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POST UTME ABU 2022 Mathematics | Objective

Prepare for your exams with POST UTME ABU questions? Reviewing past/model 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 View Details

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 View Details

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

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 View Details

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 View Details

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 View Details

Solve the equation $x^2 + 4x + 4 = 0 \$ using 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 View Details

Find the derivative of the function ( f(x) = $\frac{x^2 + 2x - 3}{x^2 - 4}$\)\) ) using 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 View Details

Solve the inequality $2x^2 + 5x - 3 > 0$ using 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 View Details

Find the area of the triangle with vertices ( A(1, 2), B(3, 4), C(2, 1) ) using 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 View Details

Solve the system of equations $x + y = 2, 2x - y = 3$ using 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 View Details

Find the sum of the infinite geometric series $1 + \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \cdots$ using 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 View Details

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 standard deviation of the dataset

Correct Answer: C

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Question 12 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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

Find the value of $\frac{d}{dx} \left \frac{1}{x^2 + 1} \right \$ ) using 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 View Details

Solve the system of equations $egin{cases} x + y + z = 6 \ x + 2y + 3z = 12 \ 2x + 3y + 4z = 20 \end{cases}$ using 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 View Details

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 View Details

Find the value of $int_{0}^{1} x^2 dx$ using 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 View Details

Find the value of x in the equation $\sin^2 x + \cos^2 x = 1$ if $$1x = \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 View Details

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 View Details

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 View Details

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 View Details

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 $km/h\\((km/h) and returns at an average speed of 40$. 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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