# Nakafa Content

## Articles

- [Framing Dynastic Politics in Local Elections within Asian Values](https://nakafa.com/en/articles/politics/dynastic-politics-asian-values): Power is passed down under the guise of practicing asian values.
- [Flawed Legal Framework and Misguided Geopolitical Direction](https://nakafa.com/en/articles/politics/flawed-legal-geopolitics): Overlapping legal bases and an emerging terrorist threat. What is behind Indonesia's bold move to move its capital to Kalimantan?
- [Afraid of Facing an Empty Box, KIM Plus Creates an Independent Candidate Scenario?](https://nakafa.com/en/articles/politics/kim-plus-empty-box): Trapped and tricked in Jakarta's political dynamics.
- ["Merah Putih" Cabinet: An Analysis of the Influence of a Multiparty and Presidential System Combination](https://nakafa.com/en/articles/politics/merah-putih-cabinet-analysis): Giant coalition forming an oversized cabinet, does transactional politics still play a role?
- [Nepotism: The Machinations of Power in the Political Chessboard of Governance](https://nakafa.com/en/articles/politics/nepotism-in-political-governance): The creeping emergence of dynastic politics behind the opaque curtain of Indonesian governmental affairs raises substantial questions. Will Indonesia's democracy collapse?
- [Pork Barrel Politics: Manipulating Social Assistance Policies to Maintain Personal Power](https://nakafa.com/en/articles/politics/pork-barrel-politics-power): The state is like a playground for those who have the keys to the game. How do "they" play the game to climb the arranged victory?
- [Political Turmoil Ahead of Regional Elections: Politics in Chaos, The People Cry Out](https://nakafa.com/en/articles/politics/regional-elections-turmoil): The political anomaly in Indonesia as it prepares for the 2024 Regional Elections.
- [Membingkai Politik Dinasti dalam Pemilihan Lokal dalam Nilai-Nilai Asia](https://nakafa.com/id/articles/politics/dynastic-politics-asian-values): Kekuasaan diwariskan dengan dalih mempraktikkan nilai-nilai Asia.
- [Kerangka Hukum yang Cacat dan Arah Geopolitik yang Keliru](https://nakafa.com/id/articles/politics/flawed-legal-geopolitics): Tumpang tindih dasar hukum dan ancaman teroris yang muncul. Apa yang ada di balik langkah berani Indonesia memindahkan ibukotanya ke Kalimantan?
- [Takut Menghadapi Kotak Kosong, KIM Plus Membuat Skenario Kandidat Independen?](https://nakafa.com/id/articles/politics/kim-plus-empty-box): Terperangkap dan terkikis dalam dinamika politik Jakarta.
- [Kabinet 'Merah Putih': Analisis Pengaruh Kombinasi Sistem Multipartai dan Presidensial](https://nakafa.com/id/articles/politics/merah-putih-cabinet-analysis): Koalisi besar membentuk kabinet yang over-size, apakah politik transaksional masih berperan?
- [Nepotisme: Permainan Kekuasaan dalam Papan Catur Politik Pemerintahan](https://nakafa.com/id/articles/politics/nepotism-in-political-governance): Kemunculan politik dinasti yang mengendap-endap di balik tirai buram urusan pemerintahan Indonesia menimbulkan pertanyaan substansial. Akankah demokrasi Indonesia runtuh?
- [Politik Gentong Babi: Memanipulasi Kebijakan Bantuan Sosial untuk Mempertahankan Kekuasaan Pribadi](https://nakafa.com/id/articles/politics/pork-barrel-politics-power): Negara ibarat taman bermain bagi mereka yang memiliki kunci permainan. Bagaimana "mereka" memainkan permainan untuk mencapai kemenangan yang telah diatur?
- [Gejolak Politik Menjelang Pilkada: Politik dalam Kekacauan, Rakyat Berteriak](https://nakafa.com/id/articles/politics/regional-elections-turmoil): Anomali politik di Indonesia saat mempersiapkan Pilkada 2024.

## Subjects

- [Exponent Concepts](https://nakafa.com/en/subject/high-school/10/mathematics/exponential-logarithm/basic-concept): Master exponent fundamentals from paper folding to viral spread. Learn base, power definitions, zero/negative/fractional exponents with real applications.
- [Exponential Decay](https://nakafa.com/en/subject/high-school/10/mathematics/exponential-logarithm/exponential-decay): Discover exponential decay through drug elimination, radioactive decay & bouncing balls. Master decreasing functions with real-world applications.
- [Exponential Growth](https://nakafa.com/en/subject/high-school/10/mathematics/exponential-logarithm/exponential-growth): Explore exponential growth through bacterial multiplication & population dynamics. Learn accelerating functions with step-by-step calculations.
- [Function Definition](https://nakafa.com/en/subject/high-school/10/mathematics/exponential-logarithm/function-definition): Master exponential function definition f(x)=a^x with domain, range & properties. Understand base conditions and real-world applications.
- [Function Exploration](https://nakafa.com/en/subject/high-school/10/mathematics/exponential-logarithm/function-exploration): Explore exponential functions through interactive virus spread visualization. Compare exponential vs linear growth with real-time charts.
- [Logarithm Definition](https://nakafa.com/en/subject/high-school/10/mathematics/exponential-logarithm/logarithm-definition): Master logarithms as the inverse of exponentiation. Learn formal definitions, exponential relationships, and practical applications in growth problems.
- [Logarithm Properties](https://nakafa.com/en/subject/high-school/10/mathematics/exponential-logarithm/logarithm-properties): Discover 8 essential logarithm properties: product, quotient, power rules with proofs. Master change of base formula and solve complex equations.
- [Property Proofs](https://nakafa.com/en/subject/high-school/10/mathematics/exponential-logarithm/proof-properties): Learn rigorous proofs of 7 exponential properties with step-by-step demonstrations. Master multiplication, division, and power rules through examples.
- [Exponent Properties](https://nakafa.com/en/subject/high-school/10/mathematics/exponential-logarithm/properties): Master 7 fundamental exponent rules with practical examples. Learn multiplication, division, power operations and rational exponents for problem solving.
- [Radical Form](https://nakafa.com/en/subject/high-school/10/mathematics/exponential-logarithm/radical-form): Convert fractional exponents to radical form and vice versa. Master simplification techniques and understand key properties with real-world applications.
- [Rationalizing Radicals](https://nakafa.com/en/subject/high-school/10/mathematics/exponential-logarithm/rationalizing-radicals): Eliminate radicals from denominators using conjugate multiplication. Master techniques for monomial and binomial cases with comprehensive examples.
- [Linear Equation Systems](https://nakafa.com/en/subject/high-school/10/mathematics/linear-equation-inequality/system-linear-equation): Master solving linear equation systems with substitution and elimination methods. Learn real-world applications with step-by-step examples and visual guides.
- [Linear Inequality Systems](https://nakafa.com/en/subject/high-school/10/mathematics/linear-equation-inequality/system-linear-inequality): Learn to solve linear inequality systems using graphical methods. Explore constraint modeling, optimization problems, and interactive visualizations.
- [Addition Rule](https://nakafa.com/en/subject/high-school/10/mathematics/probability/addition-rule): Learn probability addition rule for OR events. Master mutually exclusive vs non-mutually exclusive events with clear examples, formulas, and step-by-step solutions.
- [Probability Distribution](https://nakafa.com/en/subject/high-school/10/mathematics/probability/probability-distribution): Understand probability distributions with dice examples. Learn sample spaces, event calculations, and real-world applications through interactive scenarios.
- [Mutually Exclusive Events A and B](https://nakafa.com/en/subject/high-school/10/mathematics/probability/two-events-mutually-exclusive): Master mutually exclusive events that cannot occur together. Learn P(A or B) = P(A) + P(B) formula with coin, dice, and card examples plus calculations.
- [Non-Mutually Exclusive Events A and B](https://nakafa.com/en/subject/high-school/10/mathematics/probability/two-events-not-mutually-exclusive): Calculate overlapping events using P(A or B) = P(A) + P(B) - P(A and B). Avoid double counting with intersection examples and step-by-step solutions.
- [Quadratic Equations](https://nakafa.com/en/subject/high-school/10/mathematics/quadratic-function/quadratic-equation): Learn to solve quadratic equations using factorization, completing the square, and quadratic formula. Master ax²+bx+c=0 with step-by-step examples and real-world problems.
- [Quadratic Equation Factorization](https://nakafa.com/en/subject/high-school/10/mathematics/quadratic-function/quadratic-equation-factorization): Master factoring quadratic equations into (x-p)(x-q) form. Learn systematic steps, grouping methods, and special cases with detailed examples and practice problems.
- [Quadratic Formula](https://nakafa.com/en/subject/high-school/10/mathematics/quadratic-function/quadratic-equation-formula): Master the quadratic formula to solve any ax²+bx+c=0 equation. Learn step-by-step derivation, understand the discriminant, and apply to real-world problems.
- [Imaginary or Non-Real Roots](https://nakafa.com/en/subject/high-school/10/mathematics/quadratic-function/quadratic-equation-imaginary-root): Learn when quadratic equations have imaginary roots, how to identify them using discriminant, and solve complex numbers step-by-step with examples.
- [Completing the Square](https://nakafa.com/en/subject/high-school/10/mathematics/quadratic-function/quadratic-equation-perfect-square): Master completing the square method to solve quadratic equations by transforming them into perfect square trinomials with detailed steps and examples.
- [Types of Quadratic Equation Roots](https://nakafa.com/en/subject/high-school/10/mathematics/quadratic-function/quadratic-equation-types-of-root): Understand the types of roots in quadratic equations—real, equal, or complex—by analyzing the discriminant, with clear explanations and illustrative examples.
- [Characteristics of Quadratic Functions](https://nakafa.com/en/subject/high-school/10/mathematics/quadratic-function/quadratic-function-characteristics): Learn the key characteristics of quadratic functions, including vertex, axis of symmetry, and intercepts, with clear explanations and illustrative examples.
- [Constructing Quadratic Functions](https://nakafa.com/en/subject/high-school/10/mathematics/quadratic-function/quadratic-function-construction): Learn to construct quadratic functions using three points, vertex form, roots, and symmetry. Master different methods with step-by-step examples and solutions.
- [Determining Maximum Area](https://nakafa.com/en/subject/high-school/10/mathematics/quadratic-function/quadratic-function-maximum-area): Maximize areas using quadratic functions through real-world problems, step-by-step solutions, and graphical interpretations. Master optimization techniques.
- [Determining Minimum Area](https://nakafa.com/en/subject/high-school/10/mathematics/quadratic-function/quadratic-function-minimum-area): Minimize areas and costs using quadratic functions with practical examples, efficient solutions, and business applications. Master cost optimization techniques.
- [Arithmetic Sequence](https://nakafa.com/en/subject/high-school/10/mathematics/sequence-series/arithmetic-sequence): Master arithmetic sequences with step-by-step examples, formulas, and real-world applications. Learn to find nth terms and solve sequence problems.
- [Arithmetic Series](https://nakafa.com/en/subject/high-school/10/mathematics/sequence-series/arithmetic-series): Discover Gauss's brilliant method for calculating arithmetic series sums. Learn formulas, solve problems, and master sum calculations with examples.
- [Difference Between Convergence and Divergence](https://nakafa.com/en/subject/high-school/10/mathematics/sequence-series/convergence-divergence): Understand when infinite series converge to finite values or diverge. Explore tests, examples, and key differences with geometric and harmonic series.
- [Difference between Arithmetic and Geometric Sequence](https://nakafa.com/en/subject/high-school/10/mathematics/sequence-series/difference-arithmetic-geometric-sequence): Compare arithmetic and geometric sequences: constant differences vs ratios. Learn identification methods, formulas, and real-world applications.
- [Difference between Arithmetic and Geometric Series](https://nakafa.com/en/subject/high-school/10/mathematics/sequence-series/difference-arithmetic-geometric-series): Distinguish arithmetic vs geometric series: linear vs exponential growth patterns. Master sum formulas, calculations, and choose the right approach.
- [Difference between Sequence and Series](https://nakafa.com/en/subject/high-school/10/mathematics/sequence-series/difference-sequence-series): Clarify sequence vs series: ordered lists of terms vs their sums. Understand fundamental concepts with clear analogies and practical examples.
- [Geometric Sequence](https://nakafa.com/en/subject/high-school/10/mathematics/sequence-series/geometric-sequence): Master geometric sequences with constant ratios. Learn formulas, solve real-world problems like bacterial growth, and discover practical applications.
- [Geometric Series](https://nakafa.com/en/subject/high-school/10/mathematics/sequence-series/geometric-series): Learn geometric series formulas and calculate sums efficiently. Solve production problems, understand COVID-19 growth patterns, and master applications.
- [Infinite Geometric Series](https://nakafa.com/en/subject/high-school/10/mathematics/sequence-series/infinite-geometric-series): Discover infinite geometric series with bouncing ball examples. Learn convergence, divergence, and calculate infinite sums using practical formulas.
- [Sequence Concept](https://nakafa.com/en/subject/high-school/10/mathematics/sequence-series/sequence-concept): Explore sequence fundamentals with interactive table-chair patterns. Learn arithmetic, geometric types, and solve real-world pattern problems step-by-step.
- [Series Concept](https://nakafa.com/en/subject/high-school/10/mathematics/sequence-series/series-concept): Understand series as sequential sums through handshake examples. Discover how adding sequence terms creates arithmetic and geometric series patterns.
- [Applications of Measures of Central Tendency](https://nakafa.com/en/subject/high-school/10/mathematics/statistics/central-tendency-usage): Learn when to use mean, median, or mode in statistics. Discover how outliers affect each measure and get practical guidance for real-world data analysis.
- [Histogram](https://nakafa.com/en/subject/high-school/10/mathematics/statistics/histogram): Master histograms vs bar charts in statistics. Learn to visualize data distribution, interpret frequency patterns, and choose the right chart type.
- [Interquartile Range](https://nakafa.com/en/subject/high-school/10/mathematics/statistics/interquartile-range): Calculate interquartile range (IQR) to measure data spread. Learn Q1, Q3 quartiles, compare with range, and understand middle 50% data variation.
- [Mean (Average)](https://nakafa.com/en/subject/high-school/10/mathematics/statistics/mean): Master mean calculation in statistics with real examples. Learn the formula, understand outlier effects, and compare with median and mode effectively.
- [Mean for Grouped Data](https://nakafa.com/en/subject/high-school/10/mathematics/statistics/mean-group-data): Calculate mean for grouped data using class intervals and midpoints. Master the formula with step-by-step examples and frequency distribution tables.
- [Median and Modal Class for Grouped Data](https://nakafa.com/en/subject/high-school/10/mathematics/statistics/median-mode-group-data): Learn to find median and modal class in grouped data with step-by-step formulas. Master frequency tables and cumulative calculations for statistics.
- [Mode and Median](https://nakafa.com/en/subject/high-school/10/mathematics/statistics/mode-median): Master mode and median calculations with simple examples. Find middle values and most frequent data points using easy step-by-step methods.
- [Percentiles for Grouped Data](https://nakafa.com/en/subject/high-school/10/mathematics/statistics/percentile-data-group): Calculate percentiles in grouped data using interpolation formulas. Learn to find data positions and interpret percentile rankings with examples.
- [Quartiles for Grouped Data](https://nakafa.com/en/subject/high-school/10/mathematics/statistics/quartile-data-group): Learn quartile calculations for grouped data with interpolation methods. Master Q1, Q2, Q3 positions using cumulative frequency and class boundaries.
- [Quartiles for Ungrouped Data](https://nakafa.com/en/subject/high-school/10/mathematics/statistics/quartile-data-single): Calculate Q1, Q2, Q3 quartiles for ungrouped data with simple position formulas. Learn to divide sorted data into four equal parts step-by-step.
- [Relative Frequency](https://nakafa.com/en/subject/high-school/10/mathematics/statistics/relative-frequency): Calculate relative frequency to find data proportions and percentages. Learn to compare groups and interpret statistical results with clear examples.
- [Variance and Standard Deviation for Grouped Data](https://nakafa.com/en/subject/high-school/10/mathematics/statistics/variance-standard-deviation-data-group): Learn to calculate variance and standard deviation for grouped frequency data with step-by-step examples. Master statistical formulas for class intervals.
- [Variance and Standard Deviation for Ungrouped Data](https://nakafa.com/en/subject/high-school/10/mathematics/statistics/variance-standard-deviation-data-single): Master variance and standard deviation calculations for ungrouped data with clear formulas and real examples. Analyze data spread effectively.
- [Right Triangle Side Naming](https://nakafa.com/en/subject/high-school/10/mathematics/trigonometry/right-triangle-naming): Learn how to identify opposite, adjacent, and hypotenuse sides in right triangles. Master the foundation of trigonometry with clear examples and visual guides.
- [Trigonometric Comparison: Sin θ and Cos θ](https://nakafa.com/en/subject/high-school/10/mathematics/trigonometry/trigonometric-comparison-sin-cos): Master sine and cosine ratios with real-world pyramid examples. Compare trigonometric functions, solve practical problems, and understand their applications.
- [Special Angles in Trigonometric Comparisons](https://nakafa.com/en/subject/high-school/10/mathematics/trigonometry/trigonometric-comparison-special-angle): Memorize exact trigonometric values for 30°, 45°, and 60° angles. Get precise sin, cos, tan ratios without calculators using unit circle visualization.
- [Trigonometric Comparison: Tan θ](https://nakafa.com/en/subject/high-school/10/mathematics/trigonometry/trigonometric-comparison-tan): Calculate tangent ratios using opposite and adjacent sides. Solve height problems, slopes, and angles with step-by-step examples and practice exercises.
- [Applications of Tan θ Trigonometric Comparison](https://nakafa.com/en/subject/high-school/10/mathematics/trigonometry/trigonometric-comparison-tan-usage): Apply tangent to measure building heights using shadows. Master similar triangles and elevation angles for real-world distance and height calculations.
- [The Three Primary Trigonometric Comparisons](https://nakafa.com/en/subject/high-school/10/mathematics/trigonometry/trigonometric-comparison-three-primary): Understand sin, cos, and tan relationships in right triangles. Explore unit circle connections and master fundamental trigonometric ratios with interactive visuals.
- [Trigonometry Concept](https://nakafa.com/en/subject/high-school/10/mathematics/trigonometry/trigonometry-concept): Discover trigonometry fundamentals from Pythagorean theorem to six basic ratios. Learn similar triangles, shadow measurements, and real-world applications.
- [Column and Row Vectors](https://nakafa.com/en/subject/high-school/10/mathematics/vector-operations/column-row-vector): Learn column and row vector notation, transpose operations, unit vectors in Cartesian systems, and their applications in linear algebra calculations.
- [Equivalent Vectors](https://nakafa.com/en/subject/high-school/10/mathematics/vector-operations/equivalent-vector): Master equivalent vectors with same magnitude and direction. Learn properties, component representation, and real-world applications in physics and engineering.
- [Reciprocal Vector](https://nakafa.com/en/subject/high-school/10/mathematics/vector-operations/opposite-vector): Discover reciprocal vectors with inverse magnitude and same direction. Learn formulas, calculations, unit vector relationships, and crystallography applications.
- [Position Vector](https://nakafa.com/en/subject/high-school/10/mathematics/vector-operations/position-vector): Master position vectors from origin to points. Learn coordinate representation, displacement relationships, GPS applications, and 3D space visualization.
- [Scalar Vector Multiplication](https://nakafa.com/en/subject/high-school/10/mathematics/vector-operations/scalar-multiplication): Learn scalar multiplication of vectors: scale magnitude, change direction with negative values. Master properties, calculations, and physics applications.
- [Three-Dimensional Vector](https://nakafa.com/en/subject/high-school/10/mathematics/vector-operations/three-dimensional-vector): Learn three-dimensional vectors with interactive visualizations. Master 3D vector operations, dot & cross products, and real-world applications.
- [Two-Dimensional Vector](https://nakafa.com/en/subject/high-school/10/mathematics/vector-operations/two-dimensional-vector): Master two-dimensional vectors on coordinate planes. Learn vector components, magnitude calculations, and unit vectors with visual demonstrations.
- [Unit Vector from a Vector](https://nakafa.com/en/subject/high-school/10/mathematics/vector-operations/unit-vector): Calculate unit vectors from any vector through normalization. Learn direction representation with magnitude 1, standard unit vectors î, ĵ, k̂.
- [Vector Addition](https://nakafa.com/en/subject/high-school/10/mathematics/vector-operations/vector-addition): Master vector addition using triangle, parallelogram & polygon methods. Learn resultant calculations, component addition, and real-world applications.
- [Vector Components](https://nakafa.com/en/subject/high-school/10/mathematics/vector-operations/vector-components): Learn to break down vectors into x, y, z components, calculate magnitude using Pythagorean theorem, and find unit direction vectors with examples.
- [Vector Concept](https://nakafa.com/en/subject/high-school/10/mathematics/vector-operations/vector-concept): Discover what vectors are through real-world examples like wind maps. Learn magnitude, direction, notation methods, and identify valid vector properties.
- [Vectors and Coordinate System](https://nakafa.com/en/subject/high-school/10/mathematics/vector-operations/vector-coordinate-system): Master Cartesian coordinates in 2D and 3D space. Learn position vectors, displacement vectors, notation methods, and real-world GPS applications.
- [Vector Subtraction](https://nakafa.com/en/subject/high-school/10/mathematics/vector-operations/vector-subtraction): Master vector subtraction with step-by-step examples, geometric visualization, and real-world applications. Learn algebraic methods and properties.
