POST UTME FUTO 2020 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve for x in the equation: \( 2x^2 + 5x - 3 = 0 \)
A. -1
B. 1
C. 3
D. -3
Question 2
Let X be a random variable with probability density function (pdf) given by f(x) = \( egin{cases} 2x & 0 leq x leq 1 \ 0 & \text{otherwise} \end{cases} \). Find the probability that X takes a value greater than 0.5.
A. 0.5
B. 0.75
C. 0.875
D. 0.9375
Question 3
Find the area under the curve y = \( \sqrt{x} \) from x = 0 to x = 4.
A. 4
B. 8
C. 16
D. 32
Question 4
Find the value of x in the equation \( 2x^2 + 5x - 3 = 0 \).
A. 1
B. -1
C. -2
D. 2
Question 5
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 6
Let A = \( egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} \) and B = \( egin{bmatrix} 5 & 6 \ 7 & 8 \end{bmatrix} \). Find the product AB.
A. \( egin{bmatrix} 19 & 22 \ 43 & 50 \end{bmatrix} \)
B. \( egin{bmatrix} 23 & 26 \ 51 & 58 \end{bmatrix} \)
C. \( egin{bmatrix} 21 & 24 \ 45 & 52 \end{bmatrix} \)
D. \( egin{bmatrix} 25 & 28 \ 49 & 56 \end{bmatrix} \)
Question 7
Find the area under the curve \[ y = \sin x \] from \[ x = 0 \] to \[ x = \pi/2 \].
A. 1
B. 2
C. 3
D. 4
Question 8
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 9
A set of numbers is defined as \( S = \{ 1, 2, 3, 4, 5 \} \ \). Find the number of subsets of S.
A. 5
B. 10
C. 15
D. 20
Question 10
A circle with center O and radius 4 is inscribed in a square with side length 8. Find the area of the shaded region.
A. 16
B. 32
C. 64
D. 128
Question 11
A circle has a radius of 4cm. Find the area of the circle.
A. 16\pi cm^2
B. 32\pi cm^2
C. 64\pi cm^2
D. 128\pi cm^2
Question 12
Solve the equation \frac{1}{x+1} + \frac{1}{x-2} = \frac{3}{2}.
A. x = -1
B. x = 2
C. x = -2
D. x = 4
Question 13
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 14
A function f(x) is defined as f(x) = 2x^2 + 3x - 1. Find the derivative of f(x) u\sing the power rule.
A. 4x + 3
B. 2x^2 + 3
C. 4x + 1
D. 2x^2 - 1
Question 15
Find the mean of the data set: 2, 4, 6, 8, 10.
A. 6
B. 8
C. 10
D. 12

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