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POST UTME SKYLINE UNIVERSITY 2022 Mathematics | Objective

Prepare for your exams with POST UTME SKYLINE UNIVERSITY questions? Reviewing past/model 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.

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Question 1 View Details

In the interval $[0, 2\pi]$, 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 View Details

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

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

Correct Answer: A

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Question 4 View Details

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 View Details

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

A. 24

B. 30

Correct C. 36

D. 40

Correct Answer: C

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Question 6 View Details

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 View Details

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 View Details

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

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 View Details

A set A is defined as A = {x ∈ ℝ | \$(x^2 + 2x + 1$$\ge 0$\)}. Find the set A.

Correct A. {x ∈ ℝ |$x \ge -1$}

B. {x ∈ ℝ |$x \le -1$}

C. {x ∈ ℝ | $x \ge 1$}

D. {x ∈ ℝ | $x \le 1$}

Correct Answer: A

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Question 11 View Details

A random sample of 25 students from a university had a mean height of 175 cm with a standard deviation of 5 cm. If the population standard 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 View Details

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

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 View Details

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 View Details

A histogram of exam scores is shown below. If the mean score is 60 and the standard 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 View Details

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 View Details

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 View Details

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 View Details

Find the value of $$1\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 View Details

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 View Details

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 View Details

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

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 View Details

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 View Details

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 View Details

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 View Details

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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