POST UTME KSU 2024 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A fair six-sided die is rolled. What is the probability that the number rolled is greater than 4?
A. \frac{1}{6}
B. \frac{1}{3}
C. \frac{2}{3}
D. \frac{5}{6}
Question 2
A sequence is defined by the recurrence relation \( a_n = 2a_{n-1} + 1 \), with initial term \( a_1 = 3 \). Find the sum of the first five terms of the sequence.
A. 3 + 7 + 15 + 31 + 63
B. 3 + 5 + 11 + 23 + 47
C. 3 + 7 + 15 + 31 + 63
D. 3 + 5 + 11 + 23 + 47
Question 3
A circle has a radius of 4 cm. Find the area of the circle.
A. \[ A = 16\pi \text{ cm}^2 \]
B. \[ A = 32\pi \text{ cm}^2 \]
C. \[ A = 64\pi \text{ cm}^2 \]
D. \[ A = 128\pi \text{ cm}^2 \]
Question 4
Let ( X ) and ( Y ) be indep\endent random variables with probability density functions \( f_X\( x \ \) = egin{cases} 2x & 0 leq x leq 1 \ 0 & \text{otherwise} \end{cases} ) and \( f_Y\( y \ \) = egin{cases} 3y^2 & 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 5
A particle moves in a straight line with a velocity ( v(t) = 2t + 5 ) m/s. Find the displacement of the particle from \( t = 0 \) to \( t = 3 \) seconds.
A. 21
B. 25
C. 30
D. 35
Question 6
Solve the equation \( x^2 + 4x + 4 = 0 \) by factoring.
A. \( x + 2 \ \)^2 = 0 )
B. \( x + 1 \ \)^2 = 0 )
C. \( x - 2 \ \)^2 = 0 )
D. \( x - 1 \ \)^2 = 0 )
Question 7
Find the derivative of the function ( f(x) = \frac{1}{x^2 + 1} ) u\sing the chain rule.
A. \( \frac{-2x}{\( x^2 + 1 \ \)^2} )
B. \( \frac{2x}{\( x^2 + 1 \ \)^2} )
C. \( \frac{2}{\( x^2 + 1 \ \)^2} )
D. \( \frac{-2}{\( x^2 + 1 \ \)^2} )
Question 8
Solve the inequality \( 2x^2 - 5x - 3 > 0 \).
A. \[ x < -1 \text{ or } x > \frac{3}{2} \]
B. \[ x < -1 \text{ or } x < \frac{3}{2} \]
C. \[ x > -1 \text{ or } x > \frac{3}{2} \]
D. \[ x < -1 \text{ and } x > \frac{3}{2} \]
Question 9
Solve the system of equations: \( 2x + 3y = 7 \) and \( x - 2y = -3 \).
A. x = 1, y = 2
B. x = 2, y = 1
C. x = 3, y = 4
D. x = 4, y = 3
Question 10
Find the sum of the infinite geometric series \( 1 + \frac{1}{2} + \frac{1}{4} + \cdots \).
A. 2
B. 4
C. 6
D. 8
Question 11
Solve the inequality \( 2x^2 - 5x - 3 > 0 \) by factoring.
A. \( x - 3 \)\( x + 1 \ \) > 0 )
B. \( x - 1 \)\( x + 3 \ \) > 0 )
C. \( x + 3 \)\( x - 1 \ \) > 0 )
D. \( x + 1 \)\( x - 3 \ \) > 0 )
Question 12
Find the equation of the line pas\sing through the points ( (1, 2) ) and ( (3, 4) ).
A. \( y = \frac{2}{1}x + \frac{2}{1} \)
B. \( y = \frac{2}{1}x - \frac{2}{1} \)
C. \( y = \frac{2}{1}x + \frac{4}{1} \)
D. \( y = \frac{2}{1}x - \frac{4}{1} \)
Question 13
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 4 \) from \( x = 0 \) to \( x = 2 \).
A. 10
B. 12
C. 14
D. 16
Question 14
Solve for ( x ) in the equation \( 2^x + 3^x = 5^x \).
A. 1
B. 2
C. 3
D. 4
Question 15
Find the derivative of the function ( f(x) = \frac{1}{x^2 + 1} ) u\sing the chain rule.
A. -\frac{2x}{\( x^2 + 1 \)^2}
B. \frac{2x}{\( x^2 + 1 \)^2}
C. -\frac{2}{\( x^2 + 1 \)^2}
D. \frac{2}{\( x^2 + 1 \)^2}

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