POST UTME CALEB UNIVERSITY 2024 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
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 2
Find the determinant of the matrix \( \begin{bmatrix} 2 & 3 & 1 \ 4 & 1 & 2 \ 3 & 2 & 1 \end{bmatrix} \).
A. \( 2\( 1-4 \ \) - 3\( 8-6 \) + 1\( 8-3 \) )
B. \( 2\( 1-2 \ \) - 3\( 4-6 \) + 1\( 12-9 \) )
C. \( 2\( 1-2 \ \) - 3\( 4-3 \) + 1\( 8-12 \) )
D. \( 2\( 1-2 \ \) - 3\( 4-3 \) + 1\( 12-8 \) )
Question 3
Solve the system of equations u\sing matrices: \( \begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 5 \ 6 \end{bmatrix} \).
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 4
Solve the system of equations u\sing matrices:
A. \( egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} \)
B. \( egin{bmatrix} 2 & 1 \ 4 & 3 \end{bmatrix} \)
C. \( egin{bmatrix} 1 & 3 \ 2 & 4 \end{bmatrix} \)
D. \( egin{bmatrix} 3 & 1 \ 2 & 4 \end{bmatrix} \)
Question 5
Simplify the expression \( \frac{1}{2} \log_{10} \( x^2 \ \) ).
A. \( \frac{1}{2} \log_{10} x \)
B. \( \log_{10} x \)
C. \( \frac{1}{2} \log_{10} \( x^2 \ \) )
D. \( \log_{10} \( x^2 \ \) )
Question 6
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 7
Solve for x in the equation \( \sin^2 x + \cos^2 x = 1 \) u\sing the identity \( \sin^2 x + \cos^2 x = 1 \).
A. x = \frac{\pi}{4}
B. x = \frac{3\pi}{4}
C. x = \frac{5\pi}{4}
D. x = \frac{7\pi}{4}
Question 8
Solve the inequality $|x-2| > 3$.
A. \( -∞, -1 \) ∪ (5, ∞)
B. \( -∞, -1 \) ∪ (1, ∞)
C. \( -∞, 1 \) ∪ (5, ∞)
D. \( -∞, -1 \) ∪ (2, ∞)
Question 9
Solve the system of linear equations u\sing matrices: \begin{bmatrix} 2 & 1 \\ 1 & 2 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 3 \\ 4 \end{bmatrix}.
A. \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 1 \\ 2 \end{bmatrix}
B. \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 2 \\ 1 \end{bmatrix}
C. \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 3 \\ 4 \end{bmatrix}
D. \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 4 \\ 3 \end{bmatrix}
Question 10
Solve the quadratic equation x^2 + 4x + 4 = 0.
A. x = -2
B. x = -1
C. x = 1
D. x = 2
Question 11
Simplify the expression \frac{\sqrt{12}}{\sqrt{3}}.
A. 2\sqrt{3}
B. \sqrt{3}
C. \sqrt{12}
D. \sqrt{3} + \sqrt{12}
Question 12
Solve the system of equations \( x + y = 4 \) and \( x - y = 2 \).
A. x = 3, y = 1
B. x = 1, y = 3
C. x = 2, y = 2
D. x = 4, y = 0
Question 13
A histogram shows the distribution of exam scores. If the mean score is 80 and the s\tandard deviation is 10, what is the probability that a randomly selected score will be between 70 and 90?
A. 0.5
B. 0.6
C. 0.7
D. 0.8
Question 14
A set of 5 numbers has a mean of 10 and a s\tandard deviation of 2. Find the probability that a randomly selected number from this set is greater than 12.
A. 0.25
B. 0.5
C. 0.75
D. 0.9
Question 15
Solve for x in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 10
B. 100
C. 1000
D. 10000

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