Set 1

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Given $a = \frac{1}{2}$ , $b = 2$ , $c = 1$

The value of

\frac{a^{-2}bc^3}{ab^2c^{-1}} = ....

The simplified form of

\frac{3\sqrt{3} + \sqrt{7}}{\sqrt{7} - 2\sqrt{3}} = ....

The value of

\left(\frac{^3\log4 \cdot ^4\log81+^3\log9}{^3\log27-^3\log3}\right) = ....

The value of $x$ that satisfies

9^{2x} - 10 \cdot 9^x + 9 > 0, x \in \mathbb{R}

is ....

$\{x < 0 \text{ or } x < 1, x \in \mathbb{R}\}$

$\{x < 0 \text{ or } x > 1, x \in \mathbb{R}\}$

$\{x > 0 \text{ or } x > 1, x \in \mathbb{R}\}$

$\{0 < x < 1, x \in \mathbb{R}\}$

$\{-1 < x < 1, x \in \mathbb{R}\}$

The roots of the equation $x^2 + ax - 4 = 0$ are $p$ and $q$

If $p^2 - 2pq + q^2 = 8a$ , the value of $a$ that satisfies is ....

A mathematical model for the sea water height $H$ at a port as a function of time $t$ in hours is given by the function $H(t) = A \cos(Bt) + C$

The data shows that the maximum sea water height is $10$ meters and the minimum is $2$ meters. The complete tidal period is $12$ hours.

Analyze the values of $A$ , $B$ , and $C$ from the function based on the given data.

$A = 4, B = \frac{\pi}{6}, C = 6$

$A = 8, B = \frac{\pi}{12}, C = 2$

$A = 6, B = \frac{\pi}{6}, C = 4$

$A = 4, B = \frac{\pi}{12}, C = 8$

$A = 8, B = \frac{\pi}{6}, C = 4$

At the "Murah" bookstore, Adi buys $4$ books, $2$ pens and $3$ pencils for $\text{Rp}26{,}000$ . Bima buys $3$ books, $3$ pens and $1$ pencil for $\text{Rp}21{,}500$ . Citra buys $3$ books and $1$ pencil for $\text{Rp}12{,}500$ .

If Dina buys $2$ pens and $2$ pencils, then she must pay ....

$\text{Rp}10{,}000$

$\text{Rp}20{,}000$

$\text{Rp}30{,}000$

$\text{Rp}40{,}000$

$\text{Rp}45{,}000$

A toddler is recommended by a doctor to consume at least $60$ grams of calcium and $30$ grams of iron. A capsule contains $5$ grams of calcium and $2$ grams of iron, while a tablet contains $2$ grams of calcium and $2$ grams of iron.

If the price of a capsule is $\text{Rp}1{,}000$ and the price of a tablet is $\text{Rp}800$ , the minimum cost that must be spent to meet the needs of the toddler is ....

$\text{Rp}10{,}000$

$\text{Rp}12{,}000$

$\text{Rp}13{,}000$

$\text{Rp}14{,}000$

$\text{Rp}15{,}000$

Given functions $f: \mathbb{R} \rightarrow \mathbb{R}$ and $g: \mathbb{R} \rightarrow \mathbb{R}$ defined by $f(x) = 2x^2 - 3$ and $g(x) = 3x - 1$

The composite function $(f \circ g)(x)$ is defined as ....

$(f \circ g)(x) = 18x^2 - 12x - 21$

$(f \circ g)(x) = 18x^2 + 10x - 21$

$(f \circ g)(x) = 18x^2 - 12x - 1$

$(f \circ g)(x) = 9x^2 - 6x - 2$

$(f \circ g)(x) = 9x^2 - 6x + 2$

Given functions $f(x) = \frac{2x - 5}{x - 4}, x \neq 4$ and $g(x) = 3x + 8$

The inverse of $(f \circ g)(x)$ is ....

$(f \circ g)^{-1}(x) = \frac{6x + 11}{3x + 4}, x \neq -\frac{4}{3}$

$(f \circ g)^{-1}(x) = \frac{6x - 11}{3x + 4}, x \neq -\frac{4}{3}$

$(f \circ g)^{-1}(x) = \frac{6x - 6}{3x + 4}, x \neq -\frac{4}{3}$

$(f \circ g)^{-1}(x) = \frac{11 - 4x}{3x - 6}, x \neq 2$

$(f \circ g)^{-1}(x) = \frac{4x - 11}{3x - 6}, x \neq 2$

A square with corner points at $(0, 0)$ , $(2, 0)$ , $(2, 2)$ , and $(0, 2)$ is subjected to two linear transformations in sequence.

