POST UTME FUTO 2020 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the volume of the frustum of a cone with radii 6 cm and 3 cm, and height 8 cm.
A. 120\pi
B. 240\pi
C. 360\pi
D. 480\pi
Question 2
A histogram of exam scores has a mean of 60 and a s\tandard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score will be between 50 and 70?
A. 0.25
B. 0.5
C. 0.75
D. 0.9
Question 3
A box contains 12 red balls and 8 blue balls. If a ball is drawn at random, what is the probability that it is blue?
A. 1/2
B. 2/3
C. 1/3
D. 3/4
Question 4
A sequence is defined as \( a_n = 2n + 1 \). Find the sum of the first 5 terms of the sequence.
A. 15
B. 20
C. 25
D. 30
Question 5
Solve the inequality \( \frac{x^2 - 4x + 3}{x^2 - 4x + 2} > 0 \).
A. \( -infty, 1 \) cup (2, infty)
B. \( -infty, 2 \) cup (3, infty)
C. \( -infty, 1 \) cup (2, 3)
D. (1, 2) cup (3, infty)
Question 6
Find the volume of the frustum of a cone with height 10cm, lower base radius 4cm, and upper base radius 6cm. The frustum is cut off by a plane parallel to the base.
A. 100\pi cm^3
B. 120\pi cm^3
C. 150\pi cm^3
D. 180\pi cm^3
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 = 25
C. \( x - 2 \)^2 + \( y - 3 \)^2 = 36
D. \( x - 2 \)^2 + \( y - 3 \)^2 = 49
Question 8
A population of 1000 bacteria grows according to the equation P(t) = 500e^(0.05t), where P(t) is the population at time t. Find the rate of change of the population with respect to time when the population is 750.
A. 0.05
B. 0.1
C. 0.15
D. 0.2
Question 9
In a circle with center O and radius 6, a chord AB is drawn such that AB = 8. Find the dis\tance from O to the midpoint M of AB.
A. 4
B. 6
C. 8
D. 10
Question 10
Evaluate the definite integral \[ \int_0^1 x^2 \sin x \, dx \].
A. -1
B. 0
C. 1
D. 2
Question 11
Solve the equation \[ 2x^2 + 5x - 3 = 0 \] u\sing the quadratic formula.
A. -1/2
B. 1/2
C. -3/2
D. 3/2
Question 12
Find the derivative of the function ( f(x) = \frac{1}{\sqrt{x^2 + 1}} ) u\sing the chain rule.
A. f'(x) = \frac{-x}{\( x^2 + 1 \)^{3/2}}
B. f'(x) = \frac{x}{\( x^2 + 1 \)^{3/2}}
C. f'(x) = \frac{1}{\( x^2 + 1 \)^{3/2}}
D. f'(x) = \frac{-1}{\( x^2 + 1 \)^{3/2}}
Question 13
Find the vector projection of vector \( \vec{a} = \begin{bmatrix} 2 \\ 3 \end{bmatrix} \) onto vector \( \vec{b} = \begin{bmatrix} 4 \\ 5 \end{bmatrix} \)
A. \begin{bmatrix} 8/17 \\ 10/17 \end{bmatrix}
B. \begin{bmatrix} 10/17 \\ 8/17 \end{bmatrix}
C. \begin{bmatrix} 12/17 \\ 15/17 \end{bmatrix}
D. \begin{bmatrix} 15/17 \\ 12/17 \end{bmatrix}
Question 14
Find the mean of the data set: 2, 4, 6, 8, 10.
A. 6
B. 8
C. 10
D. 12
Question 15
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 = 4 )
D. \( x-2 \ \)^2 + \( y+3 \)^2 = 4 )

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