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POST UTME FUTA 2025 Mathematics | Objective

Prepare for your exams with POST UTME FUTA questions? Reviewing past/model questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2025 Mathematics (Objective) questions designed to simulate the real exam environment.

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Question 1 View Details

Find the derivative of the function ( f(x) = $\frac{1}${\sqrt{1 - $x^2}}$\) ) using the chain rule.

Correct A. $\frac{-x}{1 - x^2 \$^{$3/2$}} )

B. $\frac{x}{1 - x^2 \$^{$3/2$}} )

C. $\frac{1}{1 - x^2 \$^{$3/2$}} )

D. $\frac{-1}{1 - x^2 \$^{$3/2$}} )

Correct Answer: A

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Question 2 View Details

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

Correct A. $x = \frac{\pi}{4}$

B. $x = \frac{3\pi}{4}$

C. $x = \frac{5\pi}{4}$

D. $x = \frac{7\pi}{4}$

Correct Answer: A

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Question 3 View Details

Find the area of the triangle formed by the points ( A(1, 2) ), ( B(3, 4) ), and ( C(2, 1) ).

Correct A. 6

B. 8

C. 10

D. 12

Correct Answer: A

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Question 4 View Details

Solve the system of linear equations $egin{cases} 2x + 3y = 7 \ 4x - 2y = -3 \end{cases}$ using matrices.

Correct A. $x = 1, y = 2$

B. $x = 2, y = 1$

C. $x = 3, y = 4$

D. $x = 4, y = 3$

Correct Answer: A

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Question 5 View Details

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

Correct A. 0

B. 1

C. 2

D. 3

Correct Answer: A

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Question 6 View Details

In a random sample of 100 students, the mean height is 175 cm with a standard deviation of 5 cm. If the mean height of the entire population is 180 cm, what is the probability that a randomly selected student from the sample has a height greater than 180 cm?

A. $P X > 180 \$$= 0.2 )$

B. $P X > 180 \$$= 0.5 )$

Correct C. $P X > 180 \$$= 0.8 )$

D. $P X > 180 \$$= 0.9 )$

Correct Answer: C

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Question 7 View Details

Solve for x in the equation $egin{bmatrix} 2 & 1 \ 1 & 2 \end{bmatrix} egin{bmatrix} x \ 1 \end{bmatrix} = egin{bmatrix} 4 \ 4 \end{bmatrix}$.

A. $x = 2$

Correct B. $x = 3$

C. $x = 4$

D. $x = 5$

Correct Answer: B

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Question 8 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 + $y - 3$^$2 = 20$ )

C. $x - 2 \$^2 + $y - 3$^$2 = 24$ )

D. $x - 2 \$^2 + $y - 3$^$2 = 28$ )

Correct Answer: A

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Question 9 View Details

A random variable X has a probability distribution given by $P X = 1 \$$= 0.3 )$, $P X = 2 \$$= 0.4 )$, and $P X = 3 \$ = 0.3 ). Find the expected value of X.

A. $( E(X) = 1.2 )$

Correct B. $( E(X) = 1.5 )$

C. $( E(X) = 1.8 )$

D. $( E(X) = 2.1 )$

Correct Answer: B

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Question 10 View Details

Solve the system of equations $x + y = 4$ and $xy = 5$.

Correct A. $x = 2, y = 2$

B. $x = 2, y = 3$

C. $x = 3, y = 2$

D. $x = 3, y = 3$

Correct Answer: A

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Question 11 View Details

Find the area under the curve $y = \frac{1}{2}x^2 + 3x - 4$ from $x = 0$ to $x = 2$.

Correct A. 4

B. 6

C. 8

D. 10

Correct Answer: A

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Question 12 View Details

Solve for ( x ) in the equation $2^x + 3^x = 5^x$.

A. 1

Correct B. 2

C. 3

D. 4

Correct Answer: B

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Question 13 View Details

A histogram of exam scores has a mean of 70 and a standard deviation of 10. If 80% of the scores lie between 60 and 80, what is the probability that a randomly selected score lies between 70 and 80?

