POST UTME REDEEMERS UNIVERSITY 2024 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Convert the \fraction \( \frac{3}{4} \) to a decimal in base 10.
A. \( 0.75 \ \)
B. \( 0.25 \ \)
C. \( 0.50 \ \)
D. \( 0.33 \ \)
Question 2
Find the equation of the \tangent line to the curve y = x^2 at the point (1, 1).
A. y = 2x - 1
B. y = 2x + 1
C. y = x - 1
D. y = x + 1
Question 3
Find the area under the curve y = x^3 from x = 0 to x = 2.
A. 8
B. 16
C. 32
D. 64
Question 4
Let ( X ) be a random variable with probability density function ( f(x) = egin{cases} 2x, & 0 leq x leq 1 \ 0, & \text{otherwise} \end{cases} ). Find the probability that ( X ) takes on a value greater than 0.5.
A. 0.25
B. 0.5
C. 0.75
D. 1
Question 5
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 6
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
Question 7
Solve the inequality 2x^2 + 5x - 3 > 0.
A. \( -\infty, -1 \) \cup \( 3, \infty \)
B. \( -\infty, -3 \) \cup \( 1, \infty \)
C. \( -\infty, 1 \) \cup \( 3, \infty \)
D. \( -\infty, -3 \) \cup \( 1, \infty \)
Question 8
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 9
Find the determinant of the matrix [egin{pmatrix} 2 & 3 & 4 \ 5 & 6 & 7 \ 8 & 9 & 10 \end{pmatrix}].
A. 0
B. 1
C. 2
D. 3
Question 10
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 11
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 12
Solve the differential equation \frac{dy}{dx} = \frac{y^2}{x^2} with the initial condition y(1) = 1.
A. y = \frac{1}{x}
B. y = \frac{1}{x^2}
C. y = \frac{1}{x^3}
D. y = \frac{1}{x^4}
Question 13
Find the volume of the solid formed by revolving the region bounded by 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 14
Let \( S = \{1, 2, 3, \ldots, 10\} \). Find the number of subsets of ( S ) that contain exactly 3 elements.
A. 10
B. 20
C. 30
D. 40
Question 15
Find the derivative of the function ( f(x) = 2x^3 - 5x^2 + 3x - 1 ) u\sing the chain rule.
A. ( f'(x) = 6x^2 - 10x + 3 \)
B. ( f'(x) = 12x^2 - 20x + 6 \)
C. ( f'(x) = 18x^2 - 30x + 9 \)
D. ( f'(x) = 24x^2 - 40x + 12 \)

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