POST UTME ACHIEVERS UNIVERSITY 2022 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve the equation \( x^2 + 4x + 4 = 0 \) u\sing the quadratic formula.
A. \( x = -2 \)
B. \( x = -1 \)
C. \( x = 0 \)
D. \( x = 1 \)
Question 2
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. \( \frac{10}{3} \)
Question 3
Find the equation of the circle pas\sing through the points (2, 3), (4, 5), and (6, 7).
A. \( x - 4 \)^2 + \( y - 5 \)^2 = 9
B. \( x - 3 \)^2 + \( y - 4 \)^2 = 16
C. \( x - 5 \)^2 + \( y - 6 \)^2 = 25
D. \( x - 6 \)^2 + \( y - 7 \)^2 = 36
Question 4
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 5
Find the vector ( mathbf{a} ) such that \( mathbf{a} cdot mathbf{b} = 10 \) and \( mathbf{a} cdot mathbf{c} = 5 \), where \( mathbf{b} = 2mathbf{i} + 3mathbf{j} \) and \( mathbf{c} = mathbf{i} - 2mathbf{j} \).
A. \( 5mathbf{i} + 3mathbf{j} \)
B. \( 3mathbf{i} + 5mathbf{j} \)
C. \( 2mathbf{i} + 4mathbf{j} \)
D. \( 4mathbf{i} + 2mathbf{j} \)
Question 6
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 7
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 8
Find the area of the triangle with vertices (0, 0), (3, 0), and (0, 4).
A. 12
B. 16
C. 20
D. 24
Question 9
A histogram of exam scores has a mean of 75 and a s\tandard deviation of 10. If the scores are normally distributed, find the probability that a randomly selected score is greater than 85.
A. \frac{1}{4}
B. \frac{1}{2}
C. \frac{3}{4}
D. \frac{3}{5}
Question 10
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 11
Find the derivative of the function ( f(x) = \frac{1}{\sqrt{x^2 + 1}} ) u\sing the chain rule.
A. \( \frac{-x}{\( x^2 + 1 \ \)^{3/2}} )
B. \( \frac{x}{\( x^2 + 1 \ \)^{3/2}} )
C. \( \frac{1}{\( x^2 + 1 \ \)^{3/2}} )
D. \( \frac{-1}{\( x^2 + 1 \ \)^{3/2}} )
Question 12
Solve the equation \( 2 \log_{10} \( x^2 \ \) = 4 ) for ( x ).
A. \( x = 10 \)
B. \( x = 10^2 \)
C. \( x = 10^{-2} \)
D. \( x = 10^{-1} \)
Question 13
Determine the value of $\int_0^1 \frac{1}{1+x^2} dx$.
A. \frac{\pi}{4}
B. \frac{\pi}{2}
C. \frac{\pi}{3}
D. \frac{\pi}{6}
Question 14
Find the area under the curve \( y = x^2 - 2x + 1 \) from \( x = 0 \) to \( x = 2 \) u\sing integration.
A. \( \frac{4}{3} \)
B. \( \frac{2}{3} \)
C. \( \frac{1}{3} \)
D. \( \frac{1}{2} \)
Question 15
Solve the inequality $|x-2| > 3$.
A. \( -\infty, -1 \) \cup \( 5, \infty \)
B. \( -\infty, -1 \) \cup \( 1, \infty \)
C. \( -\infty, 1 \) \cup \( 5, \infty \)
D. \( -\infty, 5 \) \cup \( 1, \infty \)

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