POST UTME EKSU 2020 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( x < -1 \) or \( x > 3 \)
B. \( x < -3 \) or \( x > 1 \)
C. \( x < -5 \) or \( x > 2 \)
D. \( x < -2 \) or \( x > 4 \)
Question 2
A rec\tangular prism has dimensions 2m x 3m x 4m. Find the surface area of the prism in square meters.
A. 40
B. 50
C. 60
D. 70
Question 3
Solve the system of equations \( x + y = 2 \) and \( x - y = 1 \)
A. x = 1, y = 1
B. x = 1, y = 2
C. x = 2, y = 1
D. x = 2, y = 2
Question 4
Find the derivative of the function ( f(x) = \frac{1}{x^2 + 1} ) u\sing the chain rule.
A. ( f'(x) = \frac{-2x}{\( x^2 + 1 \)^2} )
B. ( f'(x) = \frac{2x}{\( x^2 + 1 \)^2} )
C. ( f'(x) = \frac{2}{\( x^2 + 1 \)^2} )
D. ( f'(x) = \frac{-2}{\( x^2 + 1 \)^2} )
Question 5
A histogram of exam scores has a mean of 70 and a s\tandard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score is between 60 and 80?
A. \( P\( 60 < X < 80 \ \) = \frac{1}{2} )
B. \( P\( 60 < X < 80 \ \) = \frac{3}{10} )
C. \( P\( 60 < X < 80 \ \) = \frac{5}{10} )
D. \( P\( 60 < X < 80 \ \) = \frac{7}{10} )
Question 6
Solve for ( x ) in the equation \( egin{bmatrix} 2 & 1 \ 1 & 2 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 3 \ 3 \end{bmatrix} \).
A. \( x = 1, y = 1 \)
B. \( x = 2, y = 2 \)
C. \( x = 3, y = 3 \)
D. \( x = 4, y = 4 \)
Question 7
A right-angled triangle has sides of length 3cm, 4cm, and 5cm. Find the area of the triangle in square centimeters.
A. 6
B. 12
C. 18
D. 24
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 = 32 )
C. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 64 )
D. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 128 )
Question 9
A geometric sequence has a first term of 2 and a common ratio of 3. What is the sum of the first 5 terms?
A. \( 2\( 1 + 3 + 3^2 + 3^3 + 3^4 \ \) )
B. \( 2\( 1 + 3 + 3^2 + 3^3 + 3^4 + 3^5 \ \) )
C. \( 2\( 1 + 3 + 3^2 + 3^3 + 3^4 + 3^5 + 3^6 \ \) )
D. \( 2\( 1 + 3 + 3^2 + 3^3 + 3^4 + 3^5 + 3^6 + 3^7 \ \) )
Question 10
A sphere has a radius of 3cm. Find the volume of the sphere in cubic centimeters.
A. 90
B. 120
C. 150
D. 180
Question 11
Solve the equation: \( 2^x + 2^x = 2^{x+2} \).
A. x = 1
B. x = 2
C. x = 3
D. x = 4
Question 12
A binary operation ( odot ) is defined as \( a odot b = ab + 2 \). Find the value of ( 3 odot 4 ).
A. 14
B. 16
C. 18
D. 20
Question 13
Determine the equation of the circle with center at (2, 3) and radius 4.
A. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 16 )
B. \( x - 3 \ \)^2 + \( y - 2 \)^2 = 16 )
C. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 9 )
D. \( x - 3 \ \)^2 + \( y - 2 \)^2 = 9 )
Question 14
Find the surface area of the sphere with radius 5 cm.
A. \( 4 pi \( 5^2 \ \) )
B. \( 2 pi \( 5^2 \ \) )
C. \( pi \( 5^2 \ \) )
D. \( \frac{1}{2} pi \( 5^2 \ \) )
Question 15
A circle has a radius of 4 cm. What is the area of the circle?
A. \( pi \( 4^2 \ \) )
B. \( 2 pi \( 4^2 \ \) )
C. \( \frac{1}{2} pi \( 4^2 \ \) )
D. \( \frac{1}{4} pi \( 4^2 \ \) )

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