POST UTME FUTA 2023 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the value of \( \log_{10} \( 1000x \ \) - \log_{10} (10x) ).
A. ( 2 )
B. ( 3 )
C. ( 4 )
D. ( 5 )
Question 2
Find the determinant of the matrix:
A. 0
B. 1
C. 2
D. 3
Question 3
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 4
Solve the system of linear equations:
A. [1, 2, 3]
B. [2, 3, 4]
C. [3, 4, 5]
D. [4, 5, 6]
Question 5
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 6
Solve the inequality \( x^2 - 4x + 4 > 0 \) u\sing algebraic manipulation.
A. x < 0
B. x > 0
C. x < 2
D. x > 2
Question 7
A random variable X has a probability distribution given by the following table:
A. 0.5
B. 0.6
C. 0.7
D. 0.8
Question 8
Find the value of ( x ) in the equation \( 2^x = 16 \) u\sing \logarithms.
A. 2
B. 3
C. 4
D. 5
Question 9
Find the value of \( \sin \( 2x \ \) ) given that \( \cos x = \frac{3}{5} \) and \( \sin x = \frac{4}{5} \).
A. \( \frac{24}{25} \)
B. \( \frac{16}{25} \)
C. \( \frac{20}{25} \)
D. \( \frac{12}{25} \)
Question 10
Find the area under the curve \( y = x^3 \) from \( x = 0 \) to \( x = 2 \) u\sing integration.
A. 8
B. 16
C. 32
D. 64
Question 11
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 12
Solve for x in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 10
B. 100
C. 1000
D. 10000
Question 13
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 14
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 = 20 )
C. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 24 )
D. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 28 )
Question 15
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}

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