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POST UTME UNIPORT 2019 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 2019 Mathematics (Objective) questions designed to simulate the real exam environment.

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Question 1

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

Correct A. \frac{256}{15}\pi

B. \frac{64}{3}\pi

C. \frac{32}{3}\pi

D. \frac{16}{3}\pi

Correct Answer: A

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Question 2

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

Correct A. $ -\infty,-2)\cup\( \frac{1}{2},\infty \ $

B. $ -\infty,-2)\cup\( \frac{1}{2},\infty \ $

C. $ -\infty,-2)\cup\( \frac{1}{2},\infty \ $

D. $ -\infty,-2)\cup\( \frac{1}{2},\infty \ $

Correct Answer: A

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Question 3

Find the area of the triangle with vertices $A(0,0), B(3,0), C(1,2)$.

A. 4

Correct B. 6

C. 8

D. 10

Correct Answer: B

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Question 4

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

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 5

Find the determinant of the matrix $\begin{bmatrix}1&2&3\4&5&6\7&8&9\end{bmatrix}$.

Correct A. 0

B. 1

C. -1

D. 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{3}{2} \text{ or } x > 1

B. x < -1 \text{ or } x > \frac{3}{2}

C. x < -1 \text{ or } x < \frac{3}{2}

D. x > -1 \text{ or } x > \frac{3}{2}

Correct Answer: A

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Question 8

Find the sum of the first 5 terms of the geometric series $ 2 + 6 + 18 + \ldots $.

Correct A. 2 + 6 + 18 + 54 + 162 = 242

B. 2 + 6 + 18 + 54 + 162 = 242

C. 2 + 6 + 18 + 54 + 162 = 242

D. 2 + 6 + 18 + 54 + 162 = 242

Correct Answer: A

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Question 9

Solve the system of linear equations $ x + y = 3 $ and $ 2x - 3y = -5 $.

Correct A. x = 2, y = 1

B. x = 1, y = 2

C. x = 2, y = -1

D. x = -1, y = 2

Correct Answer: A

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Question 10

Find the area of the triangle with vertices ( A(1, 2) ), ( B(3, 4) ), and ( C(2, 1) ).

Correct A. 5

B. 10

C. 15

D. 20

Correct Answer: A

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Question 11

Solve for $x$ in the equation [ \tan 2x = \frac{1}{\sqrt{3}} ] given that $0^circ le x le 90^circ$.

Correct A. $30^circ$

B. $45^circ$

C. $60^circ$

D. $75^circ$

Correct Answer: A

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Question 12

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

A. $x^2 + y^2 - 4x - 6y + 13 = 0$

Correct B. $x^2 + y^2 - 4x - 6y + 25 = 0$

C. $x^2 + y^2 - 4x - 6y + 9 = 0$

D. $x^2 + y^2 - 4x - 6y + 1 = 0$

Correct Answer: B

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Question 13

Solve the inequality [ 2x^2 - 5x - 3 > 0 ].

Correct A. $x in $ -\infty, -1 $ \cup $ 3, \infty $$

B. $x in $ -\infty, 1 $ \cup $ 3, \infty $$

C. $x in $ -\infty, -3 $ \cup $ 1, \infty $$

D. $x in $ -\infty, 3 $ \cup $ 1, \infty $$

Correct Answer: A

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Question 14

Find the value of $x$ in the equation [ \log_{10} $ x^2 $ = 4 ].

Correct A. $10^4$

B. $10^2$

C. $10^{-2}$

D. $10^{-4}$

Correct Answer: A

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Question 15

Find the mean of the data set [ 2, 4, 6, 8, 10 ].

A. $6$

Correct B. $8$

C. $10$

D. $12$

Correct Answer: B

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Question 16

Find the value of x in the equation $ \log_{10} \( x^2 \ $ = 4 ).

A. 10

B. 100

C. 1000

Correct D. 10000

Correct Answer: D

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Question 17

Solve for y in the equation $ y = \frac{1}{2} \( 3x + 5 \ $ ) when x = 2.

A. 4

Correct B. 6

C. 8

D. 10

Correct Answer: B

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Question 18

A circle has a radius of 4 cm. Find the area of the circle.

Correct A. 50.24

B. 100.48

C. 150.72

D. 201.06

Correct Answer: A

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Question 19

Find the value of x in the equation $ x^2 + 4x + 4 = 0 $.

Correct A. -2

B. -1

C. 0

D. 1

Correct Answer: A

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Question 20

A set of numbers has a mean of 10 and a s\tandard deviation of 2. Find the probability that a randomly selected number from the set is greater than 12.

A. 0.5

B. 0.6

C. 0.7

Correct D. 0.8

Correct Answer: D

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Question 21

Determine the value of $\int_{0}^{\frac{\pi}{2}} \frac{\sin^2 x}{\cos^2 x + \sin^2 x} dx$.

Correct A. \frac{\pi}{4}

B. \frac{\pi}{2}

C. \frac{\pi}{3}

D. \frac{\pi}{6}

Correct Answer: A

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Question 22

Solve the equation $\frac{1}{2} \log_{10} $ x^2 $ = 4$ for $x$.

A. 10

Correct B. 100

C. 1000

D. 10000

Correct Answer: B

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Question 23

Find the area under the curve $y = \frac{1}{x^2 + 1}$ from $x = 0$ to $x = 1$.

Correct A. \frac{\pi}{2}

B. \frac{\pi}{4}

C. \frac{\pi}{6}

D. \frac{\pi}{8}

Correct Answer: A

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Question 24

A particle moves in a straight line with a velocity given by $v(t) = 2t^2 - 5t + 3$. Find the acceleration at time $t = 2$ seconds.

Correct A. 4

B. -3

C. 2

D. -2

Correct Answer: A

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Question 25

Solve the system of equations $x + y = 2$ and $xy = 1$.

Correct A. (1, 1)

B. $ 1, -1 $

C. $ -1, 1 $

D. $ -1, -1 $

Correct Answer: A

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