POST UTME FUTO 2024 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A right triangle has a hypotenuse of 10 cm and one leg of 6 cm. What is the length of the other leg?
A. 8
B. 8.66
C. 8.94
D. 9.22
Question 2
Simplify the expression \( \frac{1}{\sqrt{2}} + \frac{1}{\sqrt{3}} \).
A. \\frac{\\sqrt{3} + \\sqrt{2}}{\\sqrt{6}}
B. \\frac{\\sqrt{3} - \\sqrt{2}}{\\sqrt{6}}
C. \\frac{\\sqrt{3} + \\sqrt{2}}{\\sqrt{6}}
D. \\frac{\\sqrt{3} - \\sqrt{2}}{\\sqrt{6}}
Question 3
Solve the inequality \( 2x - 5 > 3 \).
A. x > 4
B. x > 3
C. x > 2
D. x > 1
Question 4
Find the volume of the frustum of a cone with height 6, lower base radius 4, and upper base radius 2.
A. \frac{1}{3} \pi (6) \( 4^2 + 2^2 + 4 \cdot 2 \)
B. \frac{1}{3} \pi (6) \( 4^2 + 2^2 - 4 \cdot 2 \)
C. \frac{1}{3} \pi (6) \( 4^2 - 2^2 + 4 \cdot 2 \)
D. \frac{1}{3} \pi (6) \( 4^2 - 2^2 - 4 \cdot 2 \)
Question 5
Find the sum of the first 10 terms of the geometric progression 2, 6, 18, ...
A. 2047
B. 2057
C. 2067
D. 2077
Question 6
Solve the equation $x^2 + 4x + 5 = 0$.
A. x = -2 \pm i
B. x = -1 \pm i
C. x = -2 \pm 2i
D. x = -1 \pm 2i
Question 7
Find the equation of the circle with center ( (2, 3) ) and radius ( 4 ).
A. \left\( x - 2 \right \)^2 + \left\( y - 3 \right \)^2 = 16
B. \left\( x - 3 \right \)^2 + \left\( y - 2 \right \)^2 = 16
C. \left\( x - 4 \right \)^2 + \left\( y - 3 \right \)^2 = 16
D. \left\( x - 2 \right \)^2 + \left\( y - 4 \right \)^2 = 16
Question 8
Find the equation of the circle with center ( (2, 3) ) and radius 4.
A. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 16 \)
B. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 20 \)
C. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 24 \)
D. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 28 \)
Question 9
Find the area under the curve \[y = \frac{1}{x^2 + 1}\] from x = 0 to x = 1.
A. \frac{\pi}{4}
B. \frac{\pi}{2}
C. \frac{\pi}{6}
D. \frac{\pi}{3}
Question 10
Solve the inequality \( x^2 + 2x - 3 > 0 \).
A. \left\( -\infty, -1 \right \) \cup \left\( 3, \infty \right \)
B. \left\( -\infty, 1 \right \) \cup \left\( 3, \infty \right \)
C. \left\( -\infty, -1 \right \) \cup \left\( 1, \infty \right \)
D. \left\( -\infty, \infty \right \)
Question 11
A set A contains 5 elements, and a set B contains 7 elements. If the number of elements in the union of sets A and B is 12, find the number of elements in the intersection of sets A and B.
A. 2
B. 3
C. 4
D. 5
Question 12
Find the value of x in the equation \( \sin^2\( x \ \) + \cos^2(x) = 1 ) if \( \tan\( x \ \) = \frac{3}{4} ).
A. π/4
B. π/6
C. π/3
D. π/2
Question 13
Find the area under the curve \( y = x^2 + 2x - 3 \) from \( x = 0 \) to \( x = 2 \).
A. \( 4 \ \)
B. \( 6 \ \)
C. \( 8 \ \)
D. \( 10 \ \)
Question 14
A circle has a radius of 4 cm. What is the area of the circle?
A. 50.24
B. 50.27
C. 50.31
D. 50.35
Question 15
A rec\tangular prism has a length of 5 cm, a width of 3 cm, and a height of 2 cm. What is the surface area of the prism?
A. 62
B. 65
C. 68
D. 70

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