POST UTME REDEEMERS UNIVERSITY 2024 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve the inequality \( |x - 2| > 3 \).
A. \( -∞, -1 \) ∪ (5, ∞)
B. \( -∞, 1 \) ∪ (5, ∞)
C. \( -∞, -1 \) ∪ (2, 5)
D. \( -∞, 1 \) ∪ (2, 5)
Question 2
Solve the system of equations u\sing matrices: \( egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 5 \ 6 \end{bmatrix} \).
A. x = 1, y = 2
B. x = 2, y = 1
C. x = 3, y = 4
D. x = 4, y = 3
Question 3
A set 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 will be between 70 and 90?
A. 0.34
B. 0.68
C. 0.85
D. 0.95
Question 4
Find the volume of the solid formed by rotating the region bounded by the curves y = x^2, y = 0, and x = 2 about the x-axis.
A. 16\pi
B. 32\pi
C. 64\pi
D. 128\pi
Question 5
A circle has an equation of \( x^2 + y^2 = 4 \). Find the equation of the \tangent line to the circle at the point \( 1, \sqrt{3} \ \) ).
A. y = -√3x + 4
B. y = √3x + 4
C. y = -√3x - 4
D. y = √3x - 4
Question 6
Find the derivative of the function ( f(x) = 3x^2 + 2x - 5 ) u\sing the power rule.
A. f'(x) = 6x + 2
B. f'(x) = 6x - 2
C. f'(x) = 3x^2 + 2
D. f'(x) = 3x^2 - 2
Question 7
A rec\tangular prism has a length of 8 cm, a width of 5 cm, and a height of 3 cm. Find its volume.
A. 120 cm^3
B. 1200 cm^3
C. 12000 cm^3
D. 120000 cm^3
Question 8
Solve the vector equation \( \begin{bmatrix} 2 \ 3 \end{bmatrix} \cdot \begin{bmatrix} 4 \ 5 \end{bmatrix} = \begin{bmatrix} 1 \ 2 \end{bmatrix} \cdot \begin{bmatrix} 6 \ 7 \end{bmatrix} \).
A. \( 10 = 42 \ \)
B. \( 12 = 48 \ \)
C. \( 14 = 54 \ \)
D. \( 16 = 60 \ \)
Question 9
Find the value of ( x ) in the equation \( x^2 + 5x - 6 = 0 \).
A. x = 1
B. x = -1
C. x = 2
D. x = -2
Question 10
Solve the equation \( x^2 + 4x + 4 = 0 \).
A. \( -2, 0 \)
B. \( -1, 0 \)
C. (0, 2)
D. \( 0, -2 \)
Question 11
Solve the system of equations u\sing matrices: \( \begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 3 \ 7 \end{bmatrix} \).
A. \( x = 1, y = 2 \ \)
B. \( x = 2, y = 1 \ \)
C. \( x = 3, y = 4 \ \)
D. \( x = 4, y = 3 \ \)
Question 12
Find the sum of the first 5 terms of the geometric series \( 2 + 6 + 18 + \cdots \).
A. 62
B. 64
C. 66
D. 68
Question 13
Find the area under the curve of the function ( f(x) = \frac{1}{x^2 + 1} ) from \( x = 0 \) to \( x = 1 \).
A. 0.7854
B. 0.7857
C. 0.7859
D. 0.7851
Question 14
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( -\infty, -1 \) \cup \( 3, \infty \)
B. \( -\infty, -3 \) \cup \( 1, \infty \)
C. \( -\infty, -1 \) \cup \( 1, \infty \)
D. \( -\infty, 1 \) \cup \( 3, \infty \)
Question 15
A set of exam scores has a mean of 75 and a s\tandard deviation of 10. If a student scores 90, what is his z-score?
A. -1.5
B. 1.5
C. 2.5
D. 3.5

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