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POST UTME SKYLINE UNIVERSITY 2022 Mathematics | Objective

Are you preparing for POST UTME SKYLINE UNIVERSITY exams? Reviewing past questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2022 Mathematics (Objective) questions designed to simulate the real exam environment.

Practice these randomly selected questions to test your readiness.

Question 1

In the interval $[0, 2pi]$, find the value of $\int_0^{2\pi} \frac{\sin^2 x}{1 + \cos^2 x} dx$.

Correct A. \frac{\pi}{2}

B. \frac{\pi}{4}

C. \frac{\pi}{8}

D. \frac{\pi}{16}

Correct Answer: A

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Question 2

Solve for $x$: $\log_2 $ x^2 + 1 $ + \log_2 $ x^2 - 1 $ = 2$.

A. \frac{1}{2}

Correct B. \frac{1}{4}

C. \frac{1}{8}

D. \frac{1}{16}

Correct Answer: B

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Question 3

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}{3}

D. \frac{\pi}{6}

Correct Answer: A

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Question 4

A sequence is defined by $a_n = \frac{1}{n} + \frac{1}{n+1}$. Find the sum of the first 5 terms of the sequence.

Correct A. \frac{23}{20}

B. \frac{25}{20}

C. \frac{27}{20}

D. \frac{29}{20}

Correct Answer: A

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Question 5

In the diagram below, $ABCD$ is a rec\tangle with $AB = 6$ and $BC = 8$. Find the area of the triangle $ACD$.

A. 24

B. 30

Correct C. 36

D. 40

Correct Answer: C

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Question 6

Let X be a random variable with probability density function f(x) = $ \frac{1}{2}e^{-|x|} $ for -∞ < x < ∞. Find the probability that X lies between -1 and 1.

Correct A. 0.5

B. 0.6

C. 0.7

D. 0.8

Correct Answer: A

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Question 7

Solve the inequality $ \frac{x^2 - 4}{x^2 - 9} > 0 $ for x ≠ ±3.

Correct A. $ -∞, -3 $ ∪ (3, ∞)

B. $ -∞, -3 $ ∪ (3, ∞) ∪ (4, 6)

C. $ -∞, -3 $ ∪ (3, ∞) ∪ $ -6, -4 $

D. $ -∞, -3 $ ∪ (3, ∞) ∪ $ -6, 6 $

Correct Answer: A

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Question 8

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

Correct A. $ \frac{-2x}{\( x^2 + 1 \ $^2} )

B. $ \frac{-2x}{x^2 + 1} $

C. $ \frac{2x}{\( x^2 + 1 \ $^2} )

D. $ \frac{2x}{x^2 + 1} $

Correct Answer: A

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Question 9

A sequence is defined by the recurrence relation $ a_n = 2a_{n-1} + 1 $ with initial term $ a_1 = 3 $. Find the first five terms of the sequence.

Correct A. [3, 7, 15, 31, 63]

B. [3, 5, 7, 9, 11]

C. [3, 5, 7, 9, 11]

D. [3, 7, 15, 31, 63]

Correct Answer: A

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Question 10

A set A is defined as A = {x ∈ ℝ | x^2 + 2x + 1 ≥ 0}. Find the set A.

Correct A. {x ∈ ℝ | x ≥ -1}

B. {x ∈ ℝ | x ≤ -1}

C. {x ∈ ℝ | x ≥ 1}

D. {x ∈ ℝ | x ≤ 1}

Correct Answer: A

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Question 11

A random sample of 25 students from a university had a mean height of 175 cm with a s\tandard deviation of 5 cm. If the population s\tandard deviation is 6 cm, calculate the 95% confidence interval for the mean height of all students in the university.

Correct A. 170.35 cm, 179.65 cm

B. 168.35 cm, 181.65 cm

C. 169.35 cm, 180.65 cm

D. 171.35 cm, 178.65 cm

Correct Answer: A

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Question 12

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

Correct A. $ x = \frac{\pi}{4}, \frac{3\pi}{4} $

B. $ x = \frac{\pi}{2}, \frac{3\pi}{2} $

C. $ x = \frac{\pi}{4}, \frac{5\pi}{4} $

D. $ x = \frac{\pi}{2}, \frac{7\pi}{2} $

Correct Answer: A

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Question 13

Find the sum of the first 10 terms of the geometric series $ 2 + 6 + 18 + \cdots $.

