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POST UTME UI 2025 Mathematics | Objective

Prepare for your exams with POST UTME UI 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 equation of the line passing 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 View Details

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 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 4 View Details

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 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 + $y - 3$^$2 = 4$ )

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 View Details

Find the value of $\lim_{x\to\infty} \left \frac{$1x}{x}\right$\).

Correct A. 0

B. 1

C. ∞

D. -∞

Correct Answer: A

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Question 7 View Details

Solve the equation $x^2+2x-6 = 0$ using 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 View Details

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

Two events A and B are independent. If P(A) = 0.4 and P(B) = 0.6, find P($A \cap B$).

Correct A. 0.24

B. 0.36

C. 0.48

D. 0.60

Correct Answer: A

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Question 10 View Details

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 View Details

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 View Details

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 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 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 View Details

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

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 View Details

In a binary operation (*\) on the set of vectors $\\((*) 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 \$), the operation is defined as ((mathbf{a}, mathbf{b}) mapsto mathbf{a} ast mathbf{b} = (a_1b_1, a_2b_2\(\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 View Details

If $\(1\theta = \frac{3}{5}$ and 1\$theta =$$\frac{4}{5}$\), find the value of $$1\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 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 + $y - 3$^$2 = 4$ )

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 View Details

A random variable (X) has a probability distribution given by [$P(X = x$\) = egin{cases} 0.2 & \text{if } \$(X = x) = egin{cases} 0.2 & \(x = 1) \ 0.3 & \text{if} \\() 0.3 & \(x = 2) \ 0.5 & \text{if} \\() 0.5 & \(x = 3) \ 0.1 & \text{if} \\() 0.1 & \(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 View Details

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 View Details

Let ( X ) and ( Y ) be independent 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 $X + Y \\(text{otherwise} end{cases} ). Find the probability that \leq 1$.

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 View Details

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 View Details

Solve the equation $x^3 - 6x^2 + 11x - 6 = 0$ using 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 View Details

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

Find the area of the triangle with vertices ( (0, 0), (1, 0), ) and ( (0, 1) ) using 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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