POST UTME CHRISTOPHER UNIVERSITY 2023 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the area under the curve \( y = x^2 \) from \( x = 0 \) to \( x = 2 \).
A. ( 4 )
B. ( 8 )
C. ( 16 )
D. ( 32 )
Question 2
Solve the equation \( \tan^2 x + sec^2 x = 2 \) for ( x ) in the interval ( [0, pi] ).
A. \( x = \frac{pi}{4} \)
B. \( x = \frac{3pi}{4} \)
C. \( x = \frac{pi}{2} \)
D. \( x = \frac{5pi}{4} \)
Question 3
A rec\tangular prism has a length of 10 cm, a width of 5 cm, and a height of 8 cm. Find its volume.
A. ( 400 ) cm³
B. ( 500 ) cm³
C. ( 600 ) cm³
D. ( 800 ) cm³
Question 4
Find the equation of the circle with center \( -2,3 \) and radius 4.
A. \( x+2 \ \)^2 + \( y-3 \)^2 = 16 )
B. \( x-2 \ \)^2 + \( y+3 \)^2 = 16 )
C. \( x+2 \ \)^2 + \( y-3 \)^2 = 4 )
D. \( x-2 \ \)^2 + \( y+3 \)^2 = 4 )
Question 5
Find the equation of the circle with center ( (2, 3) ) and radius ( 4 ).
A. \[ \( x - 2 \)^2 + \( y - 3 \)^2 = 16 \]
B. \[ \( x - 2 \)^2 + \( y - 3 \)^2 = 25 \]
C. \[ \( x - 2 \)^2 + \( y - 3 \)^2 = 36 \]
D. \[ \( x - 2 \)^2 + \( y - 3 \)^2 = 49 \]
Question 6
In a survey of 50 students, the mean height was 175 cm with a s\tandard deviation of 5 cm. If the heights of the students are normally distributed, what is the probability that a randomly selected student will be taller than 180 cm?
A. 0.3085
B. 0.1915
C. 0.1359
D. 0.0228
Question 7
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( x < -\frac{3}{2} \) or \( x > \frac{1}{2} \)
B. \( x < -\frac{1}{2} \) or \( x > \frac{3}{2} \)
C. \( x < -\frac{1}{2} \) or \( x < \frac{3}{2} \)
D. \( x > -\frac{3}{2} \) or \( x < \frac{1}{2} \)
Question 8
A circle has a radius of 4 cm. Find the area of the circle.
A. 50.24
B. 50.27
C. 50.29
D. 50.31
Question 9
A circle has equation \( x^2 + y^2 - 6x + 8y - 12 = 0 \). Find its center and radius.
A. Center: \( 3, -4 \), Radius: 5
B. Center: \( 3, -4 \), Radius: 10
C. Center: \( 3, -4 \), Radius: 15
D. Center: \( 3, -4 \), Radius: 20
Question 10
Let ( f(x) = \frac{1}{x^2 + 1} \). Find the derivative of ( f(x) ) u\sing the chain rule and limits.
A. \[ f'(x) = \frac{-2x}{\( x^2 + 1 \)^2} \]
B. \[ f'(x) = \frac{2x}{\( x^2 + 1 \)^2} \]
C. \[ f'(x) = \frac{-x}{\( x^2 + 1 \)^2} \]
D. \[ f'(x) = \frac{x}{\( x^2 + 1 \)^2} \]
Question 11
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 12
Find the sum of the first 5 terms of the geometric series \( 2x + 3x^2 + 4x^3 + ldots \).
A. \( 2x + 3x^2 + 4x^3 + 5x^4 + 6x^5 \)
B. \( 2x + 3x^2 + 4x^3 + 5x^4 + 6x^5 + 7x^6 \)
C. \( 2x + 3x^2 + 4x^3 + 5x^4 + 6x^5 + 7x^6 + 8x^7 \)
D. \( 2x + 3x^2 + 4x^3 + 5x^4 + 6x^5 + 7x^6 + 8x^7 + 9x^8 \)
Question 13
Let ( f(x) = \frac{x^2 - 4}{x - 2} ). Find the derivative of ( f(x) ) u\sing the chain rule and limits.
A. \[ f'(x) = \frac{2x\( x - 2 \) - \( x^2 - 4 \)}{\( x - 2 \)^2} \]
B. \[ f'(x) = \frac{2x\( x - 2 \) + \( x^2 - 4 \)}{\( x - 2 \)^2} \]
C. \[ f'(x) = \frac{2x\( x - 2 \) - \( x^2 - 4 \)}{\( x - 2 \)^2} + \frac{\( x^2 - 4 \)}{\( x - 2 \)^2} \]
D. \[ f'(x) = \frac{2x\( x - 2 \) + \( x^2 - 4 \)}{\( x - 2 \)^2} - \frac{\( x^2 - 4 \)}{\( x - 2 \)^2} \]
Question 14
Find the mean of the data set { 2, 4, 6, 8, 10 }.
A. ( 6 )
B. ( 8 )
C. ( 10 )
D. ( 12 )
Question 15
Find the equation of the line pas\sing through the points (2, 3) and (4, 5).
A. y - 3 = \( 5 - 3 \)/\( 4 - 2 \)\( x - 2 \)
B. y - 3 = \( 5 - 3 \)/\( 4 - 2 \)\( x - 4 \)
C. y - 5 = \( 3 - 5 \)/\( 2 - 4 \)\( x - 2 \)
D. y - 5 = \( 3 - 5 \)/\( 2 - 4 \)\( x - 4 \)

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