POST UTME JOSEPH AYO BABALOLA UNIVERSITY 2019 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Determine the value of x in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 10
B. 100
C. 1000
D. 10000
Question 2
A line passes through the points ( (2, 3) ) and ( (4, 5) ). Find the equation of the line in slope-intercept form.
A. \( y = x + 1 \)
B. \( y = x - 1 \)
C. \( y = x + 2 \)
D. \( y = x - 2 \)
Question 3
A vector ( vec{a} ) has a magnitude of 5 and makes an angle of 30° with the positive x-axis. Find the x and y components of ( vec{a} ).
A. x: 4, y: 4
B. x: 4, y: 3
C. x: 3, y: 4
D. x: 3, y: 3
Question 4
A fair six-sided die is rolled. What is the probability that the number obtained is greater than 4?
A. \frac{1}{6}
B. \frac{1}{3}
C. \frac{2}{3}
D. \frac{5}{6}
Question 5
Solve for x in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 10
B. 100
C. 1000
D. 10000
Question 6
A histogram of exam scores has a mean of 75 and a s\tandard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score is between 60 and 90?
A. 0.5
B. 0.6
C. 0.7
D. 0.8
Question 7
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. \begin{pmatrix} \frac{7}{5} \\ \frac{6}{5} \end{pmatrix}
B. \begin{pmatrix} \frac{1}{5} \\ -\frac{2}{5} \end{pmatrix}
C. \begin{pmatrix} \frac{2}{5} \\ -\frac{3}{5} \end{pmatrix}
D. \begin{pmatrix} -\frac{1}{5} \\ \frac{2}{5} \end{pmatrix}
Question 8
Find the area under the curve \( y = \frac{1}{2}x^2 \) from \( x = 0 \) to \( x = 4 \).
A. \( \frac{16}{3} \)
B. \( \frac{32}{3} \)
C. \( \frac{64}{3} \)
D. \( \frac{128}{3} \)
Question 9
Solve for ( x ) in the equation \( 2x^2 + 5x - 3 = 0 \).
A. \( x = -\frac{3}{2} \)
B. \( x = \frac{1}{2} \)
C. \( x = -\frac{1}{2} \)
D. \( x = \frac{3}{2} \)
Question 10
In a right-angled triangle, the length of the hypotenuse is 10 cm and one of the acute angles is 30°. Find the length of the side opposite the 30° angle.
A. 5 cm
B. 7.5 cm
C. 10 cm
D. 12.5 cm
Question 11
A circle has a radius of 5 cm. Find the area of the circle.
A. \( 50 \pi \)
B. \( 100 \pi \)
C. \( 150 \pi \)
D. \( 200 \pi \)
Question 12
Let ( f(x) = x^2 + 2x + 1 ). Find the equation of the \tangent line to the curve at the point where \( x = 1 \).
A. y = 3x - 2
B. y = 3x + 2
C. y = 3x - 1
D. y = 3x + 1
Question 13
A right circular cylinder has a height of 10 cm and a radius of 4 cm. Find the volume of the cylinder.
A. 80\pi
B. 160\pi
C. 320\pi
D. 640\pi
Question 14
Solve the inequality \( 2x^2 + 5x - 3 > 0 \) u\sing the quadratic formula.
A. x < -1 or x > 3/2
B. x < -3/2 or x > 1
C. x < 1 or x > -3/2
D. x < 3/2 or x > -1
Question 15
Solve for y in the equation \( y = \frac{1}{2} \left\( x + \frac{1}{x} \right \ \) ) given that x = 2.
A. 2
B. 3
C. 4
D. 5

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