POST UTME BSU 2024 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve for $x$: $\sin^2 x + \cos^2 x = 1$.
A. x = \frac{\pi}{4}
B. x = \frac{\pi}{2}
C. x = \frac{3\pi}{4}
D. x = \pi
Question 2
The mean of a set of numbers is 25. If the set is increased by 10% and then decreased by 5%, what is the new mean?
A. 24.5
B. 25.5
C. 26.5
D. 27.5
Question 3
Find the equation of the circle with center \( -2, 3 \) and radius 4.
A. \( x + 2 \)^2 + \( y - 3 \)^2 = 16
B. \( x - 2 \)^2 + \( y + 3 \)^2 = 16
C. \( x + 2 \)^2 + \( y + 3 \)^2 = 16
D. \( x - 2 \)^2 + \( y - 3 \)^2 = 16
Question 4
A histogram of exam scores has a mean of 80 and a s\tandard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score is between 70 and 90?
A. 0.68
B. 0.69
C. 0.70
D. 0.71
Question 5
A particle moves along the curve y = x^2 + 2x + 1. Find the equation of the \tangent line at the point (1, 4).
A. y = 2x + 3
B. y = 2x - 3
C. y = -2x + 3
D. y = -2x - 3
Question 6
Solve for $x$: $\log_2 x + \log_2 \( x-1 \) = 2$.
A. 3
B. 4
C. 5
D. 6
Question 7
Find the equation of the circle with center ( (2, 3) ) and radius ( 4 ).
A. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 16 )
B. \( x + 2 \ \)^2 + \( y - 3 \)^2 = 16 )
C. \( x - 2 \ \)^2 + \( y + 3 \)^2 = 16 )
D. \( x + 2 \ \)^2 + \( y + 3 \)^2 = 16 )
Question 8
A right-angled triangle has sides of length ( 3 ), ( 4 ), and ( 5 ). Find the area of the triangle.
A. 6
B. 8
C. 10
D. 12
Question 9
Solve the matrix equation \( \begin{bmatrix} 2 & 1 \ 1 & 3 \end{bmatrix} \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 5 \ 7 \end{bmatrix} \).
A. \begin{bmatrix} 1 \ 2 \end{bmatrix}
B. \begin{bmatrix} 2 \ 1 \end{bmatrix}
C. \begin{bmatrix} 3 \ 4 \end{bmatrix}
D. \begin{bmatrix} 4 \ 3 \end{bmatrix}
Question 10
Solve the quadratic equation: \( x^2 + 5x + 6 = 0 \).
A. -2
B. -3
C. -1
D. 1
Question 11
A circle has a radius of 5 cm. Find the area of the circle.
A. 25\pi
B. 50\pi
C. 75\pi
D. 100\pi
Question 12
A sequence is defined recursively as \( a_n = 2a_{n-1} + 1 \), where \( a_1 = 3 \). Find the value of \( a_{10} \).
A. 1023
B. 1025
C. 1027
D. 1029
Question 13
A right circular cone has a radius of 6 cm and a height of 8 cm. Find the volume of the cone.
A. 288\pi
B. 384\pi
C. 480\pi
D. 576\pi
Question 14
Find the value of $\frac{d}{dx} \left\( \frac{1}{x} \right \)$.
A. -\frac{1}{x^2}
B. \frac{1}{x^2}
C. -\frac{1}{x}
D. \frac{1}{x}
Question 15
Solve for x in the equation: \( \sin^2\( x \ \) + \cos^2(x) = 1 ). What is the value of x?
A. 0
B. π/2
C. π
D. 3π/2

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