POST UTME RHEMA UNIVERSITY 2018 Mathematics | Objective

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Question 1
Solve the system of equations u\sing matrices:\n\begin{align*}\n2x+3y&=7\\nx-2y&=-3\n\end{align*}
A. \begin{pmatrix}1\-1\end{pmatrix}
B. \begin{pmatrix}2\-3\end{pmatrix}
C. \begin{pmatrix}3\-2\end{pmatrix}
D. \begin{pmatrix}4\-1\end{pmatrix}
Question 2
Find the vector equation of the line pas\sing through the points (P(2,3,1)) and (Q(4,5,3)).
A. \( vec{r} = vec{a} + lambda vec{b} \), where \( vec{a} = \( 2,3,1 \ \) ) and \( vec{b} = \( 2,2,2 \ \) )
B. \( vec{r} = vec{a} + lambda vec{b} \), where \( vec{a} = \( 2,3,1 \ \) ) and \( vec{b} = \( 2,1,2 \ \) )
C. \( vec{r} = vec{a} + lambda vec{b} \), where \( vec{a} = \( 2,3,1 \ \) ) and \( vec{b} = \( 1,2,2 \ \) )
D. \( vec{r} = vec{a} + lambda vec{b} \), where \( vec{a} = \( 2,3,1 \ \) ) and \( vec{b} = \( 2,2,1 \ \) )
Question 3
Find the sum of the first 5 terms of the geometric series ( 2, 6, 18, ... ).
A. ( 242 )
B. ( 242 )
C. ( 242 )
D. ( 242 )
Question 4
Find the value of x in the equation \( \sin x = \frac{1}{2} \) if ( x ) lies in the second quadrant.
A. 120°
B. 150°
C. 180°
D. 210°
Question 5
Solve the inequality \( |2x - 5| geq 3 \).
A. \( x leq -1 \) or ( x geq 4 )
B. ( x leq 1 ) or ( x geq 4 )
C. \( x leq -1 \) or ( x geq 3 )
D. ( x leq 1 ) or ( x geq 3 )
Question 6
Find the derivative of the function ( f(x) = \frac{1}{x^3 + 1} ) u\sing the chain rule.
A. -\frac{3x^2}{\( x^3 + 1 \)^2}
B. \frac{3x^2}{\( x^3 + 1 \)^2}
C. \frac{1}{\( x^3 + 1 \)^2}
D. -\frac{1}{\( x^3 + 1 \)^2}
Question 7
Solve the system of equations \( x + y = 4 \) and \( xy = 5 \).
A. \( x = 1, y = 3 \)
B. \( x = 2, y = 2 \)
C. \( x = 3, y = 1 \)
D. \( x = 4, y = 0 \)
Question 8
Solve the equation \sin^2 x + \cos^2 x = 1 for x in the interval [0, 2\pi].
A. x=\frac{\pi}{2}
B. x=\frac{3\pi}{2}
C. x=\frac{\pi}{4}
D. x=\frac{5\pi}{4}
Question 9
A histogram has a mean of 25 and a s\tandard deviation of 5. If the histogram has 10 bars, find the value of the sum of the products of the heights of the bars and their respective frequencies.
A. ( 2500 )
B. ( 3000 )
C. ( 3500 )
D. ( 4000 )
Question 10
Find the value of x in the equation \( \tan x = \frac{1}{\sqrt{3}} \) if ( x ) lies in the first quadrant.
A. 30°
B. 45°
C. 60°
D. 90°
Question 11
Evaluate the definite integral \( \int_0^1 \frac{1}{x^2 + 1} dx \).
A. \frac{\pi}{4}
B. \frac{\pi}{2}
C. \frac{\pi}{6}
D. \frac{\pi}{8}
Question 12
A car travels from city A to city B at an average speed of 60 km/h and returns from city B to city A at an average speed of 40 km/h. What is the average speed of the car for the entire trip?
A. 48 km/h
B. 50 km/h
C. 52 km/h
D. 55 km/h
Question 13
A fair six-sided die is rolled. What is the probability that the number rolled is greater than 4?
A. \frac{1}{6}
B. \frac{1}{3}
C. \frac{2}{3}
D. \frac{5}{6}
Question 14
Find the volume of the frustum of a cone with height 6 cm, lower base radius 4 cm, and upper base radius 2 cm.
A. 24\pi cm^3
B. 48\pi cm^3
C. 96\pi cm^3
D. 192\pi cm^3
Question 15
A rec\tangular solid has a length of 10 cm, a width of 5 cm, and a height of 8 cm. If the solid is cut into smaller cubes with a side length of 2 cm, how many cubes will be formed?
A. 20
B. 25
C. 30
D. 35

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