POST UTME FUTA 2023 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve the inequality \( x^2 + 4x - 5 > 0 \).
A. \( -∞, -5 \) ∪ (1, ∞)
B. \( -∞, -5 \) ∪ (1, ∞)
C. \( -∞, -5 \) ∪ \( -1, ∞ \)
D. \( -∞, -5 \) ∪ (1, ∞)
Question 2
Solve the system of equations \begin{align*} x + y &= 4 \ 2x - y &= 3 \end{align*}.
A. \left\( x, y \right \) = \left\( 2, 2 \right \)
B. \left\( x, y \right \) = \left\( 1, 3 \right \)
C. \left\( x, y \right \) = \left\( 3, 1 \right \)
D. \left\( x, y \right \) = \left\( 4, 0 \right \)
Question 3
Find the value of \( \log_{10} \( 1000x \ \) - \log_{10} (10x) ).
A. ( 2 )
B. ( 3 )
C. ( 4 )
D. ( 5 )
Question 4
Solve for x in the equation \( \sin^2 x + \cos^2 x = 1 \) u\sing the identity \( \sin^2 x + \cos^2 x = 1 \).
A. x = \frac{\pi}{4}
B. x = \\frac{3\\pi}{4}
C. x = \\frac{5\\pi}{4}
D. x = \\frac{7\\pi}{4}
Question 5
A bag contains 5 red marbles, 4 blue marbles, and 3 green marbles. If a marble is drawn at random, what is the probability that it is blue?
A. \frac{1}{3}
B. \frac{1}{4}
C. \frac{1}{5}
D. \frac{1}{6}
Question 6
Solve for x in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 10
B. 100
C. 1000
D. 10000
Question 7
Find the determinant of the matrix \begin{bmatrix} 2 & 1 & 3 \ 4 & 2 & 1 \ 3 & 1 & 2 \end{bmatrix}.
A. 10
B. 12
C. 15
D. 20
Question 8
A rec\tangular box has dimensions 3 cm, 4 cm, and 5 cm. Find the volume of the box.
A. 60 cm^3
B. 80 cm^3
C. 100 cm^3
D. 120 cm^3
Question 9
Find the derivative of the function ( f(x) = \frac{x^2}{x^2 + 1} ) u\sing the quotient rule.
A. \( \frac{2x\( x^2 + 1 \ \) - 2x^3}{\( x^2 + 1 \)^2} )
B. \( \frac{2x\( x^2 + 1 \ \) - 2x^3}{\( x^2 + 1 \)^2} )
C. \( \frac{2x^2 - 2x^3}{\( x^2 + 1 \ \)^2} )
D. \( \frac{2x^2 + 2x^3}{\( x^2 + 1 \ \)^2} )
Question 10
Solve the equation \( \sin 2x = \frac{1}{2} \).
A. \( x = \frac{pi}{12} + \frac{k pi}{2} \)
B. \( x = \frac{pi}{12} + \frac{k pi}{2} \)
C. \( x = \frac{pi}{6} + \frac{k pi}{2} \)
D. \( x = \frac{pi}{6} + \frac{k pi}{2} \)
Question 11
Solve the system of linear equations:
A. [1, 2, 3]
B. [2, 3, 4]
C. [3, 4, 5]
D. [4, 5, 6]
Question 12
Solve the equation \tan x = \sqrt{3} \sin x.
A. \frac{\pi}{4}
B. \frac{\pi}{3}
C. \frac{\pi}{2}
D. \frac{\pi}{6}
Question 13
A polynomial function f(x) has zeros at x = -2, x = 1, and x = 3. Write the function in factored form.
A. f(x) = \( x + 2 \)\( x - 1 \)\( x - 3 \)
B. f(x) = \( x - 2 \)\( x + 1 \)\( x - 3 \)
C. f(x) = \( x + 2 \)\( x + 1 \)\( x - 3 \)
D. f(x) = \( x - 2 \)\( x - 1 \)\( x + 3 \)
Question 14
A particle moves in a straight line with an initial velocity of 5 m/s. If it decelerates uniformly at a rate of 2 m/s^2, find its velocity after 4 seconds.
A. 3 m/s
B. 4 m/s
C. 5 m/s
D. 6 m/s
Question 15
Find the determinant of the matrix:
A. 0
B. 1
C. 2
D. 3

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