POST UTME CHRISTOPHER UNIVERSITY 2017 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve the equation \( \log_{2} \( x^2 - 4 \ \) = 3) for x.
A. \( \sqrt{10} \)
B. \( -\sqrt{10} \)
C. \( \sqrt{14} \)
D. \( -\sqrt{14} \)
Question 2
A sequence is defined as \( a_n = 2n + 1 \). Find the 10th term of the sequence.
A. 21
B. 23
C. 25
D. 27
Question 3
Find the area under the curve \( y = \frac{1}{2}x^2 \) from \( x = 0 \) to \( x = 4 \).
A. 16
B. 32
C. 64
D. 128
Question 4
A random variable X has a probability distribution given by P(X) = \( \frac{1}{2} left\( 1 + \frac{1}{x} \right \ \)) for x > 0. Find the expected value of X.
A. \( \frac{1}{2} \)
B. \( \frac{3}{2} \)
C. \( \frac{5}{2} \)
D. \( \frac{7}{2} \)
Question 5
Solve for ( x ) in the equation \( \sin^2 x + \cos^2 x = 1 \).
A. x = \frac{pi}{4}
B. x = \frac{pi}{2}
C. x = \frac{3pi}{4}
D. x = \frac{5pi}{4}
Question 6
A sequence is defined as \( a_n = 2n + 1 \). Find the 15th term of the sequence.
A. 31
B. 33
C. 35
D. 37
Question 7
Find the derivative of the function ( f(x) = \frac{1}{x^2} ) u\sing the chain rule.
A. -\frac{2}{x^3}
B. \frac{2}{x^3}
C. -\frac{1}{x^3}
D. \frac{1}{x^3}
Question 8
Find the volume of the solid formed by rotating the region bounded by y = x^2, y = 0, and x = 2 about the x-axis.
A. \( \frac{32pi}{3} \)
B. \( \frac{64pi}{3} \)
C. \( \frac{128pi}{3} \)
D. \( \frac{256pi}{3} \)
Question 9
A circle has a radius of 4 cm. What is the area of the circle?
A. 16π
B. 32π
C. 64π
D. 128π
Question 10
A right-angled triangle has a hypotenuse of length 10 cm and one of the other sides is 6 cm. Find the length of the third side u\sing the Pythagorean theorem.
A. 8
B. 4
C. 12
D. 16
Question 11
A circle has a radius of 4 cm. Find the circumference of the circle.
A. 25.12
B. 12.56
C. 50.24
D. 6.28
Question 12
A right-angled triangle has a hypotenuse of length 10 cm and one of the other sides is 6 cm. Find the length of the third side.
A. 8
B. 4
C. 12
D. 16
Question 13
A circle has a radius of 4 cm. Find the area of the circle.
A. 50.24
B. 25.12
C. 12.56
D. 6.28
Question 14
A histogram of exam scores has a mean of 60 and a s\tandard deviation of 10. What is the probability that a randomly selected score is between 50 and 70?
A. 0.5
B. 0.6
C. 0.7
D. 0.8
Question 15
Solve the quadratic equation \( x^2 + 5x + 6 = 0 \) u\sing the quadratic formula. What is the value of ( x )?
A. 2
B. -3
C. -2
D. 1

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