Exam Body

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POST UTME ABU 2021 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 2021 Mathematics (Objective) questions designed to simulate the real exam environment.

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Question 1

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

Correct A. ( 16 )

B. ( 20 )

C. ( 22 )

D. ( 24 )

Correct Answer: A

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Question 2

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

Correct A. \( x < -1 \) or \( x > \frac{3}{2} \)

B. \( x < -1 \) or \( x < \frac{3}{2} \)

C. \( x > -1 \) or \( x < \frac{3}{2} \)

D. \( x > -1 \) or \( x > \frac{3}{2} \)

Correct Answer: A

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Question 3

Find the volume of the frustum of a cone with radii 6 cm and 4 cm and height 10 cm.

A. ( 100pi ) cm³

Correct B. ( 120pi ) cm³

C. ( 140pi ) cm³

D. ( 160pi ) cm³

Correct Answer: B

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Question 4

Solve the system of equations \( x + y = 3 \) and \( xy = 2 \).

Correct A. \( x = 2, y = 1 \)

B. \( x = 1, y = 2 \)

C. \( x = 2, y = -1 \)

D. \( x = -1, y = 2 \)

Correct Answer: A

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Question 5

Find the determinant of the matrix \( egin{bmatrix} 2 & 1 & 3 \ 4 & 2 & 1 \ 1 & 3 & 2 \end{bmatrix} \).

Correct A. ( 0 )

B. ( 1 )

C. ( 2 )

D. ( 3 )

Correct Answer: A

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Question 6

Let \( mathbf{a} = egin{pmatrix} 2 \ 3 \end{pmatrix} \) and \( mathbf{b} = egin{pmatrix} 4 \ 5 \end{pmatrix} \). Find the unit vector in the direction of \( mathbf{a} + mathbf{b} \).

Correct A. \begin{pmatrix} \frac{6}{\sqrt{221}} \\ \frac{9}{\sqrt{221}} \end{pmatrix}

B. \begin{pmatrix} \frac{12}{\sqrt{221}} \\ \frac{15}{\sqrt{221}} \end{pmatrix}

C. \begin{pmatrix} \frac{6}{\sqrt{221}} \\ \frac{15}{\sqrt{221}} \end{pmatrix}

D. \begin{pmatrix} \frac{12}{\sqrt{221}} \\ \frac{9}{\sqrt{221}} \end{pmatrix}

Correct Answer: A

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Question 7

A rec\tangular box has dimensions 3 cm, 4 cm, and 5 cm. Find the volume of the box.

A. 60 cm^3

B. 80 cm^3

Correct C. 120 cm^3

D. 150 cm^3

Correct Answer: C

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Question 8

Find the area under the curve \( y = x^2 \) from \( x = 0 \) to \( x = 4 \).

A. 32

B. 64

Correct C. 128

D. 256

Correct Answer: C

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Question 9

Solve the equation \( x^3 - 6x^2 + 11x - 6 = 0 \).

Correct A. (1, 2, 3)

B. (1, 2, 6)

C. (1, 3, 6)

D. (2, 3, 6)

Correct Answer: A

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Question 10

Find the value of ( x ) in the equation \( 2^x = 32 \).

A. 5

Correct B. 6

C. 7

D. 8

Correct Answer: B

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Question 11

In a survey of 100 students, the mean height was 170 cm with a s\tandard deviation of 5 cm. If the heights of the students are normally distributed, what is the probability that a randomly selected student will be taller than 180 cm?

A. 0.1587

B. 0.5

Correct C. 0.8413

D. 0.9772

Correct Answer: C

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Question 12

Solve the inequality \frac{x^2-4x-3}{x^2-4x+3}>0.

Correct A. \left\( -\infty,-1\right)\cup\left\( 3,\infty\right \ \)

B. \left\( -\infty,1\right)\cup\left\( 3,\infty\right \ \)

C. \left\( -\infty,-1\right)\cup\left\( 1,\infty\right \ \)

D. \left\( -\infty,3\right)\cup\left\( 3,\infty\right \ \)

Correct Answer: A

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Question 13

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

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

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

C. \left\( x-4\right \)^2 + \left\( y-3\right \)^2 = 16

D. \left\( x-2\right \)^2 + \left\( y-4\right \)^2 = 16

Correct Answer: A

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Question 14

A sequence is defined by the recurrence relation a_n = 2a_{n-1} + 1, with initial term a_1 = 3. Find the sum of the first 5 terms of the sequence.

A. 63

B. 65

Correct C. 67

D. 69

Correct Answer: C

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Question 15

In a right-angled triangle, the length of the hypotenuse is 10 cm and one of the other sides is 6 cm. Find the length of the third side.

Correct A. 8 cm

B. 6 cm

C. 8.6 cm

D. 9.8 cm

Correct Answer: A

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Question 16

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

A. 10

B. 12

Correct C. 14

D. 16

Correct Answer: C

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Question 17

In the diagram below, the circle passes through points ( A(2, 3) ) and ( B(4, 5) ). Find the equation of the circle.

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

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

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

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

Correct Answer: A

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Question 18

Simplify the expression \( \frac{1}{2} \left\( \frac{1}{3} \right \ \)^{-2} \left\( \frac{1}{4} \right \)^{-1} \left\( \frac{1}{5} \right \)^{-3} \).

A. 120

B. 240

Correct C. 360

D. 480

Correct Answer: C

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Question 19

Find the volume of the frustum of the cone with height \( h = 6 \) cm and radii of the bases \( r_1 = 4 \) cm and \( r_2 = 2 \) cm.

A. 48\pi

B. 64\pi

Correct C. 80\pi

D. 96\pi

Correct Answer: C

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Question 20

In the sequence ( 1, 2, 4, 8, 16, ... ), find the 7th term.

A. 32

B. 64

Correct C. 128

D. 256

Correct Answer: C

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Question 21

Find the derivative of the function ( f(x) = \frac{1}{\sqrt{x^2 + 1}} ) u\sing the chain rule.

Correct A. \frac{-x}{\( x^2 + 1 \)^{3/2}}

B. \frac{x}{\( x^2 + 1 \)^{3/2}}

C. \frac{1}{\( x^2 + 1 \)^{3/2}}

D. \frac{-1}{\( x^2 + 1 \)^{3/2}}

Correct Answer: A

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Question 22

Solve the equation \( 2^x + 2^{x+1} = 3 cdot 2^{x+2} \) for ( x ).

A. x = -1

B. x = 0

Correct C. x = 1

D. x = 2

Correct Answer: C

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Question 23

Find the area of the triangle with vertices ( A(0, 0) ), ( B(2, 0) ), and ( C(1, 3) ).

A. 3

B. 6

Correct C. 9

D. 12

Correct Answer: C

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Question 24

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

A. x < -1

Correct B. x > -1

C. x < 3

D. x > 3

Correct Answer: B

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Question 25

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 = 3x - 2

D. y = 3x + 2

Correct Answer: A

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