- [Vector Types](https://nakafa.com/en/subject/high-school/10/mathematics/vector-operations/vector-types): Discover zero, negative, equivalent vectors and their properties. Learn magnitude, direction concepts with interactive visualizations and exercises.
- [Zero Vector](https://nakafa.com/en/subject/high-school/10/mathematics/vector-operations/zero-vector): Understand zero vector properties, identity element role, and real-world applications. Learn why it's unique in vector operations and physics.
- [Central Angle and Inscribed Angle](https://nakafa.com/en/subject/high-school/11/mathematics/circle/central-angle-and-inscribed-angle): Master central and inscribed angles in circles. Learn the key relationship, theorems, and solve problems with step-by-step examples and proofs.
- [Circle and Arc Circle](https://nakafa.com/en/subject/high-school/11/mathematics/circle/circle-and-arc-circle): Learn circle fundamentals, arc types, and sector calculations. Master equations, elements, and solve arc length problems with visual examples.
- [Circle and Chord](https://nakafa.com/en/subject/high-school/11/mathematics/circle/circle-and-chord): Explore circle and chord relationships. Understand theorems, properties, and solve chord length problems with clear examples and step-by-step solutions.
- [Circle and Tangent Line](https://nakafa.com/en/subject/high-school/11/mathematics/circle/circle-and-tangent-line): Discover tangent lines to circles. Learn equations, properties, and solve problems involving external points and common tangents with detailed solutions.
- [External Tangent Line and Internal Tangent Line](https://nakafa.com/en/subject/high-school/11/mathematics/circle/external-tangent-line-and-internal-tangent-line): Master external and internal tangent lines between circles. Learn formulas, calculations, and solve complex problems with comprehensive examples.
- [Properties of Angle in Circle](https://nakafa.com/en/subject/high-school/11/mathematics/circle/properties-of-angle-in-circle): Explore angle properties in circles including inscribed angles, Thales' theorem, and cyclic quadrilaterals. Master theorems with clear proofs.
- [Addition of Complex Numbers](https://nakafa.com/en/subject/high-school/11/mathematics/complex-number/addition-complex-numbers): Learn how to add complex numbers step-by-step with geometric visualization. Master real and imaginary parts addition using parallelogram rule and examples.
- [Complex Number Concept](https://nakafa.com/en/subject/high-school/11/mathematics/complex-number/complex-number-concept): Discover what complex numbers are and why they exist. Understand imaginary unit i, real vs imaginary parts, and solve equations with negative roots.
- [Complex Number Form](https://nakafa.com/en/subject/high-school/11/mathematics/complex-number/complex-number-form): Master Cartesian, polar, and exponential forms of complex numbers. Learn conversions between representations with Euler's formula and examples.
- [Complex Number Conjugate](https://nakafa.com/en/subject/high-school/11/mathematics/complex-number/conjugate-complex-numbers): Find complex number conjugates by changing imaginary signs. Explore geometric reflections, properties, and why z×z̄ produces real numbers.
- [Inverse of Complex Numbers](https://nakafa.com/en/subject/high-school/11/mathematics/complex-number/inverse-complex-numbers): Calculate complex number inverses using conjugate and modulus formulas. Master z⁻¹ = z̄/|z|² for division and reciprocal operations with examples.
- [Modulus and Argument of Complex Numbers](https://nakafa.com/en/subject/high-school/11/mathematics/complex-number/modulus-argument-complex-numbers): Calculate modulus |z| = √(x²+y²) and argument θ using quadrant rules. Master distance and angle measurements for polar form conversions.
- [Multiplication of Complex Numbers](https://nakafa.com/en/subject/high-school/11/mathematics/complex-number/multiplication-complex-numbers): Multiply complex numbers using distributive property and formula (x₁x₂-y₁y₂)+i(x₁y₂+x₂y₁). Master binomial expansion with i²=-1 examples.
- [Principal Argument of Complex Numbers](https://nakafa.com/en/subject/high-school/11/mathematics/complex-number/principal-argument-complex-numbers): Find unique principal argument Arg(z) in range [0°,360°). Convert infinite angle possibilities to one standard value for complex number equality.
- [Properties of Addition of Complex Numbers](https://nakafa.com/en/subject/high-school/11/mathematics/complex-number/properties-addition-complex-numbers): Explore algebraic properties of complex addition: commutative, associative, identity, inverse. Master scalar multiplication and prove expressions.
- [Properties of Complex Number Modulus](https://nakafa.com/en/subject/high-school/11/mathematics/complex-number/properties-modulus-complex-numbers): Master modulus laws: |z₁×z₂|=|z₁|×|z₂|, triangle inequality, |z|²=z×z̄. Simplify calculations using properties instead of complex arithmetic.
- [Properties of Multiplication of Complex Numbers](https://nakafa.com/en/subject/high-school/11/mathematics/complex-number/properties-multiplication-complex-numbers): Master commutative, associative, distributive properties and multiplicative inverse of complex numbers with step-by-step examples and algebraic proofs.
- [Properties of Principal Argument of Complex Numbers](https://nakafa.com/en/subject/high-school/11/mathematics/complex-number/properties-principal-argument-complex-numbers): Learn principal argument rules for complex number multiplication and division in polar form with range adjustments and solved practice problems.
- [Scalar Multiplication of Complex Numbers](https://nakafa.com/en/subject/high-school/11/mathematics/complex-number/scalar-multiplication-complex-numbers): Explore scalar multiplication effects on complex vectors with interactive 3D visualizations showing stretching, shrinking, and direction reversal.
- [Addition and Subtraction of Functions](https://nakafa.com/en/subject/high-school/11/mathematics/function-composition-inverse-function/addition-subtraction-function): Learn how to add and subtract functions step-by-step with domain intersection rules. Master function operations through clear examples and practice problems.
- [Domain, Codomain, and Range](https://nakafa.com/en/subject/high-school/11/mathematics/function-composition-inverse-function/domain-codomain-range): Master function domain, codomain, and range concepts with practical examples. Understand input restrictions and output sets in mathematical functions.
- [Function and Non-Function](https://nakafa.com/en/subject/high-school/11/mathematics/function-composition-inverse-function/function-and-non-function): Distinguish functions from non-functions using arrow diagrams and mathematical definitions. Learn one-to-one mapping rules with visual examples.
- [Function Composition](https://nakafa.com/en/subject/high-school/11/mathematics/function-composition-inverse-function/function-composition): Master function composition (f∘g)(x) with real-world shopping examples. Learn sequential function application and non-commutative properties.
- [Function Concept](https://nakafa.com/en/subject/high-school/11/mathematics/function-composition-inverse-function/function-concept): Understand functions as magic machines with interactive examples. Learn f(x) notation, input-output relationships, and the one-to-one rule.
- [Injective, Surjective, and Bijective Functions](https://nakafa.com/en/subject/high-school/11/mathematics/function-composition-inverse-function/injective-surjective-bijective-function): Master one-to-one, onto, and bijective function types with clear analogies. Understand mapping properties and inverse function requirements.
- [Inverse Function](https://nakafa.com/en/subject/high-school/11/mathematics/function-composition-inverse-function/inverse-function): Learn inverse functions step-by-step: definition, bijective requirements, finding formulas, and graph reflections. Master f⁻¹(x) with clear examples.
- [Multiplication and Division of Functions](https://nakafa.com/en/subject/high-school/11/mathematics/function-composition-inverse-function/multiplication-division-function): Master function multiplication and division: domain rules, zero restrictions, and practical examples. Solve (f·g)(x) and (f/g)(x) with confidence.
- [Properties of Function Composition](https://nakafa.com/en/subject/high-school/11/mathematics/function-composition-inverse-function/properties-of-function-composition): Explore function composition properties: non-commutative order, associative grouping, and identity elements. Master (f∘g) rules with proofs.
- [Properties of Inverse Function](https://nakafa.com/en/subject/high-school/11/mathematics/function-composition-inverse-function/properties-of-inverse-function): Discover inverse function properties: composition identity, double reversal, and domain-range relationships. Understand f∘f⁻¹=x with examples.
- [Absolute Value Function](https://nakafa.com/en/subject/high-school/11/mathematics/function-modeling/absolute-value-function): Master absolute value functions with interactive graphs, transformations, and step-by-step solutions. Learn properties, equations, and real applications.
- [Asymptote](https://nakafa.com/en/subject/high-school/11/mathematics/function-modeling/asymptote): Discover vertical, horizontal, and oblique asymptotes with step-by-step examples and interactive visualizations. Master rational function graphing techniques.
- [Exponential Function](https://nakafa.com/en/subject/high-school/11/mathematics/function-modeling/exponential-function): Explore exponential growth and decay with real-world applications: population dynamics, radioactive decay, and compound interest. Solve exponential equations.
- [Logarithmic Function Concept](https://nakafa.com/en/subject/high-school/11/mathematics/function-modeling/logarithmic-function-concept): Master logarithmic functions with graphs, properties, and real-world applications. Learn the inverse of exponentials through examples and practice problems.
- [Logarithmic Function Graph](https://nakafa.com/en/subject/high-school/11/mathematics/function-modeling/logarithmic-function-graph): Learn to draw logarithmic function graphs step-by-step. Explore transformations, asymptotes, and key characteristics with interactive visualizations.
- [Logarithmic Function Identity](https://nakafa.com/en/subject/high-school/11/mathematics/function-modeling/logarithmic-function-identity): Master logarithmic identities including product, quotient, power, and change of base formulas. Solve equations with practical real-world examples.
- [Piecewise Function Modeling](https://nakafa.com/en/subject/high-school/11/mathematics/function-modeling/piecewise-function-modeling): Model real-world scenarios using piecewise functions. Learn tiered pricing, tax brackets, and multi-stage processes with step-by-step examples.
- [Rational Function](https://nakafa.com/en/subject/high-school/11/mathematics/function-modeling/rational-function): Master rational functions with real-world examples, domain finding, simplification techniques, and operations. Learn through practical problems like chicken coop design.
- [Square Root Function](https://nakafa.com/en/subject/high-school/11/mathematics/function-modeling/square-root-function): Explore square root functions with interactive graphs, domain/range analysis, transformations, and equations. Master graphing techniques through rocket height problems.
- [Step Function Modeling](https://nakafa.com/en/subject/high-school/11/mathematics/function-modeling/step-function-modeling): Learn step function modeling with real-world applications like bookstore discounts, elevator capacity, and floor/ceiling functions. Master piecewise graphing.
- [Trigonometric Function of Arbitrary Angle](https://nakafa.com/en/subject/high-school/11/mathematics/function-modeling/trigonometric-function-arbitrary-angle): Master trigonometric functions for any angle using unit circle method. Learn quadrant signs, reference angles, and solve windmill rotation problems.
- [Trigonometric Function Graph](https://nakafa.com/en/subject/high-school/11/mathematics/function-modeling/trigonometric-function-graph): Master trigonometric function graphs with interactive visualizations. Learn sine, cosine, tangent graphs, amplitude, period, transformations & conversions.
- [Trigonometric Identity](https://nakafa.com/en/subject/high-school/11/mathematics/function-modeling/trigonometric-identity): Learn trigonometric identities with step-by-step proofs. Master Pythagorean, reciprocal & quotient identities to solve equations and simplify expressions.
- [Composite Transformation Matrix](https://nakafa.com/en/subject/high-school/11/mathematics/geometric-transformation/composite-transformation-matrix): Master composite transformation matrices with step-by-step examples. Learn to combine reflections, rotations & dilations using matrix multiplication.
- [Dilation](https://nakafa.com/en/subject/high-school/11/mathematics/geometric-transformation/dilation): Learn geometric dilation with scale factors and center points. Master enlargement & reduction formulas with visual examples and practice problems.
- [Dilation Matrix](https://nakafa.com/en/subject/high-school/11/mathematics/geometric-transformation/dilation-matrix): Discover how to represent dilation using matrices. Learn matrix operations for scaling shapes from origin and arbitrary points with worked examples.
- [Matrix and Transformation Connection](https://nakafa.com/en/subject/high-school/11/mathematics/geometric-transformation/matrix-transformation): Learn how 2×2 matrices perform geometric transformations like rotations and reflections on points and shapes with step-by-step examples.
- [Reflection Matrix](https://nakafa.com/en/subject/high-school/11/mathematics/geometric-transformation/reflection-matrix): Master reflection matrices for X-axis, Y-axis, y=x, and y=-x lines. Learn to transform points and triangles with detailed matrix calculations.
- [Reflection Matrix over Arbitrary Point](https://nakafa.com/en/subject/high-school/11/mathematics/geometric-transformation/reflection-matrix-arbitrary-point): Discover how to reflect points over any arbitrary point using translation and matrix operations. Master combined transformations with examples.
- [Reflection Matrix over Center Point](https://nakafa.com/en/subject/high-school/11/mathematics/geometric-transformation/reflection-matrix-center): Learn reflection matrix over origin (0,0). Master point transformation using 2x2 matrices with step-by-step calculations and visual examples.
- [Reflection over a Line](https://nakafa.com/en/subject/high-school/11/mathematics/geometric-transformation/reflection-over-line): Master geometric reflection over any line. Understand mirror lines, perpendicular bisectors, and point transformation with visual examples.
- [Reflection over Point](https://nakafa.com/en/subject/high-school/11/mathematics/geometric-transformation/reflection-over-point): Master point reflection (180° rotation). Learn half-turn transformations using coordinate formulas with step-by-step examples and visualizations.
- [Reflection over X Axis](https://nakafa.com/en/subject/high-school/11/mathematics/geometric-transformation/reflection-over-x-axis): Master X-axis reflection transformations. Learn how coordinates change (x,y) to (x,-y) with triangles, lines, and interactive visualizations.
- [Reflection over Line x = k](https://nakafa.com/en/subject/high-school/11/mathematics/geometric-transformation/reflection-over-x-equals-k): Master reflection over vertical lines x = k with step-by-step examples. Learn the transformation rule P'(2k-x, y) and solve practice problems.
- [Reflection over Y Axis](https://nakafa.com/en/subject/high-school/11/mathematics/geometric-transformation/reflection-over-y-axis): Learn y-axis reflection with complete examples for points, triangles, and lines. Master the P'(-x, y) rule with interactive visualizations.
- [Reflection over Line y = h](https://nakafa.com/en/subject/high-school/11/mathematics/geometric-transformation/reflection-over-y-equals-h): Understand horizontal line reflections y = h with worked examples and visual guides. Apply the P'(x, 2h-y) formula to solve geometry problems.
- [Reflection over Line y = -x](https://nakafa.com/en/subject/high-school/11/mathematics/geometric-transformation/reflection-over-y-equals-minus-x): Explore diagonal line reflections y = -x with comprehensive tutorials. Master coordinate swapping rule P'(-y, -x) through detailed examples.
- [Reflection over Line y = x](https://nakafa.com/en/subject/high-school/11/mathematics/geometric-transformation/reflection-over-y-equals-x): Discover coordinate exchange in y = x reflections with clear tutorials. Learn the P'(y, x) transformation for points, triangles, and equations.
- [Rotation](https://nakafa.com/en/subject/high-school/11/mathematics/geometric-transformation/rotation): Master geometric rotation transformations with step-by-step formulas, examples, and visual guides. Learn to rotate points and lines around the origin.
- [Rotation Matrix](https://nakafa.com/en/subject/high-school/11/mathematics/geometric-transformation/rotation-matrix): Learn rotation matrices for 2D transformations with derivation, formulas, and practical examples. Master rotations about origin and arbitrary points.
- [Translation](https://nakafa.com/en/subject/high-school/11/mathematics/geometric-transformation/translation): Master geometric translation transformations: learn to translate points and lines using vectors with step-by-step examples and visual demonstrations.
- [Translation Matrix](https://nakafa.com/en/subject/high-school/11/mathematics/geometric-transformation/translation-matrix): Learn translation matrix operations and homogeneous coordinates: apply vector addition and 3x3 matrices for geometric transformations with examples.
- [Cofactor Expansion Method](https://nakafa.com/en/subject/high-school/11/mathematics/matrix/cofactor-expansion-method): Learn cofactor expansion to calculate matrix determinants step-by-step. Master minors, cofactors, and determinant calculation with clear examples.
- [Matrix Addition](https://nakafa.com/en/subject/high-school/11/mathematics/matrix/matrix-addition): Master matrix addition with same-order matrices. Learn properties like commutativity & associativity, solve practical problems with detailed examples.
- [Matrix Concept](https://nakafa.com/en/subject/high-school/11/mathematics/matrix/matrix-concept): Understand matrix fundamentals from scratch. Learn rows, columns, elements, and matrix order with real-world examples and clear visual explanations.
- [Matrix Determinant](https://nakafa.com/en/subject/high-school/11/mathematics/matrix/matrix-determinant): Calculate 2x2 matrix determinants and solve linear equations using Cramer's Rule. Master determinant formulas with step-by-step examples and practice.
- [Matrix Equality](https://nakafa.com/en/subject/high-school/11/mathematics/matrix/matrix-equality): Master matrix equality conditions: same order and corresponding elements. Learn through examples, solve variable problems, and practice exercises.
- [Matrix Inverse](https://nakafa.com/en/subject/high-school/11/mathematics/matrix/matrix-inverse): Learn matrix inverse formulas for 2x2 and 3x3 matrices. Master determinant calculations, adjoint methods, and solve linear equations step-by-step.
- [Matrix Multiplication](https://nakafa.com/en/subject/high-school/11/mathematics/matrix/matrix-multiplication): Master matrix multiplication rules, conditions, and calculations. Learn step-by-step methods, properties, and real-world applications with examples.
- [Matrix Scalar Multiplication](https://nakafa.com/en/subject/high-school/11/mathematics/matrix/matrix-scalar-multiplication): Master scalar multiplication: multiply every matrix element by a number. Learn properties, solve examples, and apply distributive laws effectively.
- [Matrix Subtraction](https://nakafa.com/en/subject/high-school/11/mathematics/matrix/matrix-subtraction): Learn matrix subtraction with step-by-step examples, properties, and practice problems. Master subtracting corresponding elements and matrix operations.
- [Matrix Transpose](https://nakafa.com/en/subject/high-school/11/mathematics/matrix/matrix-transpose): Master matrix transpose by swapping rows and columns. Learn step-by-step methods, explore essential properties, and practice with detailed examples.
- [Matrix Types](https://nakafa.com/en/subject/high-school/11/mathematics/matrix/matrix-types): Discover all matrix types: row, column, square, triangular, diagonal, identity, zero, and symmetric matrices. Complete guide with definitions and examples.
- [Properties of Matrix Determinant](https://nakafa.com/en/subject/high-school/11/mathematics/matrix/properties-determinant-matrix): Explore matrix determinant properties: product rule |AB| = |A||B| and scalar multiplication |kA| = k^n|A|. Learn through step-by-step examples.
- [Sarrus Method](https://nakafa.com/en/subject/high-school/11/mathematics/matrix/sarrus-method): Master Sarrus method for calculating 3×3 matrix determinants quickly. Learn the diagonal technique with step-by-step visual approach and examples.
- [Addition and Subtraction of Polynomials](https://nakafa.com/en/subject/high-school/11/mathematics/polynomial/addition-subtraction-polynomial): Master polynomial addition and subtraction with step-by-step examples. Learn like terms, horizontal & vertical methods, plus graphical visualization.
- [Division of Polynomials](https://nakafa.com/en/subject/high-school/11/mathematics/polynomial/division-polynomial): Learn polynomial division algorithm with clear examples. Understand quotient, remainder concepts, and verify results using fractional & multiplication forms.
- [Factor Theorem](https://nakafa.com/en/subject/high-school/11/mathematics/polynomial/factor-theorem): Discover how polynomial roots connect to factors. Master the Factor Theorem to find zeros, identify linear factors, and solve complete factorization problems.
- [Horner's Method](https://nakafa.com/en/subject/high-school/11/mathematics/polynomial/horner-method): Master Horner's method for efficient polynomial division. Learn this simplified alternative to long division with step-by-step examples and practice.
- [Multiplication of Polynomials](https://nakafa.com/en/subject/high-school/11/mathematics/polynomial/multiplication-polynomial): Master polynomial multiplication using distributive property and table methods. Learn step-by-step techniques with detailed examples and practice.
- [Polynomial Concept](https://nakafa.com/en/subject/high-school/11/mathematics/polynomial/polynomial-concept): Understand polynomials from the ground up. Learn what monomials are, how they combine to form polynomials, and identify valid polynomial expressions.
- [Polynomial Degree](https://nakafa.com/en/subject/high-school/11/mathematics/polynomial/polynomial-degree): Master finding polynomial degrees by identifying the highest power term. Learn monomial degrees, multi-variable cases, and step-by-step examples.
- [Complete Polynomial Factorization](https://nakafa.com/en/subject/high-school/11/mathematics/polynomial/polynomial-factorization): Master complete polynomial factorization into linear factors using complex numbers. Learn to find all roots and apply the Fundamental Theorem of Algebra.
- [Polynomial Function](https://nakafa.com/en/subject/high-school/11/mathematics/polynomial/polynomial-function): Learn polynomial functions: understand P(x) notation, identify leading terms, coefficients, and degrees. Master function components with clear examples.
- [Polynomial Graph](https://nakafa.com/en/subject/high-school/11/mathematics/polynomial/polynomial-graph): Master polynomial graphing with point plotting, end behavior analysis, and visual patterns. Learn to sketch linear, quadratic, and cubic graphs step-by-step.
- [Polynomial Identity](https://nakafa.com/en/subject/high-school/11/mathematics/polynomial/polynomial-identity): Explore key polynomial identities like binomial squares and sum of cubes. Master these formulas to simplify expressions and solve equations efficiently.
