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POST UTME FUTO 2024 Mathematics | Objective

Prepare for your exams with POST UTME FUTO 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

A random variable X has a probability distribution given by P(X) = $1/2$^$X-1$ for $X = 1$, 2, 3, ... . Find the expected value of X.

A. 2

Correct B. 3

C. 4

D. \infty

Correct Answer: B

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Question 2 View Details

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

Correct A. \left$-\infty, -\frac{3}{2} \right$ \cup \left$\frac{3}{2}, \infty \right$

B. \left$-\infty, -1 \right$ \cup \left$1, \infty \right$

C. \left$-\infty, -\frac{1}{2} \right$ \cup \left$\frac{1}{2}, \infty \right$

D. \left$-\infty, 0 \right$ \cup \left$1, \infty \right$

Correct Answer: A

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Question 3 View Details

Find the sum of the first 10 terms of the geometric series $2x^2 + 5x - 3$.

A. 2

B. 5

Correct C. 10

D. 15

Correct Answer: C

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Question 4 View Details

A set A is defined as A = \{ x \in \mathbb{R} : $x^2 + 2x + 1$ \geq 0 \}. Find the range of A.

Correct A. \left[ -1, \infty \right)

B. \left( -\infty, -1 \right]

C. \left( -\infty, 0 \right]

D. \left( 0, \infty \right]

Correct Answer: A

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Question 5 View Details

A sequence is defined as (a_$n =$$\frac{1}{n}$\) for \$(a_n = frac{1}{n}\(n = 1, 2, 3, \ldots$. Find the sum of the first 5 terms of the sequence.

A. 1

B. 2

C. 3

Correct D. 4

Correct Answer: D

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Question 6 View Details

A random sample of 25 students from a university had a mean height of 175.5 cm with a standard deviation of 5.2 cm. If the population standard deviation is unknown, calculate the 95% confidence interval for the mean height of all students in the university.

Correct A. 173.5 cm, 177.5 cm

B. 171.5 cm, 179.5 cm

C. 174.5 cm, 176.5 cm

D. 172.5 cm, 178.5 cm

Correct Answer: A

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Question 7 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. $\frac{\pi}{6}$\)

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

Correct Answer: A

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Question 8 View Details

Solve the inequality $|x - 2| > 3$.

Correct A. $x < -1, x > 5$

B. $x < 1, x > 5$

C. $x < -1, x < 5$

D. $x > 1, x > 5$

Correct Answer: A

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Question 9 View Details

A set A contains 5 elements, and a set B contains 7 elements. If the number of elements in the union of sets A and B is 12, find the number of elements in the intersection of sets A and B.

A. 2

Correct B. 3

C. 4

D. 5

Correct Answer: B

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Question 10 View Details

Find the sum of the first 10 terms of the geometric progression 2, 6, 18, ...

Correct A. 2047

B. 2057

C. 2067

D. 2077

Correct Answer: A

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Question 11 View Details

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

Correct A. $x^2$ + \$(y^2 + 4x - 6y + 4$$= 0$\)

B. $x^2$ + \$(y^2 - 4x + 6y + 4$$= 0$\)

C. $x^2$ + \$(y^2 + 4x + 6y + 4$$= 0$\)

D. $x^2$ + \$(y^2 - 4x - 6y + 4$$= 0$\)

Correct Answer: A

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Question 12 View Details

Solve the equation $\sin^2 x + \cos^2 x = 1$ for x.

Correct A. \$sin x =$\pm $\frac{1}${$\sqrt{2}$}\)

B. \$cos x =$\pm $\frac{1}${$\sqrt{2}$}\)

C. \$tan x =$\pm 1

D. \$cot x =$\pm 1

Correct Answer: A

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Question 13 View Details

Find the volume of the frustum of a cone with height 6, lower base radius 4, and upper base radius 2.

Correct A. $\frac{1}{3}$\) \pi (6) $4^2 + 2^2 + 4 \cdot 2$

B. $\frac{1}{3}$\) \pi (6) $4^2 + 2^2 - 4 \cdot 2$

C. $\frac{1}{3}$\) \pi (6) $4^2 - 2^2 + 4 \cdot 2$

D. $\frac{1}{3}$\) \pi (6) $4^2 - 2^2 - 4 \cdot 2$

Correct Answer: A

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Question 14 View Details

Solve the matrix equation $\begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 5 \\ 6 \end{bmatrix}$ for x and y.