The first transformation $(T_1)$ is a scale with factor $2$ on the x-axis and factor $0.5$ on the y-axis. The second transformation $(T_2)$ is a shear with factor $1$ along the x-axis.

Evaluate the area of the square after both transformations!

Given that $(x - 1)$ and $(x + 3)$ are factors of the polynomial equation $x^3 - ax^2 - bx + 12 = 0$

If $x_1, x_2,$ and $x_3$ are the roots of the equation and $x_1 < x_2 < x_3$ , the value of $x_1 + x_2 + x_3$ is ....

Given matrices $A = \begin{pmatrix} 3 & y \\ 5 & -1 \end{pmatrix}$ , $B = \begin{pmatrix} x & 5 \\ -3 & 6 \end{pmatrix}$ , and $C = \begin{pmatrix} -3 & -1 \\ y & 9 \end{pmatrix}$

If $A + B + C = \begin{pmatrix} 8 & 5x \\ -x & -4 \end{pmatrix}$ , the value of $x + 2xy + y = ....$

Given matrices $A = \begin{pmatrix} 1 & 2 \\ 1 & 3 \end{pmatrix}$ and $B = \begin{pmatrix} 4 & 1 \\ 1 & 3 \end{pmatrix}$

Matrix $C$ of order $2 \times 2$ satisfies $AC = B$ , the determinant of matrix $C$ is ....

The sum of the first $n$ terms of an arithmetic series is expressed as $S_n = 2n^2 + 4n$

The 10th term of the series is ....

The path is calculated from the box to B10, forming an arithmetic sequence of distances $10, 18, 26, 34, \ldots$

mermaid

There are $10$ flags in the box that must be moved into the available bottles one by one (not all at once). All race participants start from bottle number $10$ to retrieve flags from the box.

The distance from the start to the box is ....

A merchant's profit increases every month by the same amount. If the profit in the first month is $\text{Rp}46{,}000$ and the monthly profit increase is $\text{Rp}18{,}000$ , the total profit up to the 12th month is ....

$\text{Rp}1{,}700{,}000$

$\text{Rp}1{,}740{,}000$

$\text{Rp}1{,}840{,}000$

$\text{Rp}1{,}950{,}000$

$\text{Rp}2{,}000{,}000$

The solution set of the trigonometric equation

\cos 2x - 2\cos x = -1

for $0 \leq x \leq 2\pi$ is ....

$\left\{0, \frac{1}{2}\pi, \pi\right\}$

$\left\{0, \frac{1}{2}\pi, \frac{2}{3}\pi\right\}$

$\left\{0, \frac{1}{2}\pi, \pi, \frac{3}{2}\pi\right\}$

$\left\{0, \frac{1}{2}\pi, \frac{2}{3}\pi, 2\pi\right\}$

$\left\{0, \frac{1}{2}\pi, \frac{3}{2}\pi, 2\pi\right\}$

Pay attention to the following graph!

Trigonometric Function Graph

Sine function graph with horizontal transformation.

The equation of the trigonometric function graph is ....

$y = -\sin(2x + 60^\circ)$

$y = \sin(2x + 60^\circ)$

$y = \cos(2x + 60^\circ)$

$y = \sin(2x - 60^\circ)$

$y = \cos(2x - 60^\circ)$

The value of

\sin 75^\circ - \sin 165^\circ

is ....

A circle with center at the origin $O$ and radius $r$ is given. Points $A$ and $B$ lie on the circle such that $OA$ and $OB$ are radii.

Create a vector representation to prove that the tangent line of the circle at point $A$ is perpendicular to the radius $OA$ !

By showing that the dot product of position vector A and the direction vector of the tangent line at A is positive.

By showing that the cross product of position vector A and the direction vector of the tangent line at A is the zero vector.

By showing that the dot product of position vector A and the direction vector of the tangent line at A is zero.

By showing that position vector A and the direction vector of the tangent line at A have the same direction.

By showing that position vector A and the direction vector of the tangent line at A have the same length.

Given a cube ABCD.EFGH with edge length $12$ cm. If $P$ is the midpoint of $CG$ , the distance from point $P$ to diagonal $HB$ is ....

Given a regular square pyramid P.QRST with base edge $3$ cm and lateral edge $3\sqrt{2}$ cm.

The tangent of the angle between line PT and base QRST is ....

