POST UTME COVENANT UNIVERSITY 2020 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A vector \( \vec{a} \) has a magnitude of 6 units and makes an angle of 30\circ with the positive x-axis. Find the x and y components of \( \vec{a} \).
A. 3\hat{i} + 3\hat{j}
B. 6\hat{i} + 3\hat{j}
C. 3\hat{i} + 6\hat{j}
D. 6\hat{i} + 6\hat{j}
Question 2
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 3
Find the equation of the circle with center \( (2, 3) \) and radius 4.
A. \( x - 2 \)^2 + \( y - 3 \)^2 = 16
B. \( x - 3 \)^2 + \( y - 2 \)^2 = 16
C. \( x - 4 \)^2 + \( y - 3 \)^2 = 16
D. \( x - 2 \)^2 + \( y - 4 \)^2 = 16
Question 4
Find the area under the curve \( y = x^2 \) from \( x = 0 \) to \( x = 4 \).
A. 64
B. 128
C. 256
D. 512
Question 5
Solve for x in the equation \( \log_{10} \( x^2 \) = 4 \).
A. 10
B. 100
C. 1000
D. 10000
Question 6
Find the area under the curve \( y = x^2 + 2x + 1 \) from \( x = 0 \) to \( x = 2 \).
A. 10
B. 20
C. 30
D. 40
Question 7
Solve the equation x^2 + 4x - 5 = 0 u\sing the quadratic formula.
A. x = -5, x = 1
B. x = -1, x = 5
C. x = 1, x = -5
D. x = -5, x = -1
Question 8
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 9
Find the sum of the first 5 terms of the geometric progression 3, 6, 12, ...
A. 255
B. 256
C. 257
D. 258
Question 10
Solve the quadratic equation \( x^2 + 4x + 4 = 0 \).
A. -2
B. -1
C. 0
D. 2
Question 11
Find the area under the curve $y = \sin x$ from $x = 0$ to $x = \pi$.
A. 2
B. 1
C. 0
D. -1
Question 12
Find the sum of the first 5 terms of the geometric series \( 2x^2 - 3x + 1 \).
A. 2x^2 - 3x + 1 + 2x^2 - 3x + 1 + 2x^2 - 3x + 1 + 2x^2 - 3x + 1 + 2x^2 - 3x + 1
B. 2x^2 - 3x + 1 + 2x^2 - 3x + 1 + 2x^2 - 3x + 1 + 2x^2 - 3x + 1 + 2x^2
C. 2x^2 - 3x + 1 + 2x^2 - 3x + 1 + 2x^2 - 3x + 1 + 2x^2 - 3x + 1 + 3x^2
D. 2x^2 - 3x + 1 + 2x^2 - 3x + 1 + 2x^2 - 3x + 1 + 2x^2 - 3x + 1 + 4x^2
Question 13
A particle moves in a straight line with an initial velocity of \( 5 , \text{m/s} \) and an acceleration of \( 2 , \text{m/s}^2 \). Find its velocity after ( 3 ) seconds.
A. 13
B. 15
C. 17
D. 19
Question 14
Find the determinant of the matrix $\begin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix}$.
A. 0
B. 1
C. -1
D. 2
Question 15
Find the area under the curve \( y = x^2 - 4x + 3 \) from \( x = 1 \) to \( x = 3 \).
A. 10
B. 12
C. 14
D. 16

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