- [Rational Zero Theorem](https://nakafa.com/en/subject/high-school/11/mathematics/polynomial/rational-zero): Master the Rational Zero Theorem to find polynomial roots efficiently. Learn step-by-step methods with examples to factor high-degree polynomials easily.
- [Remainder Theorem](https://nakafa.com/en/subject/high-school/11/mathematics/polynomial/remainder-theorem): Discover the Remainder Theorem to quickly find polynomial division remainders without long division. Master this shortcut with clear examples and proofs.
- [Polynomial Long Division](https://nakafa.com/en/subject/high-school/11/mathematics/polynomial/synthetic-division): Learn polynomial long division with systematic step-by-step approach. Master quotient and remainder calculations through detailed examples and practice.
- [Coefficient of Determination](https://nakafa.com/en/subject/high-school/11/mathematics/statistics/coefficient-of-determination): Learn how r² measures how well your regression line explains data variation. Master coefficient of determination with visual examples and calculations.
- [Correlation Analysis Concept](https://nakafa.com/en/subject/high-school/11/mathematics/statistics/correlation-analysis-concept): Discover how correlation analysis measures relationships between variables. Learn Pearson's r coefficient, positive/negative correlations, and why correlation ≠ causation.
- [Least Squares Method](https://nakafa.com/en/subject/high-school/11/mathematics/statistics/least-squares-method): Master the least squares method to find the best-fit line by minimizing squared residuals. Learn formulas, calculations, and real-world applications.
- [Linear Regression Concept](https://nakafa.com/en/subject/high-school/11/mathematics/statistics/linear-regression-concept): Learn linear regression to create best-fit lines through data points. Understand prediction, slope calculations, and how to model variable relationships.
- [Product Moment Correlation](https://nakafa.com/en/subject/high-school/11/mathematics/statistics/product-moment-correlation): Calculate Pearson's correlation coefficient (r) to measure linear relationships. Learn formulas, scatter plot analysis, and interpret r values from -1 to +1.
- [Scatter Diagram](https://nakafa.com/en/subject/high-school/11/mathematics/statistics/scatter-diagram): Create scatter plots to visualize relationships between two variables. Identify positive, negative, and no correlation patterns through data point analysis.
- [Definition of Circle](https://nakafa.com/en/subject/high-school/12/mathematics/analytic-geometry/definition-of-circle): Master circle fundamentals with clear explanations of center, radius, and equations. Learn how to derive (x-a)² + (y-b)² = r² with interactive examples.
- [Ellipse](https://nakafa.com/en/subject/high-school/12/mathematics/analytic-geometry/ellipse): Discover ellipse properties, foci, and equations. Learn to solve x²/a² + y²/b² = 1 problems with step-by-step examples and interactive visualizations.
- [Equation of a Tangent Line to a Circle](https://nakafa.com/en/subject/high-school/12/mathematics/analytic-geometry/equation-of-a-tangent-line-to-a-circle): Master tangent line equations using substitution, distance, and quadratic methods. Solve problems from external points with complete step-by-step solutions.
- [Equation of Circle](https://nakafa.com/en/subject/high-school/12/mathematics/analytic-geometry/equation-of-circle): Learn circle equations from (x-h)² + (y-k)² = r² to general form. Master finding center, radius, and converting between forms with practice problems.
- [Hyperbola](https://nakafa.com/en/subject/high-school/12/mathematics/analytic-geometry/hyperbola): Master hyperbola concepts: foci, asymptotes, and equations x²/a² - y²/b² = 1. Learn eccentricity, vertices, and solve problems with detailed step-by-step examples.
- [Parabola](https://nakafa.com/en/subject/high-school/12/mathematics/analytic-geometry/parabola): Master parabola equations, vertex, focus, and directrix. Learn standard forms, real-world applications, and solve problems step-by-step with examples.
- [Position of a Line to a Circle](https://nakafa.com/en/subject/high-school/12/mathematics/analytic-geometry/position-of-a-line-to-a-circle): Discover how lines intersect, touch, or miss circles using discriminant analysis. Master intersection points, tangent conditions, and solve problems.
- [Position of a Point to a Circle](https://nakafa.com/en/subject/high-school/12/mathematics/analytic-geometry/position-of-a-point-to-a-circle): Learn to determine if a point is inside, on, or outside a circle using power of a point method. Master coordinate geometry with step-by-step examples.
- [Position of a Tangent Line to a Circle](https://nakafa.com/en/subject/high-school/12/mathematics/analytic-geometry/position-of-a-tangent-line-to-a-circle): Master tangent lines to circles: find equations through points, with given slopes, and from external points. Interactive examples and step-by-step solutions.
- [Position of Two Circles](https://nakafa.com/en/subject/high-school/12/mathematics/analytic-geometry/position-of-two-circles): Discover circle relationships: intersecting, tangent (internal/external), separate, or concentric. Learn to determine positions using center distances and radii.
- [Tangent Line to Conic Sections](https://nakafa.com/en/subject/high-school/12/mathematics/analytic-geometry/tangent-line-to-conic-sections): Master tangent lines for parabolas, ellipses, and hyperbolas using the division principle. Find equations for points on curves, given slopes, and external points.
- [Arc](https://nakafa.com/en/subject/high-school/12/mathematics/circle-arc-sector/arc): Learn circle arcs, arc length formulas, and central angle relationships. Master minor, major, and semicircular arcs with step-by-step examples.
- [Central Angle on Arc](https://nakafa.com/en/subject/high-school/12/mathematics/circle-arc-sector/central-angle-on-arc): Discover central angles formed by radii and their direct relationship with arcs. Master angle-arc classifications, calculations, and real-world applications.
- [Central Angle on Sector](https://nakafa.com/en/subject/high-school/12/mathematics/circle-arc-sector/central-angle-on-sector): Master central angles that form sectors and calculate sector areas. Learn measurement techniques, proportional relationships, and real-world applications.
- [Chord](https://nakafa.com/en/subject/high-school/12/mathematics/circle-arc-sector/chord): Explore circle chords and their distance-length relationships. Master chord length formulas, intersecting theorems, and solve challenging geometry problems.
- [Circle Arc](https://nakafa.com/en/subject/high-school/12/mathematics/circle-arc-sector/circle-arc): Master arc-chord relationships, sagitta calculations, and parametric equations. Apply advanced trigonometric formulas to engineering and architectural designs.
- [Circle Sector](https://nakafa.com/en/subject/high-school/12/mathematics/circle-arc-sector/circle-sector): Calculate sector areas using proportional formulas. Understand central angle relationships and solve practical sector area problems with step-by-step methods.
- [History of Pi](https://nakafa.com/en/subject/high-school/12/mathematics/circle-arc-sector/pi-history): Discover pi's fascinating journey from ancient Babylonians to modern mathematics. Learn Archimedes' methods, Zu Chongzhi's breakthroughs, and cultural impact.
- [Relationship Between Arc Length and Sector Area](https://nakafa.com/en/subject/high-school/12/mathematics/circle-arc-sector/relationship-between-arc-length-and-sector-area): Understand proportional relationships connecting arc length and sector area. Master fundamental ratios, direct formulas, and Earth measurement applications.
- [Sector](https://nakafa.com/en/subject/high-school/12/mathematics/circle-arc-sector/sector): Learn circle sectors, their components, and central angle relationships. Explore minor and major sectors with applications in architecture and engineering.
- [Segment](https://nakafa.com/en/subject/high-school/12/mathematics/circle-arc-sector/segment): Understand circle segments bounded by chord and arc. Learn minor and major types, area calculations using sector-triangle methods, and tank applications.
- [Binomial Newton](https://nakafa.com/en/subject/high-school/12/mathematics/combinatorics/binomial-newton): Learn binomial theorem to expand (x+y)^n quickly. Master coefficients, constant terms & problem-solving with detailed step-by-step examples & practice problems.
- [Circular Permutation](https://nakafa.com/en/subject/high-school/12/mathematics/combinatorics/circular-permutation): Master circular permutation formula (n-1)! for seating arrangements & circular problems. Learn why rotations are identical with step-by-step examples & practice.
- [Combination](https://nakafa.com/en/subject/high-school/12/mathematics/combinatorics/combination): Learn combination formula C(n,k) with real examples. Master selection problems where order doesn't matter. Complete guide with detailed practice problems!
- [Slot Filling Rule](https://nakafa.com/en/subject/high-school/12/mathematics/combinatorics/filling-place-rule): Learn slot filling rule in combinatorics with table, tree diagram, and multiplication methods. Master counting arrangements with examples and exercises.
- [Permutation of n Items from n Objects](https://nakafa.com/en/subject/high-school/12/mathematics/combinatorics/permutation-of-n-items-from-n-objects): Master permutation of n items from n objects using factorial formulas. Learn complete arrangements with step-by-step examples and practical exercises.
- [Permutation with Identical Objects](https://nakafa.com/en/subject/high-school/12/mathematics/combinatorics/permutation-with-identical-objects): Learn permutation with identical objects using multinomial formula. Master counting distinct arrangements when items are indistinguishable with examples.
- [Probability of an Event](https://nakafa.com/en/subject/high-school/12/mathematics/combinatorics/probability-of-an-event): Master probability of an event with clear formulas, sample space concepts, and real-world examples. Learn to calculate event likelihoods effectively.
- [Probability of Compound Events](https://nakafa.com/en/subject/high-school/12/mathematics/combinatorics/probability-of-compound-events): Master compound event probability with clear explanations of independent and dependent events, formulas, and real-world examples to enhance understanding.
- [Probability of Independent Conditional Events](https://nakafa.com/en/subject/high-school/12/mathematics/combinatorics/probability-of-independent-conditional-events): Master conditional probability and independence concepts with clear explanations, formulas, and real-world examples to enhance your understanding.
- [Probability of Independent Events](https://nakafa.com/en/subject/high-school/12/mathematics/combinatorics/probability-of-independent-events): Master the probability of independent events with clear explanations, formulas, and real-world examples. Learn to calculate combined probabilities effectively.
- [Probability of Mutually Exclusive Events](https://nakafa.com/en/subject/high-school/12/mathematics/combinatorics/probability-of-mutually-exclusive-events): Understand mutually exclusive events in probability with clear explanations and examples. Learn how to calculate their probabilities and apply concepts effectively.
- [Binomial Distribution Function](https://nakafa.com/en/subject/high-school/12/mathematics/data-analysis-probability/binomial-distribution-function): Learn binomial distribution formula with step-by-step examples. Calculate probability of success in repeated trials with coin flips and practice problems.
- [Expected Value of Binomial Distribution](https://nakafa.com/en/subject/high-school/12/mathematics/data-analysis-probability/expected-value-of-binomial-distribution): Understand expected value of binomial distribution with clear explanations and examples. Learn to calculate mean outcomes in repeated trials using E(X)=np.
- [Expected Value of Normal Distribution](https://nakafa.com/en/subject/high-school/12/mathematics/data-analysis-probability/expected-value-of-normal-distribution): Understand expected value of normal distribution with clear explanations and examples. Learn why E(X)=μ and calculate mean outcomes in statistics problems.
- [Normal Distribution Function](https://nakafa.com/en/subject/high-school/12/mathematics/data-analysis-probability/normal-distribution-function): Learn normal distribution function with bell curve visualization and examples. Understand z-score transformation and calculate probabilities step-by-step.
- [Uniform Distribution](https://nakafa.com/en/subject/high-school/12/mathematics/data-analysis-probability/uniform-distribution): Learn uniform distribution with equal probability examples using dice and cards. Understand f(x)=1/k formula and solve probability problems step-by-step.
- [Application of Derivatives](https://nakafa.com/en/subject/high-school/12/mathematics/derivative-function/application-of-derivative): Learn how derivatives solve real-world physics problems. Calculate velocity, acceleration, and maximum heights with step-by-step examples and formulas.
- [Chain Rule in Derivative](https://nakafa.com/en/subject/high-school/12/mathematics/derivative-function/chain-rule-in-derivative): Master the chain rule to differentiate composite functions. Learn step-by-step methods for nested functions with power and trigonometric examples.
- [Concept of Derivative Function](https://nakafa.com/en/subject/high-school/12/mathematics/derivative-function/concept-of-derivative-function): Understand derivative functions as rates of change and curve slopes. Learn limits, tangent lines, and differentiation with visual examples and clear explanations.
- [Derivative of Algebraic Function](https://nakafa.com/en/subject/high-school/12/mathematics/derivative-function/derivative-of-algebraic-function): Master differentiation of algebraic functions using power, product, and quotient rules. Learn to differentiate polynomials, radicals, and rational functions.
- [Derivative of Trigonometric Function](https://nakafa.com/en/subject/high-school/12/mathematics/derivative-function/derivative-of-trigonometric-function): Master derivatives of trigonometric functions: sin, cos, tan, and more. Learn formulas, product rule, quotient rule with step-by-step examples and solutions.
- [Equation of a Tangent Line to a Curve](https://nakafa.com/en/subject/high-school/12/mathematics/derivative-function/equation-of-a-tangent-line-to-a-curve): Master finding tangent line equations using derivatives. Learn step-by-step methods, slope calculations, and solve complex problems with visual examples.
- [Extreme Points, Maximum and Minimum Turning Points](https://nakafa.com/en/subject/high-school/12/mathematics/derivative-function/extrema-maximum-and-minimum-value): Master finding extrema using derivatives. Learn first and second derivative tests to identify critical points, maximum and minimum values with visual examples.
- [Increasing, Decreasing, and Stationary Functions](https://nakafa.com/en/subject/high-school/12/mathematics/derivative-function/increasing-decreasing-and-stationary-function): Master identifying increasing, decreasing, and stationary functions using derivatives. Learn to analyze function behavior and determine monotonicity intervals.
- [Properties of Derivative Function](https://nakafa.com/en/subject/high-school/12/mathematics/derivative-function/properties-of-derivative-function): Master essential derivative properties: power, product, quotient, and chain rules. Learn shortcuts to differentiate functions efficiently with clear explanations.
- [Writing the Derivative Function](https://nakafa.com/en/subject/high-school/12/mathematics/derivative-function/writing-the-derivative-function): Learn to write derivative functions using Leibniz's and Newton's notations. Master different mathematical symbols with step-by-step examples and applications.
- [Combined Function Transformations](https://nakafa.com/en/subject/high-school/12/mathematics/function-transformation/combined-transformation-function): Master combined function transformations with step-by-step examples. Learn vertical, horizontal transformations, order effects, and solve practice exercises.
- [Horizontal Dilation](https://nakafa.com/en/subject/high-school/12/mathematics/function-transformation/horizontal-dilation): Understand horizontal dilation in functions with clear examples. Learn how to stretch or compress graphs horizontally and apply these concepts to various functions.
- [Horizontal Reflection](https://nakafa.com/en/subject/high-school/12/mathematics/function-transformation/horizontal-reflection): Master horizontal reflection in functions with clear examples. Learn how to reflect graphs across the y-axis and apply this transformation effectively.
- [Horizontal Translation](https://nakafa.com/en/subject/high-school/12/mathematics/function-transformation/horizontal-translation): Learn how horizontal translation shifts a function's graph left or right without altering its shape, enhancing your understanding of function transformations.
- [Rotation](https://nakafa.com/en/subject/high-school/12/mathematics/function-transformation/rotation): Master function rotation around fixed points with step-by-step examples. Learn rotation formulas, angles, and transformations for various function types.
- [Vertical Dilation](https://nakafa.com/en/subject/high-school/12/mathematics/function-transformation/vertical-dilation): Master vertical dilation of functions with clear examples. Learn how to stretch or compress graphs vertically using scale factors and apply transformations.
- [Vertical Reflection](https://nakafa.com/en/subject/high-school/12/mathematics/function-transformation/vertical-reflection): Discover vertical reflection techniques for flipping function graphs across the x-axis. Explore mirror transformations with practical examples and exercises.
- [Vertical Translation](https://nakafa.com/en/subject/high-school/12/mathematics/function-transformation/vertical-translation): Unlock vertical translation secrets to move function graphs up and down effortlessly. See how adding constants shifts graphs while preserving their shape.
- [Area of a Flat Surface](https://nakafa.com/en/subject/high-school/12/mathematics/integral/area-of-a-flat-surface): Calculate flat surface areas using definite integrals with step-by-step solutions. Master quadratic and irrational functions through practical examples.
- [Definite Integral](https://nakafa.com/en/subject/high-school/12/mathematics/integral/definite-integral): Transform Riemann sums into exact area calculations using definite integrals. Learn limit processes and notation with detailed worked examples.
- [Definition of Indefinite Integral](https://nakafa.com/en/subject/high-school/12/mathematics/integral/definition-of-indefinite-integral): Discover indefinite integrals as antiderivatives with the mysterious constant C. Master notation, understand why constants matter, and reverse derivatives.
- [Fundamental Theorem of Calculus](https://nakafa.com/en/subject/high-school/12/mathematics/integral/fundamental-theorem-of-calculus): Bridge derivatives and integrals with calculus' most powerful theorem. Learn how antiderivatives simplify definite integral calculations forever.
- [Integral in Economics and Business](https://nakafa.com/en/subject/high-school/12/mathematics/integral/integral-in-economics-and-business): Apply integrals to real business scenarios: calculate total sales, optimize costs, analyze revenue growth, and determine consumer surplus effectively.
- [Integral in Physics](https://nakafa.com/en/subject/high-school/12/mathematics/integral/integral-in-physics): Explore how integrals solve physics problems: calculate work with variable forces, spring energy, mass distributions, and center of mass effectively.
- [Properties of Definite Integral](https://nakafa.com/en/subject/high-school/12/mathematics/integral/properties-of-definite-integral): Master essential properties of definite integrals: identical limits, reversing bounds, constant factors, sum rules, and interval splitting techniques.
- [Properties of Indefinite Integral](https://nakafa.com/en/subject/high-school/12/mathematics/integral/properties-of-indefinite-integral): Master indefinite integral rules: power rule, constant multiples, sum/difference rules, and u-substitution techniques with step-by-step examples.
- [Riemann Sum](https://nakafa.com/en/subject/high-school/12/mathematics/integral/riemann-sum): Approximate areas under curves using rectangles with Riemann sums. Learn partitions, sample points, and visual calculations with detailed examples.
- [Application of Limit Function](https://nakafa.com/en/subject/high-school/12/mathematics/limit/application-of-limit-function): Apply limits to real-world scenarios: disease spread analysis, vaccination strategies, economic models, and marginal cost calculations with examples.
- [Concept of Limit Function](https://nakafa.com/en/subject/high-school/12/mathematics/limit/concept-of-limit-function): Understand function limits through intuitive examples and value tables. Learn left/right limits, formal definitions, and solve indeterminate forms.
- [Limit of Algebraic Function](https://nakafa.com/en/subject/high-school/12/mathematics/limit/limit-of-algebraic-function): Calculate limits of polynomial and rational functions. Master factoring, rationalization techniques, and solve indeterminate forms with detailed examples.
- [Limit of Trigonometric Function](https://nakafa.com/en/subject/high-school/12/mathematics/limit/limit-of-trigonometric-function): Master trigonometric limits using fundamental theorems. Learn sin x/x equals 1, ratio properties, identities, and advanced substitution techniques.
- [Properties of Limit Function](https://nakafa.com/en/subject/high-school/12/mathematics/limit/properties-of-limit-function): Simplify complex limit calculations with essential properties. Master sum, product, quotient, power, and root rules with step-by-step applications.
- [Arithmetic Operators](https://nakafa.com/en/subject/university/bachelor/ai-ds/ai-programming/arithmetic-operator): Master Python arithmetic operators with precedence rules, associativity, and practical examples. Learn +, -, *, /, //, %, ** operators for AI programming.
- [Creating Arrays with NumPy](https://nakafa.com/en/subject/university/bachelor/ai-ds/ai-programming/array-numpy): Learn how to create NumPy arrays: manual, built-in functions, sequences, and basic operations. Complete guide with tested code examples for AI programming and data science.
- [Array Operations with NumPy](https://nakafa.com/en/subject/university/bachelor/ai-ds/ai-programming/array-operation-numpy): Master NumPy array operations: broadcasting, vectorization, arithmetic, statistics, and shape manipulation with practical examples for data science.
- [Attributes and Data Types with NumPy](https://nakafa.com/en/subject/university/bachelor/ai-ds/ai-programming/attribute-data-type-numpy): Learn NumPy array attributes and data type systems: shape, dtype, size, ndim. Complete guide with tested code examples for AI programming and data science.
- [Comparison and Logic](https://nakafa.com/en/subject/university/bachelor/ai-ds/ai-programming/comparison-logic): Master Python comparison and boolean operators with interactive diagrams. Learn operator precedence, falsy/truthy values, and safe float comparisons.
- [Containers](https://nakafa.com/en/subject/university/bachelor/ai-ds/ai-programming/container): Learn Python container data types like list, tuple, dictionary, and set. Complete guide to indexing, slicing, and data manipulation with practical examples.
- [Control Flow](https://nakafa.com/en/subject/university/bachelor/ai-ds/ai-programming/control-flow): Learn control flow in Python including break, continue, pass, else, enumerate, while loops, zip, range, and if/elif/else with practical examples.
- [Dictionary](https://nakafa.com/en/subject/university/bachelor/ai-ds/ai-programming/dictionary): Learn dictionary data structure in Python, keys(), values(), items() methods, indexing, for loops, and get() method with practical examples.
- [Escape Sequence](https://nakafa.com/en/subject/university/bachelor/ai-ds/ai-programming/escape-sequence): Master Python escape sequences with backslash notation. Learn to handle quotes, newlines, tabs & special characters in strings with examples.
