POST UTME RSU 2025 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 derivative of the function [ f(x) = 3x^2 - 2x + 1 ].
A. ( f'(x) = 6x - 2 )
B. ( f'(x) = 6x + 2 )
C. ( f'(x) = 3x^2 - 2 )
D. ( f'(x) = 3x^2 + 2 )
Question 3
Determine the value of ( x ) in the equation \( \frac{x}{2} + 5 = 11 \).
A. 4
B. 6
C. 8
D. 10
Question 4
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( -\infty, -1 \) \cup \( 3, \infty \)
B. \( -\infty, -1 \) \cup \( 1, \infty \)
C. \( -\infty, 1 \) \cup \( 3, \infty \)
D. \( -\infty, 1 \) \cup \( 1, \infty \)
Question 5
A histogram of exam scores is shown below. If the mean score is 75, and the s\tandard deviation is 10, what is the area under the curve between 60 and 80?
A. 0.5
B. 1.0
C. 1.5
D. 2.0
Question 6
A fair six-sided die is rolled. What is the probability that the number obtained is a multiple of 3?
A. \frac{1}{6}
B. \frac{1}{3}
C. \frac{2}{3}
D. \frac{5}{6}
Question 7
Solve for x in the equation [ 2^x = 32 ].
A. \( x = 5 \)
B. \( x = 6 \)
C. \( x = 7 \)
D. \( x = 8 \)
Question 8
Find the determinant of the matrix [ egin{array}{ccc} 2 & 3 & 1 \ 4 & 5 & 2 \ 1 & 2 & 3 \end{array} ].
A. -1
B. 1
C. 2
D. 3
Question 9
Find the derivative of the function ( f(x) = \frac{1}{2x^2 + 5x + 3} ) u\sing the quotient rule.
A. \( \frac{-2x + 5}{\( 2x^2 + 5x + 3 \ \)^2} )
B. \( \frac{2x + 5}{\( 2x^2 + 5x + 3 \ \)^2} )
C. \( \frac{2x^2 + 5x + 3}{\( 2x^2 + 5x + 3 \ \)^2} )
D. \( \frac{2x^2 + 5x + 3}{\( 2x^2 + 5x + 3 \ \)^2} )
Question 10
A set of exam scores has a mean of [ 75 \] and a s\tandard deviation of [ 5 \]. Find the z-score of a score of [ 80 \].
A. 0.4
B. 0.6
C. 0.8
D. 1.0
Question 11
Solve the system of equations \( \begin{cases} x + y = 4 \ 2x - 3y = -2 \end{cases} \) u\sing matrices.
A. \begin{pmatrix} 2 \ 3 \end{pmatrix}
B. \begin{pmatrix} 1 \ 2 \end{pmatrix}
C. \begin{pmatrix} 3 \ 1 \end{pmatrix}
D. \begin{pmatrix} 4 \ 5 \end{pmatrix}
Question 12
If [ f(x) = \frac{1}{x^2-4} ], find [ lim_{x \to 2} f(x) ].
A. \( \frac{1}{4} \)
B. \( -\frac{1}{4} \)
C. \( \frac{1}{2} \)
D. \( -\frac{1}{2} \)
Question 13
Find the area under the curve \( y = x^2 \) from \( x = 0 \) to \( x = 4 \).
A. 16
B. 32
C. 64
D. 128
Question 14
Solve the system of equations u\sing matrices: \( egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 7 \ 10 \end{bmatrix} \).
A. \( egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 1 \ 2 \end{bmatrix} \)
B. \( egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 2 \ 1 \end{bmatrix} \)
C. \( egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 3 \ 4 \end{bmatrix} \)
D. \( egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 4 \ 3 \end{bmatrix} \)
Question 15
Find the equation of the line pas\sing through the points ( (2, 3) ) and ( (4, 5) ).
A. y = 2x - 1
B. y = 2x + 1
C. y = x - 2
D. y = x + 2

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