POST UTME BELLS UNIVERSITY 2018 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve the inequality $\frac{x-2}{x+1} > 0$.
A. x<-1
B. x>-1
C. x<2
D. x>2
Question 2
Find the area under the curve \[y = \frac{1}{x^2 + 1}\] from \[x = 0\] to \[x = 1\].
A. \text{The area under the curve is } \frac{\pi}{2}.
B. \text{The area under the curve is } \frac{\pi}{4}.
C. \text{The area under the curve is } \frac{\pi}{6}.
D. \text{The area under the curve is } \frac{\pi}{8}.
Question 3
Convert the \fraction \[\frac{3}{4}\] to a decimal.
A. \text{The decimal equivalent is } 0.75.
B. \text{The decimal equivalent is } 0.5.
C. \text{The decimal equivalent is } 0.25.
D. \text{The decimal equivalent is } 0.1.
Question 4
A sequence is defined by the recurrence relation \( a_n = 2a_{n-1} + 3 \) with initial term \( a_1 = 2 \). Find the value of \( a_5 \).
A. 41
B. 43
C. 45
D. 47
Question 5
Find the derivative of the function ( f(x) = \frac{x^2}{x+1} ) u\sing the quotient rule.
A. \frac{2x\( x+1 \)-x^2}{\( x+1 \)^2}
B. \frac{x^2}{\( x+1 \)^2}
C. \frac{2x}{\( x+1 \)^2}
D. \frac{x^2}{x+1}
Question 6
A 3x3 matrix is given by the following equation: [ A = egin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix} ]. What is the determinant of matrix A?
A. 0
B. 1
C. 2
D. 3
Question 7
In a survey of 100 students, the mean height was 170 cm with a s\tandard deviation of 5 cm. If the heights of the students are normally distributed, what is the probability that a randomly selected student will be taller than 180 cm?
A. 0.1587
B. 0.3413
C. 0.4772
D. 0.6827
Question 8
A sequence is given by the following equation: [ a_n = 2n + 1 ]. What is the 5th term of the sequence?
A. 11
B. 13
C. 15
D. 17
Question 9
The volume of a sphere (V) is given by the formula \( V = \frac{4}{3} \pi r^3 \ \). If the radius of the sphere is increased by 20%, what percentage increase will occur in its volume?
A. 4%
B. 12%
C. 24%
D. 48%
Question 10
Solve the system of equations: \( x + y = 4 \) and \( 2x - 3y = - 6 \).
A. \( x = 2, y = 2 \)
B. \( x = 3, y = 1 \)
C. \( x = 4, y = 0 \)
D. \( x = 5, y = -1 \)
Question 11
Solve the system of equations u\sing matrices:\n\( egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 3 \ 7 \end{bmatrix} \)
A. \( egin{bmatrix} -1 \ 2 \end{bmatrix} \)
B. \( egin{bmatrix} 1 \ -2 \end{bmatrix} \)
C. \( egin{bmatrix} 2 \ -1 \end{bmatrix} \)
D. \( egin{bmatrix} -2 \ 1 \end{bmatrix} \)
Question 12
Find the derivative of the function f(x) = \frac{x^2}{x^2 + 1} u\sing the quotient rule.
A. \frac{2x\( x^2 + 1 \) - 2x^2}{\( x^2 + 1 \)^2}
B. \frac{2x^2 - 2x^2\( x^2 + 1 \)}{\( x^2 + 1 \)^2}
C. \frac{2x\( x^2 + 1 \) - 2x^2}{\( x^2 + 1 \)^2}
D. \frac{2x^2 - 2x\( x^2 + 1 \)}{\( x^2 + 1 \)^2}
Question 13
The mean of five numbers is 20. If one of the numbers is increased by 10, what will be the new mean?
A. 20
B. 21
C. 22
D. 23
Question 14
Solve the inequality \[x^2 - 4x + 3 \geq 0\].
A. \text{The solution to the inequality is } x \leq 1 \text{ or } x \geq 3.
B. \text{The solution to the inequality is } x \leq 3 \text{ or } x \geq 1.
C. \text{The solution to the inequality is } x \leq 1 \text{ and } x \geq 3.
D. \text{The solution to the inequality is } x \leq 3 \text{ and } x \geq 1.
Question 15
A histogram is constructed from the following data: 2, 4, 5, 7, 8, 9, 10. What is the class width?
A. 1
B. 2
C. 3
D. 4

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