Exam Body

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Subject

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POST UTME UNIPORT 2024 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 2024 Mathematics (Objective) questions designed to simulate the real exam environment.

Practice these randomly selected questions to test your readiness.

Question 1

Find the equation of the circle pas\sing through the points (2,3), (4,5) and (6,7).

Correct A. $ x^2 + y^2 - 12x - 16y + 60 = 0 $

B. $ x^2 + y^2 - 14x - 20y + 80 = 0 $

C. $ x^2 + y^2 - 16x - 24y + 100 = 0 $

D. $ x^2 + y^2 - 18x - 28y + 120 = 0 $

Correct Answer: A

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Question 2

If ( f(x) = \frac{x^2 - 4}{x - 2} ), find ( f'(x) ) u\sing the chain rule.

A. ( f'(x) = \frac{x^2 - 4}{$ x - 2 $^2} )

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

C. ( f'(x) = \frac{2x - 4}{$ x - 2 $^2} )

D. ( f'(x) = \frac{2x + 4}{$ x - 2 $^2} )

Correct Answer: B

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Question 3

Solve the inequality $ |2x - 1| geq 3 $.

Correct A. $ x leq -1 $ or ( x geq 2 )

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

C. ( x leq 2 ) or $ x geq -1 $

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

Correct Answer: A

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Question 4

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

Correct A. ( 6 )

B. ( 8 )

C. ( 10 )

D. ( 12 )

Correct Answer: A

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Question 5

If ( f(x) = 2x^3 - 5x^2 + x - 1 ), find the derivative of ( f(x) ) u\sing the power rule.

Correct A. ( f'(x) = 6x^2 - 10x + 1 )

B. ( f'(x) = 6x^2 - 10x - 1 )

C. ( f'(x) = 6x^2 - 10x + 2 )

D. ( f'(x) = 6x^2 - 10x - 2 )

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 $.

A. 40

B. 50

Correct C. 60

D. 70

Correct Answer: C

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Question 7

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

Correct A. $ -∞, -2 $ ∪ (0, ∞)

B. $ -∞, -2 $ ∪ (2, ∞)

C. $ -∞, 0 $ ∪ (2, ∞)

D. $ -∞, 0 $ ∪ (0, 2)

Correct Answer: A

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Question 8

Find the derivative of the function $ y = \sqrt{2x + 1} $ u\sing the chain rule.

Correct A. 1/$ 2√\( 2x + 1 \ $)

B. 1/$ 2√\( 2x + 1 \ $) * $ 2x + 1 $

C. 1/$ 2√\( 2x + 1 \ $) * $ 2x + 1 $^2

D. 1/$ 2√\( 2x + 1 \ $) * $ 2x + 1 $^3

Correct Answer: A

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Question 9

Solve the trigonometric equation $ \sin^2 x + \cos^2 x = 1 $ for ( x ) in the interval ( [0, 2pi] ).

Correct A. 0, π/2, π, 3π/2

B. 0, π/2, 3π/2

C. 0, π, 2π

D. π/2, π, 3π/2

Correct Answer: A

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Question 10

Convert the number 1011 from base 2 to base 10.

A. 11

Correct B. 13

C. 15

D. 17

Correct Answer: B

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Question 11

Find the equation of the circle pas\sing through the points (2, 3), (4, 5), and $ -1, 1 $.

Correct A. \left$ x - 1 \right $^2 + \left$ y - 1 \right $^2 = 10

B. \left$ x + 1 \right $^2 + \left$ y - 1 \right $^2 = 10

C. \left$ x - 1 \right $^2 + \left$ y + 1 \right $^2 = 10

D. \left$ x + 1 \right $^2 + \left$ y + 1 \right $^2 = 10

Correct Answer: A

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Question 12

A rec\tangular box has a length of 10 cm, a width of 5 cm, and a height of 8 cm. Find the volume of the box.

A. 400 cm^3

B. 500 cm^3

Correct C. 600 cm^3

D. 800 cm^3

Correct Answer: C

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Question 13

Find the derivative of the function f(x) = 3x^2 + 2x - 5.

Correct A. 6x + 2

B. 6x - 2

C. 3x + 2

D. 3x - 2

Correct Answer: A

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Question 14

A fair six-sided die is rolled. Find 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 15

Find the equation of the line pas\sing through the points (2, 3) and (4, 5).

Correct A. y = \frac{2}{2}x + 1

B. y = \frac{2}{2}x - 1

C. y = \frac{2}{2}x + 2

D. y = \frac{2}{2}x - 2

Correct Answer: A

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Question 16

Find the equation of the circle with center $ -2, 3 $ and radius 4.

