POST UTME REDEEMERS UNIVERSITY 2017 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
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 2
Find the area under the curve y = x^2 + 2x - 3 from x = 0 to x = 3.
A. 27
B. 30
C. 33
D. 36
Question 3
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 4
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( x < -1 \) or \( x > \frac{3}{2} \)
B. \( x < -\frac{3}{2} \) or \( x > 1 \)
C. \( x < -\frac{1}{2} \) or \( x > 2 \)
D. \( x < 1 \) or \( x > 2 \)
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
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}\( x-4 \)
Question 7
Solve the inequality 2x^2 + 5x - 3 > 0.
A. x < -1 or x > 3/2
B. x < 1 or x > 3
C. x < -1 or x < 3/2
D. x < 1 or x > 3/2
Question 8
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 9
Find the surface area of the sphere with radius 5 cm.
A. 50\pi cm^2
B. 100\pi cm^2
C. 150\pi cm^2
D. 200\pi cm^2
Question 10
A die is rolled twice. Find the probability that the sum of the numbers on the two dice is 7.
A. \frac{1}{6}
B. \frac{1}{12}
C. \frac{1}{2}
D. \frac{5}{6}
Question 11
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 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
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 14
Find the value of x in the equation x^3 - 6x^2 + 11x - 6 = 0.
A. 1
B. 2
C. 3
D. 4
Question 15
Solve the equation \tan^2 x + 2 \tan x - 6 = 0 for x in the interval [0, \pi/2].
A. \boxed{x = \arc\tan(3)}
B. x = \arc\tan\( -2 \)
C. x = \arc\tan(2)
D. x = \arc\tan\( -3 \)

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