Correct A. 1950

B. 1960

C. 1970

D. 1980

Correct Answer: A

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Question 14

A histogram of exam scores is shown below. If the mean score is 60 and the s\tandard deviation is 10, find the area under the curve between 50 and 70.

Correct A. 0.4

B. 0.5

C. 0.6

D. 0.7

Correct Answer: A

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Question 15

Find the area under the curve $ y = \frac{1}{x} $ between $ x = 1 $ and $ x = 2 $.

Correct A. 0.693

B. 0.693

C. 0.693

D. 0.693

Correct Answer: A

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Question 16

Find the area under the curve $ y = \frac{1}{2}x^2 + 2x - 3 $ from $ x = 0 $ to $ x = 4 $.

Correct A. $ \frac{1}{2} left\( \frac{4^3}{3} + 2 cdot 4^2 - 3 cdot 4 \right \ $ )

B. $ \frac{1}{2} left\( \frac{0^3}{3} + 2 cdot 0^2 - 3 cdot 0 \right \ $ )

C. $ \frac{1}{2} left\( \frac{4^3}{3} + 2 cdot 4^2 - 3 cdot 4 \right \ $ + \frac{1}{2} left$ \frac{0^3}{3} + 2 cdot 0^2 - 3 cdot 0 \right $ )

D. $ \frac{1}{2} left\( \frac{4^3}{3} + 2 cdot 4^2 - 3 cdot 4 \right \ $ - \frac{1}{2} left$ \frac{0^3}{3} + 2 cdot 0^2 - 3 cdot 0 \right $ )

Correct Answer: A

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Question 17

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

Correct A. $ x < -\frac{3}{2} $ or $ x > \frac{1}{2} $

B. $ x < -\frac{3}{2} $ or $ x < \frac{1}{2} $

C. $ x > -\frac{3}{2} $ or $ x > \frac{1}{2} $

D. $ x < -\frac{3}{2} $ or $ x < \frac{1}{2} $

Correct Answer: A

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Question 18

Find the value of $ \sin left\( \frac{pi}{4} + \frac{pi}{6} \right \ $ ).

Correct A. $ \frac{\sqrt{3}}{2} $

B. $ \frac{1}{2} $

C. $ \frac{\sqrt{2}}{2} $

D. $ \frac{1}{\sqrt{2}} $

Correct Answer: A

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Question 19

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

Correct A. $ x = -2 $

B. $ x = -1 $

C. $ x = 0 $

D. $ x = 2 $

Correct Answer: A

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Question 20

Find the value of $ \log_{10} \( 1000 \ $ ).

Correct A. ( 3 )

B. ( 2 )

C. ( 1 )

D. ( 0 )

Correct Answer: A

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Question 21

Solve the inequality $ \frac{2x-5}{x+2} > 0 $ for $ x in \( -infty, -2 \ $ cup $ -2, infty $ ).

A. $ -5, -2 $ \cup $ 2, \infty $

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

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

D. $ -\infty, -5 $ \cup $ -2, \infty $

Correct Answer: B

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Question 22

Find the sum of the first 10 terms of the geometric series $ 2x^2 - 3x + 1 $ with common ratio $ r = -\frac{1}{2} $.

A. -\frac{1}{16}

B. -\frac{1}{32}

Correct C. -\frac{1}{64}

D. -\frac{1}{128}

Correct Answer: C

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Question 23

Solve the system of linear equations $ \begin{cases} x + 2y - 3z = 7 \ x - 2y + 3z = -3 \ 2x + 4y - 6z = 12 \end{cases} $.

Correct A. \begin{cases} x = 1 \ y = 2 \ z = 3 \end{cases}

B. \begin{cases} x = 2 \ y = 1 \ z = 4 \end{cases}

C. \begin{cases} x = 3 \ y = 2 \ z = 1 \end{cases}

D. \begin{cases} x = 4 \ y = 3 \ z = 2 \end{cases}

Correct Answer: A

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Question 24

Find the area under the curve $ y = x^2 - 4x + 3 $ from $ x = 1 $ to $ x = 3 $.

A. 4

Correct B. 6

C. 8

D. 10

Correct Answer: B

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Question 25

A box contains 5 red balls and 3 blue balls. If 2 balls are drawn at random, what is the probability that both balls are red?

Correct A. \frac{1}{4}

B. \frac{1}{6}

C. \frac{1}{8}

D. \frac{1}{10}

Correct Answer: A

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