Unit 4 · Class 7 IB MYP · MCQ Test
Linear Equations MCQ Test — Class 7 IB MYP
Practice 10 multiple-choice questions with instant answer reveal and explanations.
Linear Equations — MCQ Questions
1A scientist in Geneva is tracking the growth of a plant. The plant was 8 cm tall and grew an additional 'g' cm, reaching a total height of 21 cm. Which equation represents this situation?
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Answer: 8 + g = 21
Hint: Think about how to combine the initial height and the growth to get the final height.
Solution:
The initial height of the plant is 8 cm.
The plant grew an additional 'g' cm.
The total height is the initial height plus the growth, which is 21 cm. So, 8 + g = 21.
2Solve the equation: 3y + 5 = 23
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Answer: y = 6
Hint: First, isolate the term with 'y' by performing the inverse operation on the constant term.
Solution:
Subtract 5 from both sides of the equation to isolate the term with 'y'. — 3y + 5 - 5 = 23 - 5
This simplifies to: — 3y = 18
Divide both sides by 3 to solve for 'y'. — y = 18 ÷ 3
Therefore, 'y' equals: — y = 6
3Which of the following statements is true about the solution to the equation x/4 = 12?
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Answer: The solution is 48.
Hint: To undo division, you need to perform the inverse operation on both sides of the equation.
Solution:
The equation is x/4 = 12.
To solve for 'x', multiply both sides of the equation by 4. — x/4 × 4 = 12 × 4
This gives the solution: — x = 48
4Alex solved the equation 2(x - 3) = 10 as follows: Step 1: 2x - 3 = 10 Step 2: 2x = 13 Step 3: x = 6.5 In which step did Alex make the first mistake?
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Answer: Step 1
Hint: Remember the distributive property when multiplying a number by a term in brackets.
Solution:
The original equation is 2(x - 3) = 10.
In Step 1, Alex incorrectly applied the distributive property. It should be 2 × x - 2 × 3, not 2x - 3.
The correct Step 1 should be 2x - 6 = 10.
5A chef in Paris used 1/3 of a bag of flour for a recipe, leaving 4 kg of flour in the bag. How much flour was in the bag initially?
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Answer: 6 kg
Hint: If 1/3 was used, what fraction of the flour remains in the bag?
Solution:
If 1/3 of the flour was used, then 1 - 1/3 = 2/3 of the flour remains.
Let 'f' be the initial amount of flour. So, (2/3)f = 4 kg.
To find 'f', multiply both sides by the reciprocal of 2/3, which is 3/2. — f = 4 × (3/2)
Calculate the initial amount: — f = 12/2 = 6 kg
6Solve the equation: 5(w + 2) = 35
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Answer: w = 5
Hint: You can either distribute the 5 first or divide both sides by 5 first. Choose the method you find easier!
Solution:
Divide both sides of the equation by 5: — (5(w + 2)) / 5 = 35 / 5
This simplifies to: — w + 2 = 7
Subtract 2 from both sides to solve for 'w'. — w = 7 - 2
Therefore, 'w' equals: — w = 5
7A group of students from Berlin are fundraising. They have collected €150, which is €30 more than half of their target amount. What is their target amount?
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Answer: €240
Hint: Let 'T' be the target amount. Formulate an equation based on the given information.
Solution:
Let 'T' represent the target amount.
Half of their target amount is T/2.
They collected €150, which is €30 more than half the target, so the equation is: — 150 = T/2 + 30
Subtract 30 from both sides: — 150 - 30 = T/2
This simplifies to: — 120 = T/2
Multiply both sides by 2: — 120 × 2 = T
So, the target amount is: — T = 240
8Which operation is the inverse of multiplying by 7?
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Answer: Dividing by 7
Hint: Inverse operations 'undo' each other. Think about how to reverse the action of multiplication.
Solution:
Inverse operations are used to isolate a variable in an equation.
The inverse operation of adding is subtracting, and vice versa.
The inverse operation of multiplying is dividing. So, dividing by 7 undoes multiplying by 7.
9Consider a rectangle with length 'L' and width 'W'. If the length is 10 cm and the perimeter is 34 cm, which equation can be used to find the width 'W'?
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Answer: 2(10 + W) = 34
Hint: Recall the formula for the perimeter of a rectangle: P = 2(L + W).
Solution:
The formula for the perimeter of a rectangle is P = 2(Length + Width).
Given Length (L) = 10 cm and Perimeter (P) = 34 cm.
Substitute these values into the formula: — 34 = 2(10 + W)
10If y = 4 is the solution to the equation a(y + 1) = 20, what is the value of 'a'?
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Answer: a = 4
Hint: Substitute the given solution for 'y' into the equation and then solve for 'a'.
Solution:
The given equation is a(y + 1) = 20.
We are given that y = 4 is the solution. Substitute y = 4 into the equation: — a(4 + 1) = 20
Simplify the expression inside the bracket: — a(5) = 20
To solve for 'a', divide both sides by 5: — a = 20 ÷ 5
Therefore, 'a' equals: — a = 4
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Tips for Linear Equations 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 Linear Equations MCQs.
- 5Review your mistakes after completing the test to build lasting understanding.
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