POST UTME MOUNTAIN TOP UNIVERSITY 2019 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A particle moves along the curve \( y = x^2 + 2x + 1 \) with a velocity of 2m/s. Find the acceleration at the point where x = 1.
A. -4 m/s^2
B. -2 m/s^2
C. 2 m/s^2
D. 4 m/s^2
Question 2
Find the sum of the first 10 terms of the geometric series \( 2 + 6 + 18 + \cdots \).
A. 1023
B. 1024
C. 1025
D. 1026
Question 3
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 4
Find the equation of the \tangent to the curve \( y = x^3 - 6x^2 + 9x + 2 \) at the point where x = 2.
A. y = 3x - 5
B. y = 3x + 5
C. y = -3x + 5
D. y = -3x - 5
Question 5
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 6
A set of 4 cards is drawn from a s\tandard deck of 52 cards. What is the probability that the set contains at least one pair?
A. \frac{1}{52}
B. \frac{1}{26}
C. \frac{1}{13}
D. \frac{48}{52}
Question 7
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 8
Find the volume of the frustum of a cone with height 8cm, lower base radius 4cm, and upper base radius 2cm.
A. 64\pi cm^3
B. 128\pi cm^3
C. 256\pi cm^3
D. 512\pi cm^3
Question 9
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
Question 10
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 11
Solve the equation [ \sin^2 x + \cos^2 x = 1 ].
A. x = \frac{\pi}{4}
B. x = \frac{\pi}{2}
C. x = \frac{\pi}{3}
D. x = \frac{\pi}{6}
Question 12
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 13
Find the sum of the first 10 terms of the geometric progression 2, 6, 18, ...
A. 1040
B. 1080
C. 1100
D. 1120
Question 14
Solve the system of equations \begin{align*} x + y &= 4 \ x - y &= 2 \end{align*}.
A. \begin{align*} x &= 3, y = 1 \end{align*}
B. \begin{align*} x &= 1, y = 3 \end{align*}
C. \begin{align*} x &= 2, y = 2 \end{align*}
D. \begin{align*} x &= 4, y = 0 \end{align*}
Question 15
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 )

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