Class 11 / FSc · first-year course practice
Class 11 FSc Maths Practice MCQs — Free Online Practice
You are IN first year now — these are the HSSC Part-1 topics you are actually studying. Below are 8 Maths MCQs with worked answers, drawn from our bank of 16. The Part-1 units both maths books keep in common — complex numbers, quadratics, matrices, partial fractions, sequences & series, perms/combs, binomial and the trigonometric identities.
How this fits your first year
This is course practice, not an entry paper: first-year topics at Part-1 depth, one bank each for Maths, Physics and Chemistry. Topics follow the published FSc Part-1 curricula — restricted to the chapters the older FSc Part-1 books and the current Punjab edition keep in common, so both cohorts get their subjects. Each college or board's own syllabus is the final word on any year's exact list.
Preparing for the class-11 ENTRY test (matric/O-Level level)? That bank lives inside the practice engine — sign up free and the engine serves it with your class recorded.
Free sample Maths MCQs (with answers)
1. The nature of the roots of 2x² − 4x + 3 = 0 is:
Quadratic Equations · medium
- A. real and equal
- B. real and distinct
- C. non-real (complex conjugates)
- D. irrational but real
Correct answer: C
The discriminant b² − 4ac = (−4)² − 4(2)(3) = 16 − 24 = −8 < 0, so the square root is of a negative number: the roots are non-real complex conjugates.
2. If the roots of x² + kx + 9 = 0 are equal, then k equals:
Quadratic Equations · medium
- A. −6 only
- B. ±3
- C. ±6
- D. 6 only
Correct answer: C
Equal roots require the discriminant to be zero: k² − 4(1)(9) = 0, so k² = 36 and k = ±6. Forgetting either sign loses a root case.
3. The coefficient of x² in the binomial expansion of (1 + x)⁴ is:
Binomial Theorem · easy
- A. 6
- B. 16
- C. 4
- D. 12
Correct answer: A
The x² term carries the binomial coefficient C(4, 2) = 4!/(2!·2!) = 6, multiplying x²٠1² — the coefficient alone is 6.
4. The 20th term of the arithmetic progression 3, 7, 11, … is:
Sequences & Series · easy
- A. 80
- B. 79
- C. 83
- D. 75
Correct answer: B
AP nth term: aₙ = a + (n − 1)d with a = 3, d = 4. So a₂₀ = 3 + 19(4) = 79 — count 19 gaps, not 20.
5. sin 2θ is equal to:
Trigonometric Identities · easy
- A. 2 sin θ
- B. sin θ + cos θ
- C. 2 sin θ cos θ
- D. 2 cos θ
Correct answer: C
The double-angle formula: sin 2θ = 2 sin θ cos θ — derive it from sin(A + B) with A = B = θ. Options naming a single ratio (2 sin θ) are the classic misconception.
6. The domain of f(x) = 1/(x − 2) is:
Functions & Graphs · easy
- A. all real numbers except x = 2
- B. all real numbers except x = 0
- C. only the single value x = 2
- D. x > 2 only
Correct answer: A
A fraction is undefined where its denominator is zero; only x = 2 makes x − 2 = 0, so every other real number IS in the domain — one exclusion, not a restricted ray.
7. cos 2θ is equal to:
Trigonometric Identities · medium
- A. sin²θ − cos²θ
- B. 1 + cos²θ
- C. 1 − 2 sin²θ
- D. 1 + 2 sin²θ
Correct answer: C
One of the three standard double-angle forms: cos 2θ = cos²θ − sin²θ = 1 − 2 sin²θ = 2 cos²θ − 1. The choice (sin²θ − cos²θ) is cos 2θ NEGATED — the sign error the distractor tests.
8. For the decomposition 1/(x² − 1) = A/(x − 1) + B/(x + 1), the constants are:
Partial Fractions · hard
- A. A = 1, B = 0
- B. A = 1/2, B = −1/2
- C. A = −1/2, B = 1/2
- D. A = 1/2, B = 1/2
Correct answer: B
Clear denominators: 1 = A(x + 1) + B(x − 1) = (A + B)x + (A − B). Matching gives A + B = 0 and A − B = 1, so A = 1/2 and B = −1/2 — the two constants always oppose by the constant term.
Practise the full bank — free
All 16 first-year Maths questions sit in our free practice engine. It adapts to your level, tracks the topics you miss and builds a streak — and it stays 100% free.