POST UTME RHEMA UNIVERSITY 2020 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the derivative of the function ( f(x) = \frac{1}{\sqrt{x}} ) u\sing the chain rule.
A. x^{-\frac{3}{2}}
B. x^{-\frac{1}{2}}
C. -x^{-\frac{3}{2}}
D. -x^{-\frac{1}{2}}
Question 2
A histogram of exam scores is shown below. What is the mean score?
A. 60
B. 70
C. 80
D. 90
Question 3
A histogram of exam scores for a class of 50 students is shown below. What is the mean score?
A. 60
B. 70
C. 80
D. 90
Question 4
A line passes through the points ( (1, 2) ) and ( (3, 4) ). Find the equation of the line.
A. \( y = 2x - 1 \)
B. \( y = 2x + 1 \)
C. \( y = 3x - 1 \)
D. \( y = 3x + 1 \)
Question 5
Find the volume of the solid formed by revolving the region bounded by $y = x^2$ and $y = 4 - x^2$ about the x-axis.
A. 16\pi
B. 32\pi
C. 64\pi
D. 128\pi
Question 6
A circle has equation \( x^2 + y^2 = 4 \). Find the equation of the \tangent to the circle at the point where \( x = 2 \).
A. \( y = -x + 2 \)
B. \( y = x + 2 \)
C. \( y = -x - 2 \)
D. \( y = x - 2 \)
Question 7
A set of 5 numbers has a mean of 10 and a median of 8. If the largest number is 15, find the sum of the remaining 3 numbers.
A. 20
B. 30
C. 40
D. 50
Question 8
A random experiment consists of rolling a fair six-sided die. If the outcome is an even number, the die is rolled again. If the outcome is an odd number, the die is rolled three more times. What is the probability that the final outcome is a 6?
A. \( \frac{1}{6} \)
B. \( \frac{1}{12} \)
C. \( \frac{1}{36} \)
D. \( \frac{1}{24} \)
Question 9
A right-angled triangle has a hypotenuse of length 10cm and one leg of length 6cm. Find the length of the other leg.
A. ( 8 ) cm
B. ( 6 ) cm
C. ( 4 ) cm
D. ( 2 ) cm
Question 10
Solve the inequality \( 2x^2 + 5x - 3 > 0 \) u\sing the quadratic formula.
A. \( x < -\frac{3}{2} \) or \( x > \frac{1}{2} \)
B. \( x < -\frac{1}{2} \) or \( x > \frac{3}{2} \)
C. \( x < -\frac{3}{2} \) or \( x < \frac{1}{2} \)
D. \( x > -\frac{3}{2} \) or \( x < \frac{1}{2} \)
Question 11
Find the area of the triangle with vertices $A(0,0)$, $B(3,0)$, and $C(1,2)$.
A. 3
B. 4
C. 5
D. 6
Question 12
Find the equation of the \tangent to the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) at the point where \( x = 1 \).
A. \( y = x + 5 \)
B. \( y = 2x - 1 \)
C. \( y = 3x - 2 \)
D. \( y = x - 1 \)
Question 13
Find the area under the curve \( y = x^2 \) from \( x = 0 \) to \( x = 2 \).
A. \( \frac{8}{3} \)
B. \( \frac{16}{3} \)
C. \( \frac{32}{3} \)
D. \( \frac{64}{3} \)
Question 14
Find the derivative of the function ( f(x) = \frac{1}{\sqrt{x^2 + 1}} ) u\sing the chain rule.
A. ( f'(x) = \frac{-x}{\( x^2 + 1 \)^{3/2}} )
B. ( f'(x) = \frac{x}{\( x^2 + 1 \)^{3/2}} )
C. ( f'(x) = \frac{1}{\( x^2 + 1 \)^{3/2}} )
D. ( f'(x) = \frac{-1}{\( x^2 + 1 \)^{3/2}} )
Question 15
A histogram is constructed with 5 classes of equal width. The frequency of the classes are 10, 15, 20, 15, and 10. What is the mean of the histogram?
A. 12
B. 15
C. 18
D. 20

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