Exam Body

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Subject

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POST UTME ABU 2022 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 2022 Mathematics (Objective) questions designed to simulate the real exam environment.

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Question 1

In the diagram below, the volume of the cylinder is given by \( V = pi r^2 h \). If the radius of the cylinder is 4 cm and the height is 10 cm, calculate the volume in cubic centimeters.

A. 400\pi

Correct B. 800\pi

C. 1600\pi

D. 3200\pi

Correct Answer: B

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Question 2

Solve the inequality \( \frac{1}{x+1} > \frac{1}{x-1} \ \) for \( x \in \mathbb{R} \ \).

A. x > 1

B. x < -1

Correct C. x > -1 and x < 1

D. x < -1 or x > 1

Correct Answer: C

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Question 3

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

Correct A. 2 + 7 + 17 + 37 + 79

B. 2 + 7 + 17 + 37 + 81

C. 2 + 7 + 17 + 37 + 83

D. 2 + 7 + 17 + 37 + 85

Correct Answer: A

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Question 4

In the diagram below, the graph of the function ( f(x) = x^2 - 4x + 3 \) is shown. Find the x-coordinate of the vertex of the parabola.

A. 1

Correct B. 2

C. 3

D. 4

Correct Answer: B

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Question 5

Solve the equation \( x^2 + 4x + 4 = 0 \ \) u\sing the quadratic formula.

Correct A. x = -2

B. x = -1

C. x = 0

D. x = 1

Correct Answer: A

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Question 6

Find the derivative of the function ( f(x) = \frac{x^2 + 2x - 3}{x^2 - 4} ) u\sing the quotient rule.

A. \frac{2x\( x^2 - 4 \) - \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2}

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

Correct C. \frac{2x\( x^2 - 4 \) - \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2}

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

Correct Answer: C

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Question 7

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

A. \left\( - \frac{5}{4}, \frac{3}{2} \right \)

B. \left\( - \frac{3}{2}, \frac{5}{4} \right \)

Correct C. \left\( - \frac{5}{4}, \frac{3}{2} \right \) \cup \left\( \frac{3}{2}, \infty \right \)

D. \left\( - \frac{3}{2}, \frac{5}{4} \right \) \cup \left\( - \infty, \frac{3}{2} \right \)

Correct Answer: C

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Question 8

Find the area of the triangle with vertices ( A(1, 2), B(3, 4), C(2, 1) ) u\sing the formula for the area of a triangle.

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

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

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

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

Correct Answer: A

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Question 9

Solve the system of equations \( x + y = 2, 2x - y = 3 \) u\sing the method of substitution.

Correct A. \left\( x, y \right \) = \left\( -1, 3 \right \)

B. \left\( x, y \right \) = \left\( 1, 1 \right \)

C. \left\( x, y \right \) = \left\( -1, 1 \right \)

D. \left\( x, y \right \) = \left\( 1, 3 \right \)

Correct Answer: A

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Question 10

Find the sum of the infinite geometric series \( 1 + \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \cdots \) u\sing the formula for the sum of an infinite geometric series.

Correct A. \frac{1}{1 - \frac{1}{2}}

B. \frac{1}{1 + \frac{1}{2}}

C. \frac{1}{1 - \frac{1}{4}}

D. \frac{1}{1 + \frac{1}{4}}

Correct Answer: A

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Question 11

A histogram is a graphical representation of the distribution of a dataset. What is the primary purpose of a histogram?

A. To show the mean of the dataset

B. To show the median of the dataset

Correct C. To show the distribution of the dataset

D. To show the s\tandard deviation of the dataset

Correct Answer: C

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Question 12

A quadratic equation is given by \( ax^2 + bx + c = 0 \). What is the discriminant of the equation?

Correct A. \( b^2 - 4ac \)

B. \( a^2 - 4bc \)

C. \( b^2 + 4ac \)

D. \( a^2 + 4bc \)

Correct Answer: A

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Question 13

A right-angled triangle has a hypotenuse of length 10 cm and one of the other sides of length 6 cm. What is the length of the third side?

