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FSc Part 1 Maths MCQs with answers

Practise FSc Part 1 Maths (Part 1) with 288 exam-style MCQs, each with the answer and a short explanation. Every test is marked the moment you finish and shows your score chapter by chapter, so you know what to revise next. It is free and needs no sign-up.

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FSc Part 1 Maths MCQs with answers

Practise FSc Part 1 Maths (Part 1) with 288 exam-style MCQs, each with the answer and a short explanation. Every test is marked the moment you finish and shows your score chapter by chapter, so you know what to revise next. It is free and needs no sign-up.

288 questions · 14 chapters

What each chapter covers 14 chapters

The questions follow the syllabus chapter by chapter. You can test the whole subject or one chapter at a time.

  1. Number systems 20 questionsReal numbers, Complex numbers
  2. Sets, functions and groups 27 questionsSets and set operations, Logic, relations and functions, Binary operations and groups
  3. Matrices and determinants 27 questionsMatrices and matrix algebra, Determinants, Systems of linear equations
  4. Quadratic equations 29 questionsSolving quadratic and reducible equations, Roots of unity and polynomial theorems, Roots, coefficients and nature of roots
  5. Partial fractions 10 questionsResolving into partial fractions
  6. Sequences and series 28 questionsArithmetic progressions, Geometric progressions, Harmonic progressions and means
  7. Permutation, combination and probability 29 questionsFactorials and permutations, Combinations, Probability
  8. Mathematical induction and binomial theorem 28 questionsMathematical induction, Binomial theorem for positive integral index, Binomial series
  9. Fundamentals of trigonometry 20 questionsAngles and their measurement, Trigonometric ratios and fundamental identities
  10. Trigonometric identities 19 questionsCompound and allied angles, Double, half and triple angles; sums and products
  11. Trigonometric functions and their graphs 10 questionsDomain, range, period and graphs
  12. Application of trigonometry 20 questionsSolving triangles, Area of a triangle and connected circles
  13. Inverse trigonometric functions 11 questions
  14. Solutions of trigonometric equations 10 questionsSolving trigonometric equations
Sample FSc Part 1 Maths MCQs with answers 12 questions

12 questions from the test, one or two from each chapter. Try each one, then open the answer.

1. The number π is

  1. A
    rational, because π = 22/7
  2. B
    irrational, because its decimal expansion is non-terminating and non-recurring
  3. C
    rational, because it is the ratio of circumference to diameter
  4. D
    irrational, because its decimal expansion recurs
Show answer

Answer: B. π cannot be written as p/q with integers p, q; its decimal never ends and never repeats. 22/7 is an approximation, and circumference and diameter are not both integers.

2. Which statement about the empty set ∅ is correct?

  1. A
    ∅ is a proper subset of every set
  2. B
    ∅ is a subset of every set
  3. C
    ∅ is an element of every set
  4. D
    ∅ = {0}
Show answer

Answer: B. ∅ is a subset of every set, but it is not a proper subset of itself. {0} is not empty: it has the element 0.

3. The matrix with rows [x 2] and [8 x] is singular when

  1. A
    x = 4 only
  2. B
    x = ±4
  3. C
    x = ±2
  4. D
    x = 16
Show answer

Answer: B. |A| = x2 − 16 = 0, so x = 4 or x = −4. Forgetting the negative root gives only 4.

4. For the equation ax2 + bx + c = 0 (a ≠ 0), the quadratic formula is

  1. A
    x = (−b ± √(b2 − 4ac))/a
  2. B
    x = (b ± √(b2 − 4ac))/2a
  3. C
    x = (−b ± √(b2 + 4ac))/2a
  4. D
    x = (−b ± √(b2 − 4ac))/2a
Show answer

Answer: D. Completing the square on ax2 + bx + c = 0 gives x = (−b ± √(b2 − 4ac))/2a. Watch the −b and the 2a.

5. Which of the following is an identity?

  1. A
    x2 = 4
  2. B
    x2 − 5x + 6 = 0
  3. C
    2x + 3 = 7
  4. D
    (x + 1)2 = x2 + 2x + 1
Show answer

Answer: D. An identity is true for every value of x. The others are conditional equations, true only for particular values.

6. The three arithmetic means between 2 and 18 are

  1. A
    4, 8, 12
  2. B
    6, 11, 16
  3. C
    6, 10, 14
  4. D
    5, 9, 13
Show answer

Answer: C. With 3 means there are 5 terms, so 18 = 2 + 4d and d = 4. The means are 6, 10, 14.

7. Two fair coins are tossed. The probability of getting at least one head is

  1. A
    2/3
  2. B
    1/2
  3. C
    1/4
  4. D
    3/4
Show answer

Answer: D. The sample space is {HH, HT, TH, TT}. Three outcomes contain a head, so P = 3/4. 2/3 comes from wrongly listing only 3 outcomes.

8. The term independent of x in the expansion of (x + 1/x)6 is

  1. A
    15
  2. B
    20
  3. C
    6
  4. D
    1
Show answer

Answer: B. Tr+1 = 6Crx6−rx−r = 6Crx6−2r. For no x, 6 − 2r = 0, so r = 3 and the term is 6C3 = 20.

9. The point P(−3, 4) is on the terminal side of an angle θ in standard position. Then cos θ is

  1. A
    −4/3
  2. B
    4/5
  3. C
    −3/5
  4. D
    3/5
Show answer

Answer: C. r = √(9 + 16) = 5 and cos θ = x/r = −3/5. 4/5 is sin θ and −4/3 is tan θ.

10. sin P + sin Q is equal to

  1. A
    2 cos((P + Q)/2) cos((P − Q)/2)
  2. B
    2 cos((P + Q)/2) sin((P − Q)/2)
  3. C
    2 sin((P + Q)/2) cos((P − Q)/2)
  4. D
    sin(P + Q)
Show answer

Answer: C. sin P + sin Q = 2 sin((P + Q)/2) cos((P − Q)/2). The second option is sin P − sin Q and the third is cos P + cos Q.

11. The domain of y = sec x is

  1. A
    all real x except odd multiples of π/2
  2. B
    all real x except multiples of π
  3. C
    all real numbers
  4. D
    −1 ≤ x ≤ 1
Show answer

Answer: A. sec x = 1/cos x is undefined where cos x = 0, i.e. at x = (2n + 1)π/2. Multiples of π are excluded for cosec x and cot x.

12. In triangle ABC, a = 6, b = 8 and γ = 30°. The area of the triangle is

  1. A
    24
  2. B
    12
  3. C
    12√3
  4. D
    48
Show answer

Answer: B. Δ = ½ab sin γ = ½ × 6 × 8 × ½ = 12. Using cos 30° instead of sin 30° gives 12√3.

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Ways to practise 5 ways

When you get a question wrong, a short note called "The idea behind this" explains the topic it belongs to, with the rules to remember and a worked example.

Common questions

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Are these past paper questions?

The 288 MCQs are our own, written to the syllabus in the style of the exam.

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Instantly. You get your score, the right answer and an explanation for every question, and a list of the topics to work on.

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