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POST UTME FUTA 2025 Mathematics | Objective

Are you preparing for POST UTME FUTA exams? Reviewing past 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.

Practice these randomly selected questions to test your readiness.

Question 1

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

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. \( x = \frac{3pi}{4} \)

C. \( x = \frac{5pi}{4} \)

D. \( x = \frac{7pi}{4} \)

Correct Answer: A

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Question 3

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

Solve the system of linear equations \( egin{cases} 2x + 3y = 7 \ 4x - 2y = -3 \end{cases} \) u\sing 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

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

In a random sample of 100 students, the mean height is 175 cm with a s\tandard 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

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

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

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

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

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

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

A histogram of exam scores has a mean of 70 and a s\tandard 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

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

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

Determine the value of x in the equation \( \tan x = \frac{1}{\sqrt{3}} \) 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

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 \( t = 1 \) 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

In a circle of radius 4 cm, a chord of length 6 cm subt\ends 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

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

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

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

A. 2

Correct B. -2

C. -4

D. 4

Correct Answer: B

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Question 22

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

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

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

A histogram shows that the heights of 20 students are normally distributed with a mean of 175 cm and a s\tandard 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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