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POST UTME ABU 2018 Mathematics | Objective

Are you preparing for POST UTME ABU exams? Reviewing past questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2018 Mathematics (Objective) questions designed to simulate the real exam environment.

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Question 1

Find the equation of the circle with center \( -2, 3 \) and radius 4.

Correct A. x^2 + y^2 + 4x - 6y + 13 = 0

B. x^2 + y^2 - 4x + 6y + 13 = 0

C. x^2 + y^2 + 4x + 6y + 13 = 0

D. x^2 + y^2 - 4x - 6y + 13 = 0

Correct Answer: A

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Question 2

Solve the inequality \frac{x - 2}{x + 1} > 0.

Correct A. \( -\infty, -1 \) \cup \( 2, \infty \)

B. \( -\infty, -1 \) \cup \( -1, 2 \)

C. \( -\infty, 2 \) \cup \( 2, \infty \)

D. \( -\infty, -1 \) \cup \( 1, \infty \)

Correct Answer: A

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Question 3

Find the sum of the first 10 terms of the geometric series with first term 2 and common ratio 3.

A. 59048

Correct B. 59049

C. 59050

D. 59051

Correct Answer: B

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Question 4

Solve the system of equations \begin{align*} x + y &= 4 \ x - 2y &= 3 \end{align*}

Correct A. \begin{align*} x &= 7 \ y &= -3 \end{align*}

B. \begin{align*} x &= 3 \ y &= 1 \end{align*}

C. \begin{align*} x &= 1 \ y &= 3 \end{align*}

D. \begin{align*} x &= -1 \ y &= -3 \end{align*}

Correct Answer: A

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Question 5

Find the equation of the line pas\sing through the points (1, 2) and (3, 4).

Correct A. y = 2x - 1

B. y = 2x + 1

C. y = x - 1

D. y = x + 1

Correct Answer: A

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Question 6

Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).

Correct A. \( \frac{1}{2} \times 4^3 + 3 \times 4^2 - 2 \times 4 \)

B. \( \frac{1}{2} \times 4^2 + 3 \times 4 - 2 \)

C. \( \frac{1}{2} \times 4^3 - 3 \times 4^2 - 2 \times 4 \)

D. \( \frac{1}{2} \times 4^2 - 3 \times 4 + 2 \)

Correct Answer: A

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Question 7

Solve the inequality \( \frac{x}{x-1} > 2 \).

A. \( x < -1 \) or \( x > 2 \)

Correct B. \( x < 1 \) or \( x > 2 \)

C. \( x < -1 \) or \( x < 2 \)

D. \( x > 1 \) or \( x < 2 \)

Correct Answer: B

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Question 8

Find the volume of the solid formed by revolving the region bounded by the curve \( y = x^2 \), the x-axis, and the line \( x = 2 \) about the x-axis.

A. \( \frac{32}{3} pi \)

B. \( \frac{64}{3} pi \)

Correct C. \( \frac{128}{3} pi \)

D. \( \frac{256}{3} pi \)

Correct Answer: C

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Question 9

A vector ( mathbf{a} ) has magnitude 5 and direction \( 30^circ \) from the positive x-axis. Find the unit vector in the direction of ( mathbf{a} ).

Correct A. \( egin{pmatrix} \frac{5}{\sqrt{3}} \ \frac{5}{\sqrt{3}} \end{pmatrix} \)

B. \( egin{pmatrix} \frac{5}{\sqrt{2}} \ \frac{5}{\sqrt{2}} \end{pmatrix} \)

C. \( egin{pmatrix} \frac{5}{\sqrt{3}} \ -\frac{5}{\sqrt{3}} \end{pmatrix} \)

D. \( egin{pmatrix} \frac{5}{\sqrt{2}} \ -\frac{5}{\sqrt{2}} \end{pmatrix} \)

Correct Answer: A

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Question 10

Find the surface area of the solid formed by revolving the region bounded by the curve \( y = x^2 \), the x-axis, and the line \( x = 2 \) about the x-axis.

A. ( 16 pi )

B. ( 32 pi )

Correct C. ( 64 pi )

D. ( 128 pi )

Correct Answer: C

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Question 11

In a circle of radius 10 cm, a chord of length 8 cm subt\ends an angle of 60° at the centre. Find the area of the sector.

