POST UTME UNILAG 2024 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A vector \overrightarrow{a} has a magnitude of 5 units and makes an angle of 30° with the positive x-axis. Find the x and y components of the vector.
A. 3, 4.33
B. 4.33, 3
C. 5, 5
D. 2, 3
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
Solve the inequality \( 2x^2 - 5x - 3 > 0 \).
A. \( -∞, -1 \) ∪ (3, ∞)
B. \( -∞, 1 \) ∪ (3, ∞)
C. \( -∞, -3 \) ∪ (1, ∞)
D. \( -∞, 3 \) ∪ (1, ∞)
Question 4
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 5
Solve for x in the equation \( x^2 - 6x + 8 = 0 \)
A. 2
B. 3
C. 4
D. 5
Question 6
Find the value of x in the equation \( \frac{1}{2}x + 5 = \frac{3}{4}x - 3 \)
A. 4
B. 6
C. 8
D. 10
Question 7
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. x < -1 or x > 3/2
B. x < 1 or x > -3/2
C. x < -3/2 or x > 1
D. x < 3/2 or x > -1
Question 8
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).
A. 64
B. 80
C. 96
D. 112
Question 9
A circle has a radius of 5 cm. Find the area of the circle
A. 25
B. 50
C. 75
D. 100
Question 10
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( -∞, -1 \) ∪ (3, ∞)
B. \( -∞, -3 \) ∪ (1, ∞)
C. \( -∞, 1 \) ∪ (3, ∞)
D. \( -∞, -3 \) ∪ (1, ∞)
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 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 13
Find the volume of the solid formed by revolving the region bounded by the parabola \( y = x^2 \) and the line \( x = 2 \) about the x-axis.
A. 16π/5
B. 32π/5
C. 64π/5
D. 128π/5
Question 14
A random variable ( X ) has a probability distribution given by \( P\( X = x \ \) = \frac{1}{2} \) for \( x = 1, 2, 3, 4, 5 \ \). Find the probability that ( X ) is greater than 3.
A. \frac{1}{4}
B. \frac{1}{2}
C. \frac{3}{4}
D. \frac{5}{8}
Question 15
A solid cone has a height of 8 cm and a base radius of 4 cm. Find the volume of the cone.
A. 32π cm³
B. 64π cm³
C. 128π cm³
D. 256π cm³

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