- [Everything is an Object in Python](https://nakafa.com/en/subject/university/bachelor/ai-ds/ai-programming/everything-object-python): Discover Python's object-oriented nature with hands-on examples. Explore how numbers, strings, lists, functions become objects with methods and attributes.
- [File Input and Output](https://nakafa.com/en/subject/university/bachelor/ai-ds/ai-programming/file-input-output): Learn how to read and write files in Python, file opening modes, read(), readline() methods, and output redirection with practical examples.
- [Functions](https://nakafa.com/en/subject/university/bachelor/ai-ds/ai-programming/function): Master Python functions: parameters, return values, variable scope, closures, error handling. Complete guide with tested code examples for AI programming students.
- [Immutable, Mutable, and Identity](https://nakafa.com/en/subject/university/bachelor/ai-ds/ai-programming/immutable-mutable-identity): Master Python object mutability, identity, and memory management. Learn how lists, references, and object identity work with practical examples and code.
- [Indexing and Slicing](https://nakafa.com/en/subject/university/bachelor/ai-ds/ai-programming/indexing-slicing): Learn Python indexing and slicing techniques to access string and list elements. Master positive, negative indices and stride usage.
- [Indexing and Slicing with NumPy](https://nakafa.com/en/subject/university/bachelor/ai-ds/ai-programming/indexing-slicing-numpy): Learn NumPy indexing and slicing techniques: 1D, 2D arrays, boolean masks, advanced indexing. Complete guide with tested code examples for AI programming.
- [Iterables](https://nakafa.com/en/subject/university/bachelor/ai-ds/ai-programming/iterable): Learn iterable concepts in Python, in/not in operators, any/all functions, and unpacking operators with practical examples and real implementations.
- [Markdown and Command Line Interfaces](https://nakafa.com/en/subject/university/bachelor/ai-ds/ai-programming/markdown-cli): Learn Markdown syntax and CLI commands for efficient documentation workflows. Master file operations, automation scripts, and pandoc conversion tools.
- [Mathematical Functions](https://nakafa.com/en/subject/university/bachelor/ai-ds/ai-programming/math-function): Learn how to use Python's math module for sqrt(), round(), abs() functions, and pi constant. Complete guide to importing and practical usage.
- [Number Attributes and Methods](https://nakafa.com/en/subject/university/bachelor/ai-ds/ai-programming/number-attribute-method): Master Python number attributes like real, imag and methods like conjugate() for complex numbers. Complete guide with practical code examples.
- [Numbers](https://nakafa.com/en/subject/university/bachelor/ai-ds/ai-programming/numbers): Master Python number types: integers, floats, and complex numbers. Learn type checking, constructors, and scientific notation for AI programming.
- [Print Function](https://nakafa.com/en/subject/university/bachelor/ai-ds/ai-programming/print-function): Learn Python print function for displaying output. Master sep, end parameters and formatting techniques for precise output control.
- [First Steps in Python](https://nakafa.com/en/subject/university/bachelor/ai-ds/ai-programming/python-step-1): Start your Python journey with interactive mode, scripts, and Jupyter. Build your first programs with variables, input/output, and practical exercises.
- [String Formatting](https://nakafa.com/en/subject/university/bachelor/ai-ds/ai-programming/string-formatting): Master Python string formatting with format(), f-strings, width control, alignment options, and sign specification. Complete guide with tested examples.
- [String Methods](https://nakafa.com/en/subject/university/bachelor/ai-ds/ai-programming/string-method): Learn Python string methods for text manipulation. Master transformation, search, character validation, and advanced string operations.
- [String Objects](https://nakafa.com/en/subject/university/bachelor/ai-ds/ai-programming/string-object): Learn Python string objects complete with definition, multiline strings, concatenation literals and variables. Understand how str data type works.
- [Syntactic Sugar](https://nakafa.com/en/subject/university/bachelor/ai-ds/ai-programming/syntactic-sugar): Master Python syntactic sugar features like list comprehensions, lambda functions, and assignment operators to write cleaner, more efficient code.
- [Variables](https://nakafa.com/en/subject/university/bachelor/ai-ds/ai-programming/variable): Learn Python variable concepts, naming rules, keywords that cannot be used, and how memory works. Complete guide with practical examples.
- [All Eigenvalues Calculation](https://nakafa.com/en/subject/university/bachelor/ai-ds/linear-methods/all-eigenvalues-calculation): Master the QR method for calculating all eigenvalues through iterative matrix decomposition. Learn convergence properties and diagonal elements.
- [Best Approximation in Function and Polynomial Spaces](https://nakafa.com/en/subject/university/bachelor/ai-ds/linear-methods/approximation-function-polynomial): Discover Gauss approximation techniques for optimal function modeling using polynomial and trigonometric spaces with Euclidean norms and scalar products.
- [Characteristic Polynomial](https://nakafa.com/en/subject/university/bachelor/ai-ds/linear-methods/characteristic-polynomial): Explore characteristic polynomials to find eigenvalues, understand algebraic multiplicity, and analyze matrix trace relationships in linear algebra.
- [Cholesky Decomposition](https://nakafa.com/en/subject/university/bachelor/ai-ds/linear-methods/cholesky-decomposition): Master Cholesky decomposition for positive definite matrices with efficient algorithms, lower triangular factorization, and computational complexity analysis.
- [Complex Matrix](https://nakafa.com/en/subject/university/bachelor/ai-ds/linear-methods/complex-matrix): Learn complex matrices with adjoint operations, Hermitian transpose, Euclidean norms, and essential properties for quantum computing and signal processing.
- [Complex Vector Space](https://nakafa.com/en/subject/university/bachelor/ai-ds/linear-methods/complex-vector-space): Master complex vector spaces with complex numbers, fundamental theorem of algebra, and 8 essential axioms. Learn AI linear methods step-by-step.
- [Cramer's Rule](https://nakafa.com/en/subject/university/bachelor/ai-ds/linear-methods/cramer-rule): Solve linear systems using determinants with Cramer's rule. Learn complementary matrices, inverse formulas, and step-by-step examples for AI applications.
- [Definition of Determinant](https://nakafa.com/en/subject/university/bachelor/ai-ds/linear-methods/determinant): Understand determinants with 3 key properties: linearity, antisymmetry, and normalization. Learn matrix invertibility and calculation methods for AI.
- [Determinant Calculation](https://nakafa.com/en/subject/university/bachelor/ai-ds/linear-methods/determinant-calculation): Master determinant calculation with cofactor expansion, Gaussian elimination, and triangular matrices. Learn efficient methods for AI linear algebra.
- [Matrix Diagonalization](https://nakafa.com/en/subject/university/bachelor/ai-ds/linear-methods/diagonalization-matrix): Transform matrices using eigenvalues and eigenvectors. Learn diagonalization conditions, geometric vs algebraic multiplicity for AI computations.
- [Basic Procedure for Diagonalization](https://nakafa.com/en/subject/university/bachelor/ai-ds/linear-methods/diagonalization-procedure): Learn the 3-step matrix diagonalization procedure: compute eigenvalues, find eigenspaces, and check conditions with practical examples.
- [Eigenvalues of Diagonal and Triangular Matrices](https://nakafa.com/en/subject/university/bachelor/ai-ds/linear-methods/eigenvalue-diagonal-matrix): Discover how to read eigenvalues directly from diagonal entries of diagonal and triangular matrices, plus determinant-trace relationships.
- [Eigenvalues, Eigenvectors, and Eigenspaces](https://nakafa.com/en/subject/university/bachelor/ai-ds/linear-methods/eigenvalue-eigenvector-eigenspace): Master fundamental eigenvalue concepts: understand how matrices transform vectors, calculate eigenvectors, and explore eigenspace properties.
- [Identifiability and Ranking Capability](https://nakafa.com/en/subject/university/bachelor/ai-ds/linear-methods/identifiability-ranking): Explore matrix identifiability through singular value decomposition: determine parameter uniqueness, assess rank deficiency, and solve systems.
- [Individual Eigenvalue Calculation](https://nakafa.com/en/subject/university/bachelor/ai-ds/linear-methods/individual-eigenvalue-calculation): Learn 3 powerful eigenvalue calculation methods: inverse iteration with shift, von Mises for dominant eigenvalues, and smallest eigenvalue techniques.
- [Triangularization and Jordan Normal Form](https://nakafa.com/en/subject/university/bachelor/ai-ds/linear-methods/jordan-normal-form): Master Jordan Normal Form and matrix triangularization: canonical decomposition for non-diagonalizable matrices with Jordan blocks and eigenvalues.
- [Laplace Expansion Theorem](https://nakafa.com/en/subject/university/bachelor/ai-ds/linear-methods/laplace-expansion): Master Laplace expansion theorem: systematic determinant calculation using minors and cofactors, with row/column flexibility and Sarrus rule examples.
- [Linear Equilibrium Problem](https://nakafa.com/en/subject/university/bachelor/ai-ds/linear-methods/linear-equilibrium-problem): Solve linear equilibrium problems: least squares optimization for over-determined systems with L1, L2, L∞ norms and geometric projection methods.
- [Linear Model](https://nakafa.com/en/subject/university/bachelor/ai-ds/linear-methods/linear-model): Learn linear models: fundamental y=h(t)·x relationships, polynomial/trigonometric forms, data-to-model conversion, and linearization techniques for AI.
- [LU Decomposition](https://nakafa.com/en/subject/university/bachelor/ai-ds/linear-methods/lu-decomposition): Master LU decomposition: factorize matrices into lower/upper triangular forms using Gaussian elimination, with Python implementation and system solving.
- [Matrix Condition](https://nakafa.com/en/subject/university/bachelor/ai-ds/linear-methods/matrix-condition): Master matrix norms, condition numbers, and numerical stability. Learn spectral radius, eigenvalue analysis, and error estimation for robust AI systems.
- [Matrix Similarity](https://nakafa.com/en/subject/university/bachelor/ai-ds/linear-methods/matrix-similarity): Understand matrix similarity, basis transformations, and invariant properties. Learn eigenvalue preservation, coordinate changes, and linear transformations.
- [Normal Equation System](https://nakafa.com/en/subject/university/bachelor/ai-ds/linear-methods/normal-equation): Master normal equations for least squares optimization. Learn closed-form solutions, orthogonality principles, and when systems are solvable.
- [Normal Equation System Solution](https://nakafa.com/en/subject/university/bachelor/ai-ds/linear-methods/normal-equation-solution): Implement normal equation solutions using QR decomposition and pseudoinverse. Learn numerical methods, polynomial fitting, and stability comparisons.
- [Numerical Calculation of Eigenvalues](https://nakafa.com/en/subject/university/bachelor/ai-ds/linear-methods/numerical-eigenvalue-calculation): Master iterative eigenvalue algorithms for nonlinear problems. Learn dominant eigenvalue methods, diagonalization, and computational approaches for AI.
- [Orthogonal Polynomials](https://nakafa.com/en/subject/university/bachelor/ai-ds/linear-methods/orthogonal-polynomials): Master Chebyshev and Legendre polynomials with weighted scalar products, Gram-Schmidt process, and Gauss approximation for numerical analysis.
- [Orthogonal Projection](https://nakafa.com/en/subject/university/bachelor/ai-ds/linear-methods/orthogonal-projection): Learn orthogonal projection theory with existence theorems, orthonormal basis formulas, Gram matrices, and best approximation methods in vector spaces.
- [Orthogonal and Unitary Matrices](https://nakafa.com/en/subject/university/bachelor/ai-ds/linear-methods/orthogonal-unitary-matrix): Discover orthogonal and unitary matrices with determinant properties, eigenvalue analysis, rotation examples, and their applications in linear algebra.
- [Positive Definite Matrix](https://nakafa.com/en/subject/university/bachelor/ai-ds/linear-methods/positive-definite-matrix): Master positive definite matrices with eigenvalue criteria, leading principal minors, geometric properties, and optimization applications.
- [Principal Component Analysis](https://nakafa.com/en/subject/university/bachelor/ai-ds/linear-methods/principal-component-analysis): Learn PCA through covariance matrix diagonalization, eigenvalue analysis, coordinate transformation, and geometric visualization for data science.
- [QR Decomposition](https://nakafa.com/en/subject/university/bachelor/ai-ds/linear-methods/qr-decomposition): Master QR decomposition using Gram-Schmidt and Householder methods for matrix factorization, orthogonal transformations, and linear systems.
- [Real Axis Transformation](https://nakafa.com/en/subject/university/bachelor/ai-ds/linear-methods/real-axis-transformation): Learn quadratic forms with symmetric matrices, eigenvalue-based coordinate transformation, and conic section classification including ellipses, hyperbolas, and parabolas.
- [Regularization](https://nakafa.com/en/subject/university/bachelor/ai-ds/linear-methods/regularization): Master Tikhonov regularization for unstable linear systems. Learn to solve ill-conditioned problems, prevent overfitting, and stabilize parameter estimation.
- [Scalar Product](https://nakafa.com/en/subject/university/bachelor/ai-ds/linear-methods/scalar-product): Understand scalar products in vector spaces: bilinear forms, positive definite matrices, Hermitian properties, and real vs complex implementations.
- [Spectral Theorem for Complex Matrices](https://nakafa.com/en/subject/university/bachelor/ai-ds/linear-methods/spectral-complex-matrix): Master orthogonal diagonalization of normal matrices: prove equivalence between normality and eigenvector bases using mathematical induction.
- [Spectral Theorem for Real Matrices](https://nakafa.com/en/subject/university/bachelor/ai-ds/linear-methods/spectral-real-matrix): Discover when real matrices have orthonormal eigenvector bases: explore normality conditions, characteristic polynomials, and counterexamples.
- [Spectral Theorem](https://nakafa.com/en/subject/university/bachelor/ai-ds/linear-methods/spectral-theorem): Learn when matrices can be diagonalized with orthonormal eigenvectors. Master normal, Hermitian, and unitary matrices with real-world applications.
- [Statistical Analysis](https://nakafa.com/en/subject/university/bachelor/ai-ds/linear-methods/statistical-analysis): Master Fisher information matrix, parameter covariance, and weighted least squares. Build robust statistical models with confidence intervals.
- [Symmetric and Hermitian Matrices](https://nakafa.com/en/subject/university/bachelor/ai-ds/linear-methods/symmetric-hermitian-matrix): Discover symmetric and Hermitian matrices with real eigenvalues and orthogonal eigenvectors. Essential for quadratic forms and matrix diagonalization.
- [System of Linear Equations](https://nakafa.com/en/subject/university/bachelor/ai-ds/linear-methods/system-linear-equation): Solve overdetermined linear systems using least squares method. Learn curve fitting, polynomial models, and matrix solutions for real-world data.
- [Konsep Eksponen](https://nakafa.com/id/subject/high-school/10/mathematics/exponential-logarithm/basic-concept): Pelajari dasar eksponen dari lipatan kertas hingga penyebaran virus. Pahami bilangan pokok, pangkat nol/negatif/pecahan dengan aplikasi nyata.
- [Peluruhan Eksponen](https://nakafa.com/id/subject/high-school/10/mathematics/exponential-logarithm/exponential-decay): Pahami peluruhan eksponen melalui eliminasi obat, radioaktif & pantulan bola. Kuasai fungsi menurun dengan aplikasi kehidupan nyata.
- [Pertumbuhan Eksponen](https://nakafa.com/id/subject/high-school/10/mathematics/exponential-logarithm/exponential-growth): Jelajahi pertumbuhan eksponen melalui perkalian bakteri & dinamika populasi. Pelajari fungsi naik dengan perhitungan langkah demi langkah.
- [Definisi Fungsi](https://nakafa.com/id/subject/high-school/10/mathematics/exponential-logarithm/function-definition): Kuasai definisi fungsi eksponen f(x)=a^x dengan domain, range & sifat. Pahami syarat bilangan pokok dan aplikasi kehidupan nyata.
- [Eksplorasi Fungsi](https://nakafa.com/id/subject/high-school/10/mathematics/exponential-logarithm/function-exploration): Jelajahi fungsi eksponen melalui visualisasi penyebaran virus interaktif. Bandingkan pertumbuhan eksponensial vs linear dengan grafik.
- [Definisi Logaritma](https://nakafa.com/id/subject/high-school/10/mathematics/exponential-logarithm/logarithm-definition): Pelajari logaritma sebagai kebalikan eksponen. Pahami definisi formal, hubungan eksponensial, dan aplikasi praktis dalam masalah pertumbuhan.
- [Sifat Logaritma](https://nakafa.com/id/subject/high-school/10/mathematics/exponential-logarithm/logarithm-properties): Temukan 8 sifat penting logaritma: perkalian, pembagian, pangkat dengan bukti lengkap. Kuasai rumus perubahan basis dan selesaikan persamaan kompleks.
- [Pembuktian Sifat](https://nakafa.com/id/subject/high-school/10/mathematics/exponential-logarithm/proof-properties): Pelajari pembuktian ketat 7 sifat eksponen dengan demonstrasi langkah demi langkah. Kuasai aturan perkalian, pembagian, dan pangkat melalui contoh.
- [Sifat Eksponen](https://nakafa.com/id/subject/high-school/10/mathematics/exponential-logarithm/properties): Kuasai 7 aturan dasar eksponen dengan contoh praktis. Pelajari operasi perkalian, pembagian, pangkat dan eksponen rasional untuk pemecahan masalah.
- [Bentuk Akar](https://nakafa.com/id/subject/high-school/10/mathematics/exponential-logarithm/radical-form): Konversi eksponen pecahan ke bentuk akar dan sebaliknya. Kuasai teknik penyederhanaan dan pahami sifat penting dengan aplikasi dunia nyata.
- [Merasionalkan Akar](https://nakafa.com/id/subject/high-school/10/mathematics/exponential-logarithm/rationalizing-radicals): Hilangkan akar dari penyebut menggunakan perkalian sekawan. Kuasai teknik untuk kasus monomial dan binomial dengan contoh menyeluruh.
- [Sistem Persamaan Linear](https://nakafa.com/id/subject/high-school/10/mathematics/linear-equation-inequality/system-linear-equation): Pelajari cara menyelesaikan sistem persamaan linear dengan metode substitusi dan eliminasi. Lengkap dengan contoh aplikasi nyata dan panduan visual.
- [Sistem Pertidaksamaan Linear](https://nakafa.com/id/subject/high-school/10/mathematics/linear-equation-inequality/system-linear-inequality): Pelajari penyelesaian sistem pertidaksamaan linear dengan metode grafik. Jelajahi pemodelan batasan, optimasi, dan visualisasi interaktif.
- [Aturan Penjumlahan](https://nakafa.com/id/subject/high-school/10/mathematics/probability/addition-rule): Pelajari aturan penjumlahan peluang untuk kejadian ATAU. Kuasai perbedaan kejadian saling lepas vs tidak saling lepas dengan contoh dan rumus yang jelas.
- [Distribusi Peluang](https://nakafa.com/id/subject/high-school/10/mathematics/probability/probability-distribution): Pahami distribusi peluang dengan contoh dadu. Pelajari ruang sampel, perhitungan kejadian, dan aplikasi nyata melalui skenario interaktif yang mudah dipahami.
- [Dua Kejadian A dan B Saling Lepas](https://nakafa.com/id/subject/high-school/10/mathematics/probability/two-events-mutually-exclusive): Kuasai kejadian saling lepas yang tidak bisa terjadi bersamaan. Pelajari rumus P(A atau B) = P(A) + P(B) dengan contoh koin, dadu, dan kartu lengkap.
- [Dua Kejadian A dan B Tidak Saling Lepas](https://nakafa.com/id/subject/high-school/10/mathematics/probability/two-events-not-mutually-exclusive): Hitung kejadian beririsan dengan P(A atau B) = P(A) + P(B) - P(A dan B). Hindari penghitungan ganda dengan contoh irisan dan solusi langkah demi langkah.
- [Persamaan Kuadrat](https://nakafa.com/id/subject/high-school/10/mathematics/quadratic-function/quadratic-equation): Pelajari cara menyelesaikan persamaan kuadrat dengan faktorisasi, melengkapkan kuadrat, dan rumus ABC. Kuasai ax²+bx+c=0 dengan contoh lengkap dan soal praktis.
- [Faktorisasi Persamaan Kuadrat](https://nakafa.com/id/subject/high-school/10/mathematics/quadratic-function/quadratic-equation-factorization): Kuasai faktorisasi persamaan kuadrat ke bentuk (x-p)(x-q). Pelajari langkah sistematis, metode pengelompokan, dan kasus khusus dengan contoh detail dan latihan soal.
- [Rumus Persamaan Kuadrat](https://nakafa.com/id/subject/high-school/10/mathematics/quadratic-function/quadratic-equation-formula): Kuasai rumus kuadrat untuk menyelesaikan persamaan ax²+bx+c=0. Pelajari penurunan langkah demi langkah, pahami diskriminan, dan terapkan pada masalah nyata.
- [Akar Tidak Nyata atau Imajiner](https://nakafa.com/id/subject/high-school/10/mathematics/quadratic-function/quadratic-equation-imaginary-root): Pelajari kapan persamaan kuadrat memiliki akar imajiner, cara mengidentifikasi dengan diskriminan, dan menyelesaikan bilangan kompleks langkah demi langkah.
- [Melengkapi Kuadrat Sempurna](https://nakafa.com/id/subject/high-school/10/mathematics/quadratic-function/quadratic-equation-perfect-square): Kuasai metode melengkapi kuadrat sempurna untuk menyelesaikan persamaan kuadrat dengan mengubahnya menjadi trinomial kuadrat sempurna langkah demi langkah.
