POST UTME MOUNTAIN TOP UNIVERSITY 2019 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Determine the equation of the line pas\sing through points ( (1, 2) ) and ( (3, 4) ).
A. \( y = 2x - 1 \)
B. \( y = 2x + 1 \)
C. \( y = 2x - 2 \)
D. \( y = 2x + 2 \)
Question 2
Solve the inequality [ 2x^2 - 5x - 3 > 0 \].
A. x < -1 or x > \frac{3}{2}
B. x < -1 or x < \frac{3}{2}
C. x > -1 or x < \frac{3}{2}
D. x > -1 or x > \frac{3}{2}
Question 3
A right-angled triangle has sides 3 cm, 4 cm, and 5 cm. Find the area of the triangle.
A. 6 cm^2
B. 8 cm^2
C. 10 cm^2
D. 12 cm^2
Question 4
Find the equation of the parabola with vertex ( (2, 3) ) and focus ( (4, 3) ).
A. \( y = \frac{1}{4}\( x-2 \ \)^2 + 3 )
B. \( y = \frac{1}{4}\( x-4 \ \)^2 + 3 )
C. \( y = \frac{1}{4}\( x-2 \ \)^2 + 4 )
D. \( y = \frac{1}{4}\( x-4 \ \)^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
Solve the inequality \( 2x^2 - 5x - 3 > 0 \) u\sing the quadratic formula.
A. x < \frac{3}{2} \text{ or } x > 1
B. x < -1 \text{ or } x > \frac{3}{2}
C. x < -1 \text{ or } x < \frac{3}{2}
D. x > -1 \text{ or } x < \frac{3}{2}
Question 7
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 8
A rec\tangular prism has a length of 10 cm, a width of 5 cm, and a height of 8 cm. Calculate its volume and surface area.
A. 400 cm^3, 240 cm^2
B. 500 cm^3, 300 cm^2
C. 600 cm^3, 360 cm^2
D. 800 cm^3, 480 cm^2
Question 9
Solve the quadratic equation \( x^2 + 5x + 6 = 0 \) u\sing the quadratic formula.
A. \( x = -3 \)
B. \( x = -2 \)
C. \( x = -1 \)
D. \( x = 1 \)
Question 10
Find the sum of the first 10 terms of the geometric progression 2, 6, 18, ...
A. 1040
B. 1080
C. 1100
D. 1120
Question 11
Find the area under the curve \( y = 2x^2 + 3x - 1 \) from x = 0 to x = 2.
A. 13
B. 15
C. 17
D. 19
Question 12
Find the volume of the sphere with radius 4.
A. 268.082
B. 268.082
C. 268.082
D. 268.082
Question 13
Determine the volume of the frustum of a cone with height 10 cm, lower base radius 4 cm, and upper base radius 2 cm.
A. 50\pi cm^3
B. 75\pi cm^3
C. 100\pi cm^3
D. 125\pi cm^3
Question 14
Convert the \fraction \frac{3}{8} to a decimal and a percentage.
A. 0.375, 37.5%
B. 0.5, 50%
C. 0.625, 62.5%
D. 0.75, 75%
Question 15
A random sample of 25 students from a university had a mean height of 175 cm with a s\tandard deviation of 5 cm. If the population s\tandard deviation is 6 cm, calculate the s\tandard error of the mean.
A. 2.08
B. 2.5
C. 3.0
D. 3.5

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