POST UTME UI 2019 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve the inequality \( \frac{x^2 - 4x + 3}{x^2 - 4x + 4} > 0 \).
A. \( -∞, 1 \) ∪ (3, ∞)
B. \( -∞, 2 \) ∪ (3, ∞)
C. \( -∞, 1 \) ∪ (2, ∞)
D. \( -∞, 3 \) ∪ (4, ∞)
Question 2
Find the sum of the infinite geometric series \( sum_{n=1}^{infty} \frac{1}{2^n} \).
A. 1
B. 2
C. 3
D. 4
Question 3
The mean of a set of 5 numbers is 12. If one of the numbers is 15, find the sum of the remaining 4 numbers.
A. 45
B. 50
C. 55
D. 60
Question 4
Find the volume of the solid formed by revolving the region bounded by $y = \sqrt{x}$, $y = 0$, and $x = 4$ about the $x$-axis.
A. 128\pi
B. 256\pi
C. 512\pi
D. 1024\pi
Question 5
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).
A. 64
B. 80
C. 96
D. 112
Question 6
Solve the inequality $\frac{1}{x^2-4x+3}\geq 0$.
A. $x\in \( -\infty, 1)\cup \( 3, \infty \ \)$
B. $x\in \( -\infty, 1)\cup \( 1, 3)\cup (3, \infty \ \)$
C. $x\in \( -\infty, 1)\cup \( 3, \infty \ \)$
D. $x\in \( -\infty, 3)\cup \( 3, \infty \ \)$
Question 7
A snail is at the bottom of a 20-foot well. Each day, it climbs up 3 feet, but at night, it slips back 2 feet. How many days will it take for the snail to reach the top of the well?
A. 18
B. 20
C. 22
D. 24
Question 8
Find the surface area of the solid formed by revolving the region bounded by $y = x^2$ and $y = 0$ about the $x$-axis.
A. $\frac{4\pi}{3}$
B. $\frac{8\pi}{3}$
C. $\frac{16\pi}{3}$
D. $\frac{32\pi}{3}$
Question 9
Find the derivative of $f(x) = \frac{x^2}{x^2+1}$ u\sing the quotient rule.
A. $\frac{2x\( x^2+1 \)-2x^2x}{\( x^2+1 \)^2}$
B. $\frac{2x\( x^2+1 \)+2x^2x}{\( x^2+1 \)^2}$
C. $\frac{2x\( x^2+1 \)-2x^2x}{\( x^2+1 \)^2}$
D. $\frac{2x\( x^2+1 \)+2x^2x}{\( x^2+1 \)^2}$
Question 10
Find the area under the curve of the function ( f(x) = 2x^2 + 3x - 1 ) from \( x = 0 \) to \( x = 2 \).
A. 10
B. 12
C. 14
D. 16
Question 11
A firm produces two products, A and B. The profit from the sale of A is ₦50 per unit, and the profit from the sale of B is ₦75 per unit. If the total profit is ₦1,500 and the number of units of A produced is 20 more than the number of units of B produced, find the number of units of B produced.
A. 30
B. 40
C. 50
D. 60
Question 12
Solve the trigonometric equation \( \sin^2 x + \cos^2 x = 1 \) for ( x ).
A. x = 0
B. x = π/2
C. x = π
D. x = 2π
Question 13
Find the equation of the \tangent to the curve \( y = \frac{1}{x} \) at the point where \( x = 2 \).
A. y - 1/2 = -1/4\( x - 2 \)
B. y - 1/2 = 1/4\( x - 2 \)
C. y + 1/2 = -1/4\( x - 2 \)
D. y + 1/2 = 1/4\( x - 2 \)
Question 14
A rec\tangular solid has a length of 8 cm, a width of 5 cm, and a height of 3 cm. Calculate the surface area of the solid.
A. 104 cm^2
B. 120 cm^2
C. 140 cm^2
D. 160 cm^2
Question 15
A set of 5 numbers has an average of 10. If one number is removed, the average becomes 12. What is the sum of the remaining 4 numbers?
A. 48
B. 50
C. 52
D. 54

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