POST UTME UNILAG 2024 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
In the diagram below, ABC is a right-angled triangle with AB = 6 cm and BC = 8 cm. Find the length of AC.
A. 4 cm
B. 6 cm
C. 8 cm
D. 10 cm
Question 2
Let ( f(x) = \frac{x^2 - 4}{x - 2} ). Find the derivative of ( f(x) ) u\sing the chain rule, and simplify your answer.
A. ( f'(x) = \frac{2x}{x - 2} \)
B. ( f'(x) = \frac{x^2 - 4}{\( x - 2 \)^2} \)
C. ( f'(x) = \frac{2x\( x - 2 \)}{\( x - 2 \)^2} \)
D. ( f'(x) = \frac{x^2 - 4}{x^2 - 4x + 4} \)
Question 3
Find the determinant of the matrix \[ \begin{array}{ccc} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \ \end{array} \]
A. 0
B. 1
C. 2
D. 3
Question 4
A histogram of exam scores has a mean of 70 and a s\tandard deviation of 10. If 95% of the scores lie within 2 s\tandard deviations of the mean, what is the lower limit of the interval?
A. 50
B. 60
C. 65
D. 55
Question 5
Solve the inequality \( 2x^2 - 5x - 3 > 0 \).
A. \( -∞, -1 \) ∪ (3, ∞)
B. \( -∞, 1 \) ∪ (3, ∞)
C. \( -∞, -3 \) ∪ (1, ∞)
D. \( -∞, 3 \) ∪ (1, ∞)
Question 6
A histogram of exam scores is shown below. Find the mean score.
A. ( 60 )
B. ( 70 )
C. ( 80 )
D. ( 90 )
Question 7
Find the surface area of the solid formed by revolving the region bounded by the curve \( y = x^2 \) and the line \( x = 2 \) about the x-axis.
A. 16\pi
B. 32\pi
C. 64\pi
D. 128\pi
Question 8
Find the derivative of the function ( f(x) = \frac{1}{x^2 + 1} ) u\sing the chain rule.
A. -2x/\( x^2 + 1 \)^2
B. 2x/\( x^2 + 1 \)^2
C. -2/\( x^2 + 1 \)^2
D. 2/\( x^2 + 1 \)^2
Question 9
Solve the system of equations \( egin{cases} x + y = 4 \ x - y = 2 \end{cases} \).
A. {(2, 2), (3, 1)}
B. {(1, 3), (2, 2)}
C. {(2, 2), (1, 3)}
D. {(3, 1), (1, 3)}
Question 10
Find the volume of the solid formed by revolving the region bounded by the curve \( y = x^2 \) and the line \( x = 2 \) about the x-axis.
A. 16\pi
B. 32\pi
C. 64\pi
D. 128\pi
Question 11
A right-angled triangle has sides of length 3, 4, and 5. Find the area of the triangle.
A. 6
B. 12
C. 18
D. 24
Question 12
Solve the equation \( x^2 - 4x + 4 = 0 \).
A. x = 2
B. x = 1
C. x = 0
D. x = -2
Question 13
Solve for x in the equation: 2^x + 5^x = 7^x.
A. x = 1
B. x = 2
C. x = 3
D. x = 4
Question 14
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).
A. 40
B. 50
C. 60
D. 70
Question 15
Solve for x in the equation \( x^2 - 6x + 8 = 0 \)
A. 2
B. 3
C. 4
D. 5

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