- [Jenis-Jenis Akar Persamaan Kuadrat](https://nakafa.com/id/subject/high-school/10/mathematics/quadratic-function/quadratic-equation-types-of-root): Pahami jenis-jenis akar dalam persamaan kuadrat—real, sama, atau kompleks—dengan menganalisis diskriminan, disertai penjelasan jelas dan contoh ilustratif.
- [Karakteristik Fungsi Kuadrat](https://nakafa.com/id/subject/high-school/10/mathematics/quadratic-function/quadratic-function-characteristics): Pelajari karakteristik utama fungsi kuadrat, termasuk titik puncak, sumbu simetri, dan titik potong, dengan penjelasan jelas dan contoh visual.
- [Mengonstruksi Fungsi Kuadrat](https://nakafa.com/id/subject/high-school/10/mathematics/quadratic-function/quadratic-function-construction): Pelajari cara mengonstruksi fungsi kuadrat dengan tiga titik, bentuk vertex, akar-akar, dan simetri. Kuasai berbagai metode dengan contoh dan solusi lengkap.
- [Menentukan Luas Maksimum](https://nakafa.com/id/subject/high-school/10/mathematics/quadratic-function/quadratic-function-maximum-area): Maksimalkan luas dengan fungsi kuadrat melalui masalah nyata, solusi langkah demi langkah, dan interpretasi grafik. Kuasai teknik optimasi luas.
- [Menentukan Luas Minimum](https://nakafa.com/id/subject/high-school/10/mathematics/quadratic-function/quadratic-function-minimum-area): Minimalkan luas dan biaya dengan fungsi kuadrat melalui contoh praktis, solusi efisien, dan aplikasi bisnis. Kuasai teknik optimasi biaya.
- [Barisan Aritmetika](https://nakafa.com/id/subject/high-school/10/mathematics/sequence-series/arithmetic-sequence): Pelajari barisan aritmetika dengan contoh langkah demi langkah, rumus suku ke-n, dan aplikasi nyata. Kuasai konsep beda dan pola bilangan.
- [Deret Aritmetika](https://nakafa.com/id/subject/high-school/10/mathematics/sequence-series/arithmetic-series): Temukan metode cemerlang Gauss untuk menghitung jumlah deret aritmetika. Pelajari rumus, selesaikan soal, dan kuasai perhitungan jumlah deret.
- [Perbedaan Konvergen dan Divergen](https://nakafa.com/id/subject/high-school/10/mathematics/sequence-series/convergence-divergence): Pahami kapan deret tak hingga konvergen ke nilai terbatas atau divergen. Jelajahi tes, contoh, dan perbedaan deret geometri serta harmonik.
- [Perbedaan Barisan Aritmetika dan Geometri](https://nakafa.com/id/subject/high-school/10/mathematics/sequence-series/difference-arithmetic-geometric-sequence): Bandingkan barisan aritmetika dan geometri: beda tetap vs rasio tetap. Pelajari cara mengenali, rumus, dan aplikasi dalam kehidupan nyata.
- [Perbedaan Deret Aritmetika dan Geometri](https://nakafa.com/id/subject/high-school/10/mathematics/sequence-series/difference-arithmetic-geometric-series): Bedakan deret aritmetika vs geometri: pola pertumbuhan linear vs eksponensial. Kuasai rumus jumlah, perhitungan, dan pilih pendekatan tepat.
- [Perbedaan Barisan dan Deret](https://nakafa.com/id/subject/high-school/10/mathematics/sequence-series/difference-sequence-series): Jelaskan barisan vs deret: urutan suku vs penjumlahannya. Pahami konsep fundamental dengan analogi jelas dan contoh praktis yang mudah dipahami.
- [Barisan Geometri](https://nakafa.com/id/subject/high-school/10/mathematics/sequence-series/geometric-sequence): Pelajari barisan geometri dengan rasio tetap. Kuasai rumus, selesaikan soal pertumbuhan bakteri, dan temukan penerapan dalam kehidupan nyata.
- [Deret Geometri](https://nakafa.com/id/subject/high-school/10/mathematics/sequence-series/geometric-series): Pelajari rumus deret geometri untuk menghitung jumlah suku dengan efisien. Selesaikan masalah produksi, pola COVID-19, dan kuasai penerapannya.
- [Deret Geometri Tak Hingga](https://nakafa.com/id/subject/high-school/10/mathematics/sequence-series/infinite-geometric-series): Temukan deret geometri tak hingga dengan contoh bola memantul. Pelajari konvergen, divergen, dan hitung jumlah tak hingga menggunakan rumus praktis.
- [Konsep Barisan](https://nakafa.com/id/subject/high-school/10/mathematics/sequence-series/sequence-concept): Jelajahi dasar-dasar barisan dengan pola meja-kursi interaktif. Pelajari jenis aritmetika, geometri, dan selesaikan masalah pola kehidupan nyata.
- [Konsep Deret](https://nakafa.com/id/subject/high-school/10/mathematics/sequence-series/series-concept): Pahami deret sebagai penjumlahan berurutan melalui contoh jabat tangan. Temukan bagaimana menjumlahkan suku barisan membentuk pola deret aritmetika dan geometri.
- [Penggunaan Ukuran Pemusatan](https://nakafa.com/id/subject/high-school/10/mathematics/statistics/central-tendency-usage): Pelajari kapan menggunakan mean, median, atau modus dalam statistika. Pahami pengaruh pencilan dan dapatkan panduan praktis analisis data.
- [Histogram](https://nakafa.com/id/subject/high-school/10/mathematics/statistics/histogram): Kuasai histogram vs diagram batang dalam statistika. Pelajari cara visualisasi distribusi data dan interpretasi pola frekuensi dengan tepat.
- [Jangkauan Interkuartil](https://nakafa.com/id/subject/high-school/10/mathematics/statistics/interquartile-range): Hitung jangkauan interkuartil (IQR) untuk ukur sebaran data. Pelajari kuartil Q1, Q3, bandingkan dengan range, dan pahami variasi 50% data tengah.
- [Mean (Rerata atau Rata-rata)](https://nakafa.com/id/subject/high-school/10/mathematics/statistics/mean): Kuasai perhitungan mean dalam statistika dengan contoh nyata. Pelajari rumus, pahami pengaruh pencilan, dan bandingkan dengan median serta modus.
- [Mean/Rata-Rata Data Kelompok](https://nakafa.com/id/subject/high-school/10/mathematics/statistics/mean-group-data): Hitung rata-rata data berkelompok menggunakan nilai tengah kelas. Kuasai rumus dengan contoh langkah demi langkah dan tabel distribusi frekuensi.
- [Median dan Kelas Modus Data Kelompok](https://nakafa.com/id/subject/high-school/10/mathematics/statistics/median-mode-group-data): Pelajari cara mencari median dan kelas modus data kelompok dengan rumus lengkap. Kuasai tabel frekuensi dan perhitungan kumulatif untuk statistika.
- [Modus dan Median](https://nakafa.com/id/subject/high-school/10/mathematics/statistics/mode-median): Kuasai perhitungan modus dan median dengan contoh mudah. Temukan nilai tengah dan data paling sering muncul dengan metode langkah demi langkah.
- [Persentil Data Kelompok](https://nakafa.com/id/subject/high-school/10/mathematics/statistics/percentile-data-group): Hitung persentil data kelompok dengan rumus interpolasi. Pelajari cara menentukan posisi data dan interpretasi peringkat persentil dengan contoh.
- [Kuartil Data Kelompok](https://nakafa.com/id/subject/high-school/10/mathematics/statistics/quartile-data-group): Pelajari perhitungan kuartil data kelompok dengan metode interpolasi. Kuasai posisi Q1, Q2, Q3 menggunakan frekuensi kumulatif dan tepi kelas.
- [Kuartil Data Tunggal](https://nakafa.com/id/subject/high-school/10/mathematics/statistics/quartile-data-single): Hitung kuartil Q1, Q2, Q3 data tunggal dengan rumus posisi sederhana. Pelajari cara membagi data terurut menjadi empat bagian sama besar langkah demi langkah.
- [Frekuensi Relatif](https://nakafa.com/id/subject/high-school/10/mathematics/statistics/relative-frequency): Hitung frekuensi relatif untuk mencari proporsi dan persentase data. Pelajari cara membandingkan kelompok dan interpretasi hasil statistik dengan contoh jelas.
- [Varian dan Simpangan Baku Data Kelompok](https://nakafa.com/id/subject/high-school/10/mathematics/statistics/variance-standard-deviation-data-group): Pelajari cara menghitung varian dan simpangan baku untuk data berkelompok dengan contoh praktis. Kuasai rumus statistika untuk interval kelas data.
- [Varian dan Simpangan Baku Data Tunggal](https://nakafa.com/id/subject/high-school/10/mathematics/statistics/variance-standard-deviation-data-single): Kuasai perhitungan varian dan simpangan baku untuk data tunggal dengan rumus jelas dan contoh nyata. Analisis sebaran data secara efektif.
- [Penamaan Sisi Segitiga Siku-siku](https://nakafa.com/id/subject/high-school/10/mathematics/trigonometry/right-triangle-naming): Pelajari cara mengidentifikasi sisi depan, samping, dan miring pada segitiga siku-siku. Kuasai dasar trigonometri dengan penjelasan jelas dan panduan visual.
- [Perbandingan Trigonometri: Sin θ dan Cos θ](https://nakafa.com/id/subject/high-school/10/mathematics/trigonometry/trigonometric-comparison-sin-cos): Kuasai rasio sinus dan cosinus dengan contoh piramida nyata. Bandingkan fungsi trigonometri, selesaikan masalah praktis, dan pahami aplikasinya.
- [Sudut Istimewa Perbandingan Trigonometri](https://nakafa.com/id/subject/high-school/10/mathematics/trigonometry/trigonometric-comparison-special-angle): Hafalkan nilai eksak trigonometri untuk sudut 30°, 45°, dan 60°. Dapatkan rasio sin, cos, tan tepat tanpa kalkulator dengan visualisasi lingkaran satuan.
- [Perbandingan Trigonometri: Tan θ](https://nakafa.com/id/subject/high-school/10/mathematics/trigonometry/trigonometric-comparison-tan): Hitung rasio tangen menggunakan sisi depan dan samping. Selesaikan masalah tinggi, kemiringan, dan sudut dengan contoh langkah demi langkah dan latihan.
- [Kegunaan Perbandingan Trigonometri Tan θ](https://nakafa.com/id/subject/high-school/10/mathematics/trigonometry/trigonometric-comparison-tan-usage): Terapkan tangen untuk mengukur tinggi gedung menggunakan bayangan. Kuasai segitiga sebangun dan sudut elevasi untuk perhitungan jarak dan tinggi nyata.
- [Tiga Serangkai Perbandingan Trigonometri](https://nakafa.com/id/subject/high-school/10/mathematics/trigonometry/trigonometric-comparison-three-primary): Pahami hubungan sin, cos, dan tan dalam segitiga siku-siku. Jelajahi koneksi lingkaran satuan dan kuasai rasio trigonometri dasar dengan visual interaktif.
- [Konsep Trigonometri](https://nakafa.com/id/subject/high-school/10/mathematics/trigonometry/trigonometry-concept): Temukan dasar trigonometri dari teorema Pythagoras hingga enam rasio dasar. Pelajari segitiga sebangun, pengukuran bayangan, dan aplikasi dunia nyata.
- [Vektor Kolom dan Vektor Baris](https://nakafa.com/id/subject/high-school/10/mathematics/vector-operations/column-row-vector): Pelajari notasi vektor kolom dan baris, operasi transpos, vektor satuan dalam sistem Kartesius, dan aplikasinya dalam perhitungan aljabar linear.
- [Vektor Ekuivalen](https://nakafa.com/id/subject/high-school/10/mathematics/vector-operations/equivalent-vector): Kuasai vektor ekuivalen dengan besar dan arah sama. Pelajari sifat-sifat, representasi komponen, dan aplikasi nyata dalam fisika dan teknik.
- [Vektor Berkebalikan](https://nakafa.com/id/subject/high-school/10/mathematics/vector-operations/opposite-vector): Temukan vektor berkebalikan dengan magnitudo terbalik dan arah sama. Pelajari rumus, perhitungan, hubungan vektor satuan, dan aplikasi kristalografi.
- [Vektor Posisi](https://nakafa.com/id/subject/high-school/10/mathematics/vector-operations/position-vector): Kuasai vektor posisi dari titik asal ke titik lain. Pelajari representasi koordinat, hubungan perpindahan, aplikasi GPS, dan visualisasi ruang 3D.
- [Perkalian Skalar Vektor](https://nakafa.com/id/subject/high-school/10/mathematics/vector-operations/scalar-multiplication): Pelajari perkalian skalar vektor: skala magnitudo, ubah arah dengan nilai negatif. Kuasai sifat-sifat, perhitungan, dan aplikasi fisika.
- [Vektor Tiga Dimensi](https://nakafa.com/id/subject/high-school/10/mathematics/vector-operations/three-dimensional-vector): Pelajari vektor tiga dimensi dengan visualisasi interaktif. Kuasai operasi vektor 3D, perkalian titik & silang, serta aplikasi dunia nyata.
- [Vektor Dua Dimensi](https://nakafa.com/id/subject/high-school/10/mathematics/vector-operations/two-dimensional-vector): Kuasai vektor dua dimensi pada bidang koordinat. Pelajari komponen vektor, perhitungan panjang, dan vektor satuan dengan demonstrasi visual.
- [Vektor Satuan dari Suatu Vektor](https://nakafa.com/id/subject/high-school/10/mathematics/vector-operations/unit-vector): Hitung vektor satuan dari vektor apapun melalui normalisasi. Pelajari representasi arah dengan besar 1, vektor satuan standar î, ĵ, k̂.
- [Penjumlahan Vektor](https://nakafa.com/id/subject/high-school/10/mathematics/vector-operations/vector-addition): Kuasai penjumlahan vektor dengan metode segitiga, jajar genjang & poligon. Pelajari perhitungan resultan, komponen, dan aplikasi dunia nyata.
- [Komponen Vektor](https://nakafa.com/id/subject/high-school/10/mathematics/vector-operations/vector-components): Pelajari cara menguraikan vektor menjadi komponen x, y, z, menghitung panjang vektor dengan teorema Pythagoras, dan membuat vektor satuan arah.
- [Konsep Vektor](https://nakafa.com/id/subject/high-school/10/mathematics/vector-operations/vector-concept): Pahami vektor melalui contoh nyata seperti peta angin. Pelajari besar, arah, cara penulisan notasi, dan ciri-ciri vektor yang benar dengan latihan.
- [Vektor dan Sistem Koordinat](https://nakafa.com/id/subject/high-school/10/mathematics/vector-operations/vector-coordinate-system): Kuasai koordinat Kartesius 2D dan 3D. Pelajari vektor posisi, perpindahan, cara penulisan notasi, dan aplikasi nyata seperti GPS dan peta digital.
- [Pengurangan Vektor](https://nakafa.com/id/subject/high-school/10/mathematics/vector-operations/vector-subtraction): Pelajari pengurangan vektor dengan contoh langkah demi langkah, visualisasi geometris, dan aplikasi nyata. Pahami metode aljabar dan sifat-sifatnya.
- [Jenis-jenis Vektor](https://nakafa.com/id/subject/high-school/10/mathematics/vector-operations/vector-types): Temukan vektor nol, negatif, ekuivalen dan sifat-sifatnya. Pelajari konsep panjang, arah dengan visualisasi interaktif dan latihan soal.
- [Vektor Nol](https://nakafa.com/id/subject/high-school/10/mathematics/vector-operations/zero-vector): Pahami sifat vektor nol, peran elemen identitas, dan aplikasi nyata. Pelajari mengapa unik dalam operasi vektor dan fisika dengan contoh jelas.
- [Sudut Pusat dan Sudut Keliling](https://nakafa.com/id/subject/high-school/11/mathematics/circle/central-angle-and-inscribed-angle): Pelajari sudut pusat dan keliling lingkaran. Pahami hubungan, teorema, dan cara menghitung dengan contoh soal lengkap dan pembuktian matematis.
- [Lingkaran dan Busur Lingkaran](https://nakafa.com/id/subject/high-school/11/mathematics/circle/circle-and-arc-circle): Pelajari dasar lingkaran, jenis busur, dan perhitungan juring. Kuasai persamaan, unsur-unsur, serta menyelesaikan soal panjang busur lengkap.
- [Lingkaran dan Tali Busur](https://nakafa.com/id/subject/high-school/11/mathematics/circle/circle-and-chord): Jelajahi hubungan lingkaran dan tali busur. Pahami teorema, sifat, dan selesaikan soal panjang tali busur dengan contoh jelas dan solusi langkah demi langkah.
- [Lingkaran dan Garis Singgung](https://nakafa.com/id/subject/high-school/11/mathematics/circle/circle-and-tangent-line): Temukan garis singgung lingkaran. Pelajari persamaan, sifat, dan selesaikan soal titik luar serta garis singgung persekutuan dengan solusi detail.
- [Garis Singgung Persekutuan Luar dan Dalam](https://nakafa.com/id/subject/high-school/11/mathematics/circle/external-tangent-line-and-internal-tangent-line): Kuasai garis singgung persekutuan luar dan dalam antar lingkaran. Pelajari rumus, perhitungan, dan selesaikan soal kompleks dengan contoh lengkap.
- [Sifat Sudut dalam Lingkaran](https://nakafa.com/id/subject/high-school/11/mathematics/circle/properties-of-angle-in-circle): Jelajahi sifat sudut dalam lingkaran termasuk sudut keliling, teorema Thales, dan segiempat tali busur. Kuasai teorema dengan bukti jelas.
- [Penjumlahan Bilangan Kompleks](https://nakafa.com/id/subject/high-school/11/mathematics/complex-number/addition-complex-numbers): Pelajari cara menjumlahkan bilangan kompleks dengan mudah. Pahami penjumlahan bagian real dan imajiner dengan visualisasi geometris dan contoh soal.
- [Konsep Bilangan Kompleks](https://nakafa.com/id/subject/high-school/11/mathematics/complex-number/complex-number-concept): Temukan apa itu bilangan kompleks dan mengapa diperlukan. Pahami satuan imajiner i, bagian real vs imajiner, dan selesaikan akar negatif.
- [Bentuk Bilangan Kompleks](https://nakafa.com/id/subject/high-school/11/mathematics/complex-number/complex-number-form): Kuasai bentuk Kartesius, polar, dan eksponen bilangan kompleks. Pelajari konversi antar representasi dengan formula Euler dan contoh lengkap.
- [Konjugat Bilangan Kompleks](https://nakafa.com/id/subject/high-school/11/mathematics/complex-number/conjugate-complex-numbers): Temukan konjugat bilangan kompleks dengan mengubah tanda imajiner. Jelajahi pencerminan geometris, sifat, dan mengapa z×z̄ menghasilkan real.
- [Invers Bilangan Kompleks](https://nakafa.com/id/subject/high-school/11/mathematics/complex-number/inverse-complex-numbers): Hitung invers bilangan kompleks menggunakan rumus konjugat dan modulus. Kuasai z⁻¹ = z̄/|z|² untuk pembagian dan operasi kebalikan dengan contoh.
- [Modulus dan Argumen Bilangan Kompleks](https://nakafa.com/id/subject/high-school/11/mathematics/complex-number/modulus-argument-complex-numbers): Hitung modulus |z| = √(x²+y²) dan argumen θ dengan aturan kuadran. Kuasai pengukuran jarak dan sudut untuk konversi bentuk polar.
- [Perkalian Bilangan Kompleks](https://nakafa.com/id/subject/high-school/11/mathematics/complex-number/multiplication-complex-numbers): Kalikan bilangan kompleks dengan sifat distributif dan rumus (x₁x₂-y₁y₂)+i(x₁y₂+x₂y₁). Kuasai ekspansi binomial dengan contoh i²=-1.
- [Argumen Utama Bilangan Kompleks](https://nakafa.com/id/subject/high-school/11/mathematics/complex-number/principal-argument-complex-numbers): Temukan argumen utama Arg(z) unik dalam rentang [0°,360°). Ubah kemungkinan sudut tak hingga menjadi satu nilai standar untuk kesamaan kompleks.
- [Sifat Penjumlahan Bilangan Kompleks](https://nakafa.com/id/subject/high-school/11/mathematics/complex-number/properties-addition-complex-numbers): Jelajahi sifat aljabar penjumlahan kompleks: komutatif, asosiatif, identitas, invers. Kuasai perkalian skalar dan buktikan ekspresi.
- [Sifat Operasi Modulus Bilangan Kompleks](https://nakafa.com/id/subject/high-school/11/mathematics/complex-number/properties-modulus-complex-numbers): Kuasai hukum modulus: |z₁×z₂|=|z₁|×|z₂|, ketaksamaan segitiga, |z|²=z×z̄. Sederhanakan perhitungan dengan sifat tanpa aritmetika kompleks.
- [Sifat Perkalian Bilangan Kompleks](https://nakafa.com/id/subject/high-school/11/mathematics/complex-number/properties-multiplication-complex-numbers): Pelajari sifat komutatif, asosiatif, distributif dan invers perkalian bilangan kompleks dengan contoh langkah demi langkah dan pembuktian aljabar.
- [Sifat Argumen Utama Bilangan Kompleks](https://nakafa.com/id/subject/high-school/11/mathematics/complex-number/properties-principal-argument-complex-numbers): Pahami aturan argumen utama untuk perkalian dan pembagian bilangan kompleks dalam bentuk polar dengan penyesuaian rentang dan latihan terpecahkan.
- [Perkalian Skalar Bilangan Kompleks](https://nakafa.com/id/subject/high-school/11/mathematics/complex-number/scalar-multiplication-complex-numbers): Jelajahi efek perkalian skalar pada vektor kompleks dengan visualisasi 3D interaktif yang menunjukkan perpanjangan, perpendekkan, dan pembalikan arah.
