POST UTME ACHIEVERS UNIVERSITY 2022 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Determine the value of x in the equation \( egin{bmatrix} 2 & 1 \ 3 & 2 \end{bmatrix} egin{bmatrix} x \ 1 \end{bmatrix} = egin{bmatrix} 4 \ 8 \end{bmatrix} \).
A. 1
B. 2
C. 3
D. 4
Question 2
Two events, A and B, are indep\endent. If ( P(A) = 0.3 ) and ( P(B) = 0.4 ), find ( P(A cap B) ).
A. 0.12
B. 0.24
C. 0.36
D. 0.48
Question 3
Find the derivative of the function ( f(x) = \frac{x^2 + 2x - 3}{x^2 - 4} ) u\sing the quotient rule.
A. \( \frac{\( x^2 - 4 \)\( 2x + 2 \ \) - \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2} )
B. \( \frac{\( x^2 - 4 \)\( 2x + 2 \ \) + \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2} )
C. \( \frac{\( x^2 - 4 \)\( 2x + 2 \ \) - \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2} )
D. \( \frac{\( x^2 - 4 \)\( 2x + 2 \ \) + \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2} )
Question 4
Find the equation of the circle with center (1, 2) and radius 3.
A. \( x-1 \)^2 + \( y-2 \)^2 = 9
B. \( x+1 \)^2 + \( y+2 \)^2 = 9
C. \( x-1 \)^2 + \( y+2 \)^2 = 9
D. \( x+1 \)^2 + \( y-2 \)^2 = 9
Question 5
Find the volume of the frustum of a cone with height 8 cm, lower base radius 4 cm, and upper base radius 2 cm.
A. 64\pi cm^3
B. 128\pi cm^3
C. 256\pi cm^3
D. 512\pi cm^3
Question 6
Solve the equation \( \sin^2 x + \cos^2 x = 1 \) for ( x ) in the interval ( [0, 2π] ).
A. 0
B. π/2
C. π
D. 3π/2
Question 7
Find the volume of the frustum of a cone with height 10 cm, lower base radius 4 cm, and upper base radius 2 cm.
A. 100π
B. 120π
C. 140π
D. 160π
Question 8
Solve the system of linear equations u\sing matrices: \begin{align*} x + 2y - z &= 3 \ 2x - 3y + 4z &= 5 \ -x + y - 2z &= -2 \end{align*}
A. \begin{pmatrix} 1 \ 2 \ -1 \end{pmatrix}
B. \begin{pmatrix} 2 \ -1 \ 3 \end{pmatrix}
C. \begin{pmatrix} 3 \ 4 \ 5 \end{pmatrix}
D. \begin{pmatrix} 5 \ 6 \ 7 \end{pmatrix}
Question 9
A circle with center ( C(2, 3) ) and radius 4 passes through the point ( P(0, 0) ). Find the equation of the circle.
A. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 16 )
B. \( x + 2 \ \)^2 + \( y - 3 \)^2 = 16 )
C. \( x - 2 \ \)^2 + \( y + 3 \)^2 = 16 )
D. \( x + 2 \ \)^2 + \( y + 3 \)^2 = 16 )
Question 10
Solve the quadratic equation: x^2 + 5x + 6 = 0.
A. x = -2
B. x = -3
C. x = 2
D. x = 3
Question 11
Solve the inequality \( x^2 - 4x + 3 > 0 \) u\sing the quadratic formula.
A. \( x < 1 \) or \( x > 3 \)
B. \( x < 3 \) or \( x > 1 \)
C. \( x > 1 \) or \( x < 3 \)
D. \( x > 3 \) or \( x < 1 \)
Question 12
Find the volume of the solid formed by revolving the region bounded by the parabola \( y = x^2 \), the x-axis, and the line \( x = 2 \) about the x-axis.
A. 16π
B. 32π
C. 64π
D. 128π
Question 13
Solve the equation \( x^2 - 2x - 3 = 0 \) u\sing the quadratic formula.
A. \( x = -1 \) or \( x = 3 \)
B. \( x = 1 \) or \( x = -3 \)
C. \( x = 3 \) or \( x = -1 \)
D. \( x = -3 \) or \( x = 1 \)
Question 14
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 + 2
D. y = x - 2
Question 15
Find the area under the curve \( y = x^3 - 6x^2 + 11x - 6 \) from \( x = 0 \) to \( x = 2 \) u\sing integration.
A. \( \frac{16}{3} \)
B. \( \frac{14}{3} \)
C. \( \frac{12}{3} \)
D. \( \frac{10}{3} \)

Master the Exam!

You've seen a preview, but there are thousands more questions plus AI tutor to break down complex solutions.

Unlock Full Access Available for Android & Windows
Help others prepare! Share this practice hub: