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POST UTME AAUA 2025 Mathematics | Objective

Are you preparing for POST UTME AAUA 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 area under the curve $ y = \frac{1}{2}x^2 + 3x - 2 $ from $ x = 0 $ to $ x = 4 $.

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

B. ( 3 )

C. $ \frac{1}{2} \times 4^2 + 3 \times 4 - 2 $

Correct D. $ \frac{1}{2} \times 4^2 + 3 \times 4 - 2 $

Correct Answer: D

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Question 2

A histogram of exam scores is shown below. What is the mean score?

A. ( 50 )

Correct B. ( 60 )

C. ( 70 )

D. ( 80 )

Correct Answer: B

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Question 3

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

Correct A. $ x < -1 $ or $ x > 3 $

B. $ x < 1 $ or $ x > 3 $

C. $ x < -1 $ or $ x < 3 $

D. $ x > 1 $ or $ x > 3 $

Correct Answer: A

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Question 4

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

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

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

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

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

Correct Answer: C

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Question 5

A quadratic equation has roots $ x = 1 $ and $ x = 2 $. Find the equation of the axis of symmetry.

A. $ x = 0.5 $

Correct B. $ x = 1.5 $

C. $ x = 2.5 $

D. $ x = 3.5 $

Correct Answer: B

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Question 6

In a random experiment, two events A and B are indep\endent. If P(A) = 0.4 and P(B) = 0.3, what is the probability that both events occur?

Correct A. 0.12

B. 0.24

C. 0.36

D. 0.48

Correct Answer: A

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Question 7

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 8

A rec\tangular prism has a length of 10 cm, a width of 5 cm, and a height of 8 cm. Find its volume.

Correct A. 400 cm^3

B. 500 cm^3

C. 600 cm^3

D. 800 cm^3

Correct Answer: A

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Question 9

Find the sum of the first 10 terms of the arithmetic progression 2, 5, 8, ...

A. 50

Correct B. 55

C. 60

D. 65

Correct Answer: B

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Question 10

Solve the system of equations u\sing matrices:\n\n2x + 3y = 7\n\nx - 2y = -3

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 11

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

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

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

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

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

Correct Answer: B

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Question 12

A sequence is defined by $ a_n = \frac{2n + 1}{n^2 + 1} $. Find the sum of the first 5 terms.

Correct A. 1.2

B. 1.5

C. 1.8

D. 2.0

Correct Answer: A

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Question 13

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

A. 16π

Correct B. 32π

C. 64π

D. 128π

Correct Answer: B

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Question 14

A vector ( mathbf{a} ) is given by $ mathbf{a} = 2mathbf{i} + 3mathbf{j} $. Find the magnitude of ( mathbf{a} ).

A. 1

Correct B. √5

C. 2√5

D. 5

Correct Answer: B

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Question 15

Solve the equation $ x^2 + 2x + 1 = 0 $ u\sing the quadratic formula.

Correct A. 0

B. -1

C. 1

D. -2

Correct Answer: A

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Question 16

Find the value of $x$ in the equation $2^x + 3^x = 5^x$.

A. 1

B. 2

Correct C. 3

D. 4

Correct Answer: C

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Question 17

A random variable $X$ has a probability distribution given by $P$ X = x $ = \frac{1}{x^2}$ for $x = 1, 2, 3, \dots$. Find the probability that $X$ is greater than 2.

A. 0.25

B. 0.5

Correct C. 0.75

D. 1

Correct Answer: C

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Question 18

Solve the system of equations $\begin{align*} x + y + z &= 6 \ x + 2y + 3z &= 11 \ x + 3y + 6z &= 16 \end{align*}$.

Correct A. [1, 2, 3]

B. [2, 3, 1]

C. [3, 1, 2]

D. [1, 3, 2]

Correct Answer: A

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Question 19

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

Correct A. 0.5

B. 1

C. 1.5

D. 2

Correct Answer: A

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Question 20

A histogram of exam scores has a mean of 60 and a s\tandard deviation of 10. Find the probability that a randomly selected score is greater than 70.

A. 0.25

B. 0.5

Correct C. 0.75

D. 1

Correct Answer: C

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Question 21

Find the determinant of the matrix $ egin{bmatrix} 2 & 3 \ 4 & 5 \end{bmatrix} $.

A. 1

Correct B. -1

C. 2

D. 3

Correct Answer: B

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Question 22

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

A. 10

B. 100

C. 1000

Correct D. 10000

Correct Answer: D

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Question 23

Find the area under the curve $ y = x^2 $ from $ x = 0 $ to $ x = 4 $.

A. 16

B. 32

Correct C. 64

D. 128

Correct Answer: C

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Question 24

Solve the inequality $ x^2 - 4x + 4 > 0 $.

Correct A. x > 2

B. x < 2

C. x > 0

D. x < 0

Correct Answer: A

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Question 25

Find the equation of the line pas\sing through the points ( (2, 3) ) and ( (4, 5) ).

Correct A. y = 2x + 1

B. y = 2x - 1

C. y = x + 1

D. y = x - 1

Correct Answer: A

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