POST UTME MOUNTAIN TOP UNIVERSITY 2017 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the sum of the infinite geometric series \( sum_{n=1}^{infty} \frac{1}{2^n} \).
A. ( 1 )
B. \( \frac{1}{2} \)
C. \( \frac{1}{4} \)
D. \( \frac{1}{8} \)
Question 2
A sequence is defined by \( a_n = 2n^2 - 3n + 1 \). Find the sum of the first five terms.
A. 55
B. 65
C. 75
D. 85
Question 3
A polynomial of degree 3 has the form \( ax^3 + bx^2 + cx + d \). What is the degree of the polynomial \( 2x^3 + 3x^2 - 4x + 1 \)?
A. 1
B. 2
C. 3
D. 4
Question 4
Solve the quadratic equation \( x^2 + 4x + 4 = 0 \).
A. 0
B. -2
C. -1
D. 2
Question 5
A survey of 100 students found that 60 students preferred Mathematics, 30 preferred Science, and 10 preferred both. What is the probability that a randomly selected student prefers either Mathematics or Science?
A. 0.7
B. 0.8
C. 0.9
D. 0.95
Question 6
Find the derivative of the function ( f(x) = \sin^2 x ) u\sing the chain rule.
A. \( 2\sin x \cos x \)
B. \( 2\sin x \)
C. \( 2\cos x \)
D. \( 2\sin x \cos x \)
Question 7
Find the equation of the circle with center \( 3, -2 \ \) ) and radius ( 4 ).
A. \( x-3 \ \)^2 + \( y+2 \)^2 = 16 )
B. \( x-3 \ \)^2 + \( y+2 \)^2 = 25 )
C. \( x-3 \ \)^2 + \( y+2 \)^2 = 36 )
D. \( x-3 \ \)^2 + \( y+2 \)^2 = 49 )
Question 8
Find the derivative of the function ( f(x) = \frac{1}{x^2 + 1} ) u\sing the chain rule.
A. \( -\frac{2x}{\( x^2 + 1 \ \)^2} )
B. \( \frac{2x}{\( x^2 + 1 \ \)^2} )
C. \( -\frac{2}{\( x^2 + 1 \ \)^2} )
D. \( \frac{2}{\( x^2 + 1 \ \)^2} )
Question 9
A circle has a radius of 4 cm. Find the area of the circle.
A. ( 16pi )
B. ( 32pi )
C. ( 64pi )
D. ( 128pi )
Question 10
A sequence is defined by the recurrence relation \( a_n = 2a_{n-1} + 3 \) with initial term \( a_1 = 2 \). Find the sum of the first five terms of the sequence.
A. \( 2 + 7 + 17 + 37 + 79 \)
B. \( 2 + 5 + 13 + 29 + 61 \)
C. \( 2 + 7 + 17 + 37 + 79 \)
D. \( 2 + 5 + 13 + 29 + 61 \)
Question 11
The equation of a circle with center \( (h, k) \) and radius \( r \) is \( x - h \)^2 + \( y - k \)^2 = r^2 \). What is 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. \( x - 2 \)^2 + \( y - 3 \)^2 = 9 \)
D. \( x - 3 \)^2 + \( y - 2 \)^2 = 9 \)
Question 12
Solve for x in the equation \( x^2 + 4x + 4 = 0 \).
A. 0
B. -2
C. -1
D. 1
Question 13
The mean of a set of numbers is 25. If the mean of a subset of these numbers is 30, and the subset has 4 more numbers than the original set, what is the mean of the original set?
A. 20
B. 22
C. 24
D. 26
Question 14
If \( f(x) = 2x^2 + 3x - 1 \), find \( f'(x) \).
A. 4x + 3
B. 2x + 1
C. 3x - 2
D. x^2 + 2x
Question 15
The histogram below shows the distribution of exam scores for a class of 50 students. What is the mean score?
A. 60
B. 70
C. 80
D. 90

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