Algebra MCQs – Equations, Expressions & Factoring
Sharpen your algebra skills with 10 MCQs on linear equations, quadratic equations, factoring, simultaneous equations, and algebraic identities — aligned with board exam standards.
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Q1
What is the solution of 2x + 6 = 14?
✓ B – x = 4
2x + 6 = 14 → 2x = 14 − 6 = 8 → x = 4. To solve linear equations, isolate the variable by applying inverse operations to both sides.
2x + 6 = 14 → 2x = 14 − 6 = 8 → x = 4. To solve linear equations, isolate the variable by applying inverse operations to both sides.
Q2
Which of the following is a quadratic equation?
✓ B – x² + 4x + 4 = 0
A quadratic equation has the form ax² + bx + c = 0 where a ≠ 0. Option B (x² + 4x + 4 = 0) satisfies this — the highest power of x is 2.
A quadratic equation has the form ax² + bx + c = 0 where a ≠ 0. Option B (x² + 4x + 4 = 0) satisfies this — the highest power of x is 2.
Q3
Factor the expression: x² − 9
✓ A – (x+3)(x−3)
x² − 9 = x² − 3² is a difference of squares. Formula: a² − b² = (a+b)(a−b). So x² − 9 = (x+3)(x−3). This identity is extremely commonly tested.
x² − 9 = x² − 3² is a difference of squares. Formula: a² − b² = (a+b)(a−b). So x² − 9 = (x+3)(x−3). This identity is extremely commonly tested.
Q4
If 3x − 7 = 2x + 5, find x.
✓ B – x = 12
3x − 7 = 2x + 5 → 3x − 2x = 5 + 7 → x = 12. Collect like terms on each side and isolate the variable.
3x − 7 = 2x + 5 → 3x − 2x = 5 + 7 → x = 12. Collect like terms on each side and isolate the variable.
Q5
The roots of x² − 5x + 6 = 0 are:
✓ A – 2 and 3
Factor: x² − 5x + 6 = (x−2)(x−3) = 0 → x = 2 or x = 3. For factoring ax² + bx + c, find two numbers that multiply to c and add to b.
Factor: x² − 5x + 6 = (x−2)(x−3) = 0 → x = 2 or x = 3. For factoring ax² + bx + c, find two numbers that multiply to c and add to b.
Q6
What is the value of (a + b)² when a = 3, b = 2?
✓ C – 25
(a+b)² = (3+2)² = 5² = 25. Alternatively use the identity: (a+b)² = a² + 2ab + b² = 9 + 12 + 4 = 25.
(a+b)² = (3+2)² = 5² = 25. Alternatively use the identity: (a+b)² = a² + 2ab + b² = 9 + 12 + 4 = 25.
Q7
Simplify: 3(x + 4) − 2(x − 1)
✓ B – x + 14
3(x+4) − 2(x−1) = 3x + 12 − 2x + 2 = x + 14. Distribute carefully, noting that −2 × −1 = +2 (sign change when distributing a negative).
3(x+4) − 2(x−1) = 3x + 12 − 2x + 2 = x + 14. Distribute carefully, noting that −2 × −1 = +2 (sign change when distributing a negative).
Q8
Solve the simultaneous equations: x + y = 7 and x − y = 3
✓ B – x=5, y=2
Add both equations: 2x = 10 → x = 5. Substitute: 5 + y = 7 → y = 2. The addition method (elimination) is ideal when coefficients of one variable match.
Add both equations: 2x = 10 → x = 5. Substitute: 5 + y = 7 → y = 2. The addition method (elimination) is ideal when coefficients of one variable match.
Q9
What is the discriminant of x² − 4x + 4 = 0?
✓ A – 0
Discriminant = b² − 4ac = (−4)² − 4(1)(4) = 16 − 16 = 0. When discriminant = 0, the equation has two equal real roots (repeated root). Here x = 2 (double root).
Discriminant = b² − 4ac = (−4)² − 4(1)(4) = 16 − 16 = 0. When discriminant = 0, the equation has two equal real roots (repeated root). Here x = 2 (double root).
Q10
Which algebraic identity represents (a − b)²?
✓ C – a² − 2ab + b²
(a−b)² = a² − 2ab + b². This is a standard identity. Note the sign difference from (a+b)² = a² + 2ab + b². The middle term is always negative for (a−b)².
(a−b)² = a² − 2ab + b². This is a standard identity. Note the sign difference from (a+b)² = a² + 2ab + b². The middle term is always negative for (a−b)².
About These Algebra MCQs
These Algebra MCQs cover essential topics from linear equations to quadratic expressions, factoring, and algebraic identities. Aligned with the Class 9 & 10 Mathematics curriculum.
Algebra forms the backbone of advanced mathematics. A strong foundation in factoring, identities, and equation solving is essential for FSc, Engineering, and medical entry tests.
Topics Covered
- Linear equations in one variable
- Quadratic equations and roots
- Factoring — difference of squares
- Algebraic identities: (a+b)², (a−b)²
- Simultaneous equations (elimination)
- Discriminant and nature of roots
Study Strategy
Practice factoring daily — it is the most tested algebra skill. Memorize the 5 key algebraic identities and practice numerical substitution for quick MCQ solving. For quadratics, always check if factoring is possible before using the formula.
Frequently Asked Questions
What is a quadratic equation? ›
A quadratic equation is a polynomial equation of degree 2 in the form ax² + bx + c = 0 where a ≠ 0. It can have 0, 1, or 2 real solutions depending on the discriminant.
What is the quadratic formula? ›
x = [−b ± √(b²−4ac)] / 2a. This formula gives the roots of any quadratic equation. The expression b²−4ac is called the discriminant.
How do you factor x² − 9? ›
This is a difference of squares: x² − 9 = (x+3)(x−3). The formula is a² − b² = (a+b)(a−b).
What does a discriminant of zero mean? ›
A discriminant (b²−4ac) of zero means the quadratic has exactly one real root (a repeated/equal root). The parabola just touches the x-axis at one point.
What are simultaneous equations? ›
Two or more equations with the same variables that must be solved together. Methods include substitution, elimination (addition/subtraction), and graphical methods.
