POST UTME MOUNTAIN TOP UNIVERSITY 2024 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve the system of equations: \( egin{cases} x + y = 2 \ 2x - 3y = - 1 \end{cases} \).
A. \( x = 1, y = 1 \)
B. \( x = 2, y = 0 \)
C. \( x = 0, y = 2 \)
D. \( x = 1, y = 2 \)
Question 2
Find the equation of the line pas\sing through the points ( (1, 2) ) and ( (3, 4) ).
A. y = 2x - 1
B. y = 2x + 1
C. y = x + 1
D. y = x - 1
Question 3
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 4
Solve the inequality \( 2x^2 - 5x - 3 > 0 \).
A. \( x < -1 \) or \( x > 3 \)
B. \( x < -1 \) or \( x < 3 \)
C. \( x > -1 \) or \( x > 3 \)
D. \( x > -1 \) or \( x < 3 \)
Question 5
Solve the equation [ x^2 + 4x + 4 = 0 ] u\sing the quadratic formula.
A. 0
B. -2
C. 2
D. -4
Question 6
Solve the inequality |x - 2| > 3.
A. x < -1 or x > 5
B. x < 1 or x > 5
C. x < -1 or x > 4
D. x < 1 or x > 4
Question 7
In the number base 8, what is the value of the expression \( 5 \times 8^2 + 3 \times 8^1 + 2 \times 8^0 \)?
A. 420
B. 422
C. 425
D. 427
Question 8
Solve for ( x ) in the equation \( 2^x + 3^x = 5^x \).
A. \( x = 2 \)
B. \( x = 3 \)
C. \( x = 4 \)
D. \( x = 5 \)
Question 9
Find the value of \( \sin 2x \) if \( \sin x = \frac{1}{2} \) and ( x ) is in the first quadrant.
A. \( \frac{1}{2} \)
B. \( \frac{\sqrt{3}}{2} \)
C. \( \frac{1}{\sqrt{2}} \)
D. \( \frac{\sqrt{2}}{2} \)
Question 10
Solve the equation \( x^3 - 6x^2 + 11x - 6 = 0 \ \) u\sing the rational root theorem.
A. \( x = 1 \)
B. \( x = 2 \)
C. \( x = 3 \)
D. \( x = 6 \)
Question 11
Find the derivative of the function ( f(x) = \frac{1}{x^2 + 1} \) u\sing the chain rule.
A. \( -\frac{2x}{\( x^2 + 1 \)^2} \)
B. \( \frac{2x}{\( x^2 + 1 \)^2} \)
C. \( -\frac{2}{\( x^2 + 1 \)^2} \)
D. \( \frac{2}{\( x^2 + 1 \)^2} \)
Question 12
A set 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 will be between 60 and 90?
A. 0.9544
B. 0.8413
C. 0.6915
D. 0.6827
Question 13
A set ( A ) contains the elements ( { 1, 2, 3, 4, 5 } ). Find the number of subsets of ( A ) that contain exactly two elements.
A. 10
B. 20
C. 30
D. 40
Question 14
Solve the inequality \( \frac{x}{x-2} > 0 \) for ( x in mathbb{R} setminus {2} ).
A. \( -\infty, 2 \) \cup \( 2, \infty \)
B. \( -\infty, 2 \) \cup (2, 4)
C. (2, 4)
D. \( -\infty, 2 \) \cup \( 4, \infty \)
Question 15
Find the equation of the circle pas\sing through the points (1, 2), (3, 4), and (5, 6).
A. \( x^2 + y^2 - 6x - 4y + 9 = 0 \)
B. \( x^2 + y^2 + 6x + 4y + 9 = 0 \)
C. \( x^2 + y^2 - 6x + 4y + 9 = 0 \)
D. \( x^2 + y^2 + 6x - 4y + 9 = 0 \)

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