A. 0.4

Correct B. 0.5

C. 0.6

D. 0.7

Correct Answer: B

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Question 14 View Details

Find the value of ( x ) that satisfies the equation $\sin^2 x + \cos^2 x = 1$.

A. 0

B. 30

Correct C. 45

D. 60

Correct Answer: C

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Question 15 View Details

A polynomial function has a degree of 4 and has roots at $x = -2, 0, 1, 3$. Find the polynomial function.

Correct A. $x+2$, x)$x-1$, x-3 \\)

B. $x-2$, x)$x+1$, x-3 \\)

C. $x+2$, x)$x-1$, x+3 \\)

D. $x-2$, x)$x+1$, x-3 \\)

Correct Answer: A

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Question 16 View Details

Determine the value of x in the equation $$1x = \frac{1}{\sqrt{3}}$ if $0 \leq x \leq \frac{\pi}{2}$.

Correct A. $\frac{\pi}{6}$

B. $\frac{\pi}{4}$

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

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

Correct Answer: A

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Question 17 View Details

A particle moves along the x-axis according to the equation ( x(t) = $(2t^3 - 5t^2 + 3t - 1$\) ). Find the velocity of the particle at time $t = 1\\((2t^3 - 5t^2 + 3t - 1) ). Find the velocity of the particle at time$ second.

A. ( 6 ) $m/s$

Correct B. ( 12 ) $m/s$

C. ( 18 ) $m/s$

D. ( 24 ) $m/s$

Correct Answer: B

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Question 18 View Details

In a circle of radius 4 cm, a chord of length 6 cm subtends an angle of $60^circ$ at the center. Find the length of the segment of the chord between the points where the chord intersects the circle.

A. ( 3 ) cm

B. ( 4 ) cm

Correct C. ( 5 ) cm

D. ( 6 ) cm

Correct Answer: C

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Question 19 View Details

A set of 5 numbers has a mean of 10 and a median of 8. If the largest number is 15, find the sum of the remaining 3 numbers.

A. ( 20 )

B. ( 25 )

Correct C. ( 30 )

D. ( 35 )

Correct Answer: C

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Question 20 View Details

A right circular cone has a height of 12 cm and a base radius of 4 cm. Find the volume of the cone.

A. ( 96 pi ) $cm^3$

B. ( 144 pi ) $cm^3$

Correct C. ( 192 pi ) $cm^3$

D. ( 240 pi ) $cm^3$

Correct Answer: C

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Question 21 View Details

In the equation (y = $\frac{1}{2}$ $x^2 + 3x - 4$\), find the value of ( x ) when \$(y = frac{1}{2} x^2 + 3x - 4\(y = 0$.

A. 2

Correct B. -2

C. -4

D. 4

Correct Answer: B

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Question 22 View Details

A set of 10 numbers has a mean of 20. If 5 is added to each number, what is the new mean?

Correct A. 22.5

B. 25

C. 27.5

D. 30

Correct Answer: A

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Question 23 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 + $y - 3$^$2 = 9$ )

C. $x - 2 \$^2 + $y - 3$^$2 = 25$ )

D. $x - 2 \$^2 + $y - 3$^$2 = 36$ )

Correct Answer: A

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Question 24 View Details

Solve the system of equations: $egin{cases} x + y = 4 \ 2x - 3y = 5 \end{cases}$.

Correct A. $x = 3, y = 1$

B. $x = 1, y = 3$

C. $x = 2, y = 2$

D. $x = 4, y = 0$

Correct Answer: A

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Question 25 View Details

A histogram shows that the heights of 20 students are normally distributed with a mean of 175 cm and a standard deviation of 5 cm. Find the probability that a randomly selected student is taller than 180 cm.

A. 0.1587

B. 0.3413

C. 0.5

Correct D. 0.8413

Correct Answer: D

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