Maths Assignment Solutions - Foundations of Mathematics, Semester 1

This document presents a comprehensive solution to a mathematics assignment, covering a range of topics including simple interest calculations, breakeven analysis, and algebraic equations. The solution includes detailed steps for calculating simple interest, determining the breakeven point for a business scenario, solving quadratic equations, and analyzing data to find the mode and mean. Furthermore, the assignment addresses linear equations and their solutions. The document is designed to help students understand and solve various mathematical problems, providing clear explanations and step-by-step solutions to enhance their learning experience. This resource is useful for students studying foundations of mathematics.

Running head: MATHS ASSIGNMNET 1
MATHS ASSIGNMNET

MATHS ASSIGNMNET
Table of Contents
Question 1...................................................................................................................................................3
Question 2...................................................................................................................................................3
Question 3...................................................................................................................................................3
Question 4...................................................................................................................................................4
Question 5...................................................................................................................................................4
Question 6...................................................................................................................................................4
Question 7...................................................................................................................................................5
Part A)......................................................................................................................................................5
Part B)......................................................................................................................................................5

MATHS ASSIGNMNET
Question 1
Question 1
Simple interest
Principal 3000
Rate 12.00%
Time 2
Amount P * R * T
Amount 720
Question 2
Question 2
Investment 3500
Time 2
Rate 0.015
Amount (I + (1 + R/100)^2)
Amount 3606.39
Question 3
Part A
Calculation of profit
Particulars Units Price Amount
Sales 120 15000
£
1,800,000.00
Less: variable cost 70
£
1,050,000.00
Contribution per unit 50
£
750,000.00
Less: Fixed costs
£
500,000.00
Net profit
£
250,000.00
Calculation of breakeven units
Breakeven Point
Fixed costs £ 500,000.00

MATHS ASSIGNMNET
Contribution per unit 50
Breakeven units
£
10,000.00
Part B)
1 2 3 4 5 6 7
0
200000
400000
600000
800000
1000000
1200000
1400000
1600000
1800000
Breakeven Point
Units
Revenue
Fixed
Variable
Question 4
The stationery points of the following function can be found out in the image below.
Y= -2X^3 + 15X^2 + 27
Y = -6X + 30
-6X = -30
X = 5
Question 5
-X2 + 3X + 40 = 0
Multiplying the entire equation by – sign
X2 – 3X – 40 = 0
X2 - 8X + 5X – 40 = 0
X ( X - 8 ) + 5 ( X – 8 ) = 0

MATHS ASSIGNMNET
X + 5 = 0, X – 8 = 0
X = -5, 8
Presentation through graph
Question 6
A The total people who took the survey are 14
B Males Scale Frequency
5 1
7 2
10 1
Calculation of Mode 1
C Females Scale Frequency
5 3
6 4
7 2
8 3
9 2
Calculation of Mode 3
D Calculation of mean 2.8

MATHS ASSIGNMNET
Question 7
Part A)
6X - 7 3X - 5 5X + 78
4 7 28
42X - 49 + 12X - 20 5X + 78
28 28
54X - 69 5X + 78
54X - 5X 147
49X 147
X 3
Part B)
5 (X + 7 ) ≥ 3 (X + 9 )
5X + 35 ≥ 3X + 27
Subtracting 3x from both the side
2X + 35 ≥ 27
2X ≤ 8
X ≤ 4