Calculate Test Score: 5, -2, -4 Point System with 20 Questions

Weighted Scoring with Multiple Point Values

A teacher decides to award the following points:

5 points for each correct answer.

-2 for each incorrect answer.

-4 for each unanswered question.

There were 20 questions on the exam.

What is the score of the student who answers all the questions correctly, except for 4 questions that are left unanswered?

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Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

A teacher decides to award the following points:

5 points for each correct answer.

-2 for each incorrect answer.

-4 for each unanswered question.

There were 20 questions on the exam.

What is the score of the student who answers all the questions correctly, except for 4 questions that are left unanswered?

2

Step-by-step solution

To solve this problem, we'll follow these steps:

  • Step 1: Identify the given information
  • Step 2: Calculate the number of correct answers
  • Step 3: Calculate the score from correct answers
  • Step 4: Calculate the score from unanswered questions
  • Step 5: Sum the contributions to get the total score

Now, let's work through each step:

Step 1: Identify the given information
The problem states there are 20 total questions, with 5 points for each correct, -2 for each incorrect, and -4 points for each unanswered question. The student left 4 questions unanswered.

Step 2: Calculate the number of correct answers
Since the student answered all questions except 4, the correct number of answers is 20 - 4 = 16.

Step 3: Calculate the score from correct answers
The score for correct answers is 16×5=80 16 \times 5 = 80 points.

Step 4: Calculate the score from unanswered questions
We have 4 unanswered questions, contributing 4×(4)=16 4 \times (-4) = -16 points.

Step 5: Sum the contributions to get the total score
Add the scores from the correct and unanswered questions: 80+(16)=64 80 + (-16) = 64 .

Therefore, the solution to the problem is 64 64 .

3

Final Answer

64 64

Key Points to Remember

Essential concepts to master this topic
  • Point System: Assign correct value (5), incorrect (-2), and unanswered (-4) points
  • Technique: Calculate separately: 16 × 5 = 80, then 4 × (-4) = -16
  • Check: Verify total questions add up: 16 answered + 4 unanswered = 20 ✓

Common Mistakes

Avoid these frequent errors
  • Applying incorrect point values to wrong categories
    Don't give -2 points for unanswered questions or -4 points for incorrect answers = wrong final score! Each category has its specific point value. Always match the correct point value (-4) with unanswered questions and (5) with correct answers.

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 unanswered questions get -4 points instead of 0?

+

The teacher designed this penalty system to encourage students to attempt all questions. Getting -4 for blank answers is worse than risking -2 for a wrong guess!

How do I organize all these different point values?

+

Make a simple chart: Correct answers × 5, Incorrect answers × (-2), and Unanswered × (-4). Calculate each category separately, then add them together.

What if a student got some answers wrong too?

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You'd have three calculations instead of two! For example: 10 correct (50 points) + 6 wrong (-12 points) + 4 unanswered (-16 points) = 501216=22 50 - 12 - 16 = 22 total points.

Can the final score be negative?

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Absolutely! If a student answers mostly incorrectly or leaves many blank, the negative points can outweigh the positive ones. That's how this scoring system works.

How do I double-check my arithmetic?

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First, verify your quantities add up to 20 total questions. Then recalculate each category: 80 + (-16) = 64. Finally, ask yourself if the result makes sense!

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