POST UTME AFE BABALOLA UNIVERSITY 2025 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A vector $\mathbf{a}$ has magnitude $5$ and direction $30^\circ$ counterclockwise from the positive $x$-axis. A vector $\mathbf{b}$ has magnitude $3$ and direction $60^\circ$ counterclockwise from the positive $x$-axis. What is the magnitude of the sum $\mathbf{a} + \mathbf{b}$?
A. 4
B. 5
C. 6
D. 7
Question 2
A circle has a radius of 4 cm. Calculate the area of the circle u\sing the formula A = πr^2.
A. 50.24
B. 100.48
C. 200.96
D. 251.2
Question 3
Solve the quadratic equation \( x^2 + 5x + 6 = 0 \) u\sing the quadratic formula.
A. \( x = -2, x = -3 \)
B. \( x = -1, x = -6 \)
C. \( x = 2, x = 3 \)
D. \( x = 1, x = 6 \)
Question 4
A random variable X has a probability distribution given by: \[P\( X = 1 \) = 0.3, P\( X = 2 \) = 0.4, P\( X = 3 \) = 0.3\]. Find the expected value of X.
A. 1.1
B. 1.3
C. 1.5
D. 1.7
Question 5
Solve the equation \( x^2 + 4x + 4 = 0 \).
A. -2
B. -1
C. 1
D. 2
Question 6
A quadratic equation is given by \( x^2 - 6x + 8 = 0 \). Find the sum of the roots.
A. 2
B. 3
C. 4
D. 5
Question 7
A bag contains 5 red marbles, 8 blue marbles, and 12 green marbles. If a marble is drawn at random, what is the probability that it is blue?
A. \( \frac{1}{3} \)
B. \( \frac{2}{5} \)
C. \( \frac{1}{2} \)
D. \( \frac{2}{3} \)
Question 8
A rec\tangular prism has a length of 10 cm, a width of 6 cm, and a height of 4 cm. Calculate the volume of the prism u\sing the formula V = lwh.
A. 240
B. 288
C. 336
D. 384
Question 9
A histogram of exam scores is shown below. What is the mean score?
A. 50
B. 60
C. 70
D. 80
Question 10
Let X and Y be indep\endent random variables with probability distributions P\( X = 1 \) = 0.4 and P\( Y = 1 \) = 0.3. Find the probability that X and Y are both equal to 1.
A. 0.12
B. 0.24
C. 0.36
D. 0.48
Question 11
A right-angled triangle has a base of 5 cm and a height of 12 cm. Calculate the length of the hypotenuse u\sing the Pythagorean theorem.
A. 13
B. 14
C. 15
D. 16
Question 12
Solve the system of linear equations u\sing matrices: \( egin{cases} 2x + y = 4 \ x - 3y = -2 \end{cases} \).
A. \( x = 2, y = 0 \)
B. \( x = 0, y = 2 \)
C. \( x = 2, y = 2 \)
D. \( x = 0, y = 0 \)
Question 13
A circle has an equation of the form \( x - h \)^2 + \( y - k \)^2 = r^2. If the center of the circle is at (2, 3) and the radius is 4, find the equation of the circle.
A. \( x - 2 \)^2 + \( y - 3 \)^2 = 16
B. \( x - 3 \)^2 + \( y - 2 \)^2 = 16
C. \( x - 4 \)^2 + \( y - 3 \)^2 = 16
D. \( x - 2 \)^2 + \( y - 4 \)^2 = 16
Question 14
A matrix A has the following elements: \[A = \begin{bmatrix} 2 & 3 \\ 4 & 5 \end{bmatrix}\]. If B = 2A, find the determinant of B.
A. 20
B. 40
C. 60
D. 80
Question 15
A circle has a radius of 6 cm. Calculate the circumference of the circle u\sing the formula C = 2πr.
A. 37.68
B. 75.36
C. 113.04
D. 150.72

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