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POST UTME UI 2025 Mathematics | Objective

Are you preparing for POST UTME UI 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 equation of the line pas\sing through the points ( (2,3) ) and ( (4,5) ).

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 2

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

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

B. $ x in \( -infty, -3 \ $ cup (3, 4) cup (4, infty) )

C. $ x in \( -infty, -3 \ $ cup (3, 4) )

D. $ x in \( -infty, -3 \ $ cup (4, infty) )

Correct Answer: A

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Question 3

Find the derivative of the function ( f(x) = \frac{1}{x^2 + 1} ) u\sing 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 4

Solve the system of equations $ egin{cases} x + y = 2 \ x - y = 1 \end{cases} $.

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

B. $ x = 1, y = 3 $

C. $ x = 3, y = 1 $

D. $ x = 3, y = 3 $

Correct Answer: A

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Question 5

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 = 4 )

C. $ x - 3 \ $^2 + $ y - 2 $^2 = 16 )

D. $ x - 3 \ $^2 + $ y - 2 $^2 = 4 )

Correct Answer: A

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Question 6

Find the value of $\lim_{x\to\infty} \left$ \frac{\ln x}{x}\right $$.

Correct A. 0

B. 1

C. ∞

D. -∞

Correct Answer: A

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Question 7

Solve the equation $x^2+2x-6=0$ u\sing the quadratic formula.

Correct A. x = 1 ± √7

B. x = -1 ± √7

C. x = 1 ± √5

D. x = -1 ± √5

Correct Answer: A

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Question 8

A circle has equation $x^2+y^2=16$. Find the equation of the \tangent line at the point $(4,0)$.

Correct A. y = -x + 4

B. y = x + 4

C. y = -x - 4

D. y = x - 4

Correct Answer: A

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Question 9

Two events A and B are indep\endent. If P(A) = 0.4 and P(B) = 0.6, find P(A ∩ B).

Correct A. 0.24

B. 0.36

C. 0.48

D. 0.60

Correct Answer: A

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Question 10

Solve the inequality $x^2-4x-5>0$.

Correct A. $ -∞,-1 $ ∪ (5,∞)

B. $ -∞,-5 $ ∪ (1,∞)

C. $ -∞,-1 $ ∪ (1,∞)

D. $ -∞,-5 $ ∪ (5,∞)

Correct Answer: A

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Question 11

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

A. 40

B. 50

Correct C. 60

D. 70

Correct Answer: C

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Question 12

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

A. 1

B. 2

C. 3

Correct D. 4

Correct Answer: D

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Question 13

A histogram of exam scores has a mean of 75 and a s\tandard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score is between 60 and 90?

A. 0.68

B. 0.69

Correct C. 0.70

D. 0.71

Correct Answer: C

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Question 14

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

Correct A. \frac{-2x}{$ x^2 + 1 $^2}

B. \frac{2x}{$ x^2 + 1 $^2}

C. \frac{x}{$ x^2 + 1 $^2}

D. \frac{-x}{$ x^2 + 1 $^2}

Correct Answer: A

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Question 15

A vector ( mathbf{a} ) has a magnitude of 5 and makes an angle of 30° with the positive x-axis. Find the x and y components of ( mathbf{a} ).

Correct A. 4.33, 2.5

B. 4.5, 2.5

C. 4.33, 2.33

D. 4.5, 2.33

Correct Answer: A

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Question 16

In a binary operation $ * $ on the set of vectors $ mathbb{R}^2 $, the operation is defined as ((mathbf{a}, mathbf{b}) mapsto mathbf{a} ast mathbf{b} = $ a_1b_1, a_2b_2 $). Find the value of (mathbf{a} ast (mathbf{b} ast mathbf{c})) if $ mathbf{a} = \( 2, 3 \ $), $ mathbf{b} = \( 4, 5 \ $), and $ mathbf{c} = \( 6, 7 \ $).

A. (48, 105)

B. (56, 105)

Correct C. (48, 105)

D. (56, 105)

Correct Answer: C

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Question 17

If $ \sin \theta = \frac{3}{5} $ and $ \cos \theta = \frac{4}{5} $, find the value of $ \tan \theta $.

Correct A. \frac{3}{4}

B. \frac{4}{3}

C. \frac{3}{4}

D. \frac{4}{3}

Correct Answer: A

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Question 18

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 = 4 )

C. $ x - 2 \ $^2 + $ y - 3 $^2 = 16 )

D. $ x - 2 \ $^2 + $ y - 3 $^2 = 4 )

Correct Answer: A

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Question 19

A random variable (X) has a probability distribution given by [ P$ X = x $ = egin{cases} 0.2 & \text{if } x = 1 \ 0.3 & \text{if } x = 2 \ 0.5 & \text{if } x = 3 \ 0.1 & \text{if } x = 4 \end{cases} ]. Find the expected value of (X).

A. 1.5

B. 2.5

Correct C. 3.5

D. 4.5

Correct Answer: C

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Question 20

In a binomial distribution with parameters $ n = 5 $ and $ p = 0.4 $, find the probability that exactly $ k = 2 $ successes occur.

Correct A. 0.328

B. 0.328

C. 0.328

D. 0.328

Correct Answer: A

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Question 21

Let ( X ) and ( Y ) be indep\endent random variables with probability density functions $ f_X\( x \ $ = egin{cases} 2x, & 0 leq x leq 1 \ 0, & \text{otherwise} \end{cases} ) and $ f_Y\( y \ $ = egin{cases} 3y^2, & 0 leq y leq 1 \ 0, & \text{otherwise} \end{cases} ). Find the probability that $ X + Y leq 1 $.

Correct A. \frac{1}{2}

B. \frac{1}{3}

C. \frac{2}{3}

D. \frac{3}{4}

Correct Answer: A

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Question 22

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

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 23

Solve the equation $ x^3 - 6x^2 + 11x - 6 = 0 $ u\sing the Rational Root Theorem.

A. x = 1

B. x = 2

Correct C. x = 3

D. x = 4

Correct Answer: C

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Question 24

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

A. \frac{-2x}{$ x^2 + 1 $^2}

Correct B. \frac{2x}{$ x^2 + 1 $^2}

C. \frac{1}{$ x^2 + 1 $^2}

D. \frac{-1}{$ x^2 + 1 $^2}

Correct Answer: B

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Question 25

Find the area of the triangle with vertices ( (0, 0), (1, 0), ) and ( (0, 1) ) u\sing the formula for the area of a triangle.

Correct A. \frac{1}{2}

B. \frac{1}{3}

C. \frac{1}{4}

D. \frac{1}{6}

Correct Answer: A

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