- [Penjumlahan dan Pengurangan Fungsi](https://nakafa.com/id/subject/high-school/11/mathematics/function-composition-inverse-function/addition-subtraction-function): Pelajari cara menjumlahkan dan mengurangkan fungsi dengan aturan irisan domain. Kuasai operasi fungsi melalui contoh jelas dan soal latihan lengkap.
- [Domain, Kodomain, dan Range](https://nakafa.com/id/subject/high-school/11/mathematics/function-composition-inverse-function/domain-codomain-range): Kuasai konsep domain, kodomain, dan range fungsi dengan contoh praktis. Pahami batasan input dan himpunan output dalam fungsi matematika.
- [Fungsi dan Bukan Fungsi](https://nakafa.com/id/subject/high-school/11/mathematics/function-composition-inverse-function/function-and-non-function): Bedakan fungsi dan bukan fungsi dengan diagram panah dan definisi matematis. Pelajari aturan pemetaan satu-ke-satu dengan contoh visual.
- [Komposisi Fungsi](https://nakafa.com/id/subject/high-school/11/mathematics/function-composition-inverse-function/function-composition): Kuasai komposisi fungsi (f∘g)(x) dengan contoh promo belanja nyata. Pelajari penerapan fungsi berurutan dan sifat tidak komutatif.
- [Konsep Fungsi](https://nakafa.com/id/subject/high-school/11/mathematics/function-composition-inverse-function/function-concept): Pahami fungsi sebagai mesin ajaib dengan contoh interaktif. Pelajari notasi f(x), hubungan input-output, dan aturan tepat satu.
- [Fungsi Injektif, Surjektif, dan Bijektif](https://nakafa.com/id/subject/high-school/11/mathematics/function-composition-inverse-function/injective-surjective-bijective-function): Kuasai jenis fungsi satu-ke-satu, pada, dan bijektif dengan analogi jelas. Pahami sifat pemetaan dan syarat fungsi invers.
- [Fungsi Invers](https://nakafa.com/id/subject/high-school/11/mathematics/function-composition-inverse-function/inverse-function): Pelajari fungsi invers langkah demi langkah: definisi, syarat bijektif, mencari rumus, dan refleksi grafik. Kuasai f⁻¹(x) dengan contoh jelas.
- [Perkalian dan Pembagian Fungsi](https://nakafa.com/id/subject/high-school/11/mathematics/function-composition-inverse-function/multiplication-division-function): Kuasai perkalian dan pembagian fungsi: aturan domain, batasan nol, dan contoh praktis. Selesaikan (f·g)(x) dan (f/g)(x) dengan mudah.
- [Sifat Komposisi Fungsi](https://nakafa.com/id/subject/high-school/11/mathematics/function-composition-inverse-function/properties-of-function-composition): Jelajahi sifat komposisi fungsi: urutan tidak komutatif, pengelompokan asosiatif, dan elemen identitas. Kuasai aturan (f∘g) dengan bukti.
- [Sifat Fungsi Invers](https://nakafa.com/id/subject/high-school/11/mathematics/function-composition-inverse-function/properties-of-inverse-function): Temukan sifat fungsi invers: identitas komposisi, pembalikan ganda, dan hubungan domain-range. Pahami f∘f⁻¹=x dengan contoh.
- [Fungsi Nilai Mutlak](https://nakafa.com/id/subject/high-school/11/mathematics/function-modeling/absolute-value-function): Pelajari fungsi nilai mutlak dengan grafik interaktif, transformasi, dan solusi langkah demi langkah. Pahami sifat, persamaan, dan aplikasi nyata.
- [Asimtot](https://nakafa.com/id/subject/high-school/11/mathematics/function-modeling/asymptote): Temukan asimtot vertikal, horizontal, dan miring dengan contoh langkah demi langkah dan visualisasi interaktif. Kuasai teknik grafik fungsi rasional.
- [Fungsi Eksponensial](https://nakafa.com/id/subject/high-school/11/mathematics/function-modeling/exponential-function): Jelajahi pertumbuhan dan peluruhan eksponensial dengan aplikasi nyata: dinamika populasi, peluruhan radioaktif, dan bunga majemuk. Selesaikan persamaan.
- [Konsep Fungsi Logaritma](https://nakafa.com/id/subject/high-school/11/mathematics/function-modeling/logarithmic-function-concept): Pelajari fungsi logaritma lengkap dengan grafik, sifat-sifat, dan aplikasi nyata. Pahami kebalikan dari eksponensial melalui contoh dan latihan soal.
- [Grafik Fungsi Logaritma](https://nakafa.com/id/subject/high-school/11/mathematics/function-modeling/logarithmic-function-graph): Pelajari cara menggambar grafik fungsi logaritma langkah demi langkah. Jelajahi transformasi, asimtot, dan karakteristik dengan visualisasi interaktif.
- [Identitas Fungsi Logaritma](https://nakafa.com/id/subject/high-school/11/mathematics/function-modeling/logarithmic-function-identity): Kuasai identitas logaritma meliputi rumus perkalian, pembagian, perpangkatan, dan perubahan basis. Selesaikan persamaan dengan contoh aplikasi nyata.
- [Pemodelan Fungsi Piecewise](https://nakafa.com/id/subject/high-school/11/mathematics/function-modeling/piecewise-function-modeling): Modelkan skenario dunia nyata menggunakan fungsi piecewise. Pelajari tarif bertingkat, pajak progresif, dan proses multi-tahap dengan contoh lengkap.
- [Fungsi Rasional](https://nakafa.com/id/subject/high-school/11/mathematics/function-modeling/rational-function): Pelajari fungsi rasional dengan contoh nyata, cara mencari domain, teknik penyederhanaan, dan operasi. Pahami melalui masalah praktis seperti desain kandang ayam.
- [Fungsi Akar](https://nakafa.com/id/subject/high-school/11/mathematics/function-modeling/square-root-function): Jelajahi fungsi akar dengan grafik interaktif, analisis domain/range, transformasi, dan persamaan. Kuasai teknik penggambaran melalui masalah ketinggian roket.
- [Pemodelan Fungsi Tangga](https://nakafa.com/id/subject/high-school/11/mathematics/function-modeling/step-function-modeling): Pelajari pemodelan fungsi tangga dengan aplikasi nyata seperti diskon toko buku, kapasitas lift, dan fungsi lantai/langit-langit. Kuasai grafik sepotong.
- [Fungsi Trigonometri Sebarang Sudut](https://nakafa.com/id/subject/high-school/11/mathematics/function-modeling/trigonometric-function-arbitrary-angle): Kuasai fungsi trigonometri untuk sudut apa pun dengan metode lingkaran satuan. Pelajari tanda kuadran, sudut referensi, dan selesaikan masalah rotasi kincir.
- [Grafik Fungsi Trigonometri](https://nakafa.com/id/subject/high-school/11/mathematics/function-modeling/trigonometric-function-graph): Pelajari grafik fungsi trigonometri dengan visualisasi interaktif. Pahami grafik sin, cos, tan, amplitudo, periode, transformasi & konversi sudut.
- [Identitas Trigonometri](https://nakafa.com/id/subject/high-school/11/mathematics/function-modeling/trigonometric-identity): Pelajari identitas trigonometri dengan pembuktian langkah demi langkah. Kuasai identitas Pythagoras, kebalikan & hasil bagi untuk menyelesaikan soal.
- [Matriks Transformasi Komposisi](https://nakafa.com/id/subject/high-school/11/mathematics/geometric-transformation/composite-transformation-matrix): Pelajari cara menggabungkan transformasi geometri menggunakan matriks. Panduan lengkap refleksi, rotasi, dan dilatasi dengan contoh perhitungan detail.
- [Dilatasi](https://nakafa.com/id/subject/high-school/11/mathematics/geometric-transformation/dilation): Kuasai konsep dilatasi geometri dengan faktor skala dan pusat dilatasi. Pelajari perbesaran, pengecilan, dan rumus dengan visualisasi interaktif.
- [Matriks Dilatasi](https://nakafa.com/id/subject/high-school/11/mathematics/geometric-transformation/dilation-matrix): Temukan cara merepresentasikan dilatasi menggunakan matriks. Pelajari operasi matriks untuk mengubah ukuran dari titik pusat dan sembarang dengan contoh.
- [Kaitan Matriks dengan Transformasi](https://nakafa.com/id/subject/high-school/11/mathematics/geometric-transformation/matrix-transformation): Pelajari cara matriks 2×2 melakukan transformasi geometri seperti rotasi dan refleksi pada titik dan bangun dengan contoh langkah demi langkah.
- [Matriks Pencerminan](https://nakafa.com/id/subject/high-school/11/mathematics/geometric-transformation/reflection-matrix): Kuasai matriks pencerminan sumbu X, Y, garis y=x, dan y=-x. Pelajari cara mentransformasi titik dan segitiga dengan perhitungan matriks detail.
- [Matriks Pencerminan terhadap Sebarang Titik](https://nakafa.com/id/subject/high-school/11/mathematics/geometric-transformation/reflection-matrix-arbitrary-point): Temukan cara mencerminkan titik terhadap sebarang titik menggunakan translasi dan operasi matriks. Kuasai transformasi gabungan dengan contoh.
- [Matriks Pencerminan terhadap Titik Pusat](https://nakafa.com/id/subject/high-school/11/mathematics/geometric-transformation/reflection-matrix-center): Pelajari matriks pencerminan terhadap titik pusat O(0,0). Kuasai transformasi titik menggunakan matriks 2x2 dengan perhitungan dan contoh visual.
- [Pencerminan terhadap Garis](https://nakafa.com/id/subject/high-school/11/mathematics/geometric-transformation/reflection-over-line): Kuasai pencerminan geometri terhadap garis apapun. Pahami garis cermin, sumbu simetri, dan transformasi titik dengan contoh visual lengkap.
- [Pencerminan terhadap Titik](https://nakafa.com/id/subject/high-school/11/mathematics/geometric-transformation/reflection-over-point): Kuasai pencerminan titik (rotasi 180°). Pelajari transformasi setengah putar menggunakan rumus koordinat dengan contoh dan visualisasi lengkap.
- [Pencerminan terhadap Sumbu X](https://nakafa.com/id/subject/high-school/11/mathematics/geometric-transformation/reflection-over-x-axis): Kuasai transformasi pencerminan sumbu X. Pelajari perubahan koordinat (x,y) menjadi (x,-y) dengan segitiga, garis, dan visualisasi interaktif.
- [Pencerminan terhadap Garis x = k](https://nakafa.com/id/subject/high-school/11/mathematics/geometric-transformation/reflection-over-x-equals-k): Kuasai pencerminan terhadap garis vertikal x = k dengan contoh langkah demi langkah. Pelajari aturan transformasi P'(2k-x, y) dan latihan soal.
- [Pencerminan terhadap Sumbu Y](https://nakafa.com/id/subject/high-school/11/mathematics/geometric-transformation/reflection-over-y-axis): Pelajari pencerminan sumbu y dengan contoh lengkap untuk titik, segitiga, dan garis. Kuasai aturan P'(-x, y) dengan visualisasi interaktif.
- [Pencerminan terhadap Garis y = h](https://nakafa.com/id/subject/high-school/11/mathematics/geometric-transformation/reflection-over-y-equals-h): Pahami pencerminan garis horizontal y = h dengan contoh terperinci dan panduan visual. Terapkan rumus P'(x, 2h-y) untuk soal geometri.
- [Pencerminan terhadap Garis y = -x](https://nakafa.com/id/subject/high-school/11/mathematics/geometric-transformation/reflection-over-y-equals-minus-x): Jelajahi pencerminan garis diagonal y = -x dengan tutorial komprehensif. Kuasai aturan tukar koordinat P'(-y, -x) melalui contoh detail.
- [Pencerminan terhadap Garis y = x](https://nakafa.com/id/subject/high-school/11/mathematics/geometric-transformation/reflection-over-y-equals-x): Temukan pertukaran koordinat pada pencerminan y = x dengan tutorial jelas. Pelajari transformasi P'(y, x) untuk titik, segitiga, dan persamaan.
- [Rotasi](https://nakafa.com/id/subject/high-school/11/mathematics/geometric-transformation/rotation): Pelajari transformasi rotasi geometri dengan rumus lengkap, contoh soal, dan visualisasi interaktif. Kuasai rotasi titik dan garis terhadap titik asal.
- [Matriks Rotasi](https://nakafa.com/id/subject/high-school/11/mathematics/geometric-transformation/rotation-matrix): Pelajari matriks rotasi untuk transformasi 2D dengan penurunan rumus, contoh praktis, dan penerapan pada titik asal serta titik sebarang.
- [Translasi](https://nakafa.com/id/subject/high-school/11/mathematics/geometric-transformation/translation): Kuasai transformasi translasi geometri: pelajari cara mentranslasi titik dan garis menggunakan vektor dengan contoh langkah demi langkah dan visualisasi.
- [Matriks Translasi](https://nakafa.com/id/subject/high-school/11/mathematics/geometric-transformation/translation-matrix): Pelajari operasi matriks translasi dan koordinat homogen: terapkan penjumlahan vektor dan matriks 3x3 untuk transformasi geometri dengan contoh.
- [Metode Ekspansi Kofaktor](https://nakafa.com/id/subject/high-school/11/mathematics/matrix/cofactor-expansion-method): Pelajari metode ekspansi kofaktor untuk menghitung determinan matriks. Pahami minor, kofaktor, dan perhitungan determinan dengan contoh lengkap.
- [Penjumlahan Matriks](https://nakafa.com/id/subject/high-school/11/mathematics/matrix/matrix-addition): Kuasai penjumlahan matriks seordo dengan mudah. Pelajari sifat komutatif & asosiatif, selesaikan soal praktis dengan contoh detail dan latihan.
- [Konsep Matriks](https://nakafa.com/id/subject/high-school/11/mathematics/matrix/matrix-concept): Pahami dasar-dasar matriks dari nol. Pelajari baris, kolom, elemen, dan ordo matriks dengan contoh nyata dan penjelasan visual yang mudah dipahami.
- [Determinan Matriks](https://nakafa.com/id/subject/high-school/11/mathematics/matrix/matrix-determinant): Hitung determinan matriks 2x2 dan selesaikan SPLDV dengan Aturan Cramer. Kuasai rumus determinan dengan contoh langkah demi langkah dan latihan.
- [Kesamaan Dua Matriks](https://nakafa.com/id/subject/high-school/11/mathematics/matrix/matrix-equality): Pelajari syarat kesamaan matriks: ordo sama dan elemen seletak sama. Lengkap dengan contoh soal, penentuan variabel, dan latihan praktis.
- [Invers Matriks](https://nakafa.com/id/subject/high-school/11/mathematics/matrix/matrix-inverse): Pelajari rumus invers matriks 2x2 dan 3x3. Kuasai perhitungan determinan, metode adjoin, dan penyelesaian sistem persamaan linear langkah demi langkah.
- [Perkalian Matriks](https://nakafa.com/id/subject/high-school/11/mathematics/matrix/matrix-multiplication): Kuasai aturan perkalian matriks, syarat, dan perhitungan. Pelajari metode langkah demi langkah, sifat-sifat, dan aplikasi nyata dengan contoh.
- [Perkalian Matriks dengan Skalar](https://nakafa.com/id/subject/high-school/11/mathematics/matrix/matrix-scalar-multiplication): Kuasai perkalian skalar: kalikan setiap elemen matriks dengan bilangan. Pelajari sifat-sifat, selesaikan contoh, dan terapkan hukum distributif.
- [Pengurangan Matriks](https://nakafa.com/id/subject/high-school/11/mathematics/matrix/matrix-subtraction): Pelajari pengurangan matriks dengan contoh langkah demi langkah, sifat-sifat, dan soal latihan. Kuasai operasi pengurangan elemen matriks seletak.
- [Matriks Transpos](https://nakafa.com/id/subject/high-school/11/mathematics/matrix/matrix-transpose): Kuasai transpos matriks dengan menukar baris dan kolom. Pelajari metode langkah demi langkah, jelajahi sifat penting, dan berlatih dengan contoh.
- [Jenis-Jenis Matriks](https://nakafa.com/id/subject/high-school/11/mathematics/matrix/matrix-types): Temukan semua jenis matriks: baris, kolom, persegi, segitiga, diagonal, identitas, nol, dan simetris. Panduan lengkap dengan definisi dan contoh.
- [Sifat Determinan Matriks](https://nakafa.com/id/subject/high-school/11/mathematics/matrix/properties-determinant-matrix): Jelajahi sifat determinan matriks: aturan perkalian |AB| = |A||B| dan perkalian skalar |kA| = k^n|A|. Pelajari dengan contoh langkah demi langkah.
- [Metode Sarrus](https://nakafa.com/id/subject/high-school/11/mathematics/matrix/sarrus-method): Kuasai metode Sarrus untuk menghitung determinan matriks 3×3 dengan cepat. Pelajari teknik diagonal dengan pendekatan visual langkah demi langkah.
- [Penjumlahan dan Pengurangan Polinomial](https://nakafa.com/id/subject/high-school/11/mathematics/polynomial/addition-subtraction-polynomial): Pelajari penjumlahan dan pengurangan polinomial dengan contoh langkah demi langkah. Pahami suku sejenis, metode horizontal & vertikal, plus visualisasi grafik.
- [Pembagian Polinomial](https://nakafa.com/id/subject/high-school/11/mathematics/polynomial/division-polynomial): Pelajari algoritma pembagian polinomial dengan contoh jelas. Pahami konsep hasil bagi, sisa, dan verifikasi hasil menggunakan bentuk pecahan & perkalian.
- [Teorema Faktor](https://nakafa.com/id/subject/high-school/11/mathematics/polynomial/factor-theorem): Temukan hubungan akar polinomial dengan faktornya. Kuasai Teorema Faktor untuk mencari pembuat nol, identifikasi faktor linier, dan faktorisasi lengkap.
- [Metode Horner](https://nakafa.com/id/subject/high-school/11/mathematics/polynomial/horner-method): Kuasai metode Horner untuk pembagian polinomial yang efisien. Pelajari alternatif sederhana dari pembagian bersusun dengan contoh dan latihan.
- [Perkalian Polinomial](https://nakafa.com/id/subject/high-school/11/mathematics/polynomial/multiplication-polynomial): Kuasai perkalian polinomial dengan sifat distributif dan metode tabel. Pelajari teknik langkah demi langkah dengan contoh detail dan latihan.
- [Konsep Polinomial](https://nakafa.com/id/subject/high-school/11/mathematics/polynomial/polynomial-concept): Pahami polinomial dari dasar. Pelajari apa itu monomial, bagaimana mereka bergabung membentuk polinomial, dan identifikasi ekspresi polinomial yang valid.
- [Derajat Polinomial](https://nakafa.com/id/subject/high-school/11/mathematics/polynomial/polynomial-degree): Kuasai cara mencari derajat polinomial dengan mengidentifikasi suku berpangkat tertinggi. Pelajari derajat monomial, kasus multi-variabel, dan contoh.
- [Faktorisasi Penuh Polinomial](https://nakafa.com/id/subject/high-school/11/mathematics/polynomial/polynomial-factorization): Kuasai faktorisasi penuh polinomial menjadi faktor linier menggunakan bilangan kompleks. Pelajari cara mencari semua akar dan Teorema Fundamental Aljabar.
- [Fungsi Polinomial](https://nakafa.com/id/subject/high-school/11/mathematics/polynomial/polynomial-function): Pelajari fungsi polinomial: pahami notasi P(x), identifikasi suku utama, koefisien, dan derajat. Kuasai komponen fungsi dengan contoh jelas.
- [Grafik Fungsi Polinomial](https://nakafa.com/id/subject/high-school/11/mathematics/polynomial/polynomial-graph): Kuasai cara menggambar grafik polinomial dengan plotting titik, analisis perilaku ujung, dan pola visual. Pelajari sketsa grafik linear, kuadrat, kubik.
- [Identitas Polinomial](https://nakafa.com/id/subject/high-school/11/mathematics/polynomial/polynomial-identity): Jelajahi identitas polinomial utama seperti kuadrat binomial dan jumlah kubus. Kuasai rumus ini untuk menyederhanakan ekspresi dan menyelesaikan persamaan.
- [Pembuat Nol Rasional](https://nakafa.com/id/subject/high-school/11/mathematics/polynomial/rational-zero): Kuasai Teorema Pembuat Nol Rasional untuk mencari akar polinomial dengan efisien. Pelajari metode langkah demi langkah dengan contoh praktis.
- [Teorema Sisa](https://nakafa.com/id/subject/high-school/11/mathematics/polynomial/remainder-theorem): Temukan cara cepat menghitung sisa pembagian polinomial tanpa pembagian panjang. Pelajari Teorema Sisa dengan contoh dan pembuktian yang jelas.
- [Pembagian Bersusun](https://nakafa.com/id/subject/high-school/11/mathematics/polynomial/synthetic-division): Pelajari pembagian polinomial bersusun dengan pendekatan sistematis. Kuasai perhitungan hasil bagi dan sisa melalui contoh detail dan latihan.
- [Koefisien Determinasi](https://nakafa.com/id/subject/high-school/11/mathematics/statistics/coefficient-of-determination): Pelajari bagaimana r² mengukur seberapa baik garis regresi menjelaskan variasi data. Pahami koefisien determinasi dengan contoh visual dan perhitungan.
