Math Quiz Solution with Detailed Answers - Foundations of Mathematics

This document contains the solution to a math quiz, covering a range of mathematical concepts. The solution includes step-by-step explanations for each problem, such as temperature conversion, calculating hourly wages based on overtime, determining population growth, and solving basic arithmetic problems. It also involves calculating slopes between two points and deriving equations of lines, including complex number arithmetic and finding points on a linear equation. The quiz covers topics typically found in a foundations of mathematics course.

MATHS QUIZ
STUDENT ID:
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Question 1
The requisite conversion formula is shown below.
(Temperature in Fahrenheit – 32) *(5/9) = Temperature in Celsius
Current temperature = 15oCelsius
Hence, (Temperature in Fahrenheit – 32) *(5/9) = 15
(Temperature in Fahrenheit – 32) = 27
Temperature in Fahrenheit = 27 +32 = 59
Considering the above temperature, there does not seem to be any need of wearing a jacket.
Question 2
Let the hourly salary be X dollars
The salary for hours above 40 would be 1.5X dollars
Hence, 40X + 1.5X*6 = 440
40X + 9X = 440
49X=440
X = (440/49) = 8.98 dollars
Question 3
Population in year 1 = 100
Population in year 3 = 300
Since the trend is linear, hence let the yearly increase in population be X
Hence, 100 +2X = 300
2X = 300-100 =200

X = 100
Population in Nth year = 100 + (N-1)*100 = 100N
Population in 10th year =100*10 = 1000
Question 4
-(-50) = 50
Hence, answer is50.
Question 5
The given points are (2,3) and (7,5)
Slope = (5-3)/(7-2) = 2/5
Question 6
The given points are (3,7) and (7,5)
Slope = (5-7)/(7-3) = -1/2
Question 7
The given points are (-2,5) and (4,5)
Slope = (5-5)/(4+2) = 0
The equation of the line passing though the above two points is shown below.
y-5 = 0(x+2)
y=5 is the required equation of line

Question 8
(-4+2i) – (5-4i)
= (-4-5)+(2i+4i)
= -9 + 6i
Question 9
(3+4i)-(5-2i)
= (3-5)+(4i+2i)
= -2 + 6i
Question 10
y=2x-3
Point 1 is (0,-3)
Point 2 is (1,-1)
Point 3 is (2,1)
Point 4 is (3,3)
Point 5 is (4,5)