POST UTME AFE BABALOLA UNIVERSITY 2018 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A histogram is a graphical representation of the distribution of a set of data. What is the primary advantage of u\sing a histogram over a bar chart?
A. It provides a more detailed view of the data distribution
B. It is easier to read and unders\tand
C. It is more suitable for large datasets
D. It is more visually appealing
Question 2
A histogram is constructed with a bin width of 5 units. If the mean of the data is 15 and the median is 10, what is the mode?
A. 5
B. 10
C. 15
D. 20
Question 3
Find the mean and s\tandard deviation of the random variable X with probability density function f_X(x) = \frac{1}{2}x, 0 < x < 2.
A. \mu = 1, \sigma = \frac{1}{\sqrt{3}}
B. \mu = 1, \sigma = \frac{1}{\sqrt{2}}
C. \mu = 1, \sigma = \frac{1}{\sqrt{5}}
D. \mu = 1, \sigma = \frac{1}{\sqrt{6}}
Question 4
Find the determinant of the matrix \begin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix}.
A. 0
B. 1
C. -1
D. 2
Question 5
If ( f(x) = \frac{1}{x^2 + 1} ), find ( f'(x) ) u\sing the chain rule.
A. -\frac{2x}{\( x^2 + 1 \)^2}
B. \frac{2x}{\( x^2 + 1 \)^2}
C. \frac{2}{\( x^2 + 1 \)^2}
D. -\frac{2}{\( x^2 + 1 \)^2}
Question 6
A right circular cone has a radius of 6 cm and a height of 8 cm. Find the volume of the cone.
A. 452.389
B. 452.390
C. 452.391
D. 452.392
Question 7
Find the sum of the first 10 terms of the arithmetic sequence 3, 6, 9, ...
A. 60
B. 90
C. 120
D. 150
Question 8
Find the vector projection of vector \mathbf{b} = \begin{pmatrix} 2 \ 3 \ 4 \end{pmatrix} onto vector \mathbf{a} = \begin{pmatrix} 1 \ 2 \ 3 \end{pmatrix}.
A. \begin{pmatrix} 0.4 \ 0.8 \ 1.2 \end{pmatrix}
B. \begin{pmatrix} 0.2 \ 0.4 \ 0.6 \end{pmatrix}
C. \begin{pmatrix} 0.6 \ 1.2 \ 1.8 \end{pmatrix}
D. \begin{pmatrix} 0.8 \ 1.6 \ 2.4 \end{pmatrix}
Question 9
Find the equation of the line pas\sing through the points (2, 3) and (4, 5).
A. y = 2x - 1
B. y = 2x + 1
C. y = -2x + 1
D. y = -2x - 1
Question 10
Solve the matrix equation \( egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 7 \ 10 \end{bmatrix} \).
A. x = 3, y = 2
B. x = 2, y = 3
C. x = 1, y = 4
D. x = 4, y = 1
Question 11
In a circle with center at point O and radius 6 units, what is the length of the arc intercepted by a central angle of 60 degrees?
A. 6\pi
B. 3\pi
C. 2\pi
D. \pi
Question 12
Find the equation of the circle with center ( (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. \( x - 4 \)^2 + \( y - 3 \)^2 = 16
D. \( x - 2 \)^2 + \( y - 4 \)^2 = 16
Question 13
Find the area under the curve y = x^2 + 2x + 1 from x = 0 to x = 3.
A. 27
B. 30
C. 33
D. 36
Question 14
Solve the system of linear equations \( egin{cases} x + 2y = 4 \ 3x - 2y = 5 \end{cases} \).
A. x = 2, y = 1
B. x = 1, y = 2
C. x = 2, y = 2
D. x = 1, y = 1
Question 15
Find the area of the triangle with vertices ( A(0, 0) ), ( B(3, 0) ), and ( C(0, 4) ).
A. 6
B. 8
C. 12
D. 16

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