Correct A. \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 1 \\ 2 \end{bmatrix}

B. \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 2 \\ 1 \end{bmatrix}

C. \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 3 \\ 4 \end{bmatrix}

D. \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 4 \\ 3 \end{bmatrix}

Correct Answer: A

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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 - 3 =$$\frac{2}{2}$\)$x - 2$

B. $y - 3 =$$\frac{2}{2}$\)$x - 4$

C. $y - 5 =$$\frac{2}{2}$\)$x - 2$

D. $y - 5 =$$\frac{2}{2}$\)$x - 4$

Correct Answer: A

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Question 16 View Details

Find the value of $\int_0^1 \frac{1}{x^2+4x+5} dx$.

Correct A. $\frac{1}{2}$\) \ln|2x+1| + $\frac{1}{2}$\) \ln|x+1| + C

B. $\frac{1}{2}$\) \ln|2x+1| - $\frac{1}{2}$\) \ln|x+1| + C

C. $\frac{1}{2}$\) \ln|2x+1| + C

D. $\frac{1}{2}$\) \ln|x+1| + C

Correct Answer: A

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Question 17 View Details

Solve the inequality $|x-2| > 3$.

Correct A. $-\infty, -1$ \cup $5, \infty$

B. $-\infty, 1$ \cup $5, \infty$

C. $-\infty, -1$ \cup $1, \infty$

D. $-\infty, 1$ \cup $1, \infty$

Correct Answer: A

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Question 18 View Details

Find the value of $\sum_{n = 1}^\infty \frac{1}{n^2}$.

Correct A. $\frac{\pi^2}{6}$\)\)

B. $\frac{\pi^2}{12}$\)\)

C. $\frac{\pi^2}{24}$\)\)

D. $\frac{\pi^2}{48}$\)\)

Correct Answer: A

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Question 19 View Details

Solve the equation $x^2 + 4x + 5 = 0$.

Correct A. $x = -2$\pm i

B. $x = -1$\pm i

C. $x = -2$\pm 2i

D. $x = -1$\pm 2i

Correct Answer: A

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Question 20 View Details

Find the value of $\int_0^\pi \sin^2 x dx$.

A. $\frac{\pi}{2}$\)

Correct B. $\frac{\pi}{4}$\)

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

D. $\frac{\pi}{8}$\)

Correct Answer: B

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Question 21 View Details

Find the value of x in the equation $\sin^2 x \$ + \$\cos^2(x)$ = 1 ) if $$1x \$ = $\frac{3}{4}$\) ).

Correct A. π/4

B. π/6

C. π/3

D. π/2

Correct Answer: A

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Question 22 View Details

A histogram of exam scores has a mean of 75 and a standard deviation of 10. If 80% of the scores fall below 90, what is the value of x in the equation $P x < 90 \$$= 0.8 )$?

A. 70

Correct B. 80

C. 85

D. 90

Correct Answer: B

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Question 23 View Details

A rectangular prism has a length of 5 cm, a width of 3 cm, and a height of 2 cm. What is the surface area of the prism?

A. 62

B. 65

Correct C. 68

D. 70

Correct Answer: C

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Question 24 View Details

Solve the quadratic equation $x^2 + 5x + 6 = 0$.

Correct A. $x = -2$

B. $x = -3$

C. $x = 2$

D. $x = 3$

Correct Answer: A

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Question 25 View Details

Simplify the expression $\frac{1}{\sqrt{2}} + \frac{1}{\sqrt{3}}$.

Correct A. \$\frac{\sqrt{3}$ + \$\sqrt{2}$}{\$\sqrt{6}$}\)

B. \$\frac{\sqrt{3}$ - \$\sqrt{2}$}{\$\sqrt{6}$}\)

C. \$\frac{\sqrt{3}$ + \$\sqrt{2}$}{\$\sqrt{6}$}\)

D. \$\frac{\sqrt{3}$ - \$\sqrt{2}$}{\$\sqrt{6}$}\)

Correct Answer: A

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