Let's go step by step to solve this quiz problem.

a) Maximum score you could get on the quiz:

To maximize the score, you need to answer all 25 questions correctly. Each correct answer scores 3 points, so: $\text{Maximum score} = 25 \times 3 = 75$ This has already been filled in correctly.

b) Minimum score you could get on the quiz:

To minimize the score, you should answer all 25 questions incorrectly. Each incorrect answer deducts 2 points, so: $\text{Minimum score} = 25 \times (-2) = -50$

c) A student answers 15 questions, 10 are correct:

• For the 10 correct answers, the student scores $10 \times 3 = 30$ points.
• For the 5 incorrect answers (since 15 - 10 = 5), the student loses $5 \times 2 = 10$ points. $\text{Total score} = 30 - 10 = 20$

d) Another student answers 21 questions, 6 are correct:

• For the 6 correct answers, the student scores $6 \times 3 = 18$ points.
• For the 15 incorrect answers (since 21 - 6 = 15), the student loses $15 \times 2 = 30$ points. $\text{Total score} = 18 - 30 = -12$

Final answers:

• a) Maximum score: $75$
• b) Minimum score: $-50$
• c) Total score for 15 questions (10 correct): $20$
• d) Total score for 21 questions (6 correct): $-12$

Would you like further details or explanations?

Here are some related questions for practice:

1. What if a student answers 12 questions, with 8 correct?
2. What is the score if all answers are left blank?
3. If a student answers 20 questions and 7 are correct, what is the score?
4. How many correct answers are needed to ensure a positive score, assuming 25 answers are given?
5. What if a student answers only 5 questions, all incorrect?

Tip: Always check the impact of penalties on your score before deciding how many questions to attempt.