How many practice questions are available for Algebraic Expressions?

SparkEd Math offers 60+ practice questions for Algebraic Expressions across 3 difficulty levels (Easy, Medium, Hard) plus a timed test mode. Each question comes with visual step-by-step solutions and AI coaching hints.

Is Algebraic Expressions content free on SparkEd Math?

Yes! All Algebraic Expressions content on SparkEd Math is 100% free, including practice questions, visual solutions, lessons, and AI coaching. No credit card required.

How does SparkEd Math teach Algebraic Expressions differently from textbooks?

SparkEd Math uses visual step-by-step solutions for every Algebraic Expressions problem, making complex concepts easy to understand. The platform includes 3 difficulty levels for progressive learning, a Super Power Help AI coach for instant doubt-clearing, and interactive practice rather than passive reading.

Is SparkEd's Algebraic Expressions content aligned with the Olympiad syllabus?

Yes, all Algebraic Expressions questions and lessons on SparkEd Math are fully aligned with the Mathematical Olympiad Preparation (Olympiad) syllabus for Class 7. The content follows the official curriculum structure and exam pattern.

Algebraic Expressions — Class 7 Olympiad (2025-26)

About Algebraic Expressions — Class 7 Olympiad

Form, simplify, and evaluate algebraic expressions; solve pattern-based and expression manipulation problems. This topic is part of the Olympiad Class 7 mathematics syllabus (chapter: Module 5). On this page you can practice 48 questions across three difficulty levels — 19 easy, 19 medium, and 10 hard — each with a visual step-by-step solution, plus a timed 26-question mastery test with a live leaderboard. Worked examples and sample questions from the topic are below.

Algebraic Expressions — solved examples for Class 7 Olympiad

Example 1easy

Consider the algebraic expression 5x³y² - 7x²y + 2xy² - 9y + 11. What is the sum of the coefficients of all terms that contain 'y'?

A)2
B)-7
C)-9
D)11

Step-by-step solution

The terms containing 'y' in the expression are 5x³y², -7x²y, 2xy², and -9y.
Their respective coefficients are 5, -7, 2, and -9.
To find the sum, add these coefficients: 5 + (-7) + 2 + (-9).
Sum = 5 - 7 + 2 - 9 = -2 + 2 - 9 = 0 - 9 = -9.

Answer: -9

Example 2medium

A rectangular field has length (5x + 2y) meters and width (3x - y) meters. If the cost of fencing is ₹(2x + y) per meter, what is the total cost of fencing the field?

A)₹(16x² + 16xy + 3y²)
B)₹(8x² + 10xy + 3y²)
C)₹(32x² + 20xy + 2y²)
D)₹(16x² + 20xy + 2y²)

Step-by-step solution

Perimeter of the field = 2 × (Length + Width)
P = 2 × [(5x + 2y) + (3x - y)] = 2 × (8x + y) = (16x + 2y) meters.
Cost of fencing per meter = ₹(2x + y).
Total cost = Perimeter × Cost per meter = (16x + 2y) × (2x + y) = 16x(2x) + 16x(y) + 2y(2x) + 2y(y) = 32x² + 16xy + 4xy + 2y² = 32x² + 20xy + 2y².

Answer: ₹(32x² + 20xy + 2y²)

Example 3hard

A sequence of algebraic expressions is defined as follows:
E₁ = x - y
E_n = E_{n-1} + (x + y) if n is even
E_n = E_{n-1} - (x - y) if n is odd and n > 1
What is the simplified form of E₂₀₂₃?

A)x - 2023y
B)2x + 2022y
C)x + 2021y
D)2x - 2020y

Step-by-step solution

Let's list the first few expressions to find the pattern:
E₁ = x - y
E₂ = E₁ + (x + y) = (x - y) + (x + y) = 2x
E₃ = E₂ - (x - y) = 2x - (x - y) = x + y
E₄ = E₃ + (x + y) = (x + y) + (x + y) = 2x + 2y
E₅ = E₄ - (x - y) = (2x + 2y) - (x - y) = x + 3y
Observing the pattern:
For odd 'n' (n ≥ 1): E_n = x + (n - 2)y. (E₁ = x - y, E₃ = x + y, E₅ = x + 3y)
For even 'n' (n ≥ 2): E_n = 2x + (n - 2)y. (E₂ = 2x, E₄ = 2x + 2y)
Since 2023 is an odd number, we use the formula for odd 'n':
E₂₀₂₃ = x + (2023 - 2)y
$E₂₀₂₃ = x + 2021y$