A. 8 cm

Correct B. 12 cm

C. 16 cm

D. 20 cm

Correct Answer: B

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Question 14

A solid cylinder has a radius of 4 cm and a height of 10 cm. What is the volume of the cylinder?

Correct A. 800π cm^3

B. 1600π cm^3

C. 3200π cm^3

D. 6400π cm^3

Correct Answer: A

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Question 15

A quadratic equation is given by \( x^2 + 4x + 4 = 0 \). What is the solution to the equation?

Correct A. \( x = -2 \)

B. \( x = -1 \)

C. \( x = 1 \)

D. \( x = 2 \)

Correct Answer: A

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Question 16

Solve the inequality \( \frac{x-2}{x+1} > 0 \) for \( x in \( -infty, -1 \ \) cup \( -1, 2 \) cup (2, infty) ).

A. \( x in \( -infty, -1 \ \) cup (2, infty) )

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

C. \( x in \( -infty, -1 \ \) cup (2, infty) )

Correct D. \( x in \( -infty, -1 \ \) cup \( -1, 2 \) cup (2, infty) )

Correct Answer: D

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Question 17

Find the value of \( \frac{d}{dx} left\( \frac{1}{x^2 + 1} \right \ \) ) u\sing the chain rule.

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

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

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

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

Correct Answer: A

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Question 18

Solve the system of equations \( egin{cases} x + y + z = 6 \ x + 2y + 3z = 12 \ 2x + 3y + 4z = 20 \end{cases} \) u\sing matrices.

Correct A. \( x = 1, y = 2, z = 3 \)

B. \( x = 2, y = 3, z = 1 \)

C. \( x = 3, y = 1, z = 2 \)

D. \( x = 1, y = 3, z = 2 \)

Correct Answer: A

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Question 19

A fair six-sided die is rolled. What is the probability that the number rolled is greater than 4?

A. \( \frac{1}{6} \)

B. \( \frac{2}{6} \)

C. \( \frac{3}{6} \)

Correct D. \( \frac{4}{6} \)

Correct Answer: D

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Question 20

Find the value of \( int_{0}^{1} x^2 dx \) u\sing the power rule.

Correct A. \( left[ \frac{x^3}{3} \right]_{0}^{1} = \frac{1}{3} \)

B. \( left[ \frac{x^3}{3} \right]_{0}^{1} = \frac{2}{3} \)

C. \( left[ \frac{x^3}{3} \right]_{0}^{1} = \frac{3}{3} \)

D. \( left[ \frac{x^3}{3} \right]_{0}^{1} = \frac{4}{3} \)

Correct Answer: A

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Question 21

Find the value of x in the equation \( \sin^2 x + \cos^2 x = 1 \) if \( \sin x = \frac{3}{5} \).

A. 0

Correct B. \frac{\pi}{6}

C. \frac{\pi}{4}

D. \frac{\pi}{3}

Correct Answer: B

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Question 22

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

Correct A. \left\( -\infty, -1 \right \) \cup \left\( \frac{3}{2}, \infty \right \)

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

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

D. \left\( -\infty, 2 \right \) \cup \left\( 3, \infty \right \)

Correct Answer: A

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Question 23

Find the equation of the \tangent line to the curve \( y = x^2 - 2x + 1 \) at the point ( (1, 0) ).

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 24

A bakery sells 250 loaves of bread per day. If they make a profit of ₦5 per loaf, how much profit do they make in a day?

Correct A. ₦1250

B. ₦12500

C. ₦125000

D. ₦1250000

Correct Answer: A

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Question 25

A car travels from city A to city B at an average speed of 60 km/h and returns at an average speed of 40 km/h. What is the average speed for the round trip?

A. 48 km/h

B. 50 km/h

Correct C. 52 km/h

D. 54 km/h

Correct Answer: C

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