POST UTME BOWEN UNIVERSITY 2024 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A circle has a diameter of 14cm. Find the area of the circle.
A. 22\pi \text{cm}^2
B. 49\pi \text{cm}^2
C. 98\pi \text{cm}^2
D. 196\pi \text{cm}^2
Question 2
Given that \( \sin^2 x + \cos^2 x = 1 \), find the value of \( \tan x \) when \( \sin x = \frac{3}{5} \).
A. 3
B. 4
C. 5
D. 6
Question 3
A cone has a radius of 4cm and height of 6cm. Find the volume of the cone.
A. 16\pi \text{cm}^3
B. 32\pi \text{cm}^3
C. 48\pi \text{cm}^3
D. 64\pi \text{cm}^3
Question 4
Solve the inequality $\frac{2x + 1}{x - 1} > 0$.
A. \( -\infty, -1 \) \cup \( 1, \infty \)
B. \( -\infty, 1 \) \cup \( 1, \infty \)
C. \( -\infty, -1 \) \cup \( 1, \infty \)
D. \( -\infty, 1 \) \cup \( 1, \infty \)
Question 5
Find the value of $\log_{10} \( x^2 \) = 4$.
A. 10^4
B. 10^8
C. 10^2
D. 10^6
Question 6
Solve for x in the equation \( \log_{10} \( x^2 \) = 4 \).
A. 10
B. 100
C. 1000
D. 10000
Question 7
Solve the equation $x^2 - 4x + 4 = 0$.
A. x = 2
B. x = 1
C. x = 3
D. x = 4
Question 8
A random sample of 25 students from a large population has a mean height of 175 cm with a s\tandard deviation of 5 cm. Calculate the probability that a randomly selected student from this sample has a height greater than 180 cm.
A. 0.1587
B. 0.3413
C. 0.4772
D. 0.6915
Question 9
Find the value of \( \sin 2\theta \) given that \( \sin \theta = \frac{3}{5} \) and \( \cos \theta = \frac{4}{5} \)
A. \frac{24}{25}
B. \frac{16}{25}
C. \frac{20}{25}
D. \frac{12}{25}
Question 10
Find the derivative of the function ( f(x) = \frac{1}{2x^2 + 3x - 1} ) u\sing the chain rule.
A. \( \frac{-2x + 3}{\( 2x^2 + 3x - 1 \ \)^2} )
B. \( \frac{2x + 3}{\( 2x^2 + 3x - 1 \ \)^2} )
C. \( \frac{2x - 3}{\( 2x^2 + 3x - 1 \ \)^2} )
D. \( \frac{2x + 1}{\( 2x^2 + 3x - 1 \ \)^2} )
Question 11
In the complex plane, let $z = x + yi$ be a complex number. If $|z| = 2$ and $z$ lies on the line $y = 2x$, find the value of $x$.
A. 1
B. 2
C. 3
D. 4
Question 12
Solve the equation \( \log_2\( x \ \) + \log_2\( x^2 \) = 5 ).
A. x = 16
B. x = 8
C. x = 4
D. x = 2
Question 13
Let $A = egin{pmatrix} 1 & 2 \ 3 & 4 \end{pmatrix}$ and $B = egin{pmatrix} 5 & 6 \ 7 & 8 \end{pmatrix}$. Find the determinant of the matrix $AB$.
A. -12
B. -16
C. -20
D. -24
Question 14
Let \( A = egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} \) and \( B = egin{bmatrix} 5 & 6 \ 7 & 8 \end{bmatrix} \). Find ( det(AB) ) if ( det(A) = -1 ) and ( det(B) = 2 ).
A. -2
B. 2
C. 4
D. -4
Question 15
Solve the system of equations \( \begin{cases} x + y = 4 \ 2x - 3y = -3 \end{cases} \).
A. \{ (1, 3), (2, 2) \}
B. \{ (1, 2), (2, 3) \}
C. \{ (2, 1), (3, 2) \}
D. \{ (3, 1), (4, 2) \}

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