Algebra MCQs with Answers – Solved from Past Papers
53 solved Algebra MCQs collected from real PPSC, FPSC, SPSC, KPPSC, BPSC & NTS past papers (2004–2026). Tap an option to attempt — see correct answer instantly. Download the full PDF for offline revision.
If x=7-4v3 find the value of x-1/x?
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x = 7 − 4√3 = (2 − √3)². So √x = 2 − √3 and 1/√x = 2 + √3. But the question asks x − 1/x: 1/x = 1/(7 − 4√3) = (7 + 4√3)/((7)² − (4√3)²) = (7 + 4√3)/(49 − 48) = 7 + 4√3. Then x − 1/x = (7 − 4√3) − (7 + 4√3) = −8√3.
Solve: x(x?)?/x3?
If 3(x-1)=-6, find value of x is?
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3(x − 1) = −6 → x − 1 = −2 → x = −1. Matches option B.
Simplified expression of Solve the equation (5p-6q)? + (5p+6q)?? 50p?
If f(x)=x then the value of f(F(-1)) is equal to?
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If f(x) = x, then f(−1) = −1 and f(f(−1)) = f(−1) = −1.
How many solutions of given pair of equation 3x-6y=15 and -2x+4y=-10?
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Divide first eqn by 3: x − 2y = 5. Divide second by −2: x − 2y = 5. Same line → infinite solutions.
If y=(x+1)(x+6), then its graph will intercept the y-axis how many times?
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Y-intercept occurs at x = 0: y = (1)(6) = 6. A function intercepts the y-axis exactly once.
If 2log(x+1) + 3log(x?+3) – log(x+1)? changes into single form² log(x?
x+y=13x-y=1 What is the solution set?
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x + y = 13, x − y = 1 → 2x = 14 → x = 7, y = 6. Solution (7, 6).
Given f(x) =3x?+2x+4 what is the value of f (3)?
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f(x) = 3x² + 2x + 4 → f(3) = 27 + 6 + 4 = 37.
Solve 4/5 – 3/7?
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4/5 − 3/7 = (28 − 15)/35 = 13/35.
Solve ((37)?)??
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((3^?)^?) producing 6561 = 3^8 = (3²)^4 = 9^4. So expression equals 3^8 = 6561.
If x+1 is a factor of 2x?+kx, then the value of k is?
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If x + 1 is a factor of 2x² + kx, substitute x = −1: 2 − k = 0 → k = 2.
To Solve the value (27)*(-1/3)?
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27^(−1/3) = 1/27^(1/3) = 1/3.
If Sin X =4/5 find the value of Cos(2x)?
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sin x = 4/5 → cos(2x) = 1 − 2sin²x = 1 − 2(16/25) = 1 − 32/25 = −7/25.
If x=7-4v3, then find the value of x+1/x?
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x = 7 − 4√3, 1/x = 7 + 4√3. x + 1/x = 14.
For x=1 in 2x+y=6, we have y?
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2(1) + y = 6 → y = 4.
Factorization of the expression y?+y—6 is?
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y² + y − 6 = (y + 3)(y − 2).
Solve *v64 + 3?
The power of linear equation is?
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A linear equation has degree (power) 1.
Solve the equation -8/20 -(+9/2)-1/2?
The value of satisfying the equation 7x+1=4x-8 is?
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7x + 1 = 4x − 8 → 3x = −9 → x = −3.
The difference between three times a number and four more than two times the number can be represented by the PREPARATION WI1 expression 3x-(2x+4), where x is the number?
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3x − (2x + 4) = 3x − 2x − 4 = x − 4.
What is the value of X + 3Y + Zif X =3, Y =3, and Z=4?
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X + 3Y + Z = 3 + 9 + 4 = 16.
At present the age of Ali is x-10 years. What will be his age after 12 years?
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Current age x − 10. After 12 years: x − 10 + 12 = x + 2.
The algebraic expression of word expression “subtract eight times of the number b from ten times of the number c” is?
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'10c minus 8b' = 10c − 8b.
Let x =—4x + 4, the value of x will be?
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x = −4x + 4 → 5x = 4 → x = 4/5.
-3(x?)-2(x)+1, Find f(1)?
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f(x) = −3x² − 2x + 1. f(1) = −3 − 2 + 1 = −4.
