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Algebra Practice Questions

GCSE · GCSE Mathematics · 138 free MCQs with instant results and detailed explanations.

138
Total
32
Easy
76
Medium
30
Hard

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Sample Questions from Algebra

Here are 10 sample questions. Start a quiz to get randomized questions with scoring.

Q1
Easy
What is the expanded form of the expression (x + 3)(x + 2)?
A. x^2 + 6x + 6
B. x^2 + 5x + 6
C. x^2 + 5x + 5
D. x^2 + 7x + 6
Show Answer & Explanation
Correct Answer: B
Using the distributive property (FOIL), multiply the terms: x*x + x*2 + 3*x + 3*2 = x^2 + 2x + 3x + 6 = x^2 + 5x + 6.
Q2
Easy
Which of the following expressions is equivalent to 5(2 + x)?
A. 10 + 5x
B. 5x + 5
C. 10x + 5
D. 2 + 5x
Show Answer & Explanation
Correct Answer: A
Distributing 5 into the parentheses gives 5 * 2 + 5 * x = 10 + 5x, which is the correct equivalent expression.
Q3
Easy
Which of the following is equivalent to the expression 5(a + 2)?
A. 5a + 10
B. 2a + 5
C. 10a
D. 5a + 2
Show Answer & Explanation
Correct Answer: A
Using the distributive property, 5(a + 2) expands to 5a + 10, making option A the correct answer.
Q4
Medium
What is the value of x in the equation 3x + 5 = 20?
A. 5
B. 10
C. 15
D. 25
Show Answer & Explanation
Correct Answer: A
To solve for x, subtract 5 from both sides to get 3x = 15. Then, divide both sides by 3 to find x = 5.
Q5
Medium
Which of the following represents the total cost C of buying x apples at a price of 3 pounds each?
A. C = 3x
B. C = 3 + x
C. C = 3x^2
D. C = 3/x
Show Answer & Explanation
Correct Answer: A
The total cost C is directly proportional to the number of apples purchased, which is represented by multiplying the price per apple (3 pounds) by the quantity x.
Q6
Medium
If 5x + 2 = 4x + 8, what is the value of x?
A. 6
B. 5
C. 4
D. 3
Show Answer & Explanation
Correct Answer: A
First, move the 4x to the left side to get x + 2 = 8. Then, subtract 2 from both sides to find x = 6.
Q7
Medium
The expression 4(2y - 3) + 6y = 10 simplifies to what value of y?
A. 1
B. 2
C. 3
D. 4
Show Answer & Explanation
Correct Answer: C
Expanding the left side gives 8y - 12 + 6y = 10. Combining like terms results in 14y - 12 = 10. Adding 12 to both sides yields 14y = 22, thus y = 22/14 = 3/7, which simplifies to 1.5.
Q8
Hard
If the quadratic equation x² - 6x + k = 0 has two equal roots, what is the value of k?
A. 9
B. 6
C. 0
D. 3
Show Answer & Explanation
Correct Answer: A
For a quadratic equation to have two equal roots, the discriminant must be zero. The discriminant is given by b² - 4ac. Here, a = 1, b = -6, and c = k. Therefore, (-6)² - 4(1)(k) = 0 leads to 36 - 4k = 0. Solving this gives k = 9.
Q9
Hard
The quadratic equation x² - 5x + 6 = 0 can be factored. What are the roots of the equation?
A. 2 and 3
B. 1 and 6
C. 3 and 5
D. 0 and 6
Show Answer & Explanation
Correct Answer: A
The equation can be factored as (x - 2)(x - 3) = 0. Setting each factor to zero gives the roots x = 2 and x = 3.
Q10
Hard
If the expression 5x + 3 = 2(x + 6) is simplified, what is the value of x?
A. 3
B. 2
C. 4
D. 1
Show Answer & Explanation
Correct Answer: A
To solve, first expand the right side: 2(x + 6) = 2x + 12. Rearranging gives 5x - 2x = 12 - 3, leading to 3x = 9, thus x = 3.

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More GCSE Mathematics Chapters

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2 Ratio Proportion and Rates of Change
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Algebra — GCSE GCSE Mathematics Practice Questions Online

This page contains 138 practice MCQs for the chapter Algebra in GCSE GCSE Mathematics. The questions are organized by difficulty — 32 easy, 76 medium, 30 hard — so you can choose the right level for your preparation.

Every question includes a detailed explanation to help you understand the concept, not just memorize answers. Take a timed quiz to simulate exam conditions, or practice at your own pace with no time limit.