POST UTME ABU 2017 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the volume of the solid formed by revolving the region bounded by the parabola y = x^2, the x-axis, and the line x = 2 about the x-axis.
A. 32\pi
B. 64\pi
C. 128\pi
D. 256\pi
Question 2
Determine the value of y in the equation \( y = 2x^2 + 5x - 3 \) when x = -1.
A. -1
B. 0
C. 1
D. 2
Question 3
A circle has a radius of 4 cm. If the area of the circle is 50.24 cm^2, what is the circumference of the circle?
A. 12.56 cm
B. 25.12 cm
C. 50.24 cm
D. 100.48 cm
Question 4
Solve the system of equations \( x + y = 2 \) and \( xy = 1 \).
A. (1, 1)
B. \( 1, -1 \)
C. \( -1, 1 \)
D. \( -1, -1 \)
Question 5
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{1}{\( x^2 + 1 \)^2}
D. \frac{1}{\( x^2 + 1 \)^2}
Question 6
Find the sum of the first 5 terms of the geometric progression 2, 6, 18, ...
A. 126
B. 128
C. 130
D. 132
Question 7
A water \tank can hold 2000 liters of water. If 3/4 of the \tank is already filled, how many more liters of water can be added?
A. 1000 liters
B. 1200 liters
C. 1500 liters
D. 2000 liters
Question 8
A set A contains the elements {1, 2, 3, 4, 5}. Find the number of subsets of A.
A. 2^5
B. 5^2
C. 10
D. 20
Question 9
Find the value of x in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 10
B. 100
C. 1000
D. 10000
Question 10
Determine the volume of the frustum of a cone with a height of 10 cm, a lower base radius of 4 cm, and an upper base radius of 6 cm.
A. 200π cm^3
B. 300π cm^3
C. 400π cm^3
D. 500π cm^3
Question 11
Find the sum of the first 10 terms of the geometric progression 2, 6, 18, ...
A. 1023
B. 2046
C. 3079
D. 4092
Question 12
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( -∞, -1 \) ∪ (3, ∞)
B. \( -∞, -3 \) ∪ (1, ∞)
C. \( -∞, 1 \) ∪ (3, ∞)
D. \( -∞, -3 \) ∪ (1, ∞)
Question 13
A car travels from city A to city B at an average speed of 60 km/h and returns at an average speed of 40 km/h. What is the average speed of the car for the entire trip?
A. 48 km/h
B. 50 km/h
C. 52 km/h
D. 54 km/h
Question 14
Solve for x in the equation \( x^2 + 4x + 4 = 0 \)
A. -2
B. 0
C. 2
D. 4
Question 15
Find the volume of the solid formed by revolving the region bounded by the curve \( y = \frac{1}{2}x^2 \) and the line \( x = 2 \) about the x-axis.
A. 8π
B. 16π
C. 32π
D. 64π

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