3 Marks Question

Question 13 Marks

In a test, (+4) marks are given for every correct answer and (-2) marks are given for every incorrect answer:
Anil scored (-10) marks even though he had 5 correct answers. How many of his answers were incorrect? Did he leave any questions unanswered?

Answer

Anil had 5 correct answers, and each correct answer is worth + 4 marks they 5 × 4 = 20 marks.
From incorrect answers = -10 – 20 = -30.
Each incorrect answer is worth -2 marks
$\therefore \frac{-30}{-2}=15$
Hence, Anil had 15 incorrect answers.
Yes, he leaves some questions unanswered.
Anil answered the question = (Total No. of Questions) – (Anil’s correct answers + Anil’s incorrect answers)
= 25 – (5 + 15)
= 25 – 20
= 5
Hence, Anil left 5 questions unanswered.

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Question 23 Marks

In a test, (+4) marks are given for every correct answer and (-2) marks are given for every incorrect answer:
Anita answered all the questions in the test. She scored 40 marks even though 15 of her answers were correct. How many of her answers were incorrect? How many questions are in the test?

Answer

Anita had 15 correct answers, and each correct answer is worth +4 marks.
Marks from correct answers = 15 × 4 = 60
∴ Anita total score = 40
Marks lost = 60 – 40 = 20
Each incorrect answer is worth -2 marks
∴ No. of incorrect answers $=\frac{20}{2}=10$
Anita had 10 incorrect answers.
Total no. of questions = sum of correct and incorrect answers
= 15 + 10
= 25
Hence, Anita had 10 incorrect answers out of 25 questions on the test.

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Question 33 Marks

Using the token interpretation, find the values of:
(-4) × (-1)

Answer

For (-4) × (-1), we need to remove 1 negative from the box 4 times.
Since there are no red tokens in the bag.
We need to place 1 zero pair and remove 1 negative, and we need to do this 4 times.

Taking 1 red token from the zero pairs 4 times.
∴ (-4) × (-1) = 4

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Question 43 Marks

Using the token interpretation, find the values of:
(-5) × (-2)

Answer

For (-5) × (-2), we need to remove 2 negatives from the box 5 times.
Since there are no red tokens in the bag, we need to place 2 zero pairs and remove 2 negatives, and we need to do this 5 times.

Taking 2 red tokens from the zero pairs 5 times.
∴ (-5) × (-2) = 10

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Question 53 Marks

Using the token interpretation, find the values of:
3 × (-2)

Answer

Two red tokens 3 times = -6

There are now 6 red tokens or 6 negatives in the box, i.e., -6

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Question 63 Marks

If 123 × 456 = 56088, without calculating, find the value of:
(a) (-123) × 456
(b) (-123) × (-456)
(c) (123) × (-456)

Answer

(a) Given 123 × 456 = 56088 …..(i)
Then(a) (-123) × 456
This is the product of a negative and a positive integer, so the result will be negative.
i.e. -(123) × 456 = -(123 × 456) = -56088
(b) (-123) × (-456)
This is the product of two negative integers, so the result will be positive.
∴ (-123) × (-456) = 123 × 456 = 56088
(c) 123 × (-456)
This is the product of a positive and a negative integer, so the result will be negative.
∴ 123 × (-456) = -(123 × 456) = -56088

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Question 73 Marks

Using the token interpretation, find the values of:
(-7) × 3

Answer

For (-7) × 3, we need to remove 3 positive numbers from the box 7 times.

Taking 3 positives from the zero pairs 7 times = (-7) × 3 = -21.

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MATHS 3 Marks Question

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