POST UTME ACHIEVERS UNIVERSITY 2023 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve the inequality \( 2x^2 + 5x - 3 > 0 \) u\sing the quadratic formula.
A. \left\( -\frac{5}{4}, \frac{3}{2} \right \)
B. \left\( -\frac{3}{2}, \frac{5}{4} \right \)
C. \left\( -\infty, -\frac{3}{2} \right \) \cup \left\( \frac{5}{4}, \infty \right \)
D. \left\( -\infty, \frac{5}{4} \right \) \cup \left\( -\frac{3}{2}, \infty \right \)
Question 2
A right triangle has a hypotenuse of length 10 cm and one leg of length 6 cm. What is the length of the other leg?
A. 8
B. 8.66
C. 8.94
D. 9.22
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 = 4 )
C. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 9 )
D. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 25 )
Question 4
Find the derivative of the function f(x) = \sin\( x^2 \) u\sing the chain rule.
A. 2x \cos\( x^2 \)
B. x^2 \cos\( x^2 \)
C. x \cos\( x^2 \)
D. \cos\( x^2 \)
Question 5
Find the derivative of the function f(x) = \frac{\sin(x)}{x^2} u\sing the chain rule.
A. \frac{\cos(x)}{x^2} - \frac{2\sin(x)}{x^3}
B. \frac{\cos(x)}{x^2} + \frac{2\sin(x)}{x^3}
C. \frac{\cos(x)}{x^2} - \frac{\sin(x)}{x^3}
D. \frac{\cos(x)}{x^2} + \frac{\sin(x)}{x^3}
Question 6
Find the volume of the solid formed by rotating the region bounded by the curves \( y = x^2 \) and \( y = 2x \) about the x-axis.
A. \( \frac{1}{3} \)
B. \( \frac{2}{3} \)
C. \( \frac{4}{3} \)
D. \( \frac{8}{3} \)
Question 7
Let ( f(x) = egin{cases} x^2 & x geq 0 \ 0 & x < 0 \end{cases} ). Find ( f'(x) ) u\sing the chain rule.
A. ( f'(x) = egin{cases} 2x & x > 0 \ 0 & x < 0 \end{cases} )
B. ( f'(x) = egin{cases} 2x & x < 0 \ 0 & x > 0 \end{cases} )
C. ( f'(x) = egin{cases} 2x & x geq 0 \ 0 & x < 0 \end{cases} )
D. ( f'(x) = egin{cases} 0 & x geq 0 \ 2x & x < 0 \end{cases} )
Question 8
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).
A. 40
B. 50
C. 60
D. 70
Question 9
Let \( mathbf{a} = egin{pmatrix} 2 \ 3 \end{pmatrix} \) and \( mathbf{b} = egin{pmatrix} -1 \ 4 \end{pmatrix} \). Find the projection of ( mathbf{b} ) onto ( mathbf{a} ).
A. 0.8
B. -0.6
C. 0.6
D. 1.2
Question 10
Solve the equation \( 2^x + 2^{x+1} = 100 \).
A. 4
B. 5
C. 6
D. 7
Question 11
Find the value of ( x ) in the equation \( 2^x + 3^x = 5^x \).
A. 1
B. 2
C. 3
D. 4
Question 12
Solve the system of linear equations u\sing the method of substitution: x + y = 2 and x - y = 1.
A. x = 1, y = 1
B. x = 1, y = -1
C. x = -1, y = 1
D. x = -1, y = -1
Question 13
Find the mean of the following data set: 2, 4, 6, 8, 10.
A. 6
B. 5
C. 7
D. 8
Question 14
Solve the system of linear equations \( egin{cases} 2x + 3y = 7 \ 4x - 2y = -3 \end{cases} \) u\sing substitution or elimination.
A. \left\( x, y \right \) = \left\( 1, 2 \right \)
B. \left\( x, y \right \) = \left\( 2, 1 \right \)
C. \left\( x, y \right \) = \left\( 3, -1 \right \)
D. \left\( x, y \right \) = \left\( -1, 3 \right \)
Question 15
A matrix A has the following form: \begin{pmatrix}a&b\ c&d\end{pmatrix}. If the determinant of A is 6, what is the value of ad-bc?
A. 6
B. 12
C. 18
D. 24

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