a) In a Mathematics test, students are required to answer 50 questions. 3 points will be given for each correct answer, $$ 1 \frac{1}{2} $$ marks deducted for each wrong answer and $$ \frac{1}{5} $$ marks will be deducted for each question that was not answered. Set Hui answered 35 questions correctly and 8 questions wrongly. Calculate the marks obtained by Set Hui.

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UpStudy AI · Accepted Answer

To calculate the marks obtained by Set Hui, we'll break down each component based on the given information.

### Given:
- **Total Questions:** 50
- **Correct Answers:** 35
- **Wrong Answers:** 8
- **Unanswered Questions:** $$ 50 - (35 + 8) = 7 $$

### Scoring Scheme:
- **Correct Answer:** $$ +3 $$ points each
- **Wrong Answer:** $$ -\frac{3}{2} $$ points each (which is $$ -1.5 $$ points)
- **Unanswered Question:** $$ -\frac{1}{5} $$ points each (which is $$ -0.2 $$ points)

### Calculations:

1. **Marks from Correct Answers:**
   $$
   35 \text{ correct answers} \times 3 \text{ points} = 105 \text{ points}
   $$

2. **Marks Deducted for Wrong Answers:**
   $$
   8 \text{ wrong answers} \times \left(-\frac{3}{2}\right) \text{ points} = -12 \text{ points}
   $$

3. **Marks Deducted for Unanswered Questions:**
   $$
   7 \text{ unanswered questions} \times \left(-\frac{1}{5}\right) \text{ points} = -1.4 \text{ points}
   $$

4. **Total Marks Obtained:**
   $$
   105 \text{ (from correct answers)} - 12 \text{ (deducted for wrong answers)} - 1.4 \text{ (deducted for unanswered)} = 91.6 \text{ points}
   $$

### Final Answer:
Set Hui obtained **91.6 marks**.

Alternatively, expressing it as a fraction:
$$
91.6 = 91 \frac{3}{5} \text{ marks}
$$

**Answer:**  
Set Hui obtained 91 3⁄5 marks.
Set Hui obtained 91.6 marks.

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