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POST UTME UNIPORT 2024 Mathematics | Objective

Prepare for your exams with POST UTME UNIPORT questions? Reviewing past/model questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2024 Mathematics (Objective) questions designed to simulate the real exam environment.

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Question 1 View Details

Find the equation of the circle passing through the points (2,3), (4,5) and (6,7).

Correct A. $x^2 + y^2 - 12x - 16y + 60 = 0$

B. $x^2 + y^2 - 14x - 20y + 80 = 0$

C. $x^2 + y^2 - 16x - 24y + 100 = 0$

D. $x^2 + y^2 - 18x - 28y + 120 = 0$

Correct Answer: A

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Question 2 View Details

If ( f(x) = $\frac{x^2 - 4}{x - 2}$\)\) ), find ( f'(x) ) using the chain rule.

A. ( f'$(x) =$$\frac{x^2 - 4}{$ x - 2 ^2}\)\) )

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

C. ( f'$(x) =$$\frac{2x - 4}{x - 2 ^2}$\) )

D. ( f'$(x) =$$\frac{2x + 4}{x - 2 ^2}$\) )

Correct Answer: B

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Question 3 View Details

Solve the inequality $|2x - 1| \geq 3$.

Correct A. $x \leq -1$ or ( x geq 2 )

B. $x < -1$ or $x > 2$

C. ( x leq 2 ) or $x \geq -1$

D. $x < 2$ or $x > -1$

Correct Answer: A

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Question 4 View Details

Find the area of the triangle with vertices (0,0), (3,0), and (0,4).

Correct A. ( 6 )

B. ( 8 )

C. ( 10 )

D. ( 12 )

Correct Answer: A

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Question 5 View Details

If ( f(x) = $2x^3 - 5x^2 + x - 1$ ), find the derivative of ( f(x) ) using the power rule.

Correct A. ( f'$(x) =$$6x^2 - 10x + 1$ )

B. ( f'$(x) =$$6x^2 - 10x - 1$ )

C. ( f'$(x) =$$6x^2 - 10x + 2$ )

D. ( f'$(x) =$$6x^2 - 10x - 2$ )

Correct Answer: A

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Question 6 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 7 View Details

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

Correct A. $-∞, -2$ ∪ (0, ∞)

B. $-∞, -2$ ∪ (2, ∞)

C. $-∞, 0$ ∪ (2, ∞)

D. $-∞, 0$ ∪ (0, 2)

Correct Answer: A

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Question 8 View Details

Find the derivative of the function $y = \sqrt{2x + 1}$ using the chain rule.

Correct A. 1/$2√ 2x + 1 \$)

B. 1/$2√ 2x + 1 \$) * $2x + 1$

C. 1/$2√ 2x + 1 \$) * $2x + 1$^2

D. 1/$2√ 2x + 1 \$) * $2x + 1$^3

Correct Answer: A

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Question 9 View Details

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

Correct A. 0, π/2, π, 3π/2

B. 0, π/2, 3π/2

C. 0, π, 2π

D. π/2, π, 3π/2

Correct Answer: A

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Question 10 View Details

Convert the number 1011 from base 2 to base 10.

A. 11

Correct B. 13

C. 15

D. 17

Correct Answer: B

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Question 11 View Details

Find the equation of the circle passing through the points (2, 3), (4, 5), and $-1, 1$.

Correct A. \left$x - 1 \right$^2 + \left$y - 1 \right$^$2 = 10$

B. \left$x + 1 \right$^2 + \left$y - 1 \right$^$2 = 10$

C. \left$x - 1 \right$^2 + \left$y + 1 \right$^$2 = 10$

D. \left$x + 1 \right$^2 + \left$y + 1 \right$^$2 = 10$

Correct Answer: A

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Question 12 View Details

A rectangular box has a length of 10 cm, a width of 5 cm, and a height of 8 cm. Find the volume of the box.

A. 400 $cm^3$

B. 500 $cm^3$

Correct C. 600 $cm^3$

D. 800 $cm^3$

Correct Answer: C

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Question 13 View Details

Find the derivative of the function f(x) = $3x^2 + 2x - 5$.

Correct A. 6x + 2

B. 6x - 2

C. 3x + 2

D. 3x - 2

Correct Answer: A

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Question 14 View Details

A fair six-sided die is rolled. Find the probability that the number rolled is greater than 4.

A. $\frac{1}{6}$\)

B. $\frac{2}{6}$\)

C. $\frac{3}{6}$\)

Correct D. $\frac{4}{6}$\)

Correct Answer: D

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Question 15 View Details

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

Correct A. $y =$$\frac{2}{2}$\) x + 1

B. $y =$$\frac{2}{2}$\) x - 1

C. $y =$$\frac{2}{2}$\) x + 2

D. $y =$$\frac{2}{2}$\) x - 2

Correct Answer: A

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Question 16 View Details

Find the equation of the circle with center $-2, 3$ and radius 4.

