Calculate Test Score: 5 Points Right, -2 Points Wrong in 20-Question Exam

Q: Why do we add negative points instead of subtracting?

The penalty is already negative (-2 points), so when we calculate 4 × (-2) = -8, we then add this negative result: 80 + (-8) = 72. Adding a negative is the same as subtracting!

Q: How do I know how many questions were answered correctly?

Since there were 20 total questions and 4 were wrong, the correct answers = 20 - 4 = 16. Always account for all questions in the exam.

Q: What if some questions were left blank?

Blank questions get -4 points each. You'd need to calculate: (Correct × 5) + (Wrong × -2) + (Blank × -4) = Total Score. Make sure correct + wrong + blank = total questions.

Q: Can the final score be negative?

Yes! If a student gets too many wrong or blank answers, the penalties can outweigh the positive points. For example, getting all 20 wrong would give 20 × (-2) = -40 points.

Q: How do I check if my answer makes sense?

The maximum possible score is 20 × 5 = 100 points (all correct). Your answer should be less than this. Also verify: 72 = 80 - 8, which matches our calculation!

Scoring Systems with Positive and Negative Points

In math class it was decided to give:

5 Points for each correct answer,

(-2) for each incorrect answer,

(-4) for each answer without a solution.

In the exam there were 20 questions.

What is the grade of the student who solved all questions correctly, except 4 questions he/she got wrong?

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

In math class it was decided to give:

5 Points for each correct answer,

(-2) for each incorrect answer,

(-4) for each answer without a solution.

In the exam there were 20 questions.

What is the grade of the student who solved all questions correctly, except 4 questions he/she got wrong?

Step-by-step solution

Let's follow the step-by-step solution:

Calculate the points from the correct answers:

There are 16 correct answers. For each correct answer, the student gets $5$ points.

$\text{Points from correct answers} = 16 \times 5 = 80$ .

Calculate the points from incorrect answers:

There are 4 incorrect answers. For each incorrect answer, the student loses $2$ points.

$\text{Points from incorrect answers} = 4 \times (-2) = -8$ .

Calculate the total score:

The student answered all questions, so there are no unanswered questions.

The total score is the sum of the points from correct and incorrect answers.

$\text{Total Score} = 80 + (-8) = 72$ .

Thus, the total grade of the student is $72$ .

Final Answer

$72$

Key Points to Remember

Essential concepts to master this topic

Formula: Total = (Correct × Points) + (Wrong × Penalty)
Calculation: 16 correct answers = 16 × 5 = 80 points
Verification: Check that correct + wrong answers equal total questions: 16 + 4 = 20 ✓

Common Mistakes

Avoid these frequent errors

Forgetting to subtract penalty points
Don't just calculate 16 × 5 = 80 and stop there! This ignores the -2 penalty for wrong answers and gives 80 instead of 72. Always add the penalty points (which are negative) to get the complete score.

Practice Quiz

Test your knowledge with interactive questions

What will be the sign of the result of the next exercise?

$(-2)\cdot(-4)=$

FAQ

Everything you need to know about this question

Why do we add negative points instead of subtracting?

The penalty is already negative (-2 points), so when we calculate 4 × (-2) = -8, we then add this negative result: 80 + (-8) = 72. Adding a negative is the same as subtracting!

How do I know how many questions were answered correctly?

Since there were 20 total questions and 4 were wrong, the correct answers = 20 - 4 = 16. Always account for all questions in the exam.

What if some questions were left blank?

Blank questions get -4 points each. You'd need to calculate: (Correct × 5) + (Wrong × -2) + (Blank × -4) = Total Score. Make sure correct + wrong + blank = total questions.

Can the final score be negative?

Yes! If a student gets too many wrong or blank answers, the penalties can outweigh the positive points. For example, getting all 20 wrong would give 20 × (-2) = -40 points.

How do I check if my answer makes sense?

The maximum possible score is 20 × 5 = 100 points (all correct). Your answer should be less than this. Also verify: 72 = 80 - 8, which matches our calculation!

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