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Subject

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POST UTME UNILORIN 2025 Mathematics | Objective

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Question 1 View Details

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

Correct A. 10

B. 100

C. 1000

D. 10000

Correct Answer: A

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Question 2 View Details

A survey of 100 students found that 60 students preferred Mathematics, 30 preferred Science, and 10 preferred both. What is the probability that a randomly selected student prefers Mathematics or Science?

A. 0.7

Correct B. 0.8

C. 0.9

D. 1.0

Correct Answer: B

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Question 3 View Details

The histogram below shows the distribution of exam scores for a class of 50 students. What is the mean score?

A. 60

B. 70

Correct C. 80

D. 90

Correct Answer: C

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Question 4 View Details

Simplify the expression $\frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \frac{1}{16}$.

A. 1

B. 2

C. 3

Correct D. 4

Correct Answer: D

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Question 5 View Details

Evaluate the definite integral $\int_{0}^{2} x^2 dx$.

A. 4

B. 8

Correct C. 16

D. 32

Correct Answer: C

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Question 6 View Details

Determine the value of x in the equation $\sin^2 x \$ + \$\cos^2(x)$ = 1 ) if $$1x \$ = $\frac{3}{5}$\) ).

A. $\frac{4\pi}{3}$

Correct B. $\frac{5\pi}{3}$

C. $\frac{2\pi}{3}$

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

Correct Answer: B

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Question 7 View Details

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

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

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

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

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

Correct Answer: A

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Question 8 View Details

Find the determinant of the matrix $egin{bmatrix} 2 & 1 & 3 \ 4 & 2 & 1 \ 1 & 3 & 2 \end{bmatrix}$.

Correct A. ( 0 )

B. ( 1 )

C. $-1$

D. ( 2 )

Correct Answer: A

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Question 9 View Details

Determine the equation of the tangent line to the curve $y = \frac{1}{x}\\(tangent line to the curve (y =$ at the point ( (1, 1) ).

Correct A. $y = x - 1$

B. $y = x + 1$

C. $y = -x + 1$

D. $y = x - 2$

Correct Answer: A

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Question 10 View Details

A histogram of exam scores has a mean of 75 and a standard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score is greater than 90?

A. ( 0.1587 )

B. ( 0.3413 )

C. ( 0.5 )

Correct D. ( 0.8413 )

Correct Answer: D

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Question 11 View Details

In a right-angled triangle, the length of the hypotenuse is 10 cm and one of the other sides is 6 cm. Find the length of the third side using the Pythagorean theorem.

A. 8 cm

Correct B. 12 cm

C. 14 cm

D. 16 cm

Correct Answer: B

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Question 12 View Details

A fair six-sided die is rolled. What is the probability that the number obtained is a multiple of 3?

Correct A. $\frac{1}{3}$\)

B. $\frac{2}{3}$\)

C. $\frac{1}{2}$\)

D. $\frac{3}{4}$\)

Correct Answer: A

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Question 13 View Details

A cylindrical \tank has a height of 10 m and a radius of 4 m. Find the volume of the \tank in cubic meters.

A. 200\pi

B. 400\pi

Correct C. 800\pi

D. 1600\pi

Correct Answer: C

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Question 14 View Details

A set of 5 numbers has an average of 10. If one of the numbers is 15, what is the sum of the remaining 4 numbers?

Correct A. 40

B. 45

C. 50

D. 55

Correct Answer: A

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Question 15 View Details

A geometric sequence has a first term of 2 and a common ratio of 3. Find the sum of the first 5 terms.

A. 243

Correct B. 255

C. 267

D. 279

Correct Answer: B

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Question 16 View Details

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

A. 24\pi

B. 32\pi

Correct C. 40\pi

D. 48\pi

Correct Answer: C

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Question 17 View Details

Solve the inequality $\frac{x^2 - 4}{x^2 - 9}$\)\$) > 0.$

Correct A. $-\infty, -3$ \cup $-3, 2$ \cup $2, \infty$

B. $-\infty, -3$ \cup $2, \infty$

C. $-3, 2$

D. $-\infty, -3$ \cup $2, \infty$

Correct Answer: A

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Question 18 View Details

Find the area under the curve $y = x\^2 + 2x - 3$ from $x = 0$ to $x = 3$.

A. 18

B. 20

Correct C. 22

D. 24

Correct Answer: C

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Question 19 View Details

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

Correct A. \begin{pmatrix} 2 \ 2 \end{pmatrix}

B. \begin{pmatrix} 1 \ 3 \end{pmatrix}

C. \begin{pmatrix} 3 \ 1 \end{pmatrix}

D. \begin{pmatrix} 4 \ 0 \end{pmatrix}

Correct Answer: A

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Question 20 View Details

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

Correct A. $x - 2$^2 + $y - 3$^$2 = 16$

B. $x - 3$^2 + $y - 2$^$2 = 16$

C. $x + 2$^2 + $y + 3$^$2 = 16$

D. $x - 2$^2 + $y + 3$^$2 = 16$

Correct Answer: A

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Question 21 View Details

Solve the inequality $\frac{x^2 - 4}{x + 2} > 0$ for ( x in mathbb{R} ).

Correct A. $x < -2$ or $x > 2$

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

C. $x < -2$ or $x = 2$

D. $x > -2$ or $x = 2$

Correct Answer: A

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Question 22 View Details

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 23 View Details

A fair six-sided die is rolled twice. What is the probability that the sum of the two numbers shown is greater than 9?

A. $\frac{1}{6}$

B. $\frac{1}{3}$

Correct C. $\frac{5}{36}$

D. $\frac{1}{2}$

Correct Answer: C

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Question 24 View Details

Find the derivative of the function ( f(x) = $\frac{1}{x^2 + 1}$\)\) ) using 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 25 View Details

Solve the equation $2^x + 2^{-x} = 3$ for ( x in mathbb{R} ).

A. $x = \log_2 2 \$ )

Correct B. $x = \log_2 3 \$ )

C. $x = \log_2 2 \$ - \log_2(2) )

D. $x = \log_2 2 \$ + \log_2(2) )

Correct Answer: B

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