Sure, let's break down the problem step-by-step for both parts.
### Part (a)
You attempt all 12 questions and answer 8 of them correctly. Here's how to determine your total score:
1. Total questions: 12
2. Correct answers: 8
3. Incorrect answers: [tex]\(12 - 8 = 4\)[/tex]
Now, we calculate the score:
- Marks for correct answers: [tex]\(8 \text{ correct answers} \times 2 \text{ marks per correct answer} = 16 \text{ marks}\)[/tex]
- Marks for incorrect answers: [tex]\(4 \text{ incorrect answers} \times -2 \text{ marks per incorrect answer} = -8 \text{ marks}\)[/tex]
To find the total score, we sum the marks from correct and incorrect answers:
[tex]\[
\text{Total score} = 16 + (-8) = 8
\][/tex]
So, your total score is 8 marks.
### Part (b)
Your friend answers only 5 questions correctly and leaves the rest unattempted. Here's how to determine her total score:
1. Total questions: 12
2. Correct answers: 5
3. Unattempted questions: [tex]\(12 - 5 = 7\)[/tex]
4. Incorrect answers: 0 (since the remaining questions are unattempted, those don’t count as incorrect)
Now, we calculate the score:
- Marks for correct answers: [tex]\(5 \text{ correct answers} \times 2 \text{ marks per correct answer} = 10 \text{ marks}\)[/tex]
- Marks for unattempted questions: [tex]\(7 \text{ unattempted questions} \times 0 \text{ marks per unattempted question} = 0 \text{ marks}\)[/tex]
To find the total score, we sum the marks from correct answers and unattempted questions:
[tex]\[
\text{Total score} = 10 + 0 = 10
\][/tex]
Since we mistakenly used zero for points of incorrect answers, let's correct it:
Marks for incorrect answers: [tex]\(-2 \times 7 = -14\)[/tex]
[tex]\[
\text{Total score} = 10 + (-14) = -4
\][/tex]
So, her total score is -4 marks.
