Unit 10 · Class 8 IB MYP · MCQ Test
Modeling with Mathematics MCQ Test — Class 8 IB MYP
Practice 10 multiple-choice questions with instant answer reveal and explanations.
Modeling with Mathematics — MCQ Questions
1A taxi charges a flat fee of $3 plus $2 per kilometre. Write an expression for the cost \(C\) of travelling \(d\) kilometres.
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Answer: \(C = 3 + 2d\)
Hint: The flat fee is constant and the per-km charge depends on distance.
Solution:
Flat fee = $3 (constant term)
Per-km charge = $2 × d (variable term)
Total cost: — C = 3 + 2d
2A pool is being filled at a rate of 50 litres per minute. It already contains 200 litres. How many litres will it contain after \(t\) minutes?
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Answer: \(200 + 50t\)
Hint: Start with what's already in the pool and add the rate multiplied by time.
Solution:
Initial amount = 200 litres
Rate of filling = 50 litres/min
After t minutes: — V = 200 + 50t
3A rectangle's length is 3 more than twice its width \(w\). What is the perimeter in terms of \(w\)?
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Answer: \(6w + 6\)
Hint: Perimeter = 2(length + width). Express length as \(2w + 3\).
Solution:
Width = w, Length = 2w + 3
Perimeter = 2(w + 2w + 3)
= 2(3w + 3) — P = 6w + 6
4Tom earns $12 per hour. He also gets a $20 bonus each day. If he works \(h\) hours in a day, what is his daily earning?
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Answer: \(12h + 20\)
Hint: Daily earning = hourly wage × hours + bonus.
Solution:
Hourly earning = $12 × h
Daily bonus = $20
Total: — E = 12h + 20
5A car travels at a constant speed of 60 km/h. How far does it travel in \(t\) hours?
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Answer: \(60t\)
Hint: Distance = speed × time.
Solution:
Using distance = speed × time
d = 60 × t — d = 60t
6A garden is in the shape of a rectangle with length \(2x\) and width \(x + 3\). What is the area in terms of \(x\)?
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Answer: \(2x^2 + 6x\)
Hint: Area = length × width. Expand the product.
Solution:
Area = 2x(x + 3)
= 2x² + 6x — A = 2x^2 + 6x
7Three friends share a bill equally. The bill is $(3x + 12). How much does each person pay?
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Answer: \(x + 4\)
Hint: Divide the total by 3.
Solution:
Each person pays (3x + 12) ÷ 3
= x + 4 — \text{Each share} = x + 4
8A rope of length 50 m is cut into two pieces. One piece is \(x\) metres long. Express the length of the other piece.
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Answer: \(50 - x\)
Hint: The two pieces must add up to 50.
Solution:
Total = 50 m
First piece = x
Second piece = 50 − x
9A shop sells pens for $2 each and notebooks for $5 each. Emma buys \(p\) pens and \(n\) notebooks. Write the total cost.
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Answer: \(2p + 5n\)
Hint: Total = price per pen × number of pens + price per notebook × number of notebooks.
Solution:
Cost of pens = 2p
Cost of notebooks = 5n
Total: — C = 2p + 5n
10A rectangular field has a perimeter of 100 m. If the length is \(l\) metres, express the area in terms of \(l\).
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Answer: Both A and C
Hint: If perimeter = 100, then l + w = 50, so w = 50 − l. Area = l × w.
Solution:
Perimeter: 2(l + w) = 100, so l + w = 50
Width: w = 50 − l
Area = l(50 − l) = 50l − l² — A = l(50 - l) = 50l - l^2
Options A and C are equivalent expressions.
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Tips for Modeling with Mathematics MCQs
- 1Read each question carefully and identify what is being asked before looking at the options.
- 2Try to solve the problem mentally or on paper first, then match your answer with the options.
- 3Use elimination — rule out clearly wrong options to improve your chances even when unsure.
- 4Check units, signs, and edge cases — these are common traps in Modeling with Mathematics MCQs.
- 5Review your mistakes after completing the test to build lasting understanding.
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