POST UTME ACHIEVERS UNIVERSITY 2019 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A fair six-sided die is rolled. What is the probability that the number obtained is a multiple of 3?
A. \[ P\( \text{multiple of 3} \) = \frac{1}{2} \]
B. \[ P\( \text{multiple of 3} \) = \frac{1}{3} \]
C. \[ P\( \text{multiple of 3} \) = \frac{2}{3} \]
D. \[ P\( \text{multiple of 3} \) = \frac{1}{6} \]
Question 2
Solve the inequality \( |x - 2| > 3 \).
A. \( -∞, -1 \) ∪ (4, ∞)
B. \( -∞, -1 \) ∪ (1, ∞)
C. \( -∞, 1 \) ∪ (4, ∞)
D. \( -∞, 4 \) ∪ (1, ∞)
Question 3
Find the determinant of the matrix \( egin{bmatrix} 2 & 1 & 4 \ 3 & 2 & 5 \ 6 & 3 & 7 \end{bmatrix} \).
A. ( 0 )
B. ( 1 )
C. ( 2 )
D. ( 3 )
Question 4
A histogram is given below. Find the mean of the data.
A. 5
B. 10
C. 15
D. 20
Question 5
Determine the value of \( \log_{10} \( x^2 \ \) ) given that \( \log_{10} x = 2 \).
A. 4
B. 5
C. 6
D. 7
Question 6
Solve the inequality \( \frac{x}{x-2} > 1 \) for \( x > 2 \).
A. 2 < x < 4
B. x > 4
C. x > 2
D. x < 2
Question 7
Find the volume of the frustum of a cone with height 6 cm, lower base radius 4 cm, and upper base radius 2 cm.
A. 24\pi cm^3
B. 48\pi cm^3
C. 72\pi cm^3
D. 96\pi cm^3
Question 8
Determine the value of x in the equation \( \frac{x}{2} + \frac{1}{3} = \frac{7}{6} \).
A. 4
B. 5
C. 6
D. 7
Question 9
Solve the equation \( x^2 - 4x + 4 = 0 \) u\sing the quadratic formula.
A. \[ x = 2 \]
B. \[ x = 1 \]
C. \[ x = -2 \]
D. \[ x = -1 \]
Question 10
Find the volume of the frustum of a cone with height 10 cm, base radius 6 cm, and top radius 4 cm.
A. 120\pi cm^3
B. 150\pi cm^3
C. 180\pi cm^3
D. 200\pi cm^3
Question 11
In a random sample of 100 students, the mean height is 175 cm with a s\tandard deviation of 5 cm. If the heights of the students are normally distributed, what is the probability that a randomly selected student will be taller than 180 cm?
A. 0.1587
B. 0.3413
C. 0.4772
D. 0.6179
Question 12
Solve for $x$: $\log_{10} \( x^2 \) = 4$.
A. 10
B. 100
C. 1000
D. 10000
Question 13
Solve the system of linear equations \( 2x + 3y = 7 \) and \( x - 2y = -3 \).
A. \( x = 1, y = 2 \)
B. \( x = 2, y = 1 \)
C. \( x = 3, y = 4 \)
D. \( x = 4, y = 3 \)
Question 14
Solve the inequality \( 2x^2 - 5x - 3 > 0 \) u\sing the quadratic formula.
A. \[ x < \frac{3}{2} \text{ or } x > 1 \]
B. \[ x < -1 \text{ or } x > \frac{3}{2} \]
C. \[ x < -1 \text{ or } x < \frac{3}{2} \]
D. \[ x > -1 \text{ or } x < \frac{3}{2} \]
Question 15
If ( f(x) = \frac{1}{2} \sin^2 x + \frac{1}{4} \cos 2x ), find ( f''(x) ) u\sing the chain rule and the derivatives of \sine and co\sine.
A. \[ f''(x) = \sin x \cos x - \cos 2x \]
B. \[ f''(x) = \sin x \cos x + \cos 2x \]
C. \[ f''(x) = \sin^2 x - \cos 2x \]
D. \[ f''(x) = \sin^2 x + \cos 2x \]

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: