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2.9 There are 12 questions on a test. You get 2 marks for every correct answer, -2 marks for every incorrect answer, and zero marks for not answering a question.

(a) If you attempt all the questions but only 8 of your answers are correct, what will be your total score?

(b) One of your friends gets only 5 answers correct and leaves all other questions unattempted. What will be her score?



Answer :

GinnyAnswer
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.

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