POST UTME EKSU 2017 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A binary operation ( ast ) is defined as \( a ast b = a^2 + b^2 \). Find the value of ( 2 ast 3 ).
A. \( 2 ast 3 = 2^2 + 3^2 = 13 \)
B. \( 2 ast 3 = 2^2 - 3^2 = -5 \)
C. \( 2 ast 3 = 2^2 + 3^2 + 2 \times 2 \times 3 = 25 \)
D. \( 2 ast 3 = 2^2 + 3^2 - 2 \times 2 \times 3 = 1 \)
Question 2
Find the sum of the infinite geometric series $\sum_{n=1}^\infty \frac{2}{3^n}$.
A. 1
B. 2
C. 3
D. 4
Question 3
Find the derivative of the function \( y = \sin^2 x \) u\sing the chain rule.
A. \( y' = 2 \sin x \cos x \)
B. \( y' = \sin x \cos x \)
C. \( y' = 2 \cos x \)
D. \( y' = \sin x \)
Question 4
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( x > -1 \) or \( x < 3 \)
B. \( x > 1 \) or \( x < -3 \)
C. \( x > 3 \) or \( x < -1 \)
D. \( x > -3 \) or \( x < 1 \)
Question 5
Find the value of x in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 10
B. 100
C. 1000
D. 10000
Question 6
Find the determinant of the matrix \( egin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix} \).
A. (0)
B. (1)
C. \( -1 \)
D. (2)
Question 7
Find the sum of the first (10) terms of the geometric series with first term \( a = 2 \) and common ratio \( r = 3 \).
A. \( 2\( 3^{10} - 1 \ \))
B. \( 2\( 3^{10} + 1 \ \))
C. \( 2\( 3^{10} - 2 \ \))
D. \( 2\( 3^{10} + 2 \ \))
Question 8
A set of 4 numbers has a mean of 12 and a range of 8. If the largest number is 18, find the sum of the remaining 3 numbers.
A. ( 36 )
B. ( 38 )
C. ( 40 )
D. ( 42 )
Question 9
Find the value of x in the equation \( x^3 - 6x^2 + 11x - 6 = 0 \).
A. 1
B. 2
C. 3
D. 4
Question 10
Solve the inequality \( |x - 2| > 3 \).
A. \( x < -1 \text{ or } x > 5 \)
B. \( x < 1 \text{ or } x > 5 \)
C. \( x < -1 \text{ or } x > 2 \)
D. \( x < 1 \text{ or } x > 2 \)
Question 11
A random experiment has 3 possible outcomes: A, B, and C. If the probability of outcome A is 0.4, the probability of outcome B is 0.3, and the probability of outcome C is 0.3, find the probability that outcome A occurs.
A. ( 0.4 )
B. ( 0.3 )
C. ( 0.2 )
D. ( 0.1 )
Question 12
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).
A. \( \frac{1}{2} \times 4^3 + 3 \times \frac{4^2}{2} - 2 \times 4 \)
B. \( \frac{1}{2} \times 4^2 + 3 \times 4 - 2 \)
C. \( \frac{1}{2} \times 4^3 + 3 \times 4^2 - 2 \times 4 \)
D. \( \frac{1}{2} \times 4^2 + 3 \times \frac{4^2}{2} - 2 \times 4 \)
Question 13
Find the value of \( \log_{10} \( x^2 \ \) ) if \( x = 10 \).
A. 4
B. 6
C. 8
D. 10
Question 14
Find the equation of the circle with center at (2,3) and radius 4 in the form \( x - h \ \)^2 + \( y - k \)^2 = r^2).
A. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 16 )
B. \( x - 3 \ \)^2 + \( y - 2 \)^2 = 16 )
C. \( x - 2 \ \)^2 + \( y - 2 \)^2 = 16 )
D. \( x - 3 \ \)^2 + \( y - 3 \)^2 = 16 )
Question 15
A histogram is a graphical representation of the distribution of a set of data. What is the primary purpose of a histogram?
A. To show the mean of a data set
B. To show the median of a data set
C. To show the distribution of a data set
D. To show the s\tandard deviation of a data set

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