POST UTME ELIZADE UNIVERSITY 2017 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the volume of the sphere with radius 5.
A. \( \frac{4}{3} pi \( 5 \ \)^3 )
B. \( \frac{1}{3} pi \( 5 \ \)^3 )
C. \( \frac{2}{3} pi \( 5 \ \)^3 )
D. \( \frac{1}{4} pi \( 5 \ \)^3 )
Question 2
Find the equation of the circle with center at (2, 3) and radius 4.
A. \boxed{\( x - 2 \)^2 + \( y - 3 \)^2 = 16}
B. \( x - 2 \)^2 + \( y - 3 \)^2 = 25
C. \( x - 2 \)^2 + \( y - 3 \)^2 = 9
D. \( x - 2 \)^2 + \( y - 3 \)^2 = 36
Question 3
A vector ( mathbf{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 ( mathbf{a} ).
A. (4, 3)
B. (3, 4)
C. (5, 5)
D. (6, 6)
Question 4
A quadratic equation has roots $\alpha$ and $\beta$. If $\alpha + \beta = -2$ and $\alpha \beta = 3$, find the equation of the quadratic.
A. x^2 + 2x + 3 = 0
B. x^2 - 2x + 3 = 0
C. x^2 + 4x + 3 = 0
D. x^2 - 4x + 3 = 0
Question 5
Two events A and B are indep\endent. If P(A) = 0.4 and P(B) = 0.6, find P(A ∩ B).
A. 0.2
B. 0.3
C. 0.4
D. 0.5
Question 6
Find the sum of the first 10 terms of the arithmetic progression: 2, 5, 8, 11, ...
A. 55
B. 60
C. 65
D. 70
Question 7
Find the area of the triangle with vertices (0, 0), (3, 0), and (0, 4).
A. ( 6 )
B. ( 12 )
C. ( 18 )
D. ( 24 )
Question 8
Solve the system of equations: \begin{align*} x + y + z &= 6 \ 2x + 2y + 3z &= 12 \ 3x + 2y + z &= 9 \end{align*}
A. \begin{pmatrix} 1 \ 2 \ 3 \end{pmatrix}
B. \begin{pmatrix} 2 \ 3 \ 4 \end{pmatrix}
C. \begin{pmatrix} 3 \ 4 \ 5 \end{pmatrix}
D. \begin{pmatrix} 4 \ 5 \ 6 \end{pmatrix}
Question 9
Find the determinant of the matrix \[ \begin{bmatrix} 2 & 3 \ 4 & 5 \end{bmatrix} \].
A. 1
B. 2
C. 3
D. 4
Question 10
In the diagram below, the graph of \( y = \frac{1}{2} \sin 2x \) is shown. What is the amplitude of the function?
A. 1
B. 0.5
C. 2
D. 3
Question 11
Find the volume of the parallelepiped generated by the vectors \( mathbf{a} = egin{pmatrix} 1 \ 2 \ 3 \end{pmatrix} \), \( mathbf{b} = egin{pmatrix} 4 \ 5 \ 6 \end{pmatrix} \), and \( mathbf{c} = egin{pmatrix} 7 \ 8 \ 9 \end{pmatrix} \).
A. 42
B. 43
C. 44
D. 45
Question 12
Solve the quadratic equation: \( x^2 + 5x + 6 = 0 \).
A. -2
B. -3
C. -1
D. 1
Question 13
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 14
A histogram of exam scores has a mean of 60 and a s\tandard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score is between 50 and 70?
A. 0.68
B. 0.80
C. 0.90
D. 0.95
Question 15
The determinant of the matrix \( \begin{bmatrix} 2 & 1 & 1 \\ 1 & 2 & 1 \\ 1 & 1 & 2 \end{bmatrix} \) is
A. 4
B. 6
C. 8
D. 10

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: