POST UTME CHRISTOPHER UNIVERSITY 2019 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A polynomial p(x) has roots at x = -2, x = 1, and x = 3. If p(0) = 6, find the value of p(2).
A. -6
B. 6
C. 12
D. 18
Question 2
Solve the equation \( \sin^2 x + \cos^2 x = 1 \ \) for \( x \ \) in the interval \( [0, 2\pi] \ \).
A. \[ \frac{\pi}{2} \]
B. \[ \frac{\pi}{4} \]
C. \[ \frac{3\pi}{4} \]
D. \[ \frac{5\pi}{4} \]
Question 3
Solve for ( x ) in the equation \( 2^x = 16 \).
A. ( 2 )
B. ( 4 )
C. ( 8 )
D. ( 16 )
Question 4
Find the area under the curve y = x^2 - 4x + 3 from x = 0 to x = 2.
A. 4
B. 6
C. 8
D. 10
Question 5
Find the area under the curve \( y = \frac{1}{x^2} \) from \( x = 1 \) to \( x = 2 \).
A. \( \frac{1}{2} \)
B. \( \frac{1}{3} \)
C. \( \frac{1}{4} \)
D. \( \frac{1}{5} \)
Question 6
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 7
Solve the system of equations \begin{align*} x + y &= 2 \ x - 2y &= -3 \end{align*} u\sing matrices.
A. x = 1, y = 1
B. x = -1, y = 1
C. x = 1, y = -1
D. x = -1, y = -1
Question 8
A particle moves along the curve y = x^2 - 4x + 3. Find the equation of the \tangent line to the curve at the point where x = 1.
A. y = x - 1
B. y = x + 1
C. y = x - 3
D. y = x + 3
Question 9
A solid cylinder has a radius of 4 cm and a height of 10 cm. Find the volume of the cylinder.
A. \( pi \times 4^2 \times 10 \)
B. \( pi \times 4^2 \times 5 \)
C. \( pi \times 4^2 \times 10^2 \)
D. \( pi \times 4^2 \times 10^3 \)
Question 10
A binary operation * is defined as \( a * b = ab + 5 \). Find the value of \( 2 * 3 \).
A. 11
B. 13
C. 15
D. 17
Question 11
Find the volume of the frustum of a cone with height 6 cm, lower base radius 4 cm, and upper base radius 2 cm.
A. 24\pi cm^3
B. 48\pi cm^3
C. 72\pi cm^3
D. 96\pi cm^3
Question 12
Find the volume of the solid formed by rotating the region bounded by the curves y = x^2, y = 0, and x = 2 about the x-axis.
A. \frac{32\pi}{3}
B. \frac{64\pi}{3}
C. \frac{128\pi}{3}
D. \frac{256\pi}{3}
Question 13
A random experiment has two indep\endent events A and B. If P(A) = 0.4 and P(B) = 0.6, find the probability that both events occur.
A. 0.24
B. 0.36
C. 0.48
D. 0.60
Question 14
In a circle of radius 4 cm, a chord of length 6 cm is drawn. Find the dis\tance of the chord from the centre of the circle.
A. 2 cm
B. 3 cm
C. 4 cm
D. 5 cm
Question 15
A histogram is constructed with the following data: \( egin{array}{|c|c|} hline \text{Class} & \text{Frequency} \ hline 0-10 & 5 \ 10-20 & 8 \ 20-30 & 12 \ 30-40 & 15 \ 40-50 & 10 \ hline \end{array} \). Find the mean of the data.
A. 25
B. 30
C. 35
D. 40

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