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POST UTME FUTO 2024 Mathematics | Objective

Are you preparing for POST UTME FUTO exams? Reviewing past 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

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

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

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

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

A sequence is defined as $ a_n = \frac{1}{n} $ for $ 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

A random sample of 25 students from a university had a mean height of 175.5 cm with a s\tandard deviation of 5.2 cm. If the population s\tandard 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

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

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

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

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

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

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

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

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

Find the equation of the line pas\sing 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

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

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

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

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

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

Find the value of x in the equation $ \sin^2\( x \ $ + \cos^2(x) = 1 ) if $ \tan\( x \ $ = \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

A histogram of exam scores has a mean of 75 and a s\tandard 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

A rec\tangular 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

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

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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