What is meant by linear equation?
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A linear equation is a first-degree equation.
ifx-y=6andx+y=16, then?
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x − y = 6, x + y = 16 → 2x = 22 → x = 11.
Solve 5+6×3-2+2?
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5 + 6×3 − 2 + 2 = 5 + 18 − 2 + 2 = 23 (BODMAS).
In mathematics, a solution to an equation that emerges from the process of solving the problem but is not a valid solution to the problem is called solution?
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A solution arising during solving but invalid in the original equation is called an extraneous solution.
Solve the series 2, 4, 8, 16, …?
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Geometric sequence ×2: 2, 4, 8, 16, 32.
If"x" and "y" are directly proportional and x = 8, y= 2. If y = 10, find value of ay"?
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Direct proportion: y/x = 2/8 = 1/4. If y = 10, x = 40.
Solve and find the value of x, if (30x + 70)/x = 100?
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(30x + 70)/x = 100 → 30x + 70 = 100x → 70x = 70 → x = 1.
Solve %-%?
Ifxandy are the two digits of the number 347xy such that the number is completely divisible by 80, then what is the value of x + y?
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347xy divisible by 80 requires divisibility by 16 and 5. y = 0 (last digit). Then 347×0 divisible by 16: 34720/16=2170 → x = 2. So x + y = 2.
Solve this equation 4x +5=17?
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4x + 5 = 17 → 4x = 12 → x = 3.
X+1/x=2. What is the value of x?
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x + 1/x = 2 → (x − 1)² = 0 → x = 1.
Solve the equation: (1/4 + 5/8) – (1/2 + 3/4)?
Show solution
(1/4 + 5/8) − (1/2 + 3/4) = 7/8 − 5/4 = 7/8 − 10/8 = −3/8.
ifx+1/x=15, then the value of x? + 1/x? is?
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x + 1/x = 15 → x² + 1/x² = 15² − 2 = 223.
|fx+1/x = 10, then what is the value of x? + 1/x??
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x + 1/x = 10 → x² + 1/x² = 10² − 2 = 98.
Simplify the expression? 2x? + 3x?? 5x?
What is the factorized form of the expression: x? – 3x — 4?
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x² − 3x − 4 = (x − 4)(x + 1).
Solve the question 9-3+1/3+1?
Find the odd man out 1, 5, 7, 11, 12, 13,17?212 If x=3 then find the value of K from the equation 3x? + (K-1)x + 9=0?
Show solution
Substitute x = 3 into 3x² + (K − 1)x + 9 = 0: 27 + 3(K − 1) + 9 = 0 → 3K + 33 = 0 → K = −11.
Solve the equation 9 – 3+1/3+1?
If X=28 and Y=51, then (X+Y)+(X—Y)?
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(X + Y) + (X − Y) = 2X = 2(28) = 56.
If 7x-y=23 and 7y-x=31,x+y?
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7x − y = 23, 7y − x = 31. Add: 6x + 6y = 54 → x + y = 9.
If x=4, y=2, then (x?) -(y?)? 12 PREPARATION WI Solution: x2 – y?
If Meena solved 24 math problems in 15 minutes. At this rate, how many problems can she solve in 40 minutes?
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Rate: 24 problems / 15 min. In 40 min: 24 × 40 / 15 = 64.
If 4x +12 = 36, what is the value of x + 3?
Show solution
4x + 12 = 36 → 4x = 24 → x = 6. So x + 3 = 9.
x+6=7thenx?
Show solution
x + 6 = 7 → x = 1.
Algebra MCQs for PPSC, FPSC, NTS & All Pakistani Competitive Exams
Algebra is the universal language of Pakistani competitive exam Math. From PPSC Lecturer, Sub-Inspector and Tehsildar tests to FPSC CSS Screening (MPT), NTS NAT/GAT, OTS, CTS, KPPSC, SPSC, BPSC and AJKPSC — almost every paper contains 1 to 5 algebra-based questions. Mastering this one topic alone can secure 2–5 marks in any One Paper format exam because most questions reduce to a handful of identities and equation patterns.
QuizWing has compiled 53 verified algebra MCQs from real past papers spanning 2004–2026 — every question solved from scratch by AI and answer keys verified. The bank covers linear equations, quadratics, algebraic identities, exponent rules, conjugate / surd manipulation, factoring, and systems of equations.
