POST UTME GREENFIELD UNIVERSITY 2019 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. x < -1 or x > \frac{3}{2}
B. x < -1 or x < \frac{3}{2}
C. x > -1 or x > \frac{3}{2}
D. x > -1 or x < \frac{3}{2}
Question 2
A histogram represents the distribution of exam scores. If the mean score is 60 and the s\tandard deviation is 10, what is the probability that a randomly selected score is between 50 and 70?
A. 0.25
B. 0.5
C. 0.75
D. 1
Question 3
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 4
Two events A and B are indep\endent. If P(A) = 0.4 and P(B) = 0.6, find P(A ∩ B).
A. 0.24
B. 0.24
C. 0.24
D. 0.24
Question 5
Find the equation of the circle with center at ( (2, 3) ) and radius ( 4 ).
A. \( x - 2 \)^2 + \( y - 3 \)^2 = 16
B. \( x - 2 \)^2 + \( y - 3 \)^2 = 25
C. \( x - 2 \)^2 + \( y - 3 \)^2 = 36
D. \( x - 2 \)^2 + \( y - 3 \)^2 = 49
Question 6
Determine the value of x in the equation \( \frac{x}{2} + 5 = 11 \).
A. 6
B. 7
C. 8
D. 9
Question 7
Find the volume of the solid formed by revolving the region bounded by the curves y = x^2 and y = 4 - x^2 about the x-axis.
A. 16\pi
B. 32\pi
C. 64\pi
D. 128\pi
Question 8
Find the area under the curve y = x^3 from x = 0 to x = 2.
A. 8
B. 16
C. 32
D. 64
Question 9
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. \( x - 3 \ \)^2 + \( y - 2 \)^2 = 16 )
D. \( x - 3 \ \)^2 + \( y - 2 \)^2 = 4 )
Question 10
Determine the value of x in the equation \( \tan x = \frac{1}{\sqrt{3}} \) if ( x ) lies in the first quadrant.
A. \( \frac{pi}{6} \)
B. \( \frac{pi}{4} \)
C. \( \frac{pi}{3} \)
D. \( \frac{pi}{2} \)
Question 11
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 12
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 13
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 14
Solve the equation \( x^2 + 4x + 4 = 0 \).
A. \left\( -2, \infty \right \)
B. \left\( -\infty, -2 \right \)
C. \left\( -\infty, 2 \right \)
D. \left\( -\infty, -2 \right \) \cup \left\( 2, \infty \right \)
Question 15
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \left\( -\infty, -1 \right \) \cup \left\( 3, \infty \right \)
B. \left\( -\infty, -3 \right \) \cup \left\( 1, \infty \right \)
C. \left\( -\infty, -3 \right \) \cup \left\( 1, 3 \right \)
D. \left\( -\infty, -1 \right \) \cup \left\( 1, \infty \right \)

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