POST UTME UNIOSUN 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 \( x > \frac{3}{2} \)
B. \( x < -1 \) or \( x < \frac{3}{2} \)
C. \( x > -1 \) or \( x < \frac{3}{2} \)
D. \( x > -1 \) or \( x > \frac{3}{2} \)
Question 2
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 3
Solve the inequality \( \frac{x^2 - 4}{x + 2} > 0 \) for ( x in mathbb{R} ).
A. \( x < -2 \) or \( x > 2 \)
B. \( x > -2 \) and \( x < 2 \)
C. \( x < -2 \) or \( x = 2 \)
D. \( x > -2 \) or \( x = 2 \)
Question 4
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. 242
B. 243
C. 244
D. 245
Question 5
Solve the quadratic equation \( x^2 + 4x + 4 = 0 \).
A. \( x = -2 \)
B. \( x = 2 \)
C. \( x = -1 \) or \( x = 4 \)
D. \( x = -4 \) or \( x = 1 \)
Question 6
A set of 10 numbers has a mean of 20. If 5 new numbers are added to the set, the mean increases to 25. What is the sum of the original 10 numbers?
A. 150
B. 200
C. 250
D. 300
Question 7
A fair six-sided die is rolled. What is the probability that the number obtained is a multiple of 3?
A. \frac{1}{2}
B. \frac{1}{3}
C. \frac{2}{3}
D. \frac{4}{5}
Question 8
A cylindrical \tank with a radius of 4m and a height of 6m is filled with water. If the density of water is 1000kg/m^3, calculate the volume of water in the \tank.
A. 120\pi m^3
B. 240\pi m^3
C. 360\pi m^3
D. 480\pi m^3
Question 9
A binary operation ( ast ) is defined as \( a ast b = a^2 + b^2 \). Find the value of ( 2 ast 3 ).
A. 5
B. 7
C. 9
D. 11
Question 10
A bag contains 5 red marbles, 3 blue marbles, and 2 green marbles. If a marble is drawn at random, what is the probability that it is blue?
A. \( \frac{1}{10} \)
B. \( \frac{1}{5} \)
C. \( \frac{3}{10} \)
D. \( \frac{2}{5} \)
Question 11
A histogram shows the distribution of exam scores for a class of 20 students. The histogram has 5 bars, each representing a range of scores. The heights of the bars are 2, 3, 4, 5, and 6. What is the mean score of the class?
A. 4
B. 5
C. 6
D. 7
Question 12
Solve for ( x ) in the equation \( 2^x + 3^x = 5^x \).
A. 1
B. 2
C. 3
D. 4
Question 13
Find the value of \( \log_{10} \left\( \frac{1}{2} \right \ \) + \log_{10} \left\( \frac{1}{3} \right \) ).
A. -1
B. -2
C. -3
D. -4
Question 14
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 15
Let \( mathbf{a} = egin{pmatrix} 2 \ 3 \end{pmatrix} \) and \( mathbf{b} = egin{pmatrix} 1 \ -2 \end{pmatrix} \). Find the projection of ( mathbf{b} ) onto ( mathbf{a} ).
A. \( egin{pmatrix} 0 \ 0 \end{pmatrix} \)
B. \( egin{pmatrix} 1 \ 2 \end{pmatrix} \)
C. \( egin{pmatrix} 2 \ -4 \end{pmatrix} \)
D. \( egin{pmatrix} 4 \ -8 \end{pmatrix} \)

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