POST UTME SKYLINE UNIVERSITY 2019 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Determine the value of $x$ in the equation $2^x + 5^x = 7^x$.
A. 1
B. 2
C. 3
D. 4
Question 2
Solve the system of equations \( egin{cases} x + y = 4 \ 2x - 3y = 5 \end{cases} \).
A. (1, 3)
B. (2, 2)
C. (3, 1)
D. (4, 0)
Question 3
Find the mean of the numbers 2, 4, 6, 8, 10, 12, 14, 16, 18, 20.
A. 10
B. 12
C. 14
D. 16
Question 4
Let \( mathbf{a} = egin{pmatrix} 2 \ 3 \end{pmatrix} \) and \( mathbf{b} = egin{pmatrix} 1 \ -2 \end{pmatrix} \). Find the vector ( mathbf{a} cdot mathbf{b} ) u\sing the dot product formula.
A. \( mathbf{a} cdot mathbf{b} = 8 \)
B. \( mathbf{a} cdot mathbf{b} = -1 \)
C. \( mathbf{a} cdot mathbf{b} = 7 \)
D. \( mathbf{a} cdot mathbf{b} = -8 \)
Question 5
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).
A. \( \frac{1}{2} \times 4^3 + 3 \times 4^2 - 2 \times 4 \)
B. \( \frac{1}{2} \times 4^2 + 3 \times 4 - 2 \)
C. \( \frac{1}{2} \times 4^3 + 3 \times 4^2 - 2 \times 4^2 \)
D. \( \frac{1}{2} \times 4^2 + 3 \times 4^3 - 2 \)
Question 6
Find the determinant of the matrix \( egin{bmatrix} 2 & 3 & 4 \ 5 & 6 & 7 \ 8 & 9 & 10 \end{bmatrix} \).
A. \( 2 \times \( 6 \times 10 - 7 \times 9 \ \) - 3 \times \( 5 \times 10 - 7 \times 8 \) + 4 \times \( 5 \times 9 - 6 \times 8 \) )
B. \( 2 \times \( 6 \times 10 - 7 \times 9 \ \) - 3 \times \( 5 \times 10 - 7 \times 8 \) - 4 \times \( 5 \times 9 - 6 \times 8 \) )
C. \( 2 \times \( 6 \times 10 - 7 \times 9 \ \) + 3 \times \( 5 \times 10 - 7 \times 8 \) + 4 \times \( 5 \times 9 - 6 \times 8 \) )
D. \( 2 \times \( 6 \times 10 - 7 \times 9 \ \) + 3 \times \( 5 \times 10 - 7 \times 8 \) - 4 \times \( 5 \times 9 - 6 \times 8 \) )
Question 7
Find the sum of the infinite geometric series \( 1 + \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + cdots \).
A. 1
B. 2
C. 3
D. 4
Question 8
Find the area under the curve \( y = \frac{1}{x} \) from \( x = 1 \) to \( x = 2 \).
A. \( \log_2 \( 2 \ \) - \log_2 (1) )
B. \( \log_2 \( 2 \ \) + \log_2 (1) )
C. \( \log_2 \( 1 \ \) - \log_2 (2) )
D. \( \log_2 \( 1 \ \) + \log_2 (2) )
Question 9
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( x < -1 \) or \( x > \frac{3}{2} \)
B. \( x > -1 \) or \( x < \frac{3}{2} \)
C. \( x < -1 \) or \( x < \frac{3}{2} \)
D. \( x > -1 \) or \( x > \frac{3}{2} \)
Question 10
A vector ( mathbf{a} ) is defined as \( mathbf{a} = 2mathbf{i} + 3mathbf{j} \). Find the magnitude of ( mathbf{a} ).
A. 5
B. 10
C. 15
D. 20
Question 11
A set ( A ) contains 5 elements. If ( A ) is a subset of a set ( B ), and ( B ) has 8 elements, what is the number of elements in the power set of ( B )?
A. 32
B. 64
C. 128
D. 256
Question 12
Solve the quadratic equation \( x^2 + 5x + 6 = 0 \) u\sing the quadratic formula.
A. \( x = \frac{-5 pm \sqrt{5^2 - 4 \times 1 \times 6}}{2 \times 1} \)
B. \( x = \frac{-5 pm \sqrt{5^2 + 4 \times 1 \times 6}}{2 \times 1} \)
C. \( x = \frac{-5 pm \sqrt{5^2 - 4 \times 1 \times 6}}{2 \times 6} \)
D. \( x = \frac{-5 pm \sqrt{5^2 + 4 \times 1 \times 6}}{2 \times 6} \)
Question 13
Find the derivative of the function ( f(x) = \sqrt{3x + 2} ) u\sing the chain rule.
A. \( \frac{3}{2\sqrt{3x + 2}} \)
B. \( \frac{3}{2\( 3x + 2 \ \)} )
C. \( \frac{3}{2\sqrt{3x + 2}} + \frac{1}{2\sqrt{3x + 2}} \)
D. \( \frac{3}{2\( 3x + 2 \ \)} - \frac{1}{2\( 3x + 2 \)} )
Question 14
Solve the inequality $\frac{x^2 - 4}{x + 2} > 0$.
A. x > -2
B. x < -2
C. x > 2
D. x < 2
Question 15
A sequence is defined as \( a_n = 2n + 1 \). Find the sum of the first 5 terms of the sequence.
A. 15
B. 25
C. 35
D. 45

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