POST UTME WELLSPRING UNIVERSITY 2023 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the area under the curve y = x^2 + 2x - 3 from x = 0 to x = 2.
A. \boxed{\frac{13}{3}}
B. \frac{11}{3}
C. \frac{15}{3}
D. \frac{17}{3}
Question 2
Find the determinant of the matrix \( \begin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix} \).
A. 0
B. 1
C. -1
D. 2
Question 3
A histogram of exam scores has a mean of 75 and a s\tandard deviation of 10. If the scores are normally distributed, find the probability that a randomly selected score is greater than 85.
A. 0.1587
B. 0.3413
C. 0.5
D. 0.8413
Question 4
If f(x) = 3x^2 + 2x - 5, find f'(x) u\sing the chain rule.
A. \text{Derivative: } f'(x) = 6x + 2
B. \text{Derivative: } f'(x) = 6x - 2
C. \text{Derivative: } f'(x) = 6x^2 + 2x
D. \text{Derivative: } f'(x) = 6x^2 - 2x
Question 5
A rec\tangular prism has a length of 5 cm, a width of 3 cm, and a height of 2 cm. Find its volume.
A. \text{Volume: } 30 \text{ cm}^3
B. \text{Volume: } 40 \text{ cm}^3
C. \text{Volume: } 50 \text{ cm}^3
D. \text{Volume: } 60 \text{ cm}^3
Question 6
Find the vector projection of vector \mathbf{a} = \begin{pmatrix} 2 \ 3 \ 4 \end{pmatrix} onto vector \mathbf{b} = \begin{pmatrix} 1 \ 2 \ 3 \end{pmatrix}.
A. \boxed{\begin{pmatrix} \frac{11}{14} \ \frac{13}{14} \ \frac{15}{14} \end{pmatrix}}
B. \begin{pmatrix} \frac{11}{14} \ \frac{13}{14} \ \frac{15}{14} \end{pmatrix}
C. \begin{pmatrix} \frac{13}{14} \ \frac{15}{14} \ \frac{17}{14} \end{pmatrix}
D. \begin{pmatrix} \frac{15}{14} \ \frac{17}{14} \ \frac{19}{14} \end{pmatrix}
Question 7
Determine the value of x in the equation \( \sin^2\( x \ \) + \cos^2(x) = 1 ) if \( \sin\( x \ \) = \frac{3}{5} ).
A. \frac{4\sqrt{11}}{11}
B. \frac{3\sqrt{11}}{11}
C. \frac{4\sqrt{11}}{11}
D. \frac{3\sqrt{11}}{11}
Question 8
Solve the inequality \( \log_{10} \( x^2 \ \) > 4 ).
A. x > 10
B. x < -10
C. x > 100
D. x < -100
Question 9
A right triangle has a hypotenuse of 10 cm and one leg of 6 cm. Find the length of the other leg.
A. \text{Length: } 8 \text{ cm}
B. \text{Length: } 6 \text{ cm}
C. \text{Length: } 4 \text{ cm}
D. \text{Length: } 2 \text{ cm}
Question 10
A circle has a radius of 4 cm. Find its area.
A. \text{Area: } 16 \pi \text{ cm}^2
B. \text{Area: } 32 \pi \text{ cm}^2
C. \text{Area: } 64 \pi \text{ cm}^2
D. \text{Area: } 128 \pi \text{ cm}^2
Question 11
A survey of 100 students found that 60 students preferred Mathematics, 30 preferred Science, and 10 preferred both. What is the probability that a randomly selected student prefers either Mathematics or Science?
A. 0.65
B. 0.7
C. 0.75
D. 0.8
Question 12
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=20
C. \( x-2 \)^2+\( y-3 \)^2=24
D. \( x-2 \)^2+\( y-3 \)^2=28
Question 13
Let \( A = \begin{pmatrix} 1 & 2 \ 3 & 4 \end{pmatrix} \) and \( B = \begin{pmatrix} 2 & 1 \ 3 & 4 \end{pmatrix} \). Find the value of \( A^2 \).
A. \begin{pmatrix} 5 & 6 \ 9 & 12 \end{pmatrix}
B. \begin{pmatrix} 4 & 5 \ 7 & 10 \end{pmatrix}
C. \begin{pmatrix} 6 & 7 \ 10 & 14 \end{pmatrix}
D. \begin{pmatrix} 7 & 8 \ 11 & 16 \end{pmatrix}
Question 14
Find the derivative of the function ( f(x) = \frac{1}{x^2 + 1} ) u\sing the chain rule.
A. \frac{-2x}{\( x^2 + 1 \)^2}
B. \frac{2x}{\( x^2 + 1 \)^2}
C. \frac{-2x}{\( x^2 + 1 \)^2}
D. \frac{2x}{\( x^2 + 1 \)^2}
Question 15
Let ( f(x) = 2x^3 - 5x^2 + x - 1 ). Find the value of \( f\( -2 \ \) ).
A. -9
B. -7
C. -5
D. -3

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