POST UTME SKYLINE UNIVERSITY 2022 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the area under the curve \( y = \frac{1}{x^2} \) from \( x = 1 \) to \( x = 2 \).
A. 0.5
B. 1
C. 1.5
D. 2
Question 2
A set A is defined as A = {x ∈ ℝ | x^2 + 2x + 1 ≥ 0}. Find the set A.
A. {x ∈ ℝ | x ≥ -1}
B. {x ∈ ℝ | x ≤ -1}
C. {x ∈ ℝ | x ≥ 1}
D. {x ∈ ℝ | x ≤ 1}
Question 3
Find the value of \( \log_{10} \( 1000 \ \) ).
A. ( 3 )
B. ( 2 )
C. ( 1 )
D. ( 0 )
Question 4
Find the area under the curve $y = \frac{1}{x^2 + 1}$ from $x = 0$ to $x = 1$.
A. \frac{\pi}{4}
B. \frac{\pi}{2}
C. \frac{\pi}{3}
D. \frac{\pi}{6}
Question 5
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.
A. [3, 7, 15, 31, 63]
B. [3, 5, 7, 9, 11]
C. [3, 5, 7, 9, 11]
D. [3, 7, 15, 31, 63]
Question 6
Solve the equation \( x^2 + 2x + 1 = 0 \).
A. x = 0
B. x = -1
C. x = 1
D. x = -2
Question 7
Find the value of \( \sin left\( \frac{pi}{4} + \frac{pi}{6} \right \ \) ).
A. \( \frac{\sqrt{3}}{2} \)
B. \( \frac{1}{2} \)
C. \( \frac{\sqrt{2}}{2} \)
D. \( \frac{1}{\sqrt{2}} \)
Question 8
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?
A. \frac{1}{4}
B. \frac{1}{6}
C. \frac{1}{8}
D. \frac{1}{10}
Question 9
Solve for $x$: $\log_2 \( x^2 + 1 \) + \log_2 \( x^2 - 1 \) = 2$.
A. \frac{1}{2}
B. \frac{1}{4}
C. \frac{1}{8}
D. \frac{1}{16}
Question 10
Solve the equation \( x^2 + 4x + 4 = 0 \).
A. \( x = -2 \)
B. \( x = -1 \)
C. \( x = 0 \)
D. \( x = 2 \)
Question 11
Find the sum of the first 10 terms of the geometric series \( 2 + 6 + 18 + ldots \).
A. 1950
B. 1960
C. 1970
D. 1980
Question 12
Find the derivative of the function ( f(x) = \frac{x^2 + 2x - 3}{x^2 - 4} ) u\sing the quotient rule.
A. \frac{2x\( x^2 - 4 \) - \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2}
B. \frac{2x\( x^2 - 4 \) + \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2}
C. \frac{2x\( x^2 - 4 \) - \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2}
D. \frac{2x\( x^2 - 4 \) + \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2}
Question 13
Find the area under the curve \( y = \frac{1}{x} \) between \( x = 1 \) and \( x = 2 \).
A. 0.693
B. 0.693
C. 0.693
D. 0.693
Question 14
Find the vector \( \mathbf{a} \times \mathbf{b} \) given that \( \mathbf{a} = 2\mathbf{i} + 3\mathbf{j} \) and \( \mathbf{b} = -4\mathbf{i} + 5\mathbf{j} \).
A. -10\mathbf{i} + 14\mathbf{j}
B. 10\mathbf{i} - 14\mathbf{j}
C. -14\mathbf{i} + 10\mathbf{j}
D. 14\mathbf{i} - 10\mathbf{j}
Question 15
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
C. 36
D. 40

Master the Exam!

You've seen a preview, but there are thousands more questions plus AI tutor to break down complex solutions.

Unlock Full Access Available for Android & Windows
Help others prepare! Share this practice hub: