POST UTME COVENANT UNIVERSITY 2022 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
If \( f(x) = 3x^2 + 2x - 5 \) and \( g(x) = 2x^2 - 3x + 1 \), find the derivative of \( f(g(x)) \) u\sing the chain rule.
A. 6x^3 + 10x^2 - 13x + 3
B. 6x^3 + 10x^2 - 13x - 3
C. 6x^3 + 10x^2 + 13x + 3
D. 6x^3 + 10x^2 - 13x - 1
Question 2
Find the equation of the circle with center ( C(2,3) ) and radius \( r = 4 \).
A. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 16 )
B. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 4 )
C. \( x - 3 \ \)^2 + \( y - 2 \)^2 = 16 )
D. \( x - 3 \ \)^2 + \( y - 2 \)^2 = 4 )
Question 3
In a base-8 number system, what is the value of the digit $x$ such that $x_8 + 12_8 = 23_8$?
A. 3
B. 4
C. 5
D. 6
Question 4
Solve for $x$ in the equation $\begin{vmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{vmatrix} = 0$.
A. -1
B. 1
C. 2
D. 3
Question 5
Find the equation of the line pas\sing through the points $(2,3)$ and $(4,5)$.
A. y = 2x - 1
B. y = 2x + 1
C. y = x + 1
D. y = x - 1
Question 6
Find the derivative of the function ( f(x) = 3x^2 - 2x + 1 ) u\sing the chain rule.
A. ( f'(x) = 6x - 2 )
B. ( f'(x) = 6x + 2 )
C. ( f'(x) = 6x^2 - 2 )
D. ( f'(x) = 6x^2 + 2 )
Question 7
In the diagram below, the vector µA = 2i + 3j and vector µB = i - 2j. What is the magnitude of the resul\tant vector µA + µB?
A. 1.0
B. 3.0
C. 5.0
D. 7.0
Question 8
A circle has equation $x^2 + y^2 + 4x - 6y - 12 = 0$. Find the coordinates of the center of the circle.
A. \( 2, -3 \)
B. \( -2, 3 \)
C. (3, 2)
D. \( -3, -2 \)
Question 9
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. 32\pi
B. 48\pi
C. 64\pi
D. 80\pi
Question 10
Determine the value of $\frac{1}{2} \log_{10} \( x^2 \) = 4$.
A. 10
B. 100
C. 1000
D. 10000
Question 11
In the polynomial $p(x) = 3x^4 - 2x^3 + 5x^2 - x + 1$, find the value of $p\( -1 \)$ u\sing the Remainder Theorem.
A. 11
B. 13
C. 15
D. 17
Question 12
Solve for $x$: $\log_{10} \( x^2 \) = 4$.
A. 2
B. 4
C. 8
D. 16
Question 13
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( x < -1 \) or \( x > 3 \)
B. \( x < 1 \) or \( x > 3 \)
C. \( x < -1 \) or \( x < 3 \)
D. \( x > 1 \) or \( x > 3 \)
Question 14
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).
A. 12
B. 14
C. 16
D. 18
Question 15
Convert the decimal number 0.375 to a \fraction in its simplest form.
A. \frac{1}{4}
B. \frac{1}{8}
C. \frac{3}{8}
D. \frac{3}{4}

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