POST UTME UNILORIN 2020 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve for x in the equation \( \sin^2 x + \cos^2 x = 1 \).
A. \( x = \frac{pi}{4} \)
B. \( x = \frac{pi}{2} \)
C. \( x = \frac{3pi}{4} \)
D. \( x = \frac{pi}{6} \)
Question 2
Solve the quadratic equation \( x^2 + 4x + 4 = 0 \).
A. 0
B. -2
C. 2
D. -4
Question 3
Find the derivative of the function ( f(x) = 3x^2 + 2x - 5 ).
A. 6x + 2
B. 6x - 2
C. 3x + 2
D. 3x - 2
Question 4
A company produces two products, A and B. The profit on product A is ₦100 per unit and the profit on product B is ₦150 per unit. If the company produces 200 units of product A and 300 units of product B, what is the total profit?
A. ₦65,000
B. ₦70,000
C. ₦75,000
D. ₦80,000
Question 5
Find the area of the triangle with vertices ( (0, 0) ), ( (3, 0) ), and ( (0, 2) ).
A. 3
B. 6
C. 9
D. 12
Question 6
Find the surface area of the sphere with radius 5 cm.
A. ( 100pi )
B. ( 50pi )
C. ( 25pi )
D. ( 10pi )
Question 7
Find the equation of the circle with center \( -2, 3 \) and radius 4.
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 8
Solve the inequality \( 2^x + 3^x \ge 5^x \).
A. \( x \le 1 \)
B. \( x \ge 1 \)
C. \( x \le 2 \)
D. \( x \ge 2 \)
Question 9
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).
A. 40
B. 50
C. 60
D. 70
Question 10
Find the derivative of the function ( f(x) = x^2 \sin x ) u\sing the product rule.
A. \( 2x \sin x + x^2 \cos x \)
B. \( 2x \cos x - x^2 \sin x \)
C. \( 2x \sin x - x^2 \cos x \)
D. \( 2x \cos x + x^2 \sin x \)
Question 11
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( -∞, -1 \) ∪ (3, ∞)
B. \( -∞, -3 \) ∪ (1, ∞)
C. \( -∞, 1 \) ∪ (3, ∞)
D. \( -∞, -3 \) ∪ (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. \( x-2 \ \)^2 + \( y-3 \)^2 = 4 )
C. \( x-3 \ \)^2 + \( y-2 \)^2 = 16 )
D. \( x-3 \ \)^2 + \( y-2 \)^2 = 4 )
Question 13
A histogram of exam scores has a mean of 60 and a s\tandard deviation of 10. If the scores are normally distributed, find the probability that a randomly selected score is greater than 70.
A. \frac{1}{4}
B. \frac{1}{2}
C. \frac{3}{4}
D. \frac{2}{3}
Question 14
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. 24π cm^3
B. 48π cm^3
C. 96π cm^3
D. 192π cm^3
Question 15
Find the volume of the frustum of a cone with height 10 cm, lower base radius 4 cm, and upper base radius 2 cm.
A. \( \frac{1}{3} pi \( 4^2 + 2^2 + 4 cdot 2 cdot 4 \ \) )
B. \( \frac{1}{3} pi \( 4^2 + 2^2 - 4 cdot 2 cdot 4 \ \) )
C. \( \frac{1}{3} pi \( 4^2 + 2^2 + 2 cdot 4 cdot 2 \ \) )
D. \( \frac{1}{3} pi \( 4^2 + 2^2 - 2 cdot 4 cdot 2 \ \) )

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