Correct A. \text{Equation: } $ x + 2 $^2 + $ y - 3 $^2 = 16

B. \text{Equation: } $ x - 2 $^2 + $ y + 3 $^2 = 16

C. \text{Equation: } $ x + 2 $^2 + $ y + 3 $^2 = 16

D. \text{Equation: } $ x - 2 $^2 + $ y - 3 $^2 = 16

Correct Answer: A

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Question 17

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

Correct A. \text{Solution: } x < -2 \text{ or } x > 1

B. \text{Solution: } x < -2 \text{ or } x < 1

C. \text{Solution: } x > -2 \text{ or } x > 1

D. \text{Solution: } x < -2 \text{ or } x < 1

Correct Answer: A

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Question 18

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

Correct A. \text{Derivative: } f'(x) = \frac{$ x^2 - 4 $$ 2x + 2 $ - $ x^2 + 2x - 3 $(2x)}{$ x^2 - 4 $^2}

B. \text{Derivative: } f'(x) = \frac{$ x^2 - 4 $$ 2x + 2 $ - $ x^2 + 2x - 3 $(2x)}{$ x^2 - 4 $^2}

C. \text{Derivative: } f'(x) = \frac{$ x^2 - 4 $$ 2x + 2 $ + $ x^2 + 2x - 3 $(2x)}{$ x^2 - 4 $^2}

D. \text{Derivative: } f'(x) = \frac{$ x^2 - 4 $$ 2x + 2 $ + $ x^2 + 2x - 3 $(2x)}{$ x^2 - 4 $^2}

Correct Answer: A

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Question 19

A histogram of exam scores has a mean of 60 and a s\tandard deviation of 10. If the scores are normally distributed, find the probability that a randomly selected score is greater than 70.

Correct A. \text{Probability: } P$ X > 70 $ = 0.1587

B. \text{Probability: } P$ X > 70 $ = 0.8413

C. \text{Probability: } P$ X > 70 $ = 0.1587

D. \text{Probability: } P$ X > 70 $ = 0.8413

Correct Answer: A

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Question 20

Find the equation of the line pas\sing through the points (2, 3) and (4, 5).

Correct A. \text{Equation: } y = \frac{2}{2}x + 1

B. \text{Equation: } y = \frac{2}{2}x + 2

C. \text{Equation: } y = \frac{2}{2}x + 3

D. \text{Equation: } y = \frac{2}{2}x + 4

Correct Answer: A

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Question 21

Determine the value of $\theta$ in the equation $\tan \theta = \frac{1}{3}$, given that $\theta$ lies in quadrant II.

A. 60°

Correct B. 120°

C. 150°

D. 180°

Correct Answer: B

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Question 22

A particle moves in a plane with its position vector given by $\mathbf{r}(t) = \langle 2t, 3t^2 \rangle$. Find the velocity vector $\mathbf{v}(t)$ and acceleration vector $\mathbf{a}(t)$.

Correct A. $\mathbf{v}(t) = \langle 2, 6t \rangle$, $\mathbf{a}(t) = \langle 0, 6 \rangle$

B. $\mathbf{v}(t) = \langle 2, 6t \rangle$, $\mathbf{a}(t) = \langle 0, 12t \rangle$

C. $\mathbf{v}(t) = \langle 2t, 6t \rangle$, $\mathbf{a}(t) = \langle 0, 6 \rangle$

D. $\mathbf{v}(t) = \langle 2t, 6t \rangle$, $\mathbf{a}(t) = \langle 0, 12t \rangle$

Correct Answer: A

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Question 23

Let $A = \begin{pmatrix} 1 & 2 \ 3 & 4 \end{pmatrix}$ and $B = \begin{pmatrix} 5 & 6 \ 7 & 8 \end{pmatrix}$. Find the product $AB$.

Correct A. $\begin{pmatrix} 19 & 22 \ 43 & 50 \end{pmatrix}$

B. $\begin{pmatrix} 23 & 26 \ 47 & 54 \end{pmatrix}$

C. $\begin{pmatrix} 21 & 24 \ 45 & 52 \end{pmatrix}$

D. $\begin{pmatrix} 25 & 28 \ 49 & 56 \end{pmatrix}$

Correct Answer: A

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Question 24

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

Correct A. $\frac{1023}{2187}$

B. $\frac{1024}{2187}$

C. $\frac{1025}{2187}$

D. $\frac{1026}{2187}$

Correct Answer: A

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Question 25

Find the derivative of the function $f(x) = \frac{1}{x^2 + 1}$.

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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