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POST UTME UNIPORT 2023 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 2023 Mathematics (Objective) questions designed to simulate the real exam environment.

Practice these randomly selected questions to test your readiness.

Question 1

Find the volume of the solid formed by revolving the region bounded by the curves $y=x^2$ and $y=4x$ about the x-axis.

Correct A. \frac{32}{15}\pi

B. \frac{64}{15}\pi

C. \frac{128}{15}\pi

D. \frac{256}{15}\pi

Correct Answer: A

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Question 2

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

Correct A. $ -\infty,-5)\cup\( 5,\infty \ $

B. $ -\infty,-1)\cup\( 1,\infty \ $

C. $ -\infty,-5)\cup\( 2,\infty \ $

D. $ -\infty,-1)\cup\( 4,\infty \ $

Correct Answer: A

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Question 3

Find the equation of the plane pas\sing through the points $A(1,2,3)$ and $B(2,3,4)$ and perp\endicular to the line $\vec{r}=\begin{pmatrix}1\ 2\ 3\end{pmatrix}+t\begin{pmatrix}1\ 1\ 1\end{pmatrix}.$

Correct A. x+y+z=6

B. x-y+z=4

C. x+y-z=2

D. x-y-z=0

Correct Answer: A

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Question 4

Solve the equation $\log_{10}$ x^2-4 $=2.$

Correct A. x=\pm 2\sqrt{10}

B. x=\pm 10

C. x=\pm 2\sqrt{5}

D. x=\pm 5

Correct Answer: A

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Question 5

Find the value of $\sqrt{\frac{\sqrt{2}}{\sqrt{3}}}.$

Correct A. \frac{\sqrt{6}}{3}

B. \frac{\sqrt{2}}{3}

C. \frac{\sqrt{3}}{2}

D. \frac{\sqrt{6}}{2}

Correct Answer: A

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Question 6

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

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

B. ( f'(x) = \frac{x}{$ x^2 + 1 $^{3/2}} )

C. ( f'(x) = \frac{1}{$ x^2 + 1 $^{3/2}} )

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

Correct Answer: A

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Question 7

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

Correct A. $ x > -\frac{5}{4} $ or $ x < \frac{3}{2} $

B. $ x < -\frac{5}{4} $ or $ x > \frac{3}{2} $

C. $ x > -\frac{5}{4} $ and $ x < \frac{3}{2} $

D. $ x < -\frac{5}{4} $ and $ x > \frac{3}{2} $

Correct Answer: A

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Question 8

Find the volume of the solid formed by revolving the region bounded by the curves $ y = x^2 $ and $ y = 4 - x^2 $ about the x-axis.

Correct A. $ \frac{16pi}{3} $

B. $ \frac{32pi}{3} $

C. $ \frac{64pi}{3} $

D. $ \frac{128pi}{3} $

Correct Answer: A

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Question 9

Solve the equation $ 2^x + 2^{-x} = 3 $ for x.

A. $ x = \log_2 2 $

Correct B. $ x = \log_2 3 $

C. $ x = \log_2 4 $

D. $ x = \log_2 6 $

Correct Answer: B

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Question 10

Find the surface area of the solid formed by revolving the region bounded by the curves $ y = x^2 $ and $ y = 4 - x^2 $ about the x-axis.

Correct A. ( 16pi )

B. ( 32pi )

C. ( 64pi )

D. ( 128pi )

Correct Answer: A

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Question 11

Let X and Y be indep\endent events with P(X) = 0.4 and P(Y) = 0.6. Find P(X ∩ Y).

Correct A. 0.24

B. 0.36

C. 0.48

D. 0.60

Correct Answer: A

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Question 12

Find the volume of the solid formed by revolving the region bounded by y = x^2, y = 0, and x = 2 about the x-axis.

A. 32π

B. 64π

Correct C. 128π

D. 256π

Correct Answer: C

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Question 13

Solve the matrix equation AX = B, where A = egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix}, X = egin{bmatrix} x \ y \end{bmatrix}, and B = egin{bmatrix} 5 \ 6 \end{bmatrix}.

Correct A. egin{bmatrix} 1 \ 2 \end{bmatrix}

B. egin{bmatrix} 2 \ 3 \end{bmatrix}

C. egin{bmatrix} 3 \ 4 \end{bmatrix}

D. egin{bmatrix} 4 \ 5 \end{bmatrix}

Correct Answer: A

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Question 14

Find the surface area of the solid formed by revolving the region bounded by y = x^2, y = 0, and x = 2 about the x-axis.

A. 64π

Correct B. 128π

C. 256π

D. 512π

Correct Answer: B

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Question 15

Find the sum of the infinite geometric series 1 + x + x^2 + ...

Correct A. 1/$ 1-x $

B. 1/$ 1+x $

C. 1/$ 1-x^2 $

D. 1/$ 1+x^2 $

Correct Answer: A

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Question 16

Find the equation of the circle with center at (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 < -1 \text{ or } x > 2

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

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

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

Correct Answer: A

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Question 18

Find the determinant of the matrix \begin{bmatrix} 2 & 3 & 4 \ 5 & 6 & 7 \ 8 & 9 & 10 \end{bmatrix}.

Correct A. 0

B. 1

C. 2

D. 3

Correct Answer: A

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Question 19

Solve the quadratic equation \begin{align*} x^2 + 4x + 4 &= 0 \end{align*}.

Correct A. \text{Solution: } x = -2

B. \text{Solution: } x = -1

C. \text{Solution: } x = 0

D. \text{Solution: } x = 1

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).

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

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

C. \text{Equation: } y = 3x + 1

D. \text{Equation: } y = 4x + 1

Correct Answer: B

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Question 21

Solve the inequality \begin{align*} x^2 - 4x + 3 &> 0 \end{align*}.

Correct A. \text{Solution: } x < 1 \text{ or } x > 3

B. \text{Solution: } x < 3 \text{ or } x > 1

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

D. \text{Solution: } x < 1 \text{ or } x < 3

Correct Answer: A

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Question 22

Find the value of \begin{align*} \frac{1}{2} \left$ \frac{1}{3} + \frac{1}{4} \right $ \end{align*}.

A. \frac{1}{4}

Correct B. \frac{1}{6}

C. \frac{1}{8}

D. \frac{1}{12}

Correct Answer: B

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Question 23

Solve the equation \begin{align*} x^2 + 2x - 6 &= 0 \end{align*}.

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

B. \text{Solution: } x = -2 \text{ or } x = 3

C. \text{Solution: } x = -1 \text{ or } x = 6

D. \text{Solution: } x = 1 \text{ or } x = -6

Correct Answer: VIEW ANSWER

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Question 24

Determine the volume of the frustum of a cone with a height of 10 cm, a base radius of 6 cm, and a top radius of 4 cm.

A. 100π cm³

Correct B. 150π cm³

C. 200π cm³

D. 250π cm³

Correct Answer: B

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Question 25

Solve the system of linear equations u\sing matrices: \[ \begin{array}{ccc} x+2y-3z&=&7\ 2x-y+z&=&5\ -x+3y-2z&=&1\ \end{array}\]

Correct A. x=1, y=2, z=3

B. x=2, y=1, z=4

C. x=3, y=2, z=5

D. x=4, y=3, z=6

Correct Answer: A

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