Algebra Practice Questions

HSC/SSC (Bangladesh) · HSC Mathematics · 137 free MCQs with instant results and detailed explanations.

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Sample Questions from Algebra

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Easy

If a = 4 and b = 3, what is the value of a^2 + b^2?

A. 25

B. 16

C. 7

D. 12

Show Answer & Explanation

Correct Answer: A

We calculate a^2 (4^2 = 16) and b^2 (3^2 = 9). Adding these gives us 16 + 9 = 25.

Easy

Which of the following is the factorization of x^2 - 9?

A. (x - 3)(x + 3)

B. (x - 9)(x + 1)

C. (x - 1)(x + 1)

D. (x + 3)(x + 3)

Show Answer & Explanation

Correct Answer: A

The expression x^2 - 9 is a difference of squares, which factors to (x - 3)(x + 3).

Easy

If a = 3 and b = 4, what is the value of a² + b²?

A. 25

B. 12

C. 7

D. 9

Show Answer & Explanation

Correct Answer: A

Calculating a² gives 3² = 9 and b² gives 4² = 16. Adding them results in 9 + 16 = 25.

Medium

If x + 2y = 10 and 2x - y = 3, what is the value of x?

A. 4

B. 5

C. 6

D. 7

Show Answer & Explanation

Correct Answer: A

By solving the equations, we can substitute y from the first equation into the second and find x. Solving gives x = 4.

Medium

If the product of two numbers is 72 and one number is 8, what is the other number?

A. 9

B. 6

C. 8

D. 7

Show Answer & Explanation

Correct Answer: A

To find the other number, divide the product by the known number: 72 / 8 = 9.

Medium

What is the value of k if (x - 3)(x + k) = 0 has roots x = 3 and x = -2?

A. -2

B. 2

C. 5

D. 1

Show Answer & Explanation

Correct Answer: A

The roots indicate that one factor is (x - 3) and the other is (x + 2), thus k must be -2 for (x + k) to match (x + 2).

Medium

If 3x + 4 = 7x - 8, what is the value of x?

A. 3

B. 4

C. 5

D. -3

Show Answer & Explanation

Correct Answer: A

By isolating x, we can solve the equation: 3x + 4 = 7x - 8 leads to x = 3 after rearranging.

Hard

If the roots of the quadratic equation ax^2 + bx + c = 0 are equal, which of the following conditions must hold true?

A. b^2 - 4ac = 0

B. b^2 - 4ac > 0

C. a + b + c = 0

D. a < 0

Show Answer & Explanation

Correct Answer: A

The condition for a quadratic equation to have equal roots is that the discriminant (b^2 - 4ac) must be zero. This means that the equation does not cross the x-axis and has one repeated root.

Hard

If the sequence defined by a_n = 3n + 2 is used to find the sum of the first 10 terms, what is the result?

A. 160

B. 170

C. 180

D. 190

Show Answer & Explanation

Correct Answer: C

The sum of the first 10 terms of the sequence can be calculated by finding the values of a_1 to a_10 and adding them. The first term a_1 = 5, ..., a_10 = 32. The total sum is 5 + 8 + ... + 32 = 180.

Q10

Hard

If the roots of the equation x^2 - (k + 1)x + k = 0 are real and equal, what is the value of k?

A. 1

B. 0

C. 2

D. -1

Show Answer & Explanation

Correct Answer: A

For the roots to be real and equal, the discriminant must be zero. The discriminant Δ = b^2 - 4ac = (-(k + 1))^2 - 4(1)(k) = (k + 1)^2 - 4k = k^2 + 2k + 1 - 4k = k^2 - 2k + 1. Setting this equal to zero gives (k - 1)^2 = 0, so k = 1.

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Algebra — HSC/SSC (Bangladesh) HSC Mathematics Practice Questions Online

This page contains 137 practice MCQs for the chapter Algebra in HSC/SSC (Bangladesh) HSC Mathematics. The questions are organized by difficulty — 35 easy, 76 medium, 26 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.