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POST UTME UNIPORT 2021 Mathematics | Objective

Are you preparing for POST UTME UNIPORT 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.

Practice these randomly selected questions to test your readiness.

Question 1

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

Correct A. ( f'(x) = \frac{-2x}{$ x^2 + 1 $^2} )

B. ( f'(x) = \frac{2x}{$ x^2 + 1 $^2} )

C. ( f'(x) = \frac{2}{$ x^2 + 1 $^2} )

D. ( f'(x) = \frac{-2}{$ x^2 + 1 $^2} )

Correct Answer: A

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Question 2

Solve the inequality $|x - 2| > 3$.

Correct A. $x < -1$ or $x > 5$

B. $x < 1$ or $x > 5$

C. $x < -1$ or $x > 2$

D. $x < 1$ or $x > 2$

Correct Answer: A

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Question 3

A sequence is defined by $a_n = \frac{1}{n} + \frac{1}{n + 1}$. Find the sum of the first 5 terms of the sequence.

Correct A. $\frac{25}{12}$

B. $\frac{23}{12}$

C. $\frac{21}{12}$

D. $\frac{19}{12}$

Correct Answer: A

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Question 4

A circle has a radius of 4 cm and a center at (0, 0). Find the equation of the circle.

Correct A. $x^2 + y^2 = 16$

B. $x^2 + y^2 = 32$

C. $x^2 + y^2 = 64$

D. $x^2 + y^2 = 256$

Correct Answer: A

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Question 5

A set of 5 numbers has a mean of 10 and a median of 8. Find the sum of the numbers.

Correct A. 50

B. 60

C. 70

D. 80

Correct Answer: A

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Question 6

A rec\tangular prism has a length of 8 cm, a width of 5 cm, and a height of 3 cm. Find the volume of the prism u\sing the formula V = lwh.

A. 100 cm^3

Correct B. 120 cm^3

C. 150 cm^3

D. 200 cm^3

Correct Answer: B

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Question 7

The mean of a set of numbers is 25. If the sum of the numbers is 150, how many numbers are in the set?

A. 4

Correct B. 6

C. 8

D. 10

Correct Answer: B

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Question 8

Find the determinant of the matrix \begin{bmatrix} 2 & 3 \ 4 & 5 \end{bmatrix}.

A. -1

Correct B. -2

C. 2

D. 4

Correct Answer: B

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Question 9

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

A. -1

Correct B. -2

C. 0

D. 2

Correct Answer: B

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Question 10

A histogram shows the distribution of exam scores for a class of 20 students. The histogram has 5 bars, each representing a score range. The heights of the bars are 2, 3, 4, 5, and 6. Find the mean of the scores.

A. 4.2

B. 4.4

Correct C. 4.6

D. 4.8

Correct Answer: C

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Question 11

Determine the value of $\frac{d}{dx} \left$ \frac{1}{x^2} \right $$ u\sing the quotient rule.

Correct A. \frac{2}{x^3}

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

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

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

Correct Answer: A

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Question 12

Solve the inequality $|2x - 3| \geq 7$.

Correct A. x \leq -2 \text{ or } x \geq 5

B. x \geq -2 \text{ or } x \leq 5

C. x \leq 2 \text{ or } x \geq -5

D. x \geq 2 \text{ or } x \leq -5

Correct Answer: A

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Question 13

Find the sum of the first 10 terms of the geometric series $\sum_{n=1}^{10} \frac{2}{3^n}$.

Correct A. \frac{63}{32}

B. \frac{63}{64}

C. \frac{63}{128}

D. \frac{63}{256}

Correct Answer: A

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Question 14

A set of 5 numbers has a mean of 10. If 2 is added to each number, what is the new mean?

A. 8

B. 10

Correct C. 12

D. 14

Correct Answer: C

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Question 15

Solve the quadratic equation $x^2 + 5x + 6 = 0$.

Correct A. x = -2 \text{ or } x = -3

B. x = 2 \text{ or } x = 3

C. x = -3 \text{ or } x = 2

D. x = 3 \text{ or } x = -2

Correct Answer: A

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Question 16

Let $ A = egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} $ and $ B = egin{bmatrix} 5 & 6 \ 7 & 8 \end{bmatrix} $. Find ( AB ) if it exists.

Correct A. \[ AB = \begin{bmatrix} 19 & 22 \\ 43 & 50 \end{bmatrix} \]

B. \[ AB = \begin{bmatrix} 11 & 14 \\ 25 & 30 \end{bmatrix} \]

C. \[ AB = \begin{bmatrix} 3 & 4 \\ 9 & 12 \end{bmatrix} \]

D. \[ AB = \begin{bmatrix} 5 & 6 \\ 15 & 18 \end{bmatrix} \]

Correct Answer: A

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Question 17

A set ( S ) contains the elements ( 1, 2, 3, 4, 5, 6 ). Find the number of subsets of ( S ) that contain exactly two elements.

A. 6

Correct B. 12

C. 20

D. 30

Correct Answer: B

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Question 18

Let ( f(x) = x^2 - 4x + 3 ) and ( g(x) = 2x - 1 ). Find ( (f circ g)(x) ).

Correct A. 2x^2 - 5x + 2

B. 2x^2 - 5x + 1

C. 2x^2 - 5x - 2

D. 2x^2 - 5x + 3

Correct Answer: A

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Question 19

A sequence is defined by $ a_n = 2n + 1 $. Find the sum of the first five terms of the sequence.

A. 30

B. 35

C. 40

Correct D. 45

Correct Answer: D

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Question 20

A random experiment has two possible outcomes: heads or tails. If the probability of getting heads is $ \frac{1}{3} $, find the probability of getting tails.

A. \frac{1}{3}

Correct B. \frac{2}{3}

C. \frac{1}{2}

D. \frac{1}{4}

Correct Answer: B

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Question 21

Find the volume of the frustum of a cone with height 6cm, lower base radius 4cm, and upper base radius 2cm.

A. 24\pi cm^3

Correct B. 48\pi cm^3

C. 72\pi cm^3

D. 96\pi cm^3

Correct Answer: B

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Question 22

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

Correct A. x<-1 or x>2

B. x<-1 or x<2

C. x>1 or x>2

D. x<-1 or x<2

Correct Answer: A

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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-2 $^2 + $ y+3 $^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

Find the area of the triangle with vertices (0,0), (3,0), and (0,4).

A. 6

Correct B. 12

C. 18

D. 24

Correct Answer: B

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Question 25

Solve the system of equations \begin{align*} x+y+z&=3\ x+2y+3z&=6\ 2x+3y+4z&=9\ \end{align*}.

Correct A. x=1, y=1, z=1

B. x=2, y=1, z=0

C. x=3, y=0, z=0

D. x=0, y=0, z=0

Correct Answer: A

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