POST UTME MOUNTAIN TOP UNIVERSITY 2017 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the determinant of the matrix \[ \begin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix} \].
A. 0
B. 1
C. 2
D. 3
Question 2
Solve the equation \( x^3 - 6x^2 + 11x - 6 = 0 \) u\sing the rational root theorem.
A. \( x = 1 \)
B. \( x = 2 \)
C. \( x = 3 \)
D. \( x = 6 \)
Question 3
A circle has a radius of 4 cm. What is the area of the circle?
A. 16π
B. 32π
C. 64π
D. 128π
Question 4
A histogram is a graphical representation of a frequency distribution. What is the name of the type of graph that is used to show the relationship between two variables?
A. Scatter plot
B. Bar chart
C. Histogram
D. Pie chart
Question 5
Solve the inequality \( \frac{x-2}{x+1} > 0 \) for ( x in mathbb{R} ).
A. \( -infty, -1 \ \) cup (2, infty) )
B. \( -infty, -1 \ \) cup (1, 2) )
C. \( -infty, -1 \ \) cup (2, infty) cup (1, 2) )
D. \( -infty, -1 \ \) cup (1, infty) )
Question 6
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 7
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 8
Solve the quadratic equation \( x^2 + 4x + 4 = 0 \).
A. 0
B. -2
C. -1
D. 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
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 11
Find the volume of the solid formed by rotating the region bounded by the curves \( y = x^2 \) and \( y = x \) about the x-axis.
A. \( \frac{1}{6} pi \)
B. \( \frac{1}{3} pi \)
C. \( \frac{1}{2} pi \)
D. \( \frac{2}{3} pi \)
Question 12
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 13
Solve the inequality \( \frac{x}{x-2} > 0 \) for ( x in mathbb{R} setminus {2} ).
A. \( -∞, 2 \) ∪ (2, ∞)
B. \( -∞, 2 \) ∩ (2, ∞)
C. (2, ∞)
D. \( -∞, 2 \)
Question 14
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 15
Solve for x in the equation \( x^2 + 4x + 4 = 0 \).
A. 0
B. -2
C. -1
D. 1

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