Correct A. text{Equation: } $x + 2$^2 + \$text{Equation:} (x + 2\(y - 3$^$2 = 16$

B. text{Equation: } $x - 2$^2 + \$text{Equation:} (x - 2\(y + 3$^$2 = 16$

C. text{Equation: } $x + 2$^2 + \$text{Equation:} (x + 2\(y + 3$^$2 = 16$

D. text{Equation: } $x - 2$^2 + \$text{Equation:} (x - 2\(y - 3$^$2 = 16$

Correct Answer: A

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Question 17 View Details

Solve the inequality $\frac{x + 2}{x - 1}$\$) > 0.$

Correct A. \text{Solution: }$x < -2$\text{ or } $x > 1$

B. \text{Solution: }$x < -2$\text{ or } $x < 1$

C. \text{Solution: }$x > -2$\text{ or } $x > 1$

D. \text{Solution: }$x < -2$\text{ or } $x < 1$

Correct Answer: A

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Question 18 View Details

Find the derivative of the function f(x) = $\frac{x^2 + 2x - 3}{x^2 - 4}$\)\).

Correct A. \text{Derivative: } f'$(x) =$$\frac{x^2 - 4$ 2x + 2 - $x^2 + 2x - 3$ (2x)}{ $x^2 - 4$ ^2}\)\)

B. \text{Derivative: } f'$(x) =$$\frac{x^2 - 4$ 2x + 2 - $x^2 + 2x - 3$ (2x)}{ $x^2 - 4$ ^2}\)\)

C. \text{Derivative: } f'$(x) =$$\frac{x^2 - 4$ 2x + 2 + $x^2 + 2x - 3$ (2x)}{ $x^2 - 4$ ^2}\)\)

D. \text{Derivative: } f'$(x) =$$\frac{x^2 - 4$ 2x + 2 + $x^2 + 2x - 3$ (2x)}{ $x^2 - 4$ ^2}\)\)

Correct Answer: A

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Question 19 View Details

A histogram of exam scores has a mean of 60 and a standard deviation of 10. If the scores are normally distributed, find the probability that a randomly selected score is greater than 70.

Correct A. \text{Probability: } P$X > 70 = 0.1587$

B. \text{Probability: } P$X > 70 = 0.8413$

C. \text{Probability: } P$X > 70 = 0.1587$

D. \text{Probability: } P$X > 70 = 0.8413$

Correct Answer: A

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Question 20 View Details

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

Correct A. text{Equation: }$y =$$\frac{2}{2}\\(text{Equation:} y = ($\) x + 1

B. text{Equation: }$y =$$\frac{2}{2}\\(text{Equation:} y = ($\) x + 2

C. text{Equation: }$y =$$\frac{2}{2}\\(text{Equation:} y = ($\) x + 3

D. text{Equation: }$y =$$\frac{2}{2}\\(text{Equation:} y = ($\) x + 4

Correct Answer: A

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Question 21 View Details

Determine the value of (\theta\) in the equation \$(theta\($1theta = \frac{1}{3}$, given that \$theta = frac{1}{3}\(\theta$ lies in quadrant II.

A. 60°

Correct B. 120°

C. 150°

D. 180°

Correct Answer: B

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Question 22 View Details

A particle moves in a plane with its position vector given by $\mathbf{r}(t) = \langle 2t, 3t^2 \rangle). Find the velocity vector \(\mathbf{v}(t)\\(). Find the velocity vector ($ and acceleration vector $\mathbf{a}(t)$.

Correct A. $\mathbf{v}(t) = \langle 2, 6t \rangle$, $\mathbf{a}(t) = \langle 0, 6 \rangle$

B. $\mathbf{v}(t) = \langle 2, 6t \rangle$, $\mathbf{a}(t) = \langle 0, 12t \rangle$

C. $\mathbf{v}(t) = \langle 2t, 6t \rangle$, $\mathbf{a}(t) = \langle 0, 6 \rangle$

D. $\mathbf{v}(t) = \langle 2t, 6t \rangle$, $\mathbf{a}(t) = \langle 0, 12t \rangle$

Correct Answer: A

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Question 23 View Details

Let $A = \begin{pmatrix} 1 & 2 \ 3 & 4 \end{pmatrix}$ and $B = \begin{pmatrix} 5 & 6 \ 7 & 8 end{pmatrix}$. Find the product $AB\\(end{pmatrix}). Find the product$.

Correct A. $\begin{pmatrix} 19 & 22 \ 43 & 50 \end{pmatrix}$

B. $\begin{pmatrix} 23 & 26 \ 47 & 54 \end{pmatrix}$

C. $\begin{pmatrix} 21 & 24 \ 45 & 52 \end{pmatrix}$

D. $\begin{pmatrix} 25 & 28 \ 49 & 56 \end{pmatrix}$

Correct Answer: A

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Question 24 View Details

Find the sum of the first 10 terms of the geometric series $\sum_{n = 1}^{10} \frac{2}{3^n}$.

Correct A. $\frac{1023}{2187}$

B. $\frac{1024}{2187}$

C. $\frac{1025}{2187}$

D. $\frac{1026}{2187}$

Correct Answer: A

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Question 25 View Details

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

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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