POST UTME CALEB UNIVERSITY 2019 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the area under the curve y = x^2 from x = 0 to x = 4.
A. 64
B. 128
C. 256
D. 512
Question 2
Let \( mathbf{a} = egin{pmatrix} 2 \ 3 \end{pmatrix} \) and \( mathbf{b} = egin{pmatrix} 1 \ -2 \end{pmatrix} \). Find the projection of ( mathbf{b} ) onto ( mathbf{a} ).
A. \( egin{pmatrix} 0 \ 0 \end{pmatrix} \)
B. \( egin{pmatrix} 1 \ -\frac{1}{2} \end{pmatrix} \)
C. \( egin{pmatrix} \frac{1}{2} \ -\frac{3}{2} \end{pmatrix} \)
D. \( egin{pmatrix} 1 \ -1 \end{pmatrix} \)
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 = 25
C. \( x - 2 \)^2 + \( y - 3 \)^2 = 36
D. \( x - 2 \)^2 + \( y - 3 \)^2 = 49
Question 4
Solve \( \sqrt{x + 2} = 3 \).
A. \( x = 7 \)
B. \( x = 5 \)
C. \( x = 3 \)
D. \( x = 1 \)
Question 5
Simplify \( \frac{3x^2 + 2x - 1}{2x^2 - 5x + 1} \).
A. \( \frac{3x + 1}{2x - 1} \)
B. \( \frac{3x - 1}{2x + 1} \)
C. \( \frac{3x + 1}{2x + 1} \)
D. \( \frac{3x - 1}{2x - 1} \)
Question 6
If \overrightarrow{a} = \begin{pmatrix} 2 \ 3 \ 4 \end{pmatrix} and \overrightarrow{b} = \begin{pmatrix} -1 \ 2 \ 1 \end{pmatrix}, find the cross product \overrightarrow{a} \times \overrightarrow{b}.
A. \begin{pmatrix} 5 \ -11 \ -1 \end{pmatrix}
B. \begin{pmatrix} -5 \ 11 \ 1 \end{pmatrix}
C. \begin{pmatrix} 5 \ 11 \ 1 \end{pmatrix}
D. \begin{pmatrix} -5 \ -11 \ 1 \end{pmatrix}
Question 7
Solve the equation \sin^2 x + \cos^2 x = 1 for x in the interval [0, 2\pi].
A. x = \frac{\pi}{4}
B. x = \frac{3\pi}{4}
C. x = \frac{5\pi}{4}
D. x = \frac{7\pi}{4}
Question 8
A vector ( vec{a} ) has a magnitude of 5 units and makes an angle of 60° with the positive x-axis. Find the x-component of the vector.
A. 2.5
B. 3.5
C. 4.5
D. 5.5
Question 9
If f(x) = 2x^2 + 3x - 1, find the derivative f'(x).
A. 4x + 3
B. 2x + 1
C. 4x - 3
D. 2x - 1
Question 10
A histogram is shown below. What is the mean of the data set?
A. 5
B. 10
C. 15
D. 20
Question 11
Solve \( x^2 + 4x + 4 = 0 \).
A. \( x = -2 \)
B. \( x = -1 \)
C. \( x = 1 \)
D. \( x = 2 \)
Question 12
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 = 16
D. \( x - 2 \)^2 + \( y - 3 \)^2 = 9
Question 13
In a binary system, what is the value of the number represented by the binary digits 1011?
A. 3
B. 5
C. 7
D. 9
Question 14
A fair six-sided die is rolled. What is the probability that the number rolled is greater than 4?
A. \( \frac{1}{6} \)
B. \( \frac{1}{3} \)
C. \( \frac{2}{3} \)
D. \( \frac{5}{6} \)
Question 15
Solve for x in the equation \( 2x^2 + 5x - 3 = 0 \).
A. \( x = -1 \)
B. \( x = 2 \)
C. \( x = -3 \)
D. \( x = 1 \)

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