POST UTME UNILORIN 2022 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A random experiment consists of rolling a fair six-sided die. If the number rolled is even, the experimenter wins. If the number rolled is odd, the experimenter loses. What is the probability of winning?
A. \( \frac{1}{2} \)
B. \( \frac{1}{3} \)
C. \( \frac{2}{3} \)
D. \( \frac{3}{4} \)
Question 2
Find the volume of the solid formed by rotating the region bounded by \( y = x^2 \) and \( y = 4 - x \) about the x-axis.
A. 16π/3
B. 32π/3
C. 64π/3
D. 128π/3
Question 3
In a random sample of 50 students, the mean height is 175 cm with a s\tandard deviation of 5 cm. If the sample is normally distributed, what is the probability that a randomly selected student will have a height between 170 cm and 180 cm?
A. 0.68
B. 0.84
C. 0.98
D. 0.99
Question 4
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. x < -1 or x > 3/2
B. x < 1 or x > 3
C. x < -1 or x < 3/2
D. x < 1 or x < 3
Question 5
Solve the inequality \( \frac{x}{x-2} > 0 \) for ( x in mathbb{R} setminus {2} ).
A. \( -∞, 2 \) ∪ (2, ∞)
B. \( -∞, 2 \) ∪ (2, ∞) ∪ {2}
C. \( -∞, 2 \) ∪ (2, ∞) ∪ \( -2, 2 \)
D. \( -∞, 2 \) ∪ (2, ∞) ∪ (2, ∞)
Question 6
Solve the system of equations \( x + y = 2 \) and \( xy = 1 \).
A. \( x = 1, y = 1 \)
B. \( x = 1, y = -1 \)
C. \( x = -1, y = 1 \)
D. \( x = -1, y = -1 \)
Question 7
A right-angled triangle has a hypotenuse of 10 cm and one leg of 6 cm. What is the length of the other leg?
A. 8 cm
B. 8.66 cm
C. 8.89 cm
D. 9.01 cm
Question 8
Find the area under the curve \( y = 2x^2 + 3x - 1 \) from \( x = 0 \) to \( x = 2 \).
A. 13/3
B. 26/3
C. 39/3
D. 52/3
Question 9
Solve for x in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 10
B. 100
C. 1000
D. 10000
Question 10
A polynomial function is defined as ( f(x) = 2x^3 - 5x^2 + 3x - 1 ). What is the value of \( f\( -1 \ \) )?
A. -3
B. -2
C. -1
D. 0
Question 11
Find the derivative of the function ( f(x) = \frac{1}{x^2} ) u\sing the chain rule.
A. ( f'(x) = -\frac{2}{x^3} )
B. ( f'(x) = \frac{2}{x^3} )
C. ( f'(x) = -\frac{1}{x^3} )
D. ( f'(x) = \frac{1}{x^3} )
Question 12
Find the volume of the solid formed by rotating the region bounded by \( y = x^2 \) and \( y = x \) about the x-axis.
A. \( \frac{1}{3} pi \)
B. \( \frac{2}{3} pi \)
C. \( \frac{4}{3} pi \)
D. \( \frac{5}{3} pi \)
Question 13
A sequence is defined by the formula \( a_n = 2n + 1 \). Find the sum of the first 5 terms of the sequence.
A. 15
B. 20
C. 25
D. 30
Question 14
Determine the mean of the following data set: {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.
A. 5
B. 6
C. 7
D. 8
Question 15
Find the value of x in the equation \( \frac{x}{x+1} = \frac{2}{3} \).
A. 2
B. 4
C. 6
D. 8

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