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OAU Post-UTME Mathematics 2019 past questions and answers

10 questions. Try each one, then open the answer to check yourself and read the explanation.

Question 1

Differentiation

Differentiate y = loge(1/x) − 1

  1. A.x logex
  2. B.−1/x
  3. C.−x
  4. D.(logex)/x
Show the answer and explanation

Answer: B (−1/x)

Explanation

loge(1/x) = −ln x, so y = −ln x − 1 and dy/dx = −1/x.

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Question 2

Differentiation

Differentiate sin (1 − 2x3)

  1. A.cos (1 − 2x3)
  2. B.−cos(1 − 2x3)
  3. C.cos(12x5 − 6x2)
  4. D.−6x2cos(1 − 2x3)
Show the answer and explanation

Answer: D (−6x2cos(1 − 2x3))

Explanation

Chain rule: the derivative of sin u is cos u × du/dx, and du/dx = −6x². So the answer is −6x² cos(1 − 2x³).

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Question 3

Integration

Evaluate ∫cos2(90 − θ)dθ

  1. A.½[θ − (sin 2θ)/2] + K
  2. B.½θ − ½ sin 2θ + k
  3. C.½θ − ½ cos 2θ + k
  4. D.½θ − ¼ cos 2θ + k
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Answer: A (½[θ − (sin 2θ)/2] + K)

Explanation

cos(90° − θ) = sin θ, and sin²θ = (1 − cos 2θ)/2. Integrating gives ½(θ − ½ sin 2θ) + K.

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Question 4

Logarithms

Evaluate log28 + log232

  1. A.8
  2. B.3
  3. C.5
  4. D.2
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Answer: A (8)

Explanation

log28 = 3 and log232 = 5, so the sum is 8.

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Question 5

Algebraic Expressions

Factorise 4x − 3ay + 4y − 3ax

  1. A.(4x + 4y)(−3ax − 3ay)
  2. B.(4 − 3a)(x + y)
  3. C.(x + y)(3a)
  4. D.(2x + 3y)(a + 1)
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Answer: B ((4 − 3a)(x + y))

Explanation

Group: 4(x + y) − 3a(x + y) = (4 − 3a)(x + y).

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Question 6

Quadratic Equations

Solve x2 − 16x + 64 = 0

  1. A.8
  2. B.−8
  3. C.8 (twice)
  4. D.−8(twice)
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Answer: C (8 (twice))

Explanation

x² − 16x + 64 = (x − 8)², so x = 8 is a repeated root.

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Question 7

Differentiation

Find the minimum point of the function 2x2 − 12x + 3.

  1. A.3
  2. B.−15
  3. C.57
  4. D.5
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Answer: A (3)

Explanation

dy/dx = 4x − 12 = 0 at x = 3, and d²y/dx² = 4 > 0, so the minimum is at x = 3 (the minimum value there is −15).

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Question 8

Logarithms

Solve log10x = 5

  1. A.105
  2. B.510
  3. C.10
  4. D.50
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Answer: A (105)

Explanation

log10x = 5 means x = 105.

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Question 9

Coordinate Geometry

Given the equation x2 + y2 = 100. What is the area of the circle in terms of π?

  1. A.10π
  2. B.πxy
  3. C.100π
  4. D.π/10
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Answer: C (100π)

Explanation

This circle has r² = 100, so area = πr² = 100π.

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Question 10

Number Bases

Convert 101012 to base 3

  1. A.2103
  2. B.1123
  3. C.111212013
  4. D.10212113
Show the answer and explanation

Answer: A (2103)

Explanation

101012 = 16 + 4 + 1 = 21. 21 = 2 × 9 + 1 × 3 + 0, so it is 2103.

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