POST UTME PAN-ATLANTIC UNIVERSITY 2024 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the area of the region bounded by the curves $y = x^2$ and $y = 2x$.
A. 4/3
B. 2/3
C. 1/3
D. 1/2
Question 2
Solve the system of equations $x + y = 2$ and $xy = 1$.
A. (1, 1)
B. \( 1, -1 \)
C. \( -1, 1 \)
D. \( -1, -1 \)
Question 3
Find the area under the curve \( y = x^2 \) from \( x = 0 \) to \( x = 4 \).
A. \frac{64}{3}
B. \frac{32}{3}
C. \frac{16}{3}
D. \frac{8}{3}
Question 4
Solve for ( x ) in the equation \( \sin^2 x + \cos^2 x = 1 \).
A. \( x = \frac{pi}{2} \)
B. \( x = \frac{pi}{4} \)
C. \( x = \frac{3pi}{4} \)
D. \( x = \frac{5pi}{4} \)
Question 5
A rec\tangular prism has a length of 5 cm, a width of 3 cm, and a height of 2 cm. Find the surface area of the prism.
A. 2\( 5 cdot 3 + 3 cdot 2 + 5 cdot 2 \)
B. 2\( 5 cdot 3 + 3 cdot 2 + 5 cdot 2 \) + 2\( 5 cdot 2 + 3 cdot 2 + 5 cdot 3 \)
C. 2\( 5 cdot 3 + 3 cdot 2 + 5 cdot 2 \) - 2\( 5 cdot 2 + 3 cdot 2 + 5 cdot 3 \)
D. 2\( 5 cdot 3 + 3 cdot 2 + 5 cdot 2 \) + 2\( 5 cdot 2 + 3 cdot 2 + 5 cdot 3 \) + 2\( 5 cdot 2 + 3 cdot 2 + 5 cdot 3 \)
Question 6
Find the value of $\int_0^1 \( 2x^3 - 5x^2 + 3x - 1 \) dx$.
A. 1
B. 2
C. 3
D. 4
Question 7
Find the value of \( \log_{10} \( 1000 \ \) ).
A. ( 3 )
B. ( 4 )
C. ( 5 )
D. ( 6 )
Question 8
A random sample of 25 students from a university had a mean height of 175.5 cm with a s\tandard deviation of 5.2 cm. If the population s\tandard deviation is unknown, calculate the 95% confidence interval for the mean height of all students in the university.
A. 169.3 cm, 181.7 cm
B. 170.5 cm, 180.5 cm
C. 171.5 cm, 179.5 cm
D. 172.5 cm, 178.5 cm
Question 9
A circle has a radius of 4 cm. Find the area of the circle.
A. \pi r^2
B. \pi r^2 + \pi r^2
C. \pi r^2 - \pi r^2
D. \pi r^2 + \pi r^2 + \pi r^2
Question 10
A set ( A ) contains the elements ( {1, 2, 3, 4, 5} ). Find the number of subsets of ( A ) that contain exactly 3 elements.
A. 10
B. 15
C. 20
D. 25
Question 11
Solve the system of equations: \( \begin{cases} x + y = 4 \ x - 2y = -3 \end{cases} \).
A. \begin{cases} x = 7 \ y = -3 \end{cases}
B. \begin{cases} x = 1 \ y = 3 \end{cases}
C. \begin{cases} x = 3 \ y = 1 \end{cases}
D. \begin{cases} x = -1 \ y = 5 \end{cases}
Question 12
Find the derivative of the function ( f(x) = \sin^2 x ) u\sing the chain rule.
A. f'(x) = 2 \sin x \cos x
B. f'(x) = 2 \sin x \cos x + 2 \cos x \sin x
C. f'(x) = 2 \sin x \cos x - 2 \cos x \sin x
D. f'(x) = 2 \sin x \cos x + 2 \cos x \sin x
Question 13
A random variable ( X ) has a probability distribution given by \( P\( X = x \ \) = \frac{1}{2} ) for \( x = 1, 2, 3 \). Find the expected value of ( X ).
A. ( 2 )
B. ( 3 )
C. ( 4 )
D. ( 5 )
Question 14
Solve the inequality $|x - 2| > 3$.
A. \( -∞, -1 \) ∪ (4, ∞)
B. \( -∞, 1 \) ∪ (4, ∞)
C. \( -∞, -1 \) ∪ (1, ∞)
D. \( -∞, 4 \) ∪ (1, ∞)
Question 15
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).
A. 40
B. 50
C. 60
D. 70

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