Correct A. \( \frac{1}{6} pi \( 10 \ \)^2 )

B. \( \frac{1}{6} pi \( 8 \ \)^2 )

C. \( \frac{1}{6} pi \( 10 \ \)^2 - \frac{1}{6} pi (8)^2 )

D. \( \frac{1}{6} pi \( 10 \ \)^2 + \frac{1}{6} pi (8)^2 )

Correct Answer: A

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Question 12

Find the value of x in the equation \( 2^x + 2^{x+1} = 3 cdot 2^{x+1} \).

A. \( x = 1 \)

Correct B. \( x = 2 \)

C. \( x = 3 \)

D. \( x = 4 \)

Correct Answer: B

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Question 13

A set A contains 5 elements and a set B contains 3 elements. Find the number of elements in the union of sets A and B.

Correct A. \( 5 + 3 - 2 \)

B. \( 5 + 3 + 2 \)

C. ( 5 cdot 3 )

D. \( 5 cdot 3 + 2 \)

Correct Answer: A

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Question 14

Find the sum of the first 10 terms of the arithmetic progression 2, 5, 8, ... .

A. ( 55 )

B. ( 65 )

Correct C. ( 75 )

D. ( 85 )

Correct Answer: C

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Question 15

A circle passes through the points (1, 2) and (3, 4). Find the equation of the circle.

Correct A. \( x^2 + y^2 - 4x - 6y + 9 = 0 \)

B. \( x^2 + y^2 - 4x - 6y + 5 = 0 \)

C. \( x^2 + y^2 - 4x - 6y + 7 = 0 \)

D. \( x^2 + y^2 - 4x - 6y + 11 = 0 \)

Correct Answer: A

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Question 16

Find the volume of the frustum of a cone with height 8 cm, lower base radius 6 cm, and upper base radius 4 cm. The frustum is cut off by a plane parallel to the base of the cone.

A. 256\pi\text{ cm}^3

B. 512\pi\text{ cm}^3

Correct C. 768\pi\text{ cm}^3

D. 1024\pi\text{ cm}^3

Correct Answer: C

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Question 17

Differentiate the function \( f(x) = \frac{\log x}{x^2} \) with respect to x.

Correct A. \frac{1 - 2\log x}{x^3}

B. \frac{2\log x - 1}{x^3}

C. \frac{1}{x^3}

D. \frac{2}{x^3}

Correct Answer: A

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Question 18

A histogram of exam scores has a mean of 60 and a s\tandard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score will be between 50 and 70?

Correct A. 0.5

B. 0.6

C. 0.7

D. 0.8

Correct Answer: A

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Question 19

Simplify the expression \( \sqrt{\frac{16x^2y^2}{25}} \) and express it in the form \( ax^by^c \).

A. \frac{4x}{5y}

Correct B. \frac{4xy}{5}

C. \frac{4x^2y}{5}

D. \frac{4xy^2}{5}

Correct Answer: B

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Question 20

Find the value of x in the equation \( 2^x = 64 \).

A. 3

Correct B. 4

C. 5

D. 6

Correct Answer: B

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Question 21

Let X and Y be indep\endent events with P(X) = 0.4 and P(Y) = 0.6. Find P(X ∩ Y).

Correct A. 0.24

B. 0.48

C. 0.64

D. 0.8

Correct Answer: A

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Question 22

Solve the equation \( 2x^2 + 5x - 3 = 0 \) u\sing the quadratic formula.

A. \\frac{-5 \\pm \\sqrt{109}}{4}

B. \\frac{-5 \\pm \\sqrt{121}}{4}

Correct C. \\frac{-5 \\pm \\sqrt{169}}{4}

D. \\frac{-5 \\pm \\sqrt{225}}{4}

Correct Answer: C

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Question 23

Find the equation of the circle with center (2, 3) and radius 4.

Correct A. \( x - 2 \)^2 + \( y - 3 \)^2 = 16

B. \( x - 3 \)^2 + \( y - 2 \)^2 = 16

C. \( x + 2 \)^2 + \( y + 3 \)^2 = 16

D. \( x - 2 \)^2 + \( y + 3 \)^2 = 16

Correct Answer: A

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Question 24

Solve the inequality \( 2x^2 - 5x - 3 > 0 \).

Correct A. \( -∞, -3 \) ∪ (1, ∞)

B. \( -∞, -1 \) ∪ (3, ∞)

C. \( -∞, 1 \) ∪ (3, ∞)

D. \( -∞, -3 \) ∪ (1, 3)

Correct Answer: A

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Question 25

Find the value of \( \sin(2x) \) when \( \cos(x) = \frac{1}{2} \).

Correct A. \frac{1}{2}

B. \frac{1}{3}

C. \frac{1}{4}

D. \frac{1}{5}

Correct Answer: A

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