Question 1:

\[
\text{If } a^2 – b^2 = 15 \text{ and } a – b = 3, \text{ then } a + b = ?
\]
\[
\text{(a) } 5, \quad \text{(b) } 8, \quad \text{(c) } 6, \quad \text{(d) } 9
\]
Answer: C

Question 2:

\[
\text{Simplify } (x + 2y)^2 – (x – 2y)^2
\]
\[
\text{(a) } 4xy, \quad \text{(b) } 8xy, \quad \text{(c) } 16xy, \quad \text{(d) } x^2 – y^2
\]
Answer: B

Question 3:

\[
\text{What is the result of } (a + b)(a – b) + b^2 \text{?}
\]
\[
\text{(a) } a^2, \quad \text{(b) } b^2, \quad \text{(c) } a^2 + b^2, \quad \text{(d) } a^2 – b^2
\]
Answer: C

Question 4:

\[
\text{If } x + \frac{1}{x} = 4, \text{ then find } x^2 + \frac{1}{x^2}
\]
\[
\text{(a) } 14, \quad \text{(b) } 16, \quad \text{(c) } 12, \quad \text{(d) } 18
\]
Answer: A

Question 5:

\[
\text{If } p + q = 7 \text{ and } pq = 10, \text{ then find } p^2 + q^2
\]
\[
\text{(a) } 39, \quad \text{(b) } 45, \quad \text{(c) } 49, \quad \text{(d) } 30
\]
Answer: A

Question 6:

\[
\text{Factorize } x^3 + 3x^2y + 3xy^2 + y^3
\]
\[
\text{(a) } (x + y)(x^2 + xy + y^2), \quad \text{(b) } (x + y)^3, \quad \text{(c) } (x + y)(x + y), \quad \text{(d) } \text{None of these}
\]
Answer: B

Question 7:

\[
\text{Simplify } (a – b)^3 + (b – c)^3 + (c – a)^3
\]
\[
\text{(a) } 3(a – b)(b – c)(c – a), \quad \text{(b) } 0, \quad \text{(c) } a^3 + b^3 + c^3, \quad \text{(d) } \text{None of these}
\]
Answer: B

Question 8:

\[
\text{If } x + y = 10 \text{ and } xy = 21, \text{ then find } x^3 + y^3
\]
\[
\text{(a) } 460, \quad \text{(b) } 730, \quad \text{(c) } 1000, \quad \text{(d) } 650
\]
Answer: C

Question 9:

\[
\text{If } 2x + 3y = 12 \text{ and } 4x – 6y = 18, \text{ then find } x
\]
\[
\text{(a) } 3, \quad \text{(b) } 2, \quad \text{(c) } 5, \quad \text{(d) } 6
\]
Answer: A

Question 10:

\[
\text{Solve for } x: \quad 3x^2 – 8x + 4 = 0
\]
\[
\text{(a) } \frac{4}{3}, \quad \text{(b) } \frac{2}{3}, \quad \text{(c) } \frac{1}{2}, \quad \text{(d) } \frac{4}{2}
\]
Answer: A

Question 11:

\[
\text{What is the remainder when } x^3 + 3x + 2 \text{ is divided by } x – 1?
\]
\[
\text{(a) } 3, \quad \text{(b) } 4, \quad \text{(c) } 6, \quad \text{(d) } 7
\]
Answer: C

Question 12:

\[
\text{If } a + b = 5 \text{ and } ab = 6, \text{ then find } a^3 + b^3
\]
\[
\text{(a) } 35, \quad \text{(b) } 47, \quad \text{(c) } 65, \quad \text{(d) } 75
\]
Answer: D

Question 13:

\[
\text{If } x^2 – 6x + 9 = 0, \text{ then find } x
\]
\[
\text{(a) } 3, \quad \text{(b) } 2, \quad \text{(c) } 5, \quad \text{(d) } 6
\]
Answer: A

Question 14:

\[
\text{Solve } x^2 – 5x + 6 = 0
\]
\[
\text{(a) } 2,3, \quad \text{(b) } 3,4, \quad \text{(c) } 4,5, \quad \text{(d) } 5,6
\]
Answer: A

Question 15:

\[
\text{Find the factors of } x^2 – 4x – 12
\]
\[
\text{(a) } (x – 6)(x + 2), \quad \text{(b) } (x – 4)(x + 3), \quad \text{(c) } (x – 3)(x + 4), \quad \text{(d) } (x – 2)(x + 6)
\]
Answer: A

More MCQs on Algebra (Collected from Past Papers)

Elementary Algebra – MCQs

Algebraic Expressions – MCQs
By: Prof. Dr. Fazal Rehman Shamil | Last updated: January 31, 2025