POST UTME UNIPORT 2024 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A quadratic equation has roots at x = 2 and x = 4. What is the equation of the axis of symmetry?
A. x = 3
B. x = 2
C. x = 4
D. x = 1
Question 2
A random variable X has a probability distribution given by P\( X = 1 \) = 0.4, P\( X = 2 \) = 0.3, P\( X = 3 \) = 0.2, and P\( X = 4 \) = 0.1. What is the expected value of X?
A. 1.5
B. 2.0
C. 2.5
D. 3.0
Question 3
Convert the number 1011 from base 2 to base 10.
A. 11
B. 13
C. 15
D. 17
Question 4
Find the equation of the circle pas\sing through the points (2,3), (4,5) and (6,7).
A. \( x^2 + y^2 - 12x - 16y + 60 = 0 \)
B. \( x^2 + y^2 - 14x - 20y + 80 = 0 \)
C. \( x^2 + y^2 - 16x - 24y + 100 = 0 \)
D. \( x^2 + y^2 - 18x - 28y + 120 = 0 \)
Question 5
Determine the volume of the frustum of a cone with a height of 10 cm, a lower base radius of 4 cm, and an upper base radius of 6 cm.
A. 100π cm³
B. 150π cm³
C. 200π cm³
D. 250π cm³
Question 6
If ( f(x) = 2x^3 - 5x^2 + x - 1 ), find the derivative of ( f(x) ) u\sing the power rule.
A. ( f'(x) = 6x^2 - 10x + 1 )
B. ( f'(x) = 6x^2 - 10x - 1 )
C. ( f'(x) = 6x^2 - 10x + 2 )
D. ( f'(x) = 6x^2 - 10x - 2 )
Question 7
Let $X$ and $Y$ be indep\endent random variables with probability density functions $f_X(x) = egin{cases} 2x & \text{if } 0 leq x leq 1 \ 0 & \text{otherwise} \end{cases}$ and $f_Y(y) = egin{cases} 3y^2 & \text{if } 0 leq y leq 1 \ 0 & \text{otherwise} \end{cases}$. Find the probability that $X + Y leq 1$.
A. \frac{1}{2}
B. \frac{1}{3}
C. \frac{2}{3}
D. \frac{3}{4}
Question 8
Solve the inequality \frac{x + 2}{x - 1} > 0.
A. \text{Solution: } x < -2 \text{ or } x > 1
B. \text{Solution: } x < -2 \text{ or } x < 1
C. \text{Solution: } x > -2 \text{ or } x > 1
D. \text{Solution: } x < -2 \text{ or } x < 1
Question 9
A fair six-sided die is rolled. Find the probability that the number rolled is greater than 4.
A. \frac{1}{6}
B. \frac{2}{6}
C. \frac{3}{6}
D. \frac{4}{6}
Question 10
Find the equation of the circle pas\sing through the points (2, 3), (4, 5), and \( -1, 1 \).
A. \left\( x - 1 \right \)^2 + \left\( y - 1 \right \)^2 = 10
B. \left\( x + 1 \right \)^2 + \left\( y - 1 \right \)^2 = 10
C. \left\( x - 1 \right \)^2 + \left\( y + 1 \right \)^2 = 10
D. \left\( x + 1 \right \)^2 + \left\( y + 1 \right \)^2 = 10
Question 11
A histogram of exam scores has a mean of 60 and a s\tandard deviation of 10. If the scores are normally distributed, find the probability that a randomly selected score is greater than 70.
A. \text{Probability: } P\( X > 70 \) = 0.1587
B. \text{Probability: } P\( X > 70 \) = 0.8413
C. \text{Probability: } P\( X > 70 \) = 0.1587
D. \text{Probability: } P\( X > 70 \) = 0.8413
Question 12
A histogram of exam scores has a mean of 60 and a s\tandard deviation of 10. What is the z-score of a score of 70?
A. 0.5
B. 1.0
C. 1.5
D. 2.0
Question 13
Solve the inequality \( \frac{x^2 - 4x - 5}{x^2 - 6x + 8} > 0 \) for ( x in mathbb{R} ).
A. \( x in \( -infty, -1 \ \) cup (2, infty) )
B. \( x in \( -infty, -2 \ \) cup (1, infty) )
C. \( x in \( -infty, -3 \ \) cup (0, infty) )
D. \( x in \( -infty, -4 \ \) cup (1, infty) )
Question 14
Find the derivative of the function \( y = \sqrt{2x + 1} \) u\sing the chain rule.
A. 1/\( 2√\( 2x + 1 \ \))
B. 1/\( 2√\( 2x + 1 \ \)) * \( 2x + 1 \)
C. 1/\( 2√\( 2x + 1 \ \)) * \( 2x + 1 \)^2
D. 1/\( 2√\( 2x + 1 \ \)) * \( 2x + 1 \)^3
Question 15
Find the equation of the line pas\sing through the points (2, 3) and (4, 5).
A. y = \frac{2}{2}x + 1
B. y = \frac{2}{2}x - 1
C. y = \frac{2}{2}x + 2
D. y = \frac{2}{2}x - 2

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