POST UTME ABU 2018 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the value of \( \sin(2x) \) when \( \cos(x) = \frac{1}{2} \).
A. \frac{1}{2}
B. \frac{1}{3}
C. \frac{1}{4}
D. \frac{1}{5}
Question 2
Solve the inequality \( \frac{x}{2} + 3 > 5 \).
A. x > 2
B. x < 2
C. x ≥ 2
D. x ≤ 2
Question 3
Find the equation of the line pas\sing through the points (1, 2) and (3, 4).
A. y = 2x - 1
B. y = 2x + 1
C. y = x - 1
D. y = x + 1
Question 4
Solve the inequality \( 2x^2 - 5x - 3 > 0 \).
A. \( -∞, -3 \) ∪ (1, ∞)
B. \( -∞, -1 \) ∪ (3, ∞)
C. \( -∞, 1 \) ∪ (3, ∞)
D. \( -∞, -3 \) ∪ (1, 3)
Question 5
A right circular cylinder has a height of 10 cm and a radius of 4 cm. Find the volume of the cylinder.
A. 160\pi
B. 320\pi
C. 480\pi
D. 640\pi
Question 6
Find the mean of the data set: 2, 4, 6, 8, 10.
A. 5
B. 6
C. 7
D. 8
Question 7
Find the sum of the first 10 terms of the geometric series with first term 2 and common ratio 1/2.
A. 2.992
B. 3.000
C. 3.008
D. 3.016
Question 8
Solve the equation \( 2x^2 + 5x - 3 = 0 \) u\sing the quadratic formula.
A. \\frac{-5 \\pm \\sqrt{109}}{4}
B. \\frac{-5 \\pm \\sqrt{121}}{4}
C. \\frac{-5 \\pm \\sqrt{169}}{4}
D. \\frac{-5 \\pm \\sqrt{225}}{4}
Question 9
Solve the inequality |x - 2| > 3.
A. x < -1 or x > 5
B. x < 1 or x > 5
C. x < 1 or x > 7
D. x < -1 or x > 7
Question 10
A circle passes through the points (1, 2) and (3, 4). Find the equation of the circle.
A. \( x^2 + y^2 - 4x - 6y + 9 = 0 \)
B. \( x^2 + y^2 - 4x - 6y + 5 = 0 \)
C. \( x^2 + y^2 - 4x - 6y + 7 = 0 \)
D. \( x^2 + y^2 - 4x - 6y + 11 = 0 \)
Question 11
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).
A. \( \frac{1}{2} \times 4^3 + 3 \times 4^2 - 2 \times 4 \)
B. \( \frac{1}{2} \times 4^2 + 3 \times 4 - 2 \)
C. \( \frac{1}{2} \times 4^3 - 3 \times 4^2 - 2 \times 4 \)
D. \( \frac{1}{2} \times 4^2 - 3 \times 4 + 2 \)
Question 12
Simplify the expression \( \sqrt{\frac{16x^2y^2}{25}} \) and express it in the form \( ax^by^c \).
A. \frac{4x}{5y}
B. \frac{4xy}{5}
C. \frac{4x^2y}{5}
D. \frac{4xy^2}{5}
Question 13
Find the equation of the circle with center \( -2, 3 \) and radius 4.
A. x^2 + y^2 + 4x - 6y + 13 = 0
B. x^2 + y^2 - 4x + 6y + 13 = 0
C. x^2 + y^2 + 4x + 6y + 13 = 0
D. x^2 + y^2 - 4x - 6y + 13 = 0
Question 14
Solve the inequality \frac{x - 2}{x + 1} > 0.
A. \( -\infty, -1 \) \cup \( 2, \infty \)
B. \( -\infty, -1 \) \cup \( -1, 2 \)
C. \( -\infty, 2 \) \cup \( 2, \infty \)
D. \( -\infty, -1 \) \cup \( 1, \infty \)
Question 15
Find the sum of the first 10 terms of the arithmetic progression 2, 5, 8, ... .
A. ( 55 )
B. ( 65 )
C. ( 75 )
D. ( 85 )

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