POST UTME GREENFIELD UNIVERSITY 2019 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve the quadratic equation \( x^2 + 5x + 6 = 0 \).
A. -2
B. -3
C. -4
D. -5
Question 2
Find the determinant of the matrix [ egin{pmatrix} 2 & 3 & 1 \ 4 & 5 & 2 \ 1 & 2 & 3 \end{pmatrix} ].
A. 18
B. -18
C. 20
D. -20
Question 3
Solve for ( x ) in the equation \( 2^x + 2^{x+2} = 2^{x+3} \).
A. \( x = -1 \)
B. \( x = 0 \)
C. \( x = 1 \)
D. \( x = 2 \)
Question 4
If f(x) = 3x^2 + 2x - 5, find f'(x) u\sing the chain rule.
A. 6x + 2
B. 6x + 2 - 5
C. 6x + 2
D. 6x + 2 - 5
Question 5
If \( vec{a} = egin{pmatrix} 2 \ 3 \end{pmatrix} \) and \( vec{b} = egin{pmatrix} -1 \ 4 \end{pmatrix} \), find the unit vector in the direction of \( vec{a} + vec{b} \).
A. \begin{pmatrix} \frac{1}{\sqrt{26}} \\ \frac{3}{\sqrt{26}} \end{pmatrix}
B. \begin{pmatrix} \frac{1}{\sqrt{26}} \\ -\frac{3}{\sqrt{26}} \end{pmatrix}
C. \begin{pmatrix} -\frac{1}{\sqrt{26}} \\ \frac{3}{\sqrt{26}} \end{pmatrix}
D. \begin{pmatrix} -\frac{1}{\sqrt{26}} \\ -\frac{3}{\sqrt{26}} \end{pmatrix}
Question 6
Find the area under the curve \( y = \sin x \) from \( x = 0 \) to \( x = \frac{pi}{2} \).
A. ( 1 )
B. \( \frac{1}{2} \)
C. \( \frac{pi}{2} \)
D. ( pi )
Question 7
If ( f(x) = 2x^2 + 3x - 1 ), find the derivative of ( f(x) ) u\sing the power rule.
A. f'(x) = 4x + 3
B. f'(x) = 4x^2 + 3
C. f'(x) = 2x + 3
D. f'(x) = 2x^2 + 3x
Question 8
Solve the inequality \( \frac{x^2 - 4}{x^2 - 9} > 0 \).
A. \( x in \( -infty, -3 \ \) cup (1, infty) )
B. \( x in \( -infty, -3 \ \) cup (3, infty) )
C. \( x in \( -infty, -1 \ \) cup (1, infty) )
D. \( x in \( -infty, -1 \ \) cup (3, infty) )
Question 9
Find the area under the curve y = x^3 from x = 0 to x = 2.
A. 8
B. 16
C. 32
D. 64
Question 10
A histogram is constructed with the following data: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20. What is the class width?
A. 2
B. 4
C. 6
D. 8
Question 11
Find the sum of the first 5 terms of the geometric progression \( 2, 6, 18, \ldots \).
A. 1020
B. 2040
C. 3060
D. 4080
Question 12
Evaluate the definite integral \( int_{0}^{1} x^2 , dx \).
A. \( \frac{1}{3} \)
B. \( \frac{1}{2} \)
C. \( \frac{2}{3} \)
D. \( \frac{1}{4} \)
Question 13
Determine the value of x in the equation \( \frac{x}{2} + 5 = 11 \).
A. 6
B. 7
C. 8
D. 9
Question 14
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 15
A rec\tangular prism has a length of 5 cm, a width of 3 cm, and a height of 2 cm. Find its volume.
A. 30
B. 60
C. 30
D. 60

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