Answer: x + 2021y

Practice questions on Algebraic Expressions

Q1.easy
A farmer has 'N' sheep. He sells one-third of them and then buys 15 more. Which algebraic expression represents the number of sheep he now has?
1. A)N/3 + 15
2. B)2N/3 + 15
3. C)N - N/3 - 15
4. D)N + 15 - 1/3
Show answer
Answer: 2N/3 + 15
Hint: First, calculate the number of sheep remaining after selling. Then, add the number of sheep he bought.
Q2.easy
Simplify the expression: 7a - [5b - (3a - 2b) + a]
1. A)3a - 7b
2. B)5a - 3b
3. C)9a - 7b
4. D)9a - 3b
Show answer
Answer: 9a - 7b
Hint: Work from the innermost parentheses outwards, being very careful with negative signs when removing brackets.
Q3.easy
If x = -2 and y = 3, find the value of (x - y)² - (x² + y²).
1. A)-12
2. B)12
3. C)24
4. D)-24
Show answer
Answer: 12
Hint: Substitute the given values for 'x' and 'y' into the expression. Pay close attention to the order of operations and the signs of numbers being squared.
Q4.medium
If x + 1/x = 4, what is the value of x² + 1/x²?
1. A)12
2. B)14
3. C)16
4. D)18
Show answer
Answer: 14
Hint: Consider squaring the given equation (x + 1/x = 4) on both sides. Remember the algebraic identity for (a+b)².
Q5.medium
Consider the sequence of expressions: 2x+1, 5x+4, 8x+7, ... If the pattern continues, what is the 10th term in this sequence?
1. A)29x + 27
2. B)30x + 28
3. C)29x + 28
4. D)32x + 31
Show answer
Answer: 29x + 28
Hint: Observe the pattern for the coefficients of 'x' and the constant terms separately. Both form arithmetic progressions.
Q6.medium
When the product (2x - 3y + 4)(x + 2y - 1) is expanded, what is the coefficient of the term 'xy'?
1. A)-4
2. B)-1
3. C)7
4. D)1
Show answer
Answer: 1
Hint: To find the coefficient of 'xy', you only need to consider the products of terms that result in 'xy'. Multiply the 'x' terms from the first expression with 'y' terms from the second, and vice-versa.
Q7.hard
An algebraic expression P was first multiplied by (3x), then (5y) was added to the result. Finally, the entire expression was multiplied by 2, yielding (6x² + 10xy + 10y). What was the original expression P?
1. A)x + 2y
2. B)2x + y
3. C)x + (3/5)y
4. D)x + (5/3)y
Show answer
Answer: x + (5/3)y
Hint: Work backwards through the operations, performing the inverse operation at each step.
Q8.hard
A student simplified the expression (4x² - 3x + 7) - (ax² + bx - c). Due to a sign error, they incorrectly added the second expression instead of subtracting it. Their incorrect simplified result was 6x² + 2x - 1. What would have been the correct simplified expression?
1. A)2x² + 5x - 1
2. B)2x² - 8x + 15
3. C)6x² - 5x + 15
4. D)4x² - 8x + 1
Show answer
Answer: 2x² - 8x + 15
Hint: First, use the incorrect result to find the values of a, b, and c. Then, apply the correct subtraction with these values.
Q9.hard
If the expression (ax² + 5x - 3) - (2x² - bx + 7) + (cx² - 4x + 10) simplifies to an expression that is independent of x, what is the value of a + b + c?
1. A)1
2. B)0
3. C)2
4. D)-1
Show answer
Answer: 1
Hint: For an expression to be independent of x, the coefficients of all terms containing x must be zero.

These are 9 of the 48 questions available for Algebraic Expressions. Start practicing above to unlock visual solutions, AI coaching, and the topic leaderboard — completely free.