POST UTME UNILORIN 2022 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
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 2
Find the area of the triangle formed by the points ( (0, 0) ), ( (3, 0) ), and ( (0, 2) ).
A. ( 6 )
B. ( 8 )
C. ( 10 )
D. ( 12 )
Question 3
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 4
A histogram represents the distribution of exam scores for a class of 50 students. The histogram shows that 10 students scored between 70-79, 15 students scored between 80-89, and 25 students scored between 90-100. What is the median score of the class?
A. 85
B. 87
C. 90
D. 92
Question 5
A rec\tangular prism has a length of 5 cm, a width of 3 cm, and a height of 2 cm. What is its surface area?
A. 62 cm^2
B. 64 cm^2
C. 66 cm^2
D. 68 cm^2
Question 6
A histogram of exam scores has a mean of 75 and a s\tandard deviation of 10. If 80% of the scores lie within 2 s\tandard deviations of the mean, what is the minimum score that 80% of the students scored?
A. 50
B. 55
C. 60
D. 65
Question 7
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 8
Determine the mean of the data set {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} u\sing the formula \( ar{x} = \frac{1}{n} sum_{i=1}^{n} x_i \).
A. 5
B. 6
C. 7
D. 8
Question 9
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 10
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 11
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 12
Solve the trigonometric equation \sin(x) = \cos(x) for 0° ≤ x ≤ 360°.
A. 45°, 225°
B. 45°, 225°
C. 45°, 225°
D. 45°, 225°
Question 13
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 14
Find the derivative of the function ( f(x) = \frac{1}{\sqrt{1-x^2}} ) u\sing the chain rule.
A. ( f'(x) = \frac{-x}{\( 1-x^2 \)^{3/2}} )
B. ( f'(x) = \frac{x}{\( 1-x^2 \)^{3/2}} )
C. ( f'(x) = \frac{1}{\( 1-x^2 \)^{3/2}} )
D. ( f'(x) = \frac{-1}{\( 1-x^2 \)^{3/2}} )
Question 15
Find the value of x in the equation \( x^2 - 4x - 5 = 0 \).
A. 1
B. 2
C. 3
D. 4

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