Mathematics MCQs for 2nd Year (Federal Board)

This page has over 1,200 multiple-choice questions for Mathematics (2nd Year (Federal Board)), arranged in 9 chapters and 11 topics. The chapters include Functions, Logarithms and Financial Mathematics, Limits and Continuity, Differentiation, Applications of Differentiation and Integration. Every question has four options, an instant answer and, where available, a short explanation.

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Chapters and topics

  • Functions, Logarithms and Financial Mathematics 1 topic · 140 MCQs
  • Limits and Continuity 1 topic · 105 MCQs
  • Differentiation 2 topics · 202 MCQs
  • Applications of Differentiation 1 topic · 158 MCQs
  • Integration 1 topic · 162 MCQs
  • Differential Equations and Numerical Methods 1 topic · 102 MCQs
  • Analytical Geometry and Vector Functions 1 topic · 104 MCQs
  • Inverse Trigonometric Functions and Trigonometric Equations 1 topic · 107 MCQs
  • Conic Sections 2 topics · 205 MCQs

Sample Mathematics MCQs

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Q1. Rs. 50,000 is invested at 10% compound interest per annum. The amount after 3 years is:

  1. Rs. 73,205.00
  2. Rs. 66,550.00
  3. Rs. 16,550.00
  4. Rs. 65,000.00
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Answer: B. Rs. 66,550.00

A = P(1 + r/100)ⁿ = 50,000 × 1.1^3 = Rs. 66,550.00.

Q2. The function f(x) = (x² − 4)/(x − 2) at x = 2 (not defined there) is:

  1. continuous
  2. continuous only from the left
  3. discontinuous (not defined)
  4. discontinuous (jump)
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Answer: C. discontinuous (not defined)

f(x) = (x² − 4)/(x − 2) at x = 2 (not defined there): discontinuous (not defined).

Q3. Which function has derivative 1/x?

  1. cos x
  2. ln x
  3. sec x
  4. sin x
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Answer: B. ln x

The correct answer is “ln x”. d/dx(ln x) = 1/x.

Q4. The stationary point of y = 2x² + 16x + 37 is a:

  1. maximum
  2. minimum
  3. discontinuity
  4. point of inflexion
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Answer: B. minimum

The correct answer is “minimum”. d²y/dx² = 4 > 0.

Q5. ∫ from 0 to π/2 of sin x dx = ?

  1. 0
  2. 1
  3. π/2
  4. 2
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Answer: B. 1

The correct answer is “1”. [−cos x] = 1.

Q6. Which term means xₙ₊₁ = xₙ − f(xₙ)/f′(xₙ)?

  1. particular solution
  2. Newton–Raphson method
  3. separable equation
  4. bisection method
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Answer: B. Newton–Raphson method

Newton–Raphson method: xₙ₊₁ = xₙ − f(xₙ)/f′(xₙ).

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