POST UTME NOUN 2018 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the equation of the circle with center \( C\( -2, 3 \ \) ) and radius \( r = 4 \).
A. \( x + 2 \)^2 + \( y - 3 \)^2 = 16
B. \( x - 2 \)^2 + \( y + 3 \)^2 = 16
C. \( x + 2 \)^2 + \( y + 3 \)^2 = 16
D. \( x - 2 \)^2 + \( y - 3 \)^2 = 16
Question 2
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( -∞, -1 \) ∪ (3, ∞)
B. \( -∞, 1 \) ∪ (3, ∞)
C. \( -∞, -1 \) ∪ (1, ∞)
D. \( -∞, 3 \) ∪ (1, ∞)
Question 3
Find the value of x in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 10
B. 100
C. 1000
D. 10000
Question 4
Solve the system of equations \( x + y = 2 \) and \( xy = 1 \).
A. (1, 1)
B. \( 1, -1 \)
C. \( -1, 1 \)
D. \( -1, -1 \)
Question 5
A random sample of 16 students from a university had a mean height of 175.5 cm with a s\tandard deviation of 5.2 cm. Calculate the probability that a randomly selected student from this population has a height greater than 180 cm.
A. 0.2389
B. 0.2618
C. 0.2915
D. 0.3191
Question 6
A set ( S ) is defined as \( S = \{ x in \mathbb{R} : x^2 + 2x - 3 = 0 \} \ \). Find the number of elements in the set ( S ).
A. 1
B. 2
C. 3
D. 4
Question 7
Solve the inequality \( \frac{x}{x+2} > 1 \) for ( x ) in the interval \( -infty, -2 \ \) cup \( -2, infty \) ).
A. x ∈ \( -∞, -2 \) ∪ (2, ∞)
B. x ∈ \( -∞, -2 \) ∪ \( -2, 2 \) ∪ (2, ∞)
C. x ∈ \( -∞, -2 \) ∪ (2, ∞)
D. x ∈ \( -∞, -2 \) ∪ (0, ∞)
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
Find the sum of the first 10 terms of the geometric series $\frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \cdots$.
A. \frac{1023}{2048}
B. \frac{2047}{4096}
C. \frac{4095}{8192}
D. \frac{8191}{16384}
Question 10
Solve the equation \( 2^x + 3^x = 5^x \) for x.
A. 2
B. 3
C. 4
D. 5
Question 11
Solve the quadratic equation \( x^2 + 5x + 6 = 0 \) u\sing the quadratic formula.
A. x = -2, x = -3
B. x = -1, x = -6
C. x = 2, x = 3
D. x = 1, x = 6
Question 12
A circle with center \( C = \( 2, 3 \ \) ) and radius \( r = 4 \) has an equation of the form \( x - h \ \)^2 + \( y - k \)^2 = r^2 ). Write the equation of the circle in s\tandard form.
A. \( x - 2 \)^2 + \( y - 3 \)^2 = 16
B. \( x - 3 \)^2 + \( y - 2 \)^2 = 16
C. \( x - 4 \)^2 + \( y - 3 \)^2 = 16
D. \( x - 3 \)^2 + \( y - 4 \)^2 = 16
Question 13
Solve the trigonometric equation \( 2\sin^2 x + 3\cos x - 1 = 0 \) for 0 \leq x \leq 2\pi.
A. \frac{\pi}{6}
B. \frac{\pi}{4}
C. \frac{\pi}{3}
D. \frac{\pi}{2}
Question 14
Solve the equation \( x^2 + 4x + 4 = 0 \).
A. \( x = -2 \)
B. \( x = 2 \)
C. \( x = -1 \)
D. \( x = 1 \)
Question 15
In a probability experiment, two events A and B are indep\endent. If P(A) = 0.4 and P(B) = 0.6, what is the probability that both events A and B occur?
A. 0.24
B. 0.48
C. 0.64
D. 0.76

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