POST UTME PAN-ATLANTIC UNIVERSITY 2019 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve the system of equations: \( x + y = 2 \) and \( xy = 1 \).
A. x = 1, y = 1
B. x = 2, y = 0
C. x = 0, y = 2
D. x = -1, y = -1
Question 2
The volume of a rec\tangular prism is given by \( V = lwh \). If the length, width, and height of the prism are in the ratio 2:3:4, and the volume is 120 cubic units, find the length of the prism.
A. 4
B. 6
C. 8
D. 10
Question 3
Find the derivative of the function ( f(x) = \frac{1}{x^2 + 1} ) with respect to ( x ).
A. \frac{-2x}{\( x^2 + 1 \)^2}
B. \frac{2x}{\( x^2 + 1 \)^2}
C. \frac{-2}{\( x^2 + 1 \)^2}
D. \frac{2}{\( x^2 + 1 \)^2}
Question 4
Find the area under the curve of ( f(x) = 2x^2 + 3x - 1 ) from \( x = 0 \) to \( x = 2 \).
A. 13
B. 14
C. 15
D. 16
Question 5
A circle has a radius of 4 cm. Find the area of the circle.
A. 50
B. 100
C. 200
D. 400
Question 6
Solve the equation \( x^2 + 4x + 4 = 0 \) u\sing the quadratic formula.
A. -2
B. -1
C. 0
D. 1
Question 7
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 6.1 cm, calculate the 95% confidence interval for the mean height of the university students.
A. 168.3 cm to 182.7 cm
B. 170.1 cm to 180.9 cm
C. 172.9 cm to 178.1 cm
D. 174.7 cm to 176.3 cm
Question 8
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 is greater than 0.5.
A. \( \frac{1}{2} \)
B. \( \frac{1}{4} \)
C. \( \frac{3}{4} \)
D. \( \frac{7}{8} \)
Question 9
Find the area under the curve [ y = \frac{1}{x} ] from [ x = 1 ] to [ x = 2 ].
A. 0.5
B. 1
C. 1.5
D. 2
Question 10
Solve the equation [ \sin^2 x + \cos^2 x = 1 ] for [ x ].
A. 0
B. \frac{\pi}{2}
C. \frac{\pi}{4}
D. \frac{\pi}{6}
Question 11
A histogram of exam scores has a mean of 75 and a s\tandard deviation of 10. If 80% of the scores fall below 85, what is the value of the z-score corresponding to 85?
A. 0.5
B. 1
C. 1.25
D. 1.5
Question 12
Solve the equation \( x^2 + 4x + 4 = 0 \).
A. \[ x = -2 \]
B. \[ x = -1 \]
C. \[ x = 0 \]
D. \[ x = 1 \]
Question 13
A company produces two products, A and B. The profit from the production of product A is ₦120 per unit, while the profit from the production of product B is ₦180 per unit. If the company produces 200 units of product A and 300 units of product B, what is the total profit?
A. ₦48,000
B. ₦54,000
C. ₦60,000
D. ₦66,000
Question 14
Find the determinant of the matrix [ egin{pmatrix} 2 & 3 & 1 \ 4 & 5 & 2 \ 1 & 2 & 3 \end{pmatrix} ].
A. -1
B. 1
C. 2
D. 3
Question 15
Find the surface area of the solid formed by rotating the region bounded by \( y = x^2 \) and \( y = x \) about the x-axis.
A. \frac{\pi}{3}
B. \frac{\pi}{6}
C. \frac{\pi}{4}
D. \frac{\pi}{2}

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