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UI Post-UTME Mathematics 2016 past questions and answers

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

Question 1

Number Bases

What is the decimal equivalent of 134five

  1. A.36
  2. B.44
  3. C.105
  4. D.11
Show the answer and explanation

Answer: B (44)

Explanation

1 × 25 + 3 × 5 + 4 = 44.

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Question 2

Number Bases

3245six = Xnine, find x

  1. A.10
  2. B.739
  3. C.1011
  4. D.160
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Answer: C (1011)

Explanation

3245₆ = 3 × 216 + 2 × 36 + 4 × 6 + 5 = 739; dividing by 9 repeatedly gives remainders 1, 1, 0, 1, so 739 = 1011₉.

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Question 3

Fractions, Decimals and Approximation

Arrange in ascending order of magnitude: 5/9, 7/15, 11/20, 3/8

  1. A.5/9, 7/15, 11/20, 3/8
  2. B.7/15, 3/8, 5/9, 11/20
  3. C.3/8, 11/20, 5/9, 7/15
  4. D.3/8, 7/15, 11/20, 5/9
Show the answer and explanation

Answer: D (3/8, 7/15, 11/20, 5/9)

Explanation

As decimals: 3/8 = 0.375, 7/15 ≈ 0.467, 11/20 = 0.55, 5/9 ≈ 0.556.

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Question 4

Ratio, Percentages and Rates

In a certain gathering, the ratio of men to women is 2:5. If there are 40 women, how many men are there?

  1. A.16
  2. B.100
  3. C.20
  4. D.200
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Answer: A (16)

Explanation

Men/40 = 2/5, so there are 16 men.

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Question 5

Ratio, Percentages and Rates

Testimony, Joy and Opeyemi share 60 notebooks in the ratio 2:4:6. How many notebooks does Opeyemi get?

  1. A.10
  2. B.20
  3. C.30
  4. D.60
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Answer: C (30)

Explanation

Opeyemi gets 6/12 of 60 = 30.

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Question 6

Surds

Evaluate 7√3 − √75

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

Explanation

√75 = 5√3, so 7√3 − 5√3 = 2√3.

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Question 7

Indices

5x+1 = 625, find x

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

Explanation

625 = 5⁴, so x + 1 = 4 and x = 3.

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Question 8

Indices

25x − 5x − 20 = 0, find x

  1. A.1
  2. B.3
  3. C.5
  4. D.7
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Answer: A (1)

Explanation

Let p = 5ˣ: p² − p − 20 = (p − 5)(p + 4) = 0. Since 5ˣ > 0, p = 5 and x = 1.

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Question 9

Commercial Arithmetic

The simple interest on a certain sum of money invested for 4 years at 6.5% per annum is ₦416. Find the amount invested.

  1. A.₦2000
  2. B.₦1600
  3. C.₦3000
  4. D.₦10000
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Answer: B (₦1600)

Explanation

P = 100 × 416/(6.5 × 4) = 41,600/26 = ₦1,600.

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Question 10

Sets

If U = {1, 2, 4, 6, 9, 12}, A = {4, 6, 12}, B = {2, 4, 9}. Find A' ∩ B

  1. A.{1, 2, 9}
  2. B.{1, 4, 6}
  3. C.{2, 9}
  4. D.∅
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Answer: C ({2, 9})

Explanation

A' = {1, 2, 9}; the elements also in B are {2, 9}.

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Question 11

Linear and Simultaneous Equations

(2x − 1)/3 − (3x − 1)/4 = 1, find x

  1. A.−13
  2. B.6
  3. C.13
  4. D.−6
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Answer: A (−13)

Explanation

Multiply by 12: 4(2x − 1) − 3(3x − 1) = 12, so −x − 1 = 12 and x = −13.

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Question 12

Linear and Simultaneous Equations

The sum of three consecutive numbers is 36. Find the numbers

  1. A.18, 11 and 7
  2. B.20, 10 and 6
  3. C.15, 10 and 11
  4. D.11, 12 and 13
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Answer: D (11, 12 and 13)

Explanation

y + (y + 1) + (y + 2) = 36 gives y = 11: 11, 12, 13.

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Question 13

Linear and Simultaneous Equations

A man is four times as old as his son. In four years time, he will be three times as old. What are their present ages?

  1. A.32 and 8
  2. B.40 and 6
  3. C.33 and 6
  4. D.30 and 10
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Answer: A (32 and 8)

Explanation

4x + 4 = 3(x + 4) gives x = 8: the son is 8 and the man 32.

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Question 14

Algebraic Expressions

Factorize 16x2 − 9y2

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

Explanation

Difference of two squares: (4x)² − (3y)² = (4x + 3y)(4x − 3y).

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Question 15

Quadratic Equations

What must be added to x2 − 22x to make it a perfect square?

  1. A.11
  2. B.121
  3. C.36
  4. D.13
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Answer: B (121)

Explanation

Add the square of half the coefficient of x: (22/2)² = 121.

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Question 16

Progressions

The 8th term of a G.P is 640. If the first term is 5, find the common ratio.

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

Explanation

5r⁷ = 640, so r⁷ = 128 = 2⁷ and r = 2.

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Question 17

Progressions

How many terms has the A.P whose first term is 15 and the last term is 57 given that the common difference is 3?

  1. A.15
  2. B.21
  3. C.11
  4. D.14
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Answer: A (15)

Explanation

57 = 15 + 3(n − 1), so n − 1 = 14 and n = 15.

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Question 18

Trigonometry

Cos m = sin(m + 22°), find m.

  1. A.68
  2. B.34
  3. C.44
  4. D.14
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Answer: B (34)

Explanation

cos m = sin(90° − m), so m + 22 = 90 − m and m = 34°.

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Question 19

Angles and Polygons

One angle of an octagon is 65°. The others are equal to each other. Find the value of each.

  1. A.65°
  2. B.56°
  3. C.145°
  4. D.54°
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Answer: C (145°)

Explanation

Interior angles of an octagon add to 6 × 180° = 1080°; (1080 − 65) ÷ 7 = 145°.

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Question 20

Logarithms

Evaluate log432 + log42

  1. A.34
  2. B.30
  3. C.3
  4. D.7
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Answer: C (3)

Explanation

log₄32 + log₄2 = log₄64 = 3.

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