# Nakafa Framework: LLM

URL: https://nakafa.com/en/exercises/high-school/snbt/quantitative-knowledge/try-out/set-10/19

Exercises: Try Out - Set 10: Real exam simulation to sharpen your skills and build confidence. - Average Score Increase

---

## Exercise 19

### Question

export const metadata = {
  title: "Average Score Increase",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/27/2025",
};

In Semester <InlineMath math="I" />, Hani took <InlineMath math="5" /> Mathematics exams and obtained an average score of <InlineMath math="7.5" />. In one academic year, Hani took a total of <InlineMath math="11" /> mathematics exams and obtained an average score of <InlineMath math="8.0" />.

What is the increase in Hani's average mathematics exam score from Semester <InlineMath math="I" /> to Semester <InlineMath math="II" />?


### Choices

- [x] $$0.92$$
- [ ] $$0.82$$
- [ ] $$0.7$$
- [ ] $$1.2$$
- [ ] $$0.96$$

### Answer & Explanation

export const metadata = {
  title: "Average Increase Explanation",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/27/2025",
};

First, let's calculate the total exam score for Semester <InlineMath math="I" />:

<MathContainer>
  <BlockMath math="\text{Total Score Semester } I = 5 \times 7.5 = 37.5" />
</MathContainer>

Next, we calculate the total exam score for the whole year (Semester <InlineMath math="I" /> & <InlineMath math="II" />):

<MathContainer>
  <BlockMath math="\text{Total Score 1 Year} = 11 \times 8 = 88" />
</MathContainer>

To find the total exam score for Semester <InlineMath math="II" />, we subtract the Semester <InlineMath math="I" /> total from the yearly total:

<MathContainer>
  <BlockMath math="\text{Total Score Semester } II = 88 - 37.5 = 50.5" />
</MathContainer>

The number of exams in Semester <InlineMath math="II" /> is the difference between the total exams and Semester <InlineMath math="I" /> exams:

<MathContainer>
  <BlockMath math="\text{Number of Exams Semester } II = 11 - 5 = 6" />
</MathContainer>

Now we can calculate the average score for Semester <InlineMath math="II" />:

<MathContainer>
  <BlockMath math="\text{Average Semester } II = \frac{50.5}{6} \approx 8.4166... \approx 8.42" />
</MathContainer>

Finally, we calculate the increase in the average score from Semester <InlineMath math="I" /> to Semester <InlineMath math="II" />:

<MathContainer>
  <BlockMath math="\text{Increase} = \text{Average Semester } II - \text{Average Semester } I" />
  <BlockMath math="\text{Increase} = 8.42 - 7.5 = 0.92" />
</MathContainer>

Therefore, the increase in Hani's mathematics exam average is <InlineMath math="0.92" />.


---