POST UTME FUTA 2022 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( -∞, -1 \) ∪ (3, ∞)
B. \( -∞, -3 \) ∪ (1, ∞)
C. \( -∞, 1 \) ∪ (3, ∞)
D. \( -∞, -3 \) ∪ (1, ∞)
Question 2
Find the volume of the solid formed by revolving the region bounded by the parabola \[ y = x^2 \] and the line \[ y = 2x \] about the x-axis.
A. \[ V = \frac{16\pi}{3} \]
B. \[ V = \frac{32\pi}{3} \]
C. \[ V = \frac{64\pi}{3} \]
D. \[ V = \frac{128\pi}{3} \]
Question 3
A company produces two products, A and B. The profit from the sale of product A is ₦100 per unit, and the profit from the sale of product B is ₦120 per unit. If the company produces 200 units of product A and 300 units of product B, what is the total profit?
A. ₦58,000
B. ₦58,400
C. ₦58,800
D. ₦59,200
Question 4
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).
A. 40
B. 60
C. 80
D. 100
Question 5
A circle with center ( C(3, 4) ) and radius \( r = 5 \) is drawn in the coordinate plane. Find the equation of the line pas\sing through the point ( P(6, 1) ) and perp\endicular to the radius of the circle at point ( P ).
A. y = -\frac{1}{5}x + \frac{31}{5}
B. y = \frac{1}{5}x + \frac{21}{5}
C. y = -\frac{1}{5}x + \frac{21}{5}
D. y = \frac{1}{5}x + \frac{31}{5}
Question 6
A sequence is defined as: \(a_n = \frac{2n + 1}{n^2 + 1}\). Find the sum of the first 5 terms of the sequence.
A. 1.2
B. 1.5
C. 1.8
D. 2.1
Question 7
A set of 5 numbers has a mean of 10 and a median of 8. If the largest number is 15, find the sum of the remaining 3 numbers.
A. 40
B. 50
C. 60
D. 70
Question 8
Find the area under the curve \( y = x^2 \) from \( x = 0 \) to \( x = 2 \).
A. 4
B. 6
C. 8
D. 10
Question 9
A set of 10 numbers has a mean of 20. If two more numbers are added to the set, the mean becomes 22. What is the sum of the two additional numbers?
A. 40
B. 60
C. 80
D. 100
Question 10
Solve the system of equations: \( egin{cases} x + y = 6 \ 2x - 3y = - 3 \end{cases} \).
A. x = 3, y = 3
B. x = 2, y = 4
C. x = 4, y = 2
D. x = 5, y = 1
Question 11
Find the area of the triangle with vertices (0, 0), (3, 0), and (0, 2).
A. \boxed{3}
B. 4
C. 5
D. 6
Question 12
Determine the value of x in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 10
B. 100
C. 1000
D. 10000
Question 13
Let ( f(x) = \frac{x^2 - 4}{x - 2} ). Find the derivative of ( f(x) ) u\sing the quotient rule.
A. f'(x) = \frac{2x - 4}{\( x - 2 \)^2}
B. f'(x) = \frac{2x + 4}{\( x - 2 \)^2}
C. f'(x) = \frac{2x^2 - 8}{\( x - 2 \)^2}
D. f'(x) = \frac{2x^2 + 8}{\( x - 2 \)^2}
Question 14
Find the value of \( \log_{10} \( x^2 \ \) ) given that \( \log_{10} x = 2 \).
A. 4
B. 6
C. 8
D. 10
Question 15
Solve the equation \( \sin^2 x + \cos^2 x = 1 \).
A. x = 0
B. x = π/2
C. x = π
D. x = 2π

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