POST UTME ACHIEVERS UNIVERSITY 2020 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the value of \( \frac{d^2}{dx^2} \( x^3 - 2x^2 + x - 1 \ \) ).
A. ( 6x )
B. ( 2x )
C. \( x^2 \)
D. ( x )
Question 2
A fair six-sided die is rolled. What is the probability that the number rolled is greater than 4?
A. 1/2
B. 1/3
C. 2/3
D. 1/6
Question 3
Find the area of the region bounded by the curves y = x^2 + 1, y = 0, and x = 2.
A. 9
B. 18
C. 27
D. 36
Question 4
Find the equation of the line pas\sing through the points (2, 3) and (4, 5).
A. \( y = x + 1 \)
B. \( y = x - 1 \)
C. \( y = x + 2 \)
D. \( y = x - 2 \)
Question 5
Find the volume of the solid generated by revolving the region bounded by the curves y = x^2, y = 0, and x = 2 about the x-axis.
A. 32\pi
B. 64\pi
C. 128\pi
D. 256\pi
Question 6
Find the value of ( k ) in the equation \( 2x^2 + 7x + k = 0 \) if the sum of the roots is \( -\frac{7}{2} \) and the product of the roots is \( -\frac{3}{4} \).
A. 1
B. 2
C. 3
D. 4
Question 7
Determine the volume of the frustum of a cone with height 6 cm, lower base radius 4 cm, and upper base radius 2 cm.
A. 24\pi cm^3
B. 48\pi cm^3
C. 96\pi cm^3
D. 192\pi cm^3
Question 8
Find the area of the region bounded by the curves y = x^2 + 1, y = 0, and x = 2.
A. 9
B. 18
C. 27
D. 36
Question 9
Find the mean deviation about the median of the data set: 2, 4, 6, 8, 10.
A. 2
B. 4
C. 6
D. 8
Question 10
Solve the inequality |x^2 - 4| < 5.
A. x < -1 or x > 4
B. x < 0 or x > 5
C. x < 1 or x > 6
D. x < 2 or x > 7
Question 11
Solve for x in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 10
B. 100
C. 1000
D. 10000
Question 12
Solve the quadratic equation \( x^2 + 4x + 4 = 0 \).
A. \( x = -2 \)
B. \( x = -1 \)
C. \( x = 0 \)
D. \( x = 1 \)
Question 13
Let $S = \{1, 2, 3, 4, 5, 6, 7, 8, 9\}$. Find the number of subsets of $S$ that contain exactly three elements.
A. 84
B. 85
C. 86
D. 87
Question 14
Find the volume of the solid generated by revolving the region bounded by the curves y = x^2, y = 0, and x = 2 about the x-axis.
A. 32\pi
B. 64\pi
C. 128\pi
D. 256\pi
Question 15
Solve the system of equations \( x + y = 4 \) and \( x - y = 2 \).
A. \( x = 3, y = 1 \)
B. \( x = 1, y = 3 \)
C. \( x = 2, y = 2 \)
D. \( x = 4, y = 0 \)

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