POST UTME UNILAG 2017 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A die is rolled twice. What is the probability that the sum of the two numbers is 7?
A. \( \frac{1}{6} \)
B. \( \frac{1}{12} \)
C. \( \frac{1}{36} \)
D. \( \frac{1}{24} \)
Question 2
Find the equation of the circle with center \( -2, 3 \ \) ) and radius 4. Express your answer in the s\tandard form \( x - h \ \)^2 + \( y - k \)^2 = r^2 ).
A. \( x + 2 \ \)^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 3
A water \tank is in the shape of a cone with height 10m and radius 5m. If the water level is at 4m, what is the volume of the water in the \tank?
A. \( \frac{1}{3} pi \( 5^2 \ \) \( 10 - 4 \) )
B. \( \frac{1}{3} pi \( 5^2 \ \) \( 10 + 4 \) )
C. \( \frac{1}{3} pi \( 5^2 \ \) \( 10 \times 4 \) )
D. \( \frac{1}{3} pi \( 5^2 \ \) \( 10 - 4 \)^2 )
Question 4
Find the volume of the frustum of a cone with height 8cm, lower base radius 4cm, and upper base radius 2cm. Given that the slant height is 6cm. Express your answer in terms of π.
A. \( \frac{1}{3} pi \( 4^2 + 2^2 + 4 \times 4 \times 2 \ \) )
B. \( \frac{1}{3} pi \( 4^2 + 2^2 - 4 \times 4 \times 2 \ \) )
C. \( \frac{1}{3} pi \( 4^2 + 2^2 + 4 \times 4 \times 6 \ \) )
D. \( \frac{1}{3} pi \( 4^2 + 2^2 - 4 \times 4 \times 6 \ \) )
Question 5
Solve the inequality \( 2x^2 + 5x - 3 > 0 \). Express your answer in interval notation.
A. \( -infty, -\frac{3}{2} \ \) cup \( \frac{3}{2}, infty \) )
B. \( -infty, \frac{3}{2} \ \) cup \( infty, -\frac{3}{2} \) )
C. \( -infty, -\frac{3}{2} \ \) cup \( \frac{3}{2}, infty \) )
D. \( -infty, \frac{3}{2} \ \) cup \( infty, -\frac{3}{2} \) )

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