POST UTME FUTO 2023 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the volume of the frustum of a cone with height 8 cm, lower base radius 4 cm, and upper base radius 2 cm.
A. 32\pi cm^3
B. 64\pi cm^3
C. 128\pi cm^3
D. 256\pi cm^3
Question 2
Solve the trigonometric equation \( \sin^2 x + \cos^2 x = 1 \).
A. x = 0
B. x = 90
C. x = 180
D. x = 270
Question 3
Solve the inequality 2x^2 + 5x - 3 > 0.
A. \( -∞, -1 \) ∪ (3, ∞)
B. \( -∞, 1 \) ∪ (3, ∞)
C. \( -∞, -3 \) ∪ (1, ∞)
D. \( -∞, 3 \) ∪ (1, ∞)
Question 4
Find the area under the curve \( y = x^2 \) from \( x = 0 \) to \( x = 2 \).
A. \( \frac{8}{3} \)
B. \( \frac{16}{3} \)
C. \( \frac{32}{3} \)
D. \( \frac{64}{3} \)
Question 5
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 6
Find the mean of the data set: 2, 4, 6, 8, 10.
A. 6
B. 7
C. 8
D. 9
Question 7
Solve the equation \sin(x) + \cos(x) = 1.
A. \frac{π}{4}
B. \frac{π}{3}
C. \frac{π}{2}
D. \frac{π}{6}
Question 8
A histogram is constructed with the following data: [ 2, 4, 6, 8, 10, 12, 14, 16, 18, 20 ]. If the width of each bar is 2, what is the area of the histogram?
A. 100
B. 200
C. 50
D. 150
Question 9
Find the derivative of the function ( f(x) = \frac{1}{2x^2 + 3x - 1} ) u\sing the quotient rule.
A. f'(x) = \frac{-4x + 3}{\( 2x^2 + 3x - 1 \)^2}
B. f'(x) = \frac{4x + 3}{\( 2x^2 + 3x - 1 \)^2}
C. f'(x) = \frac{2x^2 + 3x - 1}{\( 2x^2 + 3x - 1 \)^2}
D. f'(x) = \frac{-2x^2 - 3x + 1}{\( 2x^2 + 3x - 1 \)^2}
Question 10
Find the area of the region bounded by the curves $y=x^2+1$ and $y=2x+1$.
A. \frac{3}{2}
B. \frac{5}{2}
C. \frac{7}{2}
D. \frac{9}{2}
Question 11
Solve the inequality \( 2x^2 + 5x - 3 > 0 \ \).
A. x < -1
B. x > -1
C. x < 3
D. x > 3
Question 12
Find the value of x in the equation 2^x + 5^x = 10^x.
A. 2
B. 3
C. 4
D. 5
Question 13
Find the equation of the line pas\sing through the points $\( -2,3 \)$ and $(1,2)$.
A. y=-x+5
B. y=x-1
C. y=-x-1
D. y=x+1
Question 14
Solve the inequality x^2 - 4x - 5 > 0.
A. \( -∞, -1 \) ∪ (5, ∞)
B. \( -∞, 1 \) ∪ (5, ∞)
C. \( -∞, -5 \) ∪ (1, ∞)
D. \( -∞, 5 \) ∪ (1, ∞)
Question 15
Solve the inequality \( x^2 - 4x + 3 > 0 \).
A. \( -∞, 1 \) ∪ (3, ∞)
B. \( -∞, 3 \) ∪ (1, ∞)
C. \( -∞, 1 \) ∪ (3, ∞)
D. \( -∞, 3 \) ∪ (1, ∞)

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