What types of algebra questions appear?
- Linear equation — “If 3(x − 1) = −6, find x” → x = −1
- Quadratic equations — factor or use x = (−b ± √(b² − 4ac)) ÷ 2a
- Algebraic identities — (a + b)², (a − b)², a² − b², (a + b)³, (a − b)³
- Surd / conjugate — “If x = 7 − 4√3, find x − 1/x” → use conjugate to simplify
- Exponent rules — x^a × x^b = x^(a+b), (x^a)^b = x^(ab), simplify expressions
- Factoring — pull out HCF, then look for perfect-square trinomial or difference of squares
- System of equations — substitution or elimination to find two unknowns
Seven essential algebraic identities
Mental-math shortcuts
- x + 1/x or x − 1/x trick — if x + 1/x = k, then x² + 1/x² = k² − 2; if x − 1/x = k, then x² + 1/x² = k² + 2
- Conjugate trick — if x = a − b√c, then 1/x = (a + b√c) ÷ (a² − b²c). Useful for x ± 1/x questions.
- Quadratic by inspection — find factors of `c` that sum to `b` for ax² + bx + c when a = 1
- Plug-in answers — for multiple-choice algebra, often faster to test each option than solve symbolically
- Common perfect squares — 11² = 121, 12² = 144, 13² = 169, 14² = 196, 15² = 225, 16² = 256, 17² = 289, 18² = 324, 19² = 361, 25² = 625
- Exponent zero — anything^0 = 1 (except 0^0 which is undefined)
How to use this page for revision
Quiz mode: Tap any option — green = correct, red = wrong. Use the pagination buttons to move between sets of 25 MCQs at a time.
PDF download: Click Download PDF in the sticky bar to grab all 53 MCQs with answers for offline study.
Mixed practice: attempt our full PPSC Mock Test with all subjects + weighted distribution to simulate the real exam.
Algebra weightage by exam
| Exam | Typical Algebra MCQs | Marks Share |
|---|---|---|
| PPSC One Paper | 1–3 | 2–5 |
| FPSC Screening | 2–5 | 4–8 |
| NTS NAT / GAT | 3–6 | 5–10 |
| CSS Screening (MPT) | 3–6 | 6–12 |
| OTS / CTS | 2–4 | 3–7 |
| SPSC / KPPSC / BPSC | 1–3 | 2–5 |
All MCQs sourced from official past papers of PPSC, FPSC, SPSC, KPPSC and NTS. Found a wrong answer? WhatsApp 0302-1417839 — we fix every reported issue within 24 hours.
Frequently Asked Questions
Typically 1 to 3 algebra MCQs appear in every PPSC One Paper test (Sub-Inspector, Tehsildar, Junior Clerk, Lecturer, BPS-14/16/17). FPSC, NTS and CSS papers tend to include 2–5. Mastering this topic alone secures 2–5 guaranteed marks because most questions reduce to the same handful of identities and linear or quadratic equation patterns.
Based on our analysis of 53 past-paper MCQs (2004–2026), the three most-recurring types are: (1) linear equation solving (find x), (2) application of algebraic identities like a²−b² = (a−b)(a+b), and (3) conjugate or surd manipulation when x is given as a+b√c form.
No. Calculators are not allowed in PPSC, FPSC, NTS, OTS or any provincial commission exam. Practise mental math shortcuts — 10%, 25%, 50% calculations should take under 5 seconds.
Yes for PPSC and FPSC — 0.25 marks deducted per wrong answer. Strategy: if you can eliminate 2 out of 4 options confidently, attempt it; otherwise leave blank.
Yes — click the Download PDF button in the sticky bar at the top of the quiz section. You get all 53 MCQs with answers in a branded QuizWing PDF, free, no signup.
Yes — 100% transferable. All provincial public service commissions follow a near-identical Math syllabus. The same algebra MCQs appear (often verbatim) in SPSC, KPPSC, BPSC, AJKPSC and NTS NAT/GAT papers.
Message us on WhatsApp at 0302-1417839 with the question number and what you believe the correct answer should be. We verify against multiple sources and fix every reported issue within 24 hours.