- [Konsep Analisis Korelasi](https://nakafa.com/id/subject/high-school/11/mathematics/statistics/correlation-analysis-concept): Temukan cara analisis korelasi mengukur hubungan antar variabel. Pelajari koefisien r Pearson, korelasi positif/negatif, dan mengapa korelasi ≠ kausalitas.
- [Metode Kuadrat Terkecil](https://nakafa.com/id/subject/high-school/11/mathematics/statistics/least-squares-method): Kuasai metode kuadrat terkecil untuk mencari garis terbaik dengan meminimalkan kuadrat residu. Pelajari rumus, perhitungan, dan aplikasi nyata.
- [Konsep Regresi Linear](https://nakafa.com/id/subject/high-school/11/mathematics/statistics/linear-regression-concept): Pelajari regresi linear untuk membuat garis best-fit melalui titik data. Pahami prediksi, perhitungan slope, dan cara memodelkan hubungan variabel.
- [Korelasi Product Moment](https://nakafa.com/id/subject/high-school/11/mathematics/statistics/product-moment-correlation): Hitung koefisien korelasi Pearson (r) untuk mengukur hubungan linear. Pelajari rumus, analisis scatter plot, dan interpretasi nilai r dari -1 hingga +1.
- [Diagram Pencar atau Diagram Scatter](https://nakafa.com/id/subject/high-school/11/mathematics/statistics/scatter-diagram): Buat diagram pencar untuk memvisualisasikan hubungan antar dua variabel. Identifikasi pola korelasi positif, negatif, dan tanpa korelasi dari titik data.
- [Definisi Lingkaran](https://nakafa.com/id/subject/high-school/12/mathematics/analytic-geometry/definition-of-circle): Pelajari konsep dasar lingkaran dengan penjelasan pusat, jari-jari, dan persamaan. Pahami cara menurunkan (x-a)² + (y-b)² = r² dengan contoh interaktif.
- [Elips](https://nakafa.com/id/subject/high-school/12/mathematics/analytic-geometry/ellipse): Pahami sifat elips, fokus, dan persamaannya. Pelajari cara menyelesaikan masalah x²/a² + y²/b² = 1 dengan contoh langkah demi langkah dan visualisasi interaktif.
- [Persamaan Garis Singgung Lingkaran](https://nakafa.com/id/subject/high-school/12/mathematics/analytic-geometry/equation-of-a-tangent-line-to-a-circle): Kuasai persamaan garis singgung dengan metode substitusi, jarak, dan kuadratik. Selesaikan soal dari titik eksternal dengan pembahasan lengkap langkah demi langkah.
- [Persamaan Lingkaran](https://nakafa.com/id/subject/high-school/12/mathematics/analytic-geometry/equation-of-circle): Pelajari persamaan lingkaran dari (x-h)² + (y-k)² = r² ke bentuk umum. Kuasai cara mencari pusat, jari-jari, dan konversi bentuk dengan latihan soal.
- [Hiperbola](https://nakafa.com/id/subject/high-school/12/mathematics/analytic-geometry/hyperbola): Kuasai konsep hiperbola: fokus, asimtot, dan persamaan x²/a² - y²/b² = 1. Pelajari eksentrisitas, puncak, dan selesaikan soal dengan contoh langkah demi langkah.
- [Parabola](https://nakafa.com/id/subject/high-school/12/mathematics/analytic-geometry/parabola): Pelajari persamaan parabola, puncak, fokus, dan direktriks. Pahami bentuk standar, aplikasi nyata, dan selesaikan soal dengan contoh lengkap.
- [Kedudukan Garis Terhadap Lingkaran](https://nakafa.com/id/subject/high-school/12/mathematics/analytic-geometry/position-of-a-line-to-a-circle): Pelajari cara garis memotong, menyinggung, atau tidak bersentuhan dengan lingkaran menggunakan analisis diskriminan. Kuasai titik potong dan kondisi singgung.
- [Kedudukan Suatu Titik Terhadap Lingkaran](https://nakafa.com/id/subject/high-school/12/mathematics/analytic-geometry/position-of-a-point-to-a-circle): Pelajari cara menentukan apakah titik berada di dalam, pada, atau di luar lingkaran menggunakan metode kuasa titik dengan contoh langkah demi langkah.
- [Kedudukan Garis Singgung Lingkaran](https://nakafa.com/id/subject/high-school/12/mathematics/analytic-geometry/position-of-a-tangent-line-to-a-circle): Pelajari cara menentukan persamaan garis singgung lingkaran melalui titik, dengan gradien tertentu, dan dari titik luar. Visualisasi interaktif dan contoh lengkap.
- [Kedudukan Dua Lingkaran](https://nakafa.com/id/subject/high-school/12/mathematics/analytic-geometry/position-of-two-circles): Pahami hubungan lingkaran: berpotongan, bersinggungan (dalam/luar), terpisah, atau konsentris. Pelajari cara menentukan kedudukan dengan jarak pusat dan jari-jari.
- [Garis Singgung pada Irisan Kerucut](https://nakafa.com/id/subject/high-school/12/mathematics/analytic-geometry/tangent-line-to-conic-sections): Kuasai garis singgung parabola, elips, dan hiperbola dengan prinsip bagi adil. Temukan persamaan untuk titik pada kurva, gradien tertentu, dan titik luar.
- [Busur](https://nakafa.com/id/subject/high-school/12/mathematics/circle-arc-sector/arc): Pelajari busur lingkaran, rumus panjang busur, dan hubungan dengan sudut pusat. Kuasai busur kecil, besar, dan setengah lingkaran dengan contoh soal.
- [Sudut Pusat pada Busur](https://nakafa.com/id/subject/high-school/12/mathematics/circle-arc-sector/central-angle-on-arc): Temukan sudut pusat yang dibentuk jari-jari dan hubungan langsung dengan busur. Kuasai klasifikasi sudut-busur, perhitungan, dan aplikasi nyata.
- [Sudut Pusat pada Juring](https://nakafa.com/id/subject/high-school/12/mathematics/circle-arc-sector/central-angle-on-sector): Kuasai sudut pusat yang membentuk juring dan hitung luas juring dengan rumus tepat. Pelajari teknik pengukuran, hubungan proporsional, dan aplikasi nyata.
- [Tali Busur](https://nakafa.com/id/subject/high-school/12/mathematics/circle-arc-sector/chord): Jelajahi tali busur lingkaran dan hubungan jarak-panjang. Kuasai rumus panjang tali busur, teorema berpotongan, dan selesaikan masalah geometri menantang.
- [Busur Lingkaran](https://nakafa.com/id/subject/high-school/12/mathematics/circle-arc-sector/circle-arc): Kuasai hubungan busur-tali busur, perhitungan sagita, dan persamaan parametrik. Terapkan rumus trigonometri lanjutan untuk desain teknik dan arsitektur.
- [Juring Lingkaran](https://nakafa.com/id/subject/high-school/12/mathematics/circle-arc-sector/circle-sector): Hitung luas juring dengan rumus proporsional. Pahami hubungan sudut pusat dan selesaikan masalah luas juring praktis dengan metode langkah demi langkah.
- [Sejarah Nilai Pi](https://nakafa.com/id/subject/high-school/12/mathematics/circle-arc-sector/pi-history): Temukan perjalanan menarik pi dari peradaban Babilonia kuno hingga matematika modern. Pelajari metode Archimedes, terobosan Zu Chongzhi, dan dampak budayanya.
- [Hubungan Panjang Busur dan Luas Juring](https://nakafa.com/id/subject/high-school/12/mathematics/circle-arc-sector/relationship-between-arc-length-and-sector-area): Pahami hubungan proporsional panjang busur dan luas juring. Kuasai rasio fundamental, rumus langsung, dan aplikasi sejarah pengukuran Bumi Eratosthenes.
- [Juring](https://nakafa.com/id/subject/high-school/12/mathematics/circle-arc-sector/sector): Pelajari juring lingkaran, komponen-komponennya, dan hubungan sudut pusat. Jelajahi juring minor dan mayor dengan aplikasi praktis dalam arsitektur dan teknik.
- [Tembereng](https://nakafa.com/id/subject/high-school/12/mathematics/circle-arc-sector/segment): Pahami tembereng lingkaran yang dibatasi tali busur dan busur. Pelajari jenis minor dan mayor, perhitungan luas metode juring-segitiga, dan aplikasi tangki.
- [Binomial Newton](https://nakafa.com/id/subject/high-school/12/mathematics/combinatorics/binomial-newton): Pelajari teorema binomial untuk mengembangkan (x+y)^n dengan cepat. Kuasai koefisien, suku konstanta & strategi penyelesaian masalah dengan latihan soal detail.
- [Permutasi Siklis](https://nakafa.com/id/subject/high-school/12/mathematics/combinatorics/circular-permutation): Kuasai rumus permutasi siklis (n-1)! untuk susunan melingkar & masalah tempat duduk. Pelajari mengapa rotasi identik dengan contoh detail & latihan soal lengkap.
- [Kombinasi](https://nakafa.com/id/subject/high-school/12/mathematics/combinatorics/combination): Pelajari rumus kombinasi C(n,k) dengan contoh nyata. Kuasai masalah pemilihan tanpa memperhatikan urutan. Panduan lengkap dengan latihan soal detail dan kunci!
- [Aturan Pengisian Tempat](https://nakafa.com/id/subject/high-school/12/mathematics/combinatorics/filling-place-rule): Pelajari aturan pengisian tempat kombinatorik dengan metode tabel, diagram cabang, dan perkalian. Kuasai perhitungan susunan dengan contoh dan latihan.
- [Permutasi n Item dari n Objek](https://nakafa.com/id/subject/high-school/12/mathematics/combinatorics/permutation-of-n-items-from-n-objects): Kuasai permutasi n item dari n objek dengan rumus faktorial. Pelajari susunan lengkap dengan contoh langkah demi langkah dan latihan praktis.
- [Permutasi dengan Objek yang Sama](https://nakafa.com/id/subject/high-school/12/mathematics/combinatorics/permutation-with-identical-objects): Pelajari permutasi dengan objek yang sama menggunakan rumus multinomial. Kuasai perhitungan susunan berbeda saat objek tidak dapat dibedakan.
- [Peluang Suatu Kejadian](https://nakafa.com/id/subject/high-school/12/mathematics/combinatorics/probability-of-an-event): Kuasai peluang suatu kejadian dengan rumus jelas, konsep ruang sampel, dan contoh nyata. Pelajari cara menghitung kemungkinan kejadian efektif.
- [Peluang Kejadian Majemuk](https://nakafa.com/id/subject/high-school/12/mathematics/combinatorics/probability-of-compound-events): Kuasai peluang kejadian majemuk dengan penjelasan jelas tentang kejadian bebas dan tidak bebas, rumus, dan contoh nyata untuk pemahaman mendalam.
- [Peluang Kejadian Majemuk Saling Bebas Bersyarat](https://nakafa.com/id/subject/high-school/12/mathematics/combinatorics/probability-of-independent-conditional-events): Kuasai konsep peluang bersyarat dan independen dengan penjelasan jelas, rumus, dan contoh nyata untuk meningkatkan pemahaman kamu.
- [Peluang Kejadian Majemuk Saling Bebas](https://nakafa.com/id/subject/high-school/12/mathematics/combinatorics/probability-of-independent-events): Kuasai peluang kejadian saling bebas dengan penjelasan jelas, rumus, dan contoh nyata. Pelajari cara menghitung probabilitas gabungan efektif.
- [Peluang Kejadian Majemuk Saling Lepas](https://nakafa.com/id/subject/high-school/12/mathematics/combinatorics/probability-of-mutually-exclusive-events): Pahami kejadian saling lepas dalam peluang dengan penjelasan jelas dan contoh. Pelajari cara menghitung peluangnya dan menerapkan konsep efektif.
- [Fungsi Distribusi Binomial](https://nakafa.com/id/subject/high-school/12/mathematics/data-analysis-probability/binomial-distribution-function): Pelajari rumus distribusi binomial dengan contoh langkah demi langkah. Hitung peluang keberhasilan dalam percobaan berulang dan latihan soal lengkap.
- [Nilai Harapan Distribusi Binomial](https://nakafa.com/id/subject/high-school/12/mathematics/data-analysis-probability/expected-value-of-binomial-distribution): Pahami nilai harapan distribusi binomial dengan penjelasan dan contoh jelas. Pelajari cara menghitung hasil rata-rata percobaan berulang rumus E(X)=np.
- [Nilai Harapan Distribusi Normal](https://nakafa.com/id/subject/high-school/12/mathematics/data-analysis-probability/expected-value-of-normal-distribution): Pahami nilai harapan distribusi normal dengan penjelasan dan contoh jelas. Pelajari mengapa E(X)=μ dan cara menghitung mean dalam soal statistik.
- [Fungsi Distribusi Normal](https://nakafa.com/id/subject/high-school/12/mathematics/data-analysis-probability/normal-distribution-function): Pelajari fungsi distribusi normal dengan visualisasi kurva lonceng dan contoh soal. Pahami transformasi z-score dan cara menghitung peluang langkah demi langkah.
- [Distribusi Seragam](https://nakafa.com/id/subject/high-school/12/mathematics/data-analysis-probability/uniform-distribution): Pelajari distribusi seragam dengan contoh peluang sama menggunakan dadu dan kartu. Pahami rumus f(x)=1/k dan selesaikan soal peluang langkah demi langkah.
- [Aplikasi Turunan](https://nakafa.com/id/subject/high-school/12/mathematics/derivative-function/application-of-derivative): Pelajari cara turunan memecahkan masalah fisika nyata. Hitung kecepatan, percepatan, dan ketinggian maksimum dengan contoh dan rumus langkah demi langkah.
- [Aturan Rantai pada Turunan](https://nakafa.com/id/subject/high-school/12/mathematics/derivative-function/chain-rule-in-derivative): Kuasai aturan rantai untuk menurunkan fungsi komposisi. Pelajari metode langkah demi langkah untuk fungsi bersusun dengan contoh pangkat dan trigonometri.
- [Konsep Turunan Fungsi](https://nakafa.com/id/subject/high-school/12/mathematics/derivative-function/concept-of-derivative-function): Pahami fungsi turunan sebagai laju perubahan dan kemiringan kurva. Pelajari limit, garis singgung, dan diferensiasi dengan contoh visual dan penjelasan jelas.
- [Turunan Fungsi Aljabar](https://nakafa.com/id/subject/high-school/12/mathematics/derivative-function/derivative-of-algebraic-function): Kuasai diferensiasi fungsi aljabar menggunakan aturan pangkat, hasil kali, dan hasil bagi. Pelajari cara menurunkan polinomial, akar, dan fungsi rasional.
- [Turunan Fungsi Trigonometri](https://nakafa.com/id/subject/high-school/12/mathematics/derivative-function/derivative-of-trigonometric-function): Kuasai turunan fungsi trigonometri: sin, cos, tan, dan lainnya. Pelajari rumus, aturan hasil kali, hasil bagi dengan contoh langkah demi langkah dan solusi.
- [Persamaan Garis Singgung pada Kurva](https://nakafa.com/id/subject/high-school/12/mathematics/derivative-function/equation-of-a-tangent-line-to-a-curve): Kuasai cara mencari persamaan garis singgung menggunakan turunan. Pelajari metode langkah demi langkah, perhitungan gradien, dan soal kompleks dengan contoh visual.
- [Titik Ekstrim, Nilai Balik Maksimum dan Minimum](https://nakafa.com/id/subject/high-school/12/mathematics/derivative-function/extrema-maximum-and-minimum-value): Kuasai cara mencari ekstrim menggunakan turunan. Pelajari uji turunan pertama dan kedua untuk mengidentifikasi titik kritis, nilai maksimum dan minimum dengan contoh visual.
- [Fungsi Naik, Turun, dan Stasioner](https://nakafa.com/id/subject/high-school/12/mathematics/derivative-function/increasing-decreasing-and-stationary-function): Kuasai cara mengidentifikasi fungsi naik, turun, dan stasioner menggunakan turunan. Pelajari analisis perilaku fungsi dan penentuan interval kemonotonan.
- [Sifat Turunan Fungsi](https://nakafa.com/id/subject/high-school/12/mathematics/derivative-function/properties-of-derivative-function): Kuasai sifat-sifat turunan penting: aturan pangkat, hasil kali, hasil bagi, dan rantai. Pelajari jalan pintas menurunkan fungsi efisien dengan penjelasan jelas.
- [Penulisan Turunan Fungsi](https://nakafa.com/id/subject/high-school/12/mathematics/derivative-function/writing-the-derivative-function): Pelajari cara menulis turunan fungsi menggunakan notasi Leibniz dan Newton. Kuasai berbagai simbol matematika dengan contoh langkah demi langkah dan aplikasi.
- [Kombinasi Transformasi Fungsi](https://nakafa.com/id/subject/high-school/12/mathematics/function-transformation/combined-transformation-function): Pelajari kombinasi transformasi fungsi dengan contoh langkah demi langkah. Kuasai transformasi vertikal, horizontal, pengaruh urutan, dan kerjakan latihan soal.
- [Dilatasi Horizontal](https://nakafa.com/id/subject/high-school/12/mathematics/function-transformation/horizontal-dilation): Pahami dilatasi horizontal pada fungsi dengan contoh jelas. Pelajari cara meregangkan atau menekan grafik horizontal dan terapkan pada berbagai fungsi.
- [Refleksi Horizontal](https://nakafa.com/id/subject/high-school/12/mathematics/function-transformation/horizontal-reflection): Kuasai refleksi horizontal pada fungsi dengan contoh jelas. Pelajari cara memantulkan grafik terhadap sumbu y dan terapkan transformasi ini secara efektif.
- [Translasi Horizontal](https://nakafa.com/id/subject/high-school/12/mathematics/function-transformation/horizontal-translation): Pelajari cara translasi horizontal menggeser grafik fungsi ke kiri atau kanan tanpa mengubah bentuk, tingkatkan pemahaman transformasi fungsi Anda.
- [Rotasi](https://nakafa.com/id/subject/high-school/12/mathematics/function-transformation/rotation): Kuasai rotasi fungsi terhadap titik tetap dengan contoh langkah demi langkah. Pelajari rumus rotasi, sudut, dan transformasi untuk berbagai jenis fungsi.
- [Dilatasi Vertikal](https://nakafa.com/id/subject/high-school/12/mathematics/function-transformation/vertical-dilation): Kuasai dilatasi vertikal fungsi dengan contoh jelas. Pelajari cara meregangkan atau menekan grafik vertikal menggunakan faktor skala dan terapkan transformasi.
- [Refleksi Vertikal](https://nakafa.com/id/subject/high-school/12/mathematics/function-transformation/vertical-reflection): Jelajahi teknik refleksi vertikal untuk membalik grafik fungsi terhadap sumbu x. Temukan transformasi cermin dengan contoh praktis dan latihan soal.
- [Translasi Vertikal](https://nakafa.com/id/subject/high-school/12/mathematics/function-transformation/vertical-translation): Buka rahasia translasi vertikal untuk menggerakkan grafik fungsi naik turun dengan mudah. Lihat bagaimana menambah konstanta menggeser grafik tanpa ubah bentuk.
- [Luas Bidang Datar](https://nakafa.com/id/subject/high-school/12/mathematics/integral/area-of-a-flat-surface): Hitung luas bidang datar menggunakan integral tentu dengan solusi langkah demi langkah. Kuasai fungsi kuadrat dan irasional melalui contoh praktis.
- [Integral Tentu](https://nakafa.com/id/subject/high-school/12/mathematics/integral/definite-integral): Ubah jumlahan Riemann menjadi perhitungan luas yang eksak menggunakan integral tentu. Pelajari proses limit dan notasi dengan contoh terperinci.
- [Definisi Integral Tak Tentu](https://nakafa.com/id/subject/high-school/12/mathematics/integral/definition-of-indefinite-integral): Temukan integral tak tentu sebagai antiturunan dengan konstanta misterius C. Kuasai notasi, pahami pentingnya konstanta, dan balikkan turunan.
- [Teorema Dasar Kalkulus](https://nakafa.com/id/subject/high-school/12/mathematics/integral/fundamental-theorem-of-calculus): Hubungkan turunan dan integral dengan teorema terkuat kalkulus. Pelajari bagaimana antiturunan menyederhanakan perhitungan integral tentu selamanya.
- [Integral dalam Bidang Ekonomi dan Bisnis](https://nakafa.com/id/subject/high-school/12/mathematics/integral/integral-in-economics-and-business): Terapkan integral pada skenario bisnis nyata: hitung total penjualan, optimasi biaya, analisis pertumbuhan pendapatan, dan tentukan surplus konsumen.
- [Integral dalam Bidang Fisika](https://nakafa.com/id/subject/high-school/12/mathematics/integral/integral-in-physics): Jelajahi cara integral memecahkan masalah fisika: hitung usaha dengan gaya variabel, energi pegas, distribusi massa, dan pusat massa secara efektif.
- [Sifat-Sifat Integral Tentu](https://nakafa.com/id/subject/high-school/12/mathematics/integral/properties-of-definite-integral): Kuasai sifat penting integral tentu: batas identik, pembalikan batas, faktor konstanta, aturan jumlah, dan teknik pemecahan interval.
- [Sifat-Sifat Integral Tak Tentu](https://nakafa.com/id/subject/high-school/12/mathematics/integral/properties-of-indefinite-integral): Kuasai aturan integral tak tentu: aturan pangkat, kelipatan konstanta, aturan jumlah/kurang, dan teknik substitusi-u dengan contoh langkah demi langkah.
- [Jumlahan Riemann](https://nakafa.com/id/subject/high-school/12/mathematics/integral/riemann-sum): Perkirakan luas di bawah kurva menggunakan persegi panjang dengan jumlahan Riemann. Pelajari partisi, titik sampel, dan perhitungan visual dengan contoh detail.
