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POST UTME UNIOSUN 2023 Mathematics | Objective

Prepare for your exams with POST UTME UNIOSUN questions? Reviewing past/model 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 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 2 View Details

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 View Details

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 View Details

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 View Details

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 View Details

Determine the value of (x\) in the equation \(2^x + 5^x = 7^x\\((x) in the equation\).

A. 1

Correct B. 2

C. 3

D. 4

Correct Answer: B

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Question 7 View Details

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 View Details

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 View Details

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 View Details

Find the equation of the line passing 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 View Details

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

A set of exam scores has a mean of 75 and a standard 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 View Details

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 View Details

A histogram of exam scores has a mean of 75 and a standard 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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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

Solve the inequality \(2x^2 + 5x - 3 > 0\).

Correct A. \(-∞, -1\) ∪ (3, ∞)

B. \(-∞, -3\) ∪ (1, ∞)

C. \(-∞, -1\) \cup \(-3, ∞\)\)

D. \(-∞, -3\) ∪ (1, ∞)

Correct Answer: A

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Question 21 View Details

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 View Details

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 View Details

Find the probability of drawing two hearts from a standard 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 View Details

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 View Details

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