POST UTME CRAWFORD UNIVERSITY 2020 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
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 = -2x + 1
D. y = -2x - 1
Question 2
Solve the trigonometric equation \sin^2 x + \cos^2 x = 1.
A. \boxed{\text{True for all x}}
B. \text{False for all x}
C. \text{True for x = 0}
D. \text{False for x = 0}
Question 3
Find the volume of the frustum of the cone with height 8 cm, lower base radius 4 cm, and upper base radius 2 cm.
A. 64π cm³
B. 128π cm³
C. 256π cm³
D. 512π cm³
Question 4
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 = 16
C. \( x + 2 \)^2 + \( y + 3 \)^2 = 16
D. \( x - 2 \)^2 + \( y - 3 \)^2 = 16
Question 5
A survey of 100 students found that 60% of them preferred pizza, 20% preferred burgers, and 20% preferred sandwiches. What is the probability that a randomly selected student prefers pizza?
A. 0.6
B. 0.7
C. 0.8
D. 0.9
Question 6
Solve the equation \( \sqrt{x+1} + \sqrt{x-1} = 2 \ \).
A. \( x = 1 \ \)
B. \( x = 3 \ \)
C. \( x = 5 \ \)
D. \( x = 7 \ \)
Question 7
Find the value of x in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 10
B. 100
C. 1000
D. 10000
Question 8
A histogram of exam scores has a mean of 75 and a s\tandard deviation of 5. If the scores are normally distributed, what is the probability that a randomly selected score is between 70 and 80?
A. 0.135
B. 0.341
C. 0.674
D. 0.954
Question 9
Find the volume of the frustum of a cone with height 6 cm, lower base radius 4 cm, and upper base radius 2 cm.
A. 24π cm³
B. 48π cm³
C. 96π cm³
D. 192π cm³
Question 10
Solve for ( x ) in the equation \( \begin{vmatrix} 2 & 3 & 1 \ 4 & 1 & 3 \ 2 & 0 & 1 \ \end{vmatrix} = 0 \).
A. \( x = \frac{1}{2} \ \)
B. \( x = -\frac{1}{2} \ \)
C. \( x = 1 \ \)
D. \( x = -1 \ \)
Question 11
Find the value of \( \sin \left\( \frac{3\pi}{4} \right \ \) \cos \left\( \frac{\pi}{4} \right \) + \cos \left\( \frac{3\pi}{4} \right \) \sin \left\( \frac{\pi}{4} \right \) ).
A. \( \frac{1}{2} \ \)
B. \( \frac{\sqrt{2}}{2} \ \)
C. \( \frac{1}{\sqrt{2}} \ \)
D. \( \\frac{\\sqrt{2}}{\\sqrt{2}} \\ \)
Question 12
Solve the inequality \( x^2 - 4x - 5 > 0 \).
A. \( -∞, -1 \) ∪ (5, ∞)
B. \( -∞, -5 \) ∪ (1, ∞)
C. \( -∞, 1 \) ∪ (5, ∞)
D. \( -∞, -5 \) ∪ (1, ∞)
Question 13
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 = \frac{2}{2}\( x - 2 \) + 3
D. y = \frac{2}{2}\( x + 2 \) + 3
Question 14
A vector [ mathbf{a} = egin{bmatrix} 2 \ 3 \ 4 \end{bmatrix} ] is rotated by 90° about the x-axis. Find the new vector [ mathbf{a}' ].
A. [ egin{bmatrix} 2 \ -3 \ 4 \end{bmatrix} ]
B. [ egin{bmatrix} 2 \ 3 \ -4 \end{bmatrix} ]
C. [ egin{bmatrix} 2 \ 4 \ 3 \end{bmatrix} ]
D. [ egin{bmatrix} 2 \ -4 \ 3 \end{bmatrix} ]
Question 15
A car travels from city A to city B at an average speed of 60 km/h and returns at an average speed of 40 km/h. What is the average speed for the round trip?
A. 50
B. 60
C. 70
D. 80

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