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POST UTME UNIOSUN 2023 Mathematics | Objective

Are you preparing for POST UTME UNIOSUN exams? Reviewing past questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2023 Mathematics (Objective) questions designed to simulate the real exam environment.

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Question 1

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 2

Solve the equation $ 2^x + 2^{x+1} = 2^{x+2} + 2^{x+3} $.

A. x = -1

B. x = 0

Correct C. x = 1

D. x = 2

Correct Answer: C

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Question 3

In the diagram below, ( ABC ) is a right-angled triangle with $ AB = 3 $ and $ BC = 4 $. Find the area of the triangle.

Correct A. 6

B. 8

C. 12

D. 16

Correct Answer: A

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Question 4

A company produces two products, A and B. The profit from the sale of one unit of product A is ₦200 and the profit from the sale of one unit of product B is ₦300. If the company produces 100 units of product A and 50 units of product B, what is the total profit?

A. ₦25000

Correct B. ₦30000

C. ₦35000

D. ₦40000

Correct Answer: B

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Question 5

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

A. x = \frac{\pi}{2}

Correct B. x = \frac{\pi}{4}

C. x = \frac{\pi}{6}

D. x = \frac{\pi}{3}

Correct Answer: B

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Question 6

Determine the value of $x$ in the equation $2^x + 5^x = 7^x$.

A. 1

Correct B. 2

C. 3

D. 4

Correct Answer: B

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Question 7

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

Correct A. $$ -\infty, -2 $ \cup $ 2, \infty $$

B. $$ -\infty, -2 $ \cup $ -2, 2 $ \cup $ 2, \infty $$

C. $$ -\infty, -2 $ \cup $ 2, \infty $$

D. $$ -\infty, 2 $ \cup $ 2, \infty $$

Correct Answer: A

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Question 8

Find the value of $\log_{10} $ x^2 $ = 4$.

A. 10

Correct B. 100

C. 1000

D. 10000

Correct Answer: B

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Question 9

Solve the system of equations $\begin{cases} x + y = 2 \ x - 2y = -3 \end{cases}$.

Correct A. $\left\{ \left$ -1, \frac{5}{2} \right $ \right\}$

B. $\left\{ \left$ 1, \frac{1}{2} \right $ \right\}$

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

D. $\left\{ \left$ 1, \frac{5}{2} \right $ \right\}$

Correct Answer: A

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Question 10

Find the equation of the line pas\sing through the points $(2, 3)$ and $(4, 5)$.

Correct A. y = 2x - 1

B. y = 2x + 1

C. y = x - 1

D. y = x + 1

Correct Answer: A

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Question 11

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

A. f'(x) = -\frac{x}{$ x^2 + 1 $^{3/2}}

Correct B. f'(x) = \frac{x}{$ x^2 + 1 $^{3/2}}

C. f'(x) = \frac{1}{$ x^2 + 1 $^{3/2}}

D. f'(x) = \frac{-1}{$ x^2 + 1 $^{3/2}}

Correct Answer: B

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Question 12

A set of exam scores has a mean of 75 and a s\tandard deviation of 10. If a new score of 90 is added to the set, what is the new mean?

Correct A. 80

B. 85

C. 90

D. 95

Correct Answer: A

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Question 13

Find the sum of the first 10 terms of the geometric series $ 2x^2 + 3x^3 + 4x^4 + cdots $.

Correct A. 2x^2 + 3x^3 + 4x^4 + 5x^5 + 6x^6 + 7x^7 + 8x^8 + 9x^9 + 10x^{10}

B. 2x^2 + 3x^3 + 4x^4 + 5x^5 + 6x^6 + 7x^7 + 8x^8 + 9x^9 + 10x^{10} + 11x^{11}

C. 2x^2 + 3x^3 + 4x^4 + 5x^5 + 6x^6 + 7x^7 + 8x^8 + 9x^9 + 10x^{10} + 11x^{11} + 12x^{12}

D. 2x^2 + 3x^3 + 4x^4 + 5x^5 + 6x^6 + 7x^7 + 8x^8 + 9x^9 + 10x^{10} + 11x^{11} + 12x^{12} + 13x^{13}

Correct Answer: A

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Question 14

A histogram of exam scores has a mean of 75 and a s\tandard deviation of 10. If a new score of 90 is added to the set, what is the new mean?

Correct A. 80

B. 85

C. 90

D. 95

Correct Answer: A

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Question 15

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

A. 10

B. 20

Correct C. 30

D. 40

Correct Answer: C

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Question 16

Solve the inequality $ 2x^2 + 3x - 1 > 0 $.

A. x < -1

Correct B. x > -1

C. x < 1

D. x > 1

Correct Answer: B

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Question 17

Find the value of ( x ) that satisfies the equation $ 2^x = 16 $.

A. 2

Correct B. 3

C. 4

D. 5

Correct Answer: B

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Question 18

Solve the system of equations $ x + y = 4 $ and $ x - y = 2 $.

A. x = 3, y = 1

B. x = 1, y = 3

C. x = 2, y = 2

D. x = 4, y = 0

Correct Answer: VIEW ANSWER

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Question 19

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

Correct A. \frac{2x$ x^2 - 4 $ - 2$ x^2 + 2x - 3 $(2x)}{$ x^2 - 4 $^2}

B. \frac{2x$ x^2 - 4 $ + 2$ x^2 + 2x - 3 $(2x)}{$ x^2 - 4 $^2}

C. \frac{2x$ x^2 - 4 $ - 2$ x^2 + 2x - 3 $(2x)}{$ x^2 - 4 $^2}

D. \frac{2x$ x^2 - 4 $ + 2$ x^2 + 2x - 3 $(2x)}{$ x^2 - 4 $^2}

Correct Answer: A

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Question 20

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

Correct A. $ -∞, -1 $ ∪ (3, ∞)

B. $ -∞, -3 $ ∪ (1, ∞)

C. $ -∞, -1 $ ∪ $ -3, ∞ $

D. $ -∞, -3 $ ∪ (1, ∞)

Correct Answer: A

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Question 21

Find the area under the curve $ y = x^2 $ from $ x = 0 $ to $ x = 2 $.

Correct A. \frac{8}{3}

B. \frac{16}{3}

C. \frac{32}{3}

D. \frac{64}{3}

Correct Answer: A

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Question 22

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

A. x = \frac{π}{2}

Correct B. x = \frac{π}{4}

C. x = \frac{3π}{4}

D. x = \frac{5π}{4}

Correct Answer: B

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Question 23

Find the probability of drawing two hearts from a s\tandard deck of 52 cards.

Correct A. \frac{1}{221}

B. \frac{1}{13}

C. \frac{1}{17}

D. \frac{1}{25}

Correct Answer: A

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Question 24

Solve the system of linear equations $ 2x + 3y = 7 $ and $ x - 2y = -3 $.

Correct A. \left$ \frac{13}{7}, \frac{5}{7} \right $

B. \left$ \frac{5}{7}, \frac{13}{7} \right $

C. \left$ \frac{13}{7}, -\frac{5}{7} \right $

D. \left$ -\frac{5}{7}, \frac{13}{7} \right $

Correct Answer: A

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Question 25

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

Correct A. -\frac{2}{x^3}

B. \frac{2}{x^3}

C. -\frac{1}{x^3}

D. \frac{1}{x^3}

Correct Answer: A

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