- [Aplikasi Limit Fungsi](https://nakafa.com/id/subject/high-school/12/mathematics/limit/application-of-limit-function): Terapkan limit pada skenario dunia nyata: analisis penyebaran penyakit, strategi vaksinasi, model ekonomi, dan perhitungan biaya marginal dengan contoh.
- [Konsep Limit Fungsi](https://nakafa.com/id/subject/high-school/12/mathematics/limit/concept-of-limit-function): Pahami limit fungsi melalui contoh intuitif dan tabel nilai. Pelajari limit kiri/kanan, definisi formal, dan selesaikan bentuk tak tentu.
- [Limit Fungsi Aljabar](https://nakafa.com/id/subject/high-school/12/mathematics/limit/limit-of-algebraic-function): Hitung limit fungsi polinomial dan rasional. Kuasai teknik pemfaktoran, rasionalisasi, dan selesaikan bentuk tak tentu dengan contoh terperinci.
- [Limit Fungsi Trigonometri](https://nakafa.com/id/subject/high-school/12/mathematics/limit/limit-of-trigonometric-function): Kuasai limit trigonometri menggunakan teorema fundamental. Pelajari sin x/x sama dengan 1, sifat perbandingan, identitas, dan teknik substitusi lanjutan.
- [Sifat Limit Fungsi](https://nakafa.com/id/subject/high-school/12/mathematics/limit/properties-of-limit-function): Sederhanakan perhitungan limit kompleks dengan sifat penting. Kuasai aturan jumlah, kali, bagi, pangkat, dan akar dengan penerapan langkah demi langkah.
- [Operator Aritmatika](https://nakafa.com/id/subject/university/bachelor/ai-ds/ai-programming/arithmetic-operator): Kuasai operator aritmatika Python dengan aturan prioritas dan asosiativitas. Pelajari +, -, *, /, //, %, ** untuk pemrograman AI dengan contoh praktis.
- [Membuat Array dengan NumPy](https://nakafa.com/id/subject/university/bachelor/ai-ds/ai-programming/array-numpy): Pelajari cara membuat array NumPy: manual, fungsi bawaan, sequence, dan operasi dasar. Panduan lengkap dengan contoh kode teruji untuk pemrograman AI dan data science.
- [Operasi pada Array dengan NumPy](https://nakafa.com/id/subject/university/bachelor/ai-ds/ai-programming/array-operation-numpy): Pelajari operasi matematika pada array dengan NumPy: broadcasting, vektorisasi, aritmetika, statistik, dan manipulasi bentuk. Panduan lengkap dengan contoh kode teruji untuk pemrograman AI dan data science.
- [Atribut dan Tipe Data dengan NumPy](https://nakafa.com/id/subject/university/bachelor/ai-ds/ai-programming/attribute-data-type-numpy): Pelajari atribut array NumPy dan sistem tipe data: shape, dtype, size, ndim. Panduan lengkap dengan contoh kode teruji untuk pemrograman AI dan data science.
- [Perbandingan dan Logika](https://nakafa.com/id/subject/university/bachelor/ai-ds/ai-programming/comparison-logic): Pelajari operator perbandingan dan logika Python dengan diagram interaktif. Pahami prioritas operator, boolean, nilai falsy/truthy, dan perbandingan float.
- [Container](https://nakafa.com/id/subject/university/bachelor/ai-ds/ai-programming/container): Pelajari tipe data container Python seperti list, tuple, dictionary, dan set. Panduan lengkap indexing, slicing, dan manipulasi data dengan contoh praktis.
- [Control Flow](https://nakafa.com/id/subject/university/bachelor/ai-ds/ai-programming/control-flow): Pelajari kontrol alur dalam Python meliputi break, continue, pass, else, enumerate, while loops, zip, range, dan if/elif/else dengan contoh praktis.
- [Dictionary](https://nakafa.com/id/subject/university/bachelor/ai-ds/ai-programming/dictionary): Pelajari struktur data dictionary dalam Python, metode keys(), values(), items(), indexing, for loops, dan metode get() dengan contoh praktis.
- [Escape Sequence](https://nakafa.com/id/subject/university/bachelor/ai-ds/ai-programming/escape-sequence): Pelajari escape sequence Python dengan notasi backslash. Kuasai cara menangani tanda kutip, baris baru, tab & karakter khusus dalam string.
- [Semuanya adalah Objek di Python](https://nakafa.com/id/subject/university/bachelor/ai-ds/ai-programming/everything-object-python): Temukan sifat object-oriented Python dengan contoh praktis. Jelajahi bagaimana angka, string, list, fungsi menjadi objek dengan method dan atribut.
- [File Input dan Output](https://nakafa.com/id/subject/university/bachelor/ai-ds/ai-programming/file-input-output): Pelajari cara membaca dan menulis file dalam Python, mode pembukaan file, metode read(), readline(), dan pengalihan output dengan contoh praktis.
- [Fungsi](https://nakafa.com/id/subject/university/bachelor/ai-ds/ai-programming/function): Pelajari fungsi Python: parameter, return values, scope variabel, closure, error handling. Panduan lengkap dengan contoh kode teruji untuk mahasiswa AI programming.
- [Immutable, Mutable, dan Identity](https://nakafa.com/id/subject/university/bachelor/ai-ds/ai-programming/immutable-mutable-identity): Kuasai konsep mutabilitas, identitas, dan manajemen memori objek Python. Pelajari cara kerja list, referensi, dan identitas objek dengan contoh praktis.
- [Indexing dan Slicing](https://nakafa.com/id/subject/university/bachelor/ai-ds/ai-programming/indexing-slicing): Pelajari teknik indexing dan slicing Python untuk mengakses elemen string dan list. Kuasai penggunaan indeks positif, negatif, dan stride.
- [Indexing dan Slicing dengan NumPy](https://nakafa.com/id/subject/university/bachelor/ai-ds/ai-programming/indexing-slicing-numpy): Pelajari teknik indexing dan slicing NumPy: array 1D, 2D, boolean mask, advanced indexing. Panduan lengkap dengan contoh kode teruji untuk pemrograman AI.
- [Iterable](https://nakafa.com/id/subject/university/bachelor/ai-ds/ai-programming/iterable): Pelajari konsep iterable dalam Python, operator in/not in, fungsi any/all, dan unpacking operator dengan contoh praktis dan implementasi nyata.
- [Markdown dan Command Line Interfaces](https://nakafa.com/id/subject/university/bachelor/ai-ds/ai-programming/markdown-cli): Pelajari sintaks Markdown dan perintah CLI untuk alur kerja dokumentasi efisien. Kuasai operasi file, skrip otomasi, dan tools konversi pandoc.
- [Fungsi Matematika](https://nakafa.com/id/subject/university/bachelor/ai-ds/ai-programming/math-function): Pelajari cara menggunakan modul math Python untuk fungsi sqrt(), round(), abs(), dan konstanta pi. Panduan lengkap import dan penggunaan praktis.
- [Atribut dan Metode Bilangan](https://nakafa.com/id/subject/university/bachelor/ai-ds/ai-programming/number-attribute-method): Pelajari cara menggunakan atribut real, imag, dan metode conjugate() pada bilangan kompleks Python. Panduan lengkap dengan contoh kode praktis.
- [Numbers](https://nakafa.com/id/subject/university/bachelor/ai-ds/ai-programming/numbers): Kuasai tipe angka Python: integer, float, dan kompleks. Pelajari type checking, constructor, dan notasi ilmiah untuk pemrograman AI.
- [Fungsi Print](https://nakafa.com/id/subject/university/bachelor/ai-ds/ai-programming/print-function): Pelajari fungsi print Python untuk menampilkan output. Kuasai parameter sep, end, dan teknik formatting untuk kontrol output yang presisi.
- [Step Pertama di Python](https://nakafa.com/id/subject/university/bachelor/ai-ds/ai-programming/python-step-1): Mulai perjalanan Python dengan mode interaktif, script, dan Jupyter. Bangun program pertama dengan variabel, input/output, dan latihan praktis.
- [Pemformatan String](https://nakafa.com/id/subject/university/bachelor/ai-ds/ai-programming/string-formatting): Pelajari teknik pemformatan string Python dengan format(), f-strings, alignment, precision control, dan error handling. Panduan lengkap dengan contoh praktis.
- [Metode String](https://nakafa.com/id/subject/university/bachelor/ai-ds/ai-programming/string-method): Pelajari metode string Python untuk manipulasi teks. Kuasai transformasi, pencarian, validasi karakter, dan operasi string lanjutan.
- [Objek String](https://nakafa.com/id/subject/university/bachelor/ai-ds/ai-programming/string-object): Pelajari objek string Python lengkap dengan definisi, multiline strings, concatenation literals dan variabel. Pahami cara kerja tipe data str.
- [Syntactic Sugar](https://nakafa.com/id/subject/university/bachelor/ai-ds/ai-programming/syntactic-sugar): Pelajari fitur syntactic sugar Python seperti list comprehension, lambda functions, dan operator assignment untuk menulis kode yang lebih bersih dan efisien.
- [Variabel](https://nakafa.com/id/subject/university/bachelor/ai-ds/ai-programming/variable): Pelajari konsep variabel Python, aturan penamaan, keyword yang tidak boleh digunakan, dan cara kerja memori. Panduan lengkap dengan contoh praktis.
- [Perhitungan Semua Nilai Eigen](https://nakafa.com/id/subject/university/bachelor/ai-ds/linear-methods/all-eigenvalues-calculation): Pelajari metode QR untuk menghitung semua nilai eigen melalui iterasi dekomposisi matriks. Pahami sifat konvergensi dan elemen diagonal.
- [Perkiraan Terbaik dalam Fungsi dan Ruang Polinomial](https://nakafa.com/id/subject/university/bachelor/ai-ds/linear-methods/approximation-function-polynomial): Pelajari teknik aproksimasi Gauss untuk pemodelan fungsi optimal menggunakan ruang polinomial dan trigonometrik dengan norma Euklidean dan produk skalar.
- [Karakteristik Polinomial](https://nakafa.com/id/subject/university/bachelor/ai-ds/linear-methods/characteristic-polynomial): Jelajahi polinomial karakteristik untuk mencari nilai eigen, memahami multiplisitas aljabar, dan analisis hubungan jejak matriks dalam aljabar linear.
- [Cholesky Dekomposisi](https://nakafa.com/id/subject/university/bachelor/ai-ds/linear-methods/cholesky-decomposition): Kuasai dekomposisi Cholesky untuk matriks positif definit dengan algoritma efisien, faktorisasi segitiga bawah, dan analisis kompleksitas komputasi.
- [Matriks Kompleks](https://nakafa.com/id/subject/university/bachelor/ai-ds/linear-methods/complex-matrix): Pelajari matriks kompleks dengan operasi adjoint, transpose Hermitian, norma Euclidean, dan sifat penting untuk komputasi kuantum dan pemrosesan sinyal.
- [Ruang Vektor Kompleks](https://nakafa.com/id/subject/university/bachelor/ai-ds/linear-methods/complex-vector-space): Pelajari ruang vektor kompleks dengan bilangan kompleks, teorema fundamental aljabar, dan 8 aksioma penting. Panduan lengkap metode linear AI.
- [Aturan Cramer](https://nakafa.com/id/subject/university/bachelor/ai-ds/linear-methods/cramer-rule): Selesaikan sistem linear dengan determinan menggunakan aturan Cramer. Pelajari matriks komplementer, formula invers, dan contoh lengkap untuk AI.
- [Definisi Determinan](https://nakafa.com/id/subject/university/bachelor/ai-ds/linear-methods/determinant): Pahami determinan dengan 3 sifat kunci: linearitas, antisimetris, dan normalisasi. Pelajari keterbalikan matriks dan metode perhitungan untuk AI.
- [Perhitungan Determinan](https://nakafa.com/id/subject/university/bachelor/ai-ds/linear-methods/determinant-calculation): Kuasai perhitungan determinan dengan ekspansi kofaktor, eliminasi Gauss, dan matriks segitiga. Pelajari metode efisien untuk aljabar linear AI.
- [Diagonalisasi Matriks](https://nakafa.com/id/subject/university/bachelor/ai-ds/linear-methods/diagonalization-matrix): Transformasi matriks dengan nilai eigen dan vektor eigen. Pelajari syarat diagonalisasi, multiplisitas geometris vs aljabar untuk komputasi AI.
- [Prosedur Dasar untuk Diagonalisasi](https://nakafa.com/id/subject/university/bachelor/ai-ds/linear-methods/diagonalization-procedure): Pelajari prosedur 3 langkah diagonalisasi matriks: hitung nilai eigen, cari ruang eigen, dan periksa kondisi dengan contoh praktis.
- [Nilai Eigen dari Matriks Diagonal dan Segitiga](https://nakafa.com/id/subject/university/bachelor/ai-ds/linear-methods/eigenvalue-diagonal-matrix): Temukan cara membaca nilai eigen langsung dari entri diagonal matriks diagonal dan segitiga, plus hubungan determinan-jejak.
- [Nilai Eigen, Vektor Eigen, dan Ruang Eigen](https://nakafa.com/id/subject/university/bachelor/ai-ds/linear-methods/eigenvalue-eigenvector-eigenspace): Kuasai konsep fundamental nilai eigen: pahami transformasi vektor oleh matriks, hitung vektor eigen, dan jelajahi sifat ruang eigen.
- [Kemampuan Identifikasi dan Pemeringkatan](https://nakafa.com/id/subject/university/bachelor/ai-ds/linear-methods/identifiability-ranking): Jelajahi identifikasi matriks melalui dekomposisi nilai singular: tentukan keunikan parameter, nilai defisiensi peringkat, dan solusi sistem.
- [Perhitungan Nilai Eigen Individu](https://nakafa.com/id/subject/university/bachelor/ai-ds/linear-methods/individual-eigenvalue-calculation): Pelajari 3 metode perhitungan nilai eigen: iterasi invers dengan shift, von Mises untuk eigen dominan, dan teknik mencari eigen terkecil.
- [Trigonalisasi dan Bentuk Normal Jordan](https://nakafa.com/id/subject/university/bachelor/ai-ds/linear-methods/jordan-normal-form): Kuasai Bentuk Normal Jordan dan trigonalisasi matriks: dekomposisi kanonik untuk matriks tak dapat didiagonalisasi dengan blok Jordan dan nilai eigen.
- [Teorema Pengembangan Laplace](https://nakafa.com/id/subject/university/bachelor/ai-ds/linear-methods/laplace-expansion): Kuasai teorema pengembangan Laplace: perhitungan determinan sistematis dengan minor dan kofaktor, fleksibilitas baris/kolom dan contoh aturan Sarrus.
- [Masalah Keseimbangan Linear](https://nakafa.com/id/subject/university/bachelor/ai-ds/linear-methods/linear-equilibrium-problem): Selesaikan masalah keseimbangan linear: optimasi kuadrat terkecil untuk sistem over-determined dengan norm L1, L2, L∞ dan metode proyeksi geometris.
- [Linear Model](https://nakafa.com/id/subject/university/bachelor/ai-ds/linear-methods/linear-model): Pelajari model linear: hubungan fundamental y=h(t)·x, bentuk polinomial/trigonometri, konversi data-ke-model, dan teknik linearisasi untuk AI.
- [LU Dekomposisi](https://nakafa.com/id/subject/university/bachelor/ai-ds/linear-methods/lu-decomposition): Kuasai dekomposisi LU: faktorisasi matriks menjadi bentuk segitiga bawah/atas dengan eliminasi Gauss, implementasi Python dan penyelesaian sistem.
- [Kondisi Matriks](https://nakafa.com/id/subject/university/bachelor/ai-ds/linear-methods/matrix-condition): Pelajari norma matriks, bilangan kondisi, dan stabilitas numerik. Pahami spektralradius, analisis nilai eigen, dan estimasi error untuk sistem AI.
- [Kesamaan Matriks](https://nakafa.com/id/subject/university/bachelor/ai-ds/linear-methods/matrix-similarity): Pahami kesamaan matriks, transformasi basis, dan sifat invarian. Pelajari preservasi nilai eigen, perubahan koordinat, dan transformasi linear.
- [Sistem Persamaan Normal](https://nakafa.com/id/subject/university/bachelor/ai-ds/linear-methods/normal-equation): Kuasai persamaan normal untuk optimasi kuadrat terkecil. Pelajari solusi closed-form, prinsip ortogonalitas, dan kondisi sistem terpecahkan.
- [Solusi Sistem Persamaan Normal](https://nakafa.com/id/subject/university/bachelor/ai-ds/linear-methods/normal-equation-solution): Implementasikan solusi persamaan normal dengan dekomposisi QR dan pseudoinverse. Pelajari metode numerik, fitting polynomial, dan perbandingan stabilitas.
- [Perhitungan Numerik dari Nilai Eigen](https://nakafa.com/id/subject/university/bachelor/ai-ds/linear-methods/numerical-eigenvalue-calculation): Kuasai algoritma iteratif nilai eigen untuk masalah nonlinear. Pelajari metode nilai eigen dominan, diagonalisasi, dan pendekatan komputasi untuk AI.
- [Polinomial Ortogonal](https://nakafa.com/id/subject/university/bachelor/ai-ds/linear-methods/orthogonal-polynomials): Pelajari polinomial Chebyshev dan Legendre dengan perkalian skalar berbobot, proses Gram-Schmidt, dan aproksimasi Gauss untuk analisis numerik.
- [Proyeksi Ortogonal](https://nakafa.com/id/subject/university/bachelor/ai-ds/linear-methods/orthogonal-projection): Pelajari teori proyeksi ortogonal dengan teorema eksistensi, formula basis ortonormal, matriks Gram, dan metode pendekatan terbaik dalam ruang vektor.
- [Matriks Ortogonal dan Uniter](https://nakafa.com/id/subject/university/bachelor/ai-ds/linear-methods/orthogonal-unitary-matrix): Jelajahi matriks ortogonal dan uniter dengan sifat determinan, analisis nilai eigen, contoh rotasi, dan aplikasinya dalam aljabar linear.
- [Matriks Definit Positif](https://nakafa.com/id/subject/university/bachelor/ai-ds/linear-methods/positive-definite-matrix): Kuasai matriks definit positif dengan kriteria nilai eigen, minor utama, sifat geometris, dan aplikasi optimasi untuk solusi matematika andal.
- [Analisis Komponen Utama](https://nakafa.com/id/subject/university/bachelor/ai-ds/linear-methods/principal-component-analysis): Pelajari PCA melalui diagonalisasi matriks kovarians, analisis nilai eigen, transformasi koordinat, dan visualisasi geometris untuk sains data.
- [QR Dekomposisi](https://nakafa.com/id/subject/university/bachelor/ai-ds/linear-methods/qr-decomposition): Kuasai QR dekomposisi menggunakan metode Gram-Schmidt dan Householder untuk faktorisasi matriks, transformasi ortogonal, dan sistem linear.
- [Transformasi Sumbu Nyata](https://nakafa.com/id/subject/university/bachelor/ai-ds/linear-methods/real-axis-transformation): Pelajari bentuk kuadrat dengan matriks simetris, transformasi koordinat berbasis nilai eigen, dan klasifikasi irisan kerucut meliputi elips, hiperbola, dan parabola.
- [Regularisasi](https://nakafa.com/id/subject/university/bachelor/ai-ds/linear-methods/regularization): Kuasai regularisasi Tikhonov untuk sistem linear tidak stabil. Pelajari cara menyelesaikan masalah ill-conditioned dan menstabilkan estimasi parameter.
- [Produk Skalar](https://nakafa.com/id/subject/university/bachelor/ai-ds/linear-methods/scalar-product): Pahami produk skalar dalam ruang vektor: bentuk bilinear, matriks definit positif, sifat Hermitian, dan implementasi real vs kompleks.
- [Teorema Spektral untuk Matriks Kompleks](https://nakafa.com/id/subject/university/bachelor/ai-ds/linear-methods/spectral-complex-matrix): Kuasai diagonalisasi ortogonal matriks normal: buktikan ekuivalensi antara normalitas dan basis vektor eigen menggunakan induksi matematis.
- [Teorema Spektral untuk Matriks Nyata](https://nakafa.com/id/subject/university/bachelor/ai-ds/linear-methods/spectral-real-matrix): Temukan kapan matriks nyata memiliki basis vektor eigen ortonormal: jelajahi kondisi normalitas, polinomial karakteristik, dan contoh penyangkal.
- [Teorema Spektral](https://nakafa.com/id/subject/university/bachelor/ai-ds/linear-methods/spectral-theorem): Pelajari kapan matriks dapat didiagonalisasi dengan vektor eigen ortonormal. Kuasai matriks normal, hermitian, dan kesatuan untuk AI.
- [Analisis Statistik](https://nakafa.com/id/subject/university/bachelor/ai-ds/linear-methods/statistical-analysis): Kuasai matriks informasi Fisher, kovarian parameter, dan kuadrat terkecil berbobot. Bangun model statistik yang robust dan akurat.
- [Matriks Simetris dan Hermitian](https://nakafa.com/id/subject/university/bachelor/ai-ds/linear-methods/symmetric-hermitian-matrix): Temukan matriks simetris dan Hermitian dengan nilai eigen real dan vektor eigen ortogonal. Penting untuk bentuk kuadrat dan diagonalisasi matriks.
- [Sistem Persamaan Linear](https://nakafa.com/id/subject/university/bachelor/ai-ds/linear-methods/system-linear-equation): Selesaikan sistem linear berlebih dengan metode kuadrat terkecil. Pelajari curve fitting, model polinomial, dan solusi matriks untuk data nyata.