The weight of newborn babies at a hospital is assumed to be normally distributed with mean $(\mu)$ $3{,}200$ grams and standard deviation $(\sigma)$ $450$ grams.

Analyze the probability that a newborn baby at the hospital has a weight between $2{,}750$ grams and $3{,}650$ grams!

$P(Z < 1) - P(Z < -1)$

$P(Z < 2) - P(Z < -2)$

$P(Z < 1) + P(Z < -1)$

$P(Z < 2) + P(Z < -2)$

$P(Z < 0) - P(Z < -1)$

The equation of the tangent line to the circle

x^2 + y^2 + 2x - 6y + 2 = 0

that is parallel to the line $x - y + 3 = 0$ is ....

$x - y = 0$

$x - y - 8 = 0$

$x - y + 8 = 0$

$2x - y + 8 = 0$

$2x - y - 8 = 0$

The value of

\lim_{x \to 0} \left(\frac{5x}{3 - \sqrt{9 + x}}\right)

is ....

The value of

\lim_{x \to 0} \left(\frac{1 - \cos 2x}{x \tan 2x}\right)

is ....

The first derivative of $y = \cos^3 x$ is ....

$3\cos x \cdot \sin x$

$-3\cos x \cdot \sin x$

$2\cos x \cdot \sin 2x$

$-6\cos x \cdot \sin 2x$

$\frac{-3}{2}\cos x \cdot \sin 2x$

The equation of the tangent line to the curve $y = 6\sqrt{x}$ that passes through the point with abscissa $9$ is ....

A piece of land will be bordered by a fence using barbed wire as shown in the illustration below.

Wall

Land Area

$y$

$x$

Fence

Fence Shape

Barbed Wire

The land boundary that is fenced is the one without a wall. The available wire is $800$ meters. What is the maximum area that can be bordered by the available fence?

$2{,}500 \text{ m}^2$

$5{,}000 \text{ m}^2$

$6{,}000 \text{ m}^2$

$10{,}000 \text{ m}^2$

$15{,}000 \text{ m}^2$

The result of

\int 2x(5 - x)^3 dx = ....

$-\frac{1}{10}(6x + 5)(5 - x)^4 + C$

$-\frac{1}{10}(4x + 5)(5 - x)^4 + C$

$-\frac{1}{10}(x + 5)(5 - x)^4 + C$

$\frac{1}{10}(4x + 5)(5 - x)^4 + C$

$\frac{1}{2}(5 - x)^4 + C$

The value of

\int_1^2 (4x^2 - x + 5) dx

is ....

The result of

\int (2\sin 2x - 3\cos x) dx = ....

$2\cos 2x - 3\sin x + C$

$-2\cos 2x + 3\sin x + C$

$-2\cos 2x - 3\sin x + C$

$-\cos 2x - 3\sin x + C$

$\cos 2x + 3\sin x + C$

The result of

\int \frac{3x - 1}{(3x^2 - 2x + 7)^7} dx

is ....

$\frac{-1}{(3x^2 - 2x + 7)^6} + C$

$\frac{1}{12(3x^2 - 2x + 7)^6} + C$

$\frac{-1}{12(3x^2 - 2x + 7)^6} + C$

$\frac{-1}{6(3x^2 - 2x + 7)^6} + C$

$\frac{1}{6(3x^2 - 2x + 7)^6} + C$

The area of the region bounded by the curve $y = x^2 - 4x + 3$ and $y = 3 - x$ is ....

$\frac{7}{3}$ satuan luas

$\frac{8}{2}$ satuan luas

$\frac{9}{2}$ satuan luas

$\frac{11}{3}$ satuan luas

$\frac{11}{2}$ satuan luas

Two dice are thrown together once. The probability that the sum of the dice is 5 or 7 is ....

Consider the following histogram!

Score Distribution Histogram

Frequency distribution of student scores.

The mode of the data shown in the histogram is ....

Consider the data in the following table!

Score	Frequency
$40$ — $49$	$7$
$50$ — $59$	$11$
$60$ — $69$	$9$
$70$ — $79$	$6$
$80$ — $89$	$5$
$90$ — $99$	$2$

The upper quartile of the data in the table is ....

A curve is given by the function $f(x) = 6x - x^2$ . Evaluate the area bounded by this curve and the x-axis, for $x \geq 0$ !

In an exam, there are $10$ questions, from number $1$ to number $10$ . Exam participants are required to work on questions number $1$ , $2$ , and $3$ and only work on $7$ out of $10$ available questions. The number of ways participants can choose the questions to work on is ....

Command Palette

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