POST UTME OSUSTECH 2020 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
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. \( \frac{1}{2} \times 4^2 + 3 \times 4^3 - 2 \times 4 \)
Question 2
Solve the equation [ x^2 + 4x + 4 = 0 ].
A. x = -2
B. x = 2
C. x = -1
D. x = 1
Question 3
Solve the system of linear equations \( \begin{cases} 2x + 3y = 7 \ 4x - 2y = -3 \end{cases} \).
A. x = 1, y = 1
B. x = 2, y = 3
C. x = 3, y = 2
D. x = 4, y = 1
Question 4
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).
A. 40
B. 50
C. 60
D. 70
Question 5
Solve for x in the equation \( \log_{10} \( x^2 \) = 4 \).
A. 10^4
B. 10^8
C. 10^12
D. 10^16
Question 6
Find the vector \( \vec{a} \times \vec{b} \) given that \( \vec{a} = \begin{bmatrix} 1 \ 2 \ 3 \end{bmatrix} \) and \( \vec{b} = \begin{bmatrix} 4 \ 5 \ 6 \end{bmatrix} \).
A. \begin{bmatrix} -3 \ 6 \ -3 \end{bmatrix}
B. \begin{bmatrix} 3 \ -6 \ 3 \end{bmatrix}
C. \begin{bmatrix} 6 \ -3 \ 3 \end{bmatrix}
D. \begin{bmatrix} -6 \ 3 \ -3 \end{bmatrix}
Question 7
Find the vector ( mathbf{a} ) such that \( mathbf{a} cdot mathbf{b} = 10 \) and \( mathbf{a} cdot mathbf{c} = 20 \), where \( mathbf{b} = egin{pmatrix} 2 \ 3 \end{pmatrix} \) and \( mathbf{c} = egin{pmatrix} 4 \ 5 \end{pmatrix} \).
A. \( egin{pmatrix} 5 \ 2 \end{pmatrix} \)
B. \( egin{pmatrix} 2 \ 5 \end{pmatrix} \)
C. \( egin{pmatrix} 3 \ 4 \end{pmatrix} \)
D. \( egin{pmatrix} 4 \ 3 \end{pmatrix} \)
Question 8
A histogram of exam scores has a mean of 75 and a s\tandard deviation of 10. If 75% of the scores are above 80, what is the value of the z-score for a score of 85?
A. 1.25
B. 1.5
C. 1.75
D. 2.0
Question 9
Solve for ( x ) in the equation \( 2^x + 3^x = 5^x \).
A. \( x = 2 \)
B. \( x = 3 \)
C. \( x = 4 \)
D. \( x = 5 \)
Question 10
A bag contains 5 red balls and 3 blue balls. If a ball is drawn at random, what is the probability that it is blue?
A. \( \frac{1}{2} \)
B. \( \frac{2}{3} \)
C. \( \frac{3}{4} \)
D. \( \frac{4}{5} \)
Question 11
A curve has the equation y = 2x^2 + 3x - 1. What is the area under the curve between x = 0 and x = 2?
A. 4
B. 6
C. 8
D. 10
Question 12
A 3x3 matrix \( A \) has the following elements: \[ A = \begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{bmatrix} \]. Find the determinant of \( A \).
A. 0
B. 1
C. 2
D. 3
Question 13
A vector \( \vec{a} \) has a magnitude of 5 units and makes an angle of 30° with the positive x-axis. Find the x and y components of \( \vec{a} \).
A. 4.33 \hat{i} + 2.5 \hat{j}
B. 4.33 \hat{i} - 2.5 \hat{j}
C. 2.5 \hat{i} + 4.33 \hat{j}
D. 2.5 \hat{i} - 4.33 \hat{j}
Question 14
Find the equation of the line pas\sing through the points (2, 3) and (4, 5).
A. y = 2x - 1
B. y = 2x + 1
C. y = -2x + 3
D. y = -2x - 3
Question 15
A random sample of 25 students from a university had a mean height of 175.5 cm with a s\tandard deviation of 5.2 cm. Calculate the coefficient of variation (CV) for the sample.
A. 16.8%
B. 17.4%
C. 18.0%
D. 18.6%

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: