POST UTME UNIBEN 2019 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 system of equations \( x + y = 4 \) and \( x - y = 2 \).
A. x = 3, y = 1
B. x = 1, y = 3
C. x = 2, y = 2
D. x = 4, y = 0
Question 3
Solve for x in the equation \( x^2 + 5x + 6 = 0 \).
A. -2
B. -3
C. 1
D. 2
Question 4
A sequence is defined by the formula \( a_n = 2n + 1 \). Find the sum of the first 5 terms of the sequence.
A. 20
B. 30
C. 40
D. 50
Question 5
Find the value of x in the equation \log_{10}\( x^2 \) = 4.
A. 10^8
B. 10^4
C. 10^2
D. 10^6
Question 6
Find the vector projection of vector \vec{a} = 2\hat{i} + 3\hat{j} onto vector \vec{b} = \hat{i} + \hat{j}.
A. \frac{5}{6}\hat{i} + \frac{5}{6}\hat{j}
B. \frac{1}{6}\hat{i} + \frac{1}{6}\hat{j}
C. \frac{3}{4}\hat{i} + \frac{3}{4}\hat{j}
D. \frac{1}{2}\hat{i} + \frac{1}{2}\hat{j}
Question 7
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 8
In the diagram below, ( AB ) is a diameter of the circle with center ( O ). If \( ∠AOB = 60^{circ} \), find the measure of ( ∠ACB ).
A. 30^{circ}
B. 45^{circ}
C. 60^{circ}
D. 90^{circ}
Question 9
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. x < -1 or x > 3
B. x < 1 or x > 3
C. x < -3 or x > 1
D. x < 3 or x > 1
Question 10
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 11
Solve for x in the equation \( x^2 + 5x + 6 = 0 \).
A. \( x = -2 \)
B. \( x = -3 \)
C. \( x = 2 \)
D. \( x = 3 \)
Question 12
Find the value of x in the equation \( \frac{x}{2} + 5 = 11 \).
A. 6
B. 8
C. 10
D. 12
Question 13
Solve for x in the equation \( \frac{1}{2}x^2 + 5x - 3 = 0 \).
A. \( x = -10 \)
B. \( x = 1 \)
C. \( x = -1 \)
D. \( x = 2 \)
Question 14
A circle with center (0, 0) and radius 5 passes through which of the following points?
A. (3, 4)
B. (4, 3)
C. (5, 0)
D. (0, 5)
Question 15
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 \( x > \frac{3}{2} \ \)

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