Chapter 8 (Balbharati) · Class 7 Maharashtra SSC · MCQ Test
Algebraic Expressions (बीजगणितीय व्यंजके) MCQ Test — Class 7 Maharashtra SSC
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Algebraic Expressions (बीजगणितीय व्यंजके) — MCQ Questions
1Which of the following statements correctly describes a variable in an algebraic expression?
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Answer: It is an unknown value that can change or take different values.
Hint: Recall the basic definition of a variable and how it differs from a constant.
Solution:
A variable is a symbol, usually a letter, that represents an unknown quantity or a quantity that can change.
Unlike a constant, which has a fixed value, a variable's value can vary.
2The cost of one apple is ₹'a' and the cost of one banana is ₹'b'. What is the total cost of 5 apples and 3 bananas?
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Answer: 5a + 3b
Hint: To find the total cost, consider the cost of each item multiplied by its quantity, and then add them together.
Solution:
Cost of 5 apples = 5 × a = 5a.
Cost of 3 bananas = 3 × b = 3b.
Total cost = Cost of 5 apples + Cost of 3 bananas.
Total cost = 5a + 3b.
3In the expression 7x²y - 4xy + 9, identify the coefficient of the term 'xy'.
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Answer: -4
Hint: The coefficient is the numerical factor that multiplies the variable part of a term. Pay close attention to the sign.
Solution:
An algebraic expression consists of terms. In the given expression, the terms are 7x²y, -4xy, and 9.
For the term '-4xy', the variable part is 'xy'.
The numerical factor multiplying 'xy' is -4. Therefore, -4 is the coefficient of 'xy'.
4Which of the following pairs represents 'like terms'?
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Answer: 9ab, 4ba
Hint: Like terms must have the exact same variables raised to the same powers. Remember that the order of multiplication does not change the product.
Solution:
Like terms are terms that have the same variables raised to the same powers.
For option A (6x, 6y), the variables are different (x and y).
For option B (9ab, 4ba), the variables are 'a' and 'b' for both terms. Since 'ab' is the same as 'ba' (due to commutative property of multiplication), these are like terms.
For option C (3p², 3p), the powers of 'p' are different (p² and p).
For option D (2m, 2mn), the variables are different (m and mn).
5Simplify the expression: 7x + 2y - 3x + 5y.
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Answer: 4x + 7y
Hint: Combine the 'like terms' together. Group the terms with 'x' and the terms with 'y' separately.
Solution:
Group the like terms: (7x - 3x) + (2y + 5y).
Combine the 'x' terms: 7x - 3x = 4x.
Combine the 'y' terms: 2y + 5y = 7y.
The simplified expression is 4x + 7y.
6Rani wanted to write '8 less than thrice a number p' as an algebraic expression. She wrote 8 - 3p. What was her mistake?
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Answer: She should have written 3p - 8.
Hint: When translating 'less than', the number being subtracted comes after the term from which it is being subtracted.
Solution:
'Thrice a number p' translates to 3 × p, or 3p.
'8 less than' means that 8 is subtracted FROM the quantity. So, it should be 3p - 8.
Rani wrote 8 - 3p, which represents '3p less than 8', which is incorrect for the given statement.
7What is the fundamental difference between an algebraic expression and an algebraic equation?
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Answer: An equation contains an equals sign (=), while an expression does not.
Hint: Consider the primary symbol that defines an equation and what it signifies.
Solution:
An algebraic expression is a combination of variables, constants, and mathematical operations (like addition, subtraction, multiplication, division), but it does not contain an equals sign.
An algebraic equation, on the other hand, always contains an equals sign (=), showing that two expressions are equal in value.
We simplify expressions, but we solve equations to find the value of the variable(s).
8If an algebraic expression has terms 2m², -5m, and 12, which of the following could be the expression?
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Answer: 2m² - 5m + 12
Hint: Terms in an expression are usually separated by addition or subtraction signs. Pay attention to the signs of the individual terms.
Solution:
Terms in an algebraic expression are combined using addition or subtraction.
The term 2m² is positive, -5m is negative, and 12 is positive.
Combining these terms correctly maintains their signs: 2m² + (-5m) + 12, which simplifies to 2m² - 5m + 12.
9A cyclist travels at a constant speed of 's' kilometres per hour. How far will the cyclist travel in 'h' hours?
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Answer: s × h
Hint: Recall the basic formula relating distance, speed, and time.
Solution:
The relationship between distance, speed, and time is: Distance = Speed × Time.
Given speed = 's' km/hour and time = 'h' hours.
Therefore, the distance traveled = s × h.
10When we use a letter like 'y' in an algebraic expression, what does it primarily represent?
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Answer: An unknown value that can vary or change.
Hint: Think about why we introduce letters in algebra instead of just using numbers.
Solution:
In algebra, letters (variables) are used to represent quantities whose values are not fixed or are unknown.
This allows us to write general rules and solve problems where the exact numerical value is not yet determined or can change depending on the situation.
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Tips for Algebraic Expressions (बीजगणितीय व्यंजके) 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 (बीजगणितीय व्यंजके) MCQs.
- 5Review your mistakes after completing the test to build lasting understanding.
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