POST UTME REDEEMERS UNIVERSITY 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 and the line y = 2x about the x-axis.
A. \boxed{\frac{16\pi}{15}}
B. \frac{32\pi}{15}
C. \frac{64\pi}{15}
D. \frac{128\pi}{15}
Question 2
Find the determinant of the matrix \begin{bmatrix} 2 & 1 & 3 \ 4 & 2 & 5 \ 6 & 3 & 7 \end{bmatrix}.
A. \boxed{0}
B. 2
C. 4
D. 6
Question 3
Find the value of \( \log_{10} \( x^2 \ \) ) given that \( \log_{10} x = 2 \).
A. 4
B. 6
C. 8
D. 10
Question 4
Find the volume of the frustum of a cone with height 6 cm, lower base radius 4 cm, and upper base radius 2 cm.
A. 48\pi cm^3
B. 64\pi cm^3
C. 80\pi cm^3
D. 96\pi cm^3
Question 5
Find the equation of the circle with center \( -2, 3 \) and radius 4.
A. \boxed{\( x + 2 \)^2 + \( y - 3 \)^2 = 16}
B. \( x - 2 \)^2 + \( y + 3 \)^2 = 16
C. \( x + 2 \)^2 + \( y + 3 \)^2 = 16
D. \( x - 2 \)^2 + \( y - 3 \)^2 = 16
Question 6
Differentiate the function \( f(x) = \frac{2x^2 + 3x - 1}{x^2 - 4} \) with respect to x.
A. \frac{4x^3 + 6x^2 - 2x - 3x^2 + 12}{\( x^2 - 4 \)^2}
B. \frac{4x^3 + 6x^2 - 2x + 3x^2 - 12}{\( x^2 - 4 \)^2}
C. \frac{4x^3 + 6x^2 - 2x - 3x^2 + 12}{\( x^2 - 4 \)^2}
D. \frac{4x^3 + 6x^2 - 2x + 3x^2 - 12}{\( x^2 - 4 \)^2}
Question 7
Find the mean of the following data set: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20.
A. 10
B. 12
C. 14
D. 16
Question 8
A sequence is defined by the formula an = 2n + 1. Find the sum of the first 5 terms of the sequence.
A. 15
B. 20
C. 25
D. 30
Question 9
Simplify the expression \sqrt[3]{64x^6y^3}.
A. 4x^2\sqrt[3]{y^3}
B. 4x^2y\sqrt[3]{y^3}
C. 4x^3y\sqrt[3]{y^3}
D. 4x^3y^2\sqrt[3]{y^3}
Question 10
Find the value of ( k ) such that the equation \( x^2 + kx + 6 = 0 \) has a discriminant of ( 12 ).
A. 2
B. 3
C. 4
D. 5
Question 11
Solve the quadratic equation \( x^2 + 4x + 4 = 0 \).
A. \( x = -2 \)
B. \( x = -1 \)
C. \( x = 0 \)
D. \( x = 1 \)
Question 12
Find the equation of the circle with center ( (2, 3) ) and radius ( 4 ).
A. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 16 )
B. \( x - 3 \ \)^2 + \( y - 2 \)^2 = 16 )
C. \( x - 4 \ \)^2 + \( y - 5 \)^2 = 16 )
D. \( x - 5 \ \)^2 + \( y - 4 \)^2 = 16 )
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. U\sing the concept of variation, find the ratio of the time taken for the return journey to the time taken for the outward journey.
A. 1:2
B. 2:1
C. 3:2
D. 4:3
Question 14
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( x > -\frac{5}{4} \) or \( x < \frac{3}{2} \)
B. \( x < -\frac{5}{4} \) or \( x > \frac{3}{2} \)
C. \( x > -\frac{5}{4} \) and \( x < \frac{3}{2} \)
D. \( x < -\frac{5}{4} \) and \( x > \frac{3}{2} \)
Question 15
Find the equation of the line pas\sing through the points (2,3) and (4,5).
A. y-3=\frac{2}{2}\( x-2 \)
B. y-3=\frac{2}{2}\( x-4 \)
C. y-5=\frac{2}{2}\( x-2 \)
D. y-5=\frac{2}{2}\( x-4 \)

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