POST UTME REDEEMERS UNIVERSITY 2022 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the derivative of the function \( y = \sin^2 x \) u\sing the chain rule.
A. \( 2\sin x \cos x \)
B. \( \cos^2 x \)
C. \( \sin x \cos x \)
D. \( \sin^2 x \)
Question 2
Find the area under the curve y = x^3 - 6x^2 + 9x + 2 from x = 0 to x = 2.
A. 10
B. 20
C. 30
D. 40
Question 3
Solve for x in the quadratic equation \( x^2 + 5x + 6 = 0 \).
A. \( x = -2 \)
B. \( x = -3 \)
C. \( x = 2 \)
D. \( x = 3 \)
Question 4
A histogram has a mean of 25 and a s\tandard deviation of 5. Find the median.
A. 25
B. 30
C. 35
D. 40
Question 5
A circle with center $C$ and radius $r$ is shown below. If the point $P$ lies on the circle, find the value of $CP$.
A. r
B. 2r
C. 3r
D. 4r
Question 6
Find the volume of the solid formed by revolving the region bounded by the parabola \( y = x^2 \), the line \( x = 2 \), and the x-axis about the x-axis.
A. 16\pi
B. 32\pi
C. 64\pi
D. 128\pi
Question 7
Let X be a random variable with probability density function ( f(x) = egin{cases} 2x & 0 leq x leq 1 \ 0 & \text{otherwise} \end{cases} ). Find the probability that X is greater than 0.5.
A. \( int_{0.5}^{1} 2x , dx \)
B. \( int_{0}^{0.5} 2x , dx \)
C. \( int_{0}^{1} 2x , dx \)
D. \( int_{0.5}^{1} 2x , dx + int_{0}^{0.5} 2x , dx \)
Question 8
Find the area under the curve \( y = x^2 \) from \( x = 0 \) to \( x = 4 \).
A. \( \frac{64}{3} \)
B. \( \frac{32}{3} \)
C. \( \frac{16}{3} \)
D. \( \frac{8}{3} \)
Question 9
Find the mean of the numbers 2, 4, 6, 8, 10.
A. 5
B. 6
C. 7
D. 8
Question 10
A polynomial is defined as ( p(x) = x^3 - 6x^2 + 11x - 6 ). Find the value of ( p(2) ).
A. 0
B. 2
C. 4
D. 6
Question 11
Solve the inequality \( \log_{10} \( x^2 \ \) > 2 ).
A. \( x > 10 \)
B. \( x < -10 \)
C. \( x > 100 \)
D. \( x < -100 \)
Question 12
A circle has a radius of 4 units and a center at ( (0,0) ). Find the equation of the circle.
A. x^2 + y^2 = 16
B. x^2 + y^2 = 32
C. x^2 + y^2 = 64
D. x^2 + y^2 = 128
Question 13
A histogram of exam scores is shown below. What is the mean score if the total number of students is 50?
A. 60
B. 70
C. 80
D. 90
Question 14
Find the equation of the line pas\sing through the points ( (2, 3) ) and ( (4, 5) ).
A. \( y = x + 1 \)
B. \( y = x - 1 \)
C. \( y = x + 2 \)
D. \( y = x - 2 \)
Question 15
Find the equation of the circle with center ( (2, 3) ) and radius ( 4 ).
A. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 16 )
B. \( x - 3 \ \)^2 + \( y - 2 \)^2 = 16 )
C. \( x - 4 \ \)^2 + \( y - 5 \)^2 = 16 )
D. \( x - 5 \ \)^2 + \( y - 4 \)^2 = 16 )

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