Unit 3 · Class 7 IB MYP · MCQ Test
Algebraic Expressions MCQ Test — Class 7 IB MYP
Practice 10 multiple-choice questions with instant answer reveal and explanations.
Algebraic Expressions — MCQ Questions
1Which pair of terms are considered 'like terms' in algebraic expressions?
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Answer: A. 3x and -5x
Hint: Like terms must have the exact same variables raised to the same powers. The numerical coefficients can be different.
Solution:
Identify the variables and their powers in each term for all options.
For option A, '3x' and '-5x' both have the variable 'x' raised to the power of 1. These are like terms.
For option B, '2y' has variable 'y' while '2x' has variable 'x', so they are not like terms. Similarly for C and D, the variables or their combinations are different.
2Simplify the expression: 7a + 3b - 2a + 5b.
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Answer: B. 5a + 8b
Hint: Group the 'a' terms together and the 'b' terms together, then perform the addition or subtraction for each group separately.
Solution:
Identify like terms: (7a and -2a), and (3b and 5b).
Combine the 'a' terms: 7a - 2a = 5a.
Combine the 'b' terms: 3b + 5b = 8b.
Write the simplified expression by combining the results: 5a + 8b.
3Expand the expression: 4(2x - 3).
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Answer: C. 8x - 12
Hint: Remember to apply the distributive property by multiplying the term outside the bracket by *each* term inside the bracket.
Solution:
Multiply the term outside the bracket (4) by the first term inside (2x). — 4 × 2x = 8x
Multiply the term outside the bracket (4) by the second term inside (-3). — 4 × -3 = -12
Combine the results to get the expanded expression: 8x - 12.
4The formula for the cost of renting a bicycle in Amsterdam is C = 5h + 8, where C is the total cost in euros and h is the number of hours. If you rent a bicycle for 3 hours, what is the total cost?
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Answer: D. €23
Hint: Substitute the given value for 'h' into the formula and then calculate the result.
Solution:
The given formula is C = 5h + 8.
The number of hours (h) is 3.
Substitute h = 3 into the formula: — C = 5(3) + 8
Calculate the value: — C = 15 + 8 = 23
5A baker in Paris makes 'c' croissants each morning. He sells 15 of them and gives away 'p' croissants to his neighbours. Which expression represents the number of croissants he has left?
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Answer: A. c - 15 - p
Hint: Start with the initial number of croissants and then subtract the amounts that are sold and given away.
Solution:
Start with the initial number of croissants: c.
The baker sells 15 croissants, so subtract 15: — c - 15
He gives away 'p' croissants, so subtract 'p' from the remaining amount: — c - 15 - p
6Which statement about the algebraic expression 5x + 2y - 1 is true?
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Answer: B. It has three terms.
Hint: An expression does not have an equals sign. Terms are separated by addition or subtraction signs, and constants include their sign.
Solution:
An equation contains an equals sign (=), which this expression does not, so option A is false.
The terms in the expression are 5x, 2y, and -1. There are three distinct terms, so option B is true.
The coefficient of y is the numerical part multiplying y, which is 2, not 2y. So option C is false.
The constant term is the term without any variables, including its sign, which is -1. So option D is false.
7Alex was asked to simplify the expression 3m + 4n - m + 2n. He wrote the answer as 2m + 6n. Which statement correctly identifies Alex's work?
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Answer: A. Alex is correct; his simplification of the expression results in 2m + 6n.
Hint: Carefully group and combine the 'm' terms and the 'n' terms separately, paying attention to their signs.
Solution:
First, group the 'm' terms: 3m - m.
Combine the 'm' terms: 3m - m = 2m.
Next, group the 'n' terms: 4n + 2n.
Combine the 'n' terms: 4n + 2n = 6n. Therefore, the simplified expression is 2m + 6n. Alex's answer is correct.
8If the expression 2x + 5 has a value of 17, what is the value of x?
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Answer: C. 6
Hint: Set up an equation with the given expression and its value, then solve for the variable 'x'.
Solution:
Set up the equation: — 2x + 5 = 17
Subtract 5 from both sides of the equation: — 2x = 17 - 5
Simplify: — 2x = 12
Divide both sides by 2: — x = 12 / 2 = 6
9Simplify the expression: 6p + 3q - 2p - q + 5.
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Answer: D. 4p + 2q + 5
Hint: Group all the 'p' terms, all the 'q' terms, and any constant terms separately before combining them. Remember that '-q' is the same as '-1q'.
Solution:
Identify like terms: (6p and -2p), (3q and -q), and (5).
Combine the 'p' terms: 6p - 2p = 4p.
Combine the 'q' terms: 3q - q = 3q - 1q = 2q.
The constant term is 5.
Write the simplified expression by combining the results: 4p + 2q + 5.
10A school in Berlin is ordering supplies. They order 'n' boxes of pens, with each box containing 12 pens. They also order 'm' individual pens. If they already have 5 pens in storage, what is the total number of pens they will have?
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Answer: B. 12n + m + 5
Hint: First, express the total number of pens from the 'n' boxes. Then, add the individual pens and the pens already in storage.
Solution:
Number of pens from 'n' boxes: Since each box has 12 pens, 'n' boxes will have 12 × n = 12n pens.
Number of individual pens ordered: m.
Number of pens already in storage: 5.
Add all these quantities to find the total number of pens: — 12n + m + 5
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Tips for Algebraic Expressions 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 Algebraic Expressions MCQs.
- 5Review your mistakes after completing the test to build lasting understanding.
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