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• Level: GCSE
• Subject: Maths
• Word count: 1866

Gary's Car Sales Mathematics Coursework

Extracts from this document...

Introduction

Gary’s Car Sales Mathematics Coursework

For this experiment I was given a table of second hand cars for sale showing how the factors eg. age and mileage, effect the cost of a second hand car, compared with the same cars price when new. The table consists of 36 cars separated into 5 different manufacturers. For my investigation I will only use 3 of these manufacturers, Ford, Vauxhall, and Rover. I chose these 3 because they were the makes with the largest amount of information. Using the table I have been given I will try to find out which car is the best value for money. To do this I will have to draw two different types of graph, age against second hand price, and mileage against second hand price, draw a line of best fit, and work out formulas for these graphs.

Car no. Price   Age Make Cost when Mileage Engine Size     (£) (Years)     new   (£)       (Litres)               1 6,970 3 Ford 11,600 24,000 1.6 2 3,350 7 Peugeot 7,100 85,000 1.1 3 3,995 6 Ford 13,800 52,000 2.0 4 5,300 6 Vauxhall 16,300 70,000 2.0 5 6,500 3 Fiat 8,700 24,000 1.2 6 1,500 9 Vauxhall 8,700 82,000 1.6 7 995 9 Ford 8,500 102,000 1.8 8 3,000 7 Vauxhall 10,400 63,000 1.7 9 7,495 1 Vauxhall 9,770 8,000 1.4 10 850 10 Ford 7,540 124,000 1.6 11 5,595 4 Ford 11,000 41,000 1.6 12 4,995 3 Ford 9,880 34,000 1.4 13 5,595 4 Ford 14,000 55,000 1.6 14 4,995 4 Rover 11,500 40,000 1.4 15 2,600 7 Rover 12,000 82,000 1.6 16 1,000 10 Peugeot 6,200 119,000 1.1 17 750 11 Peugeot 5,100 96,000 1.0 18 1,350 8 Ford 9,140 108,000 1.6 19 2,950 8 Ford 17,750 96,000 2.9 20 3,250 7 Vauxhall 9,990 86,000 1.6 21 5,650 3 Vauxhall 11,150 34,000 1.6 22 4,600 2 Rover 7,300 17,000 1.1 23 5,400 1 Rover 7,300 11,000 1.1 24 4,800 1 Rover 7,300 26,000 1.1 25 2,700 5 Fiat 13,000 51,000 2.0 26 11,000 1 Peugeot 13,800 9,000 1.8 27 2,800 5 Fiat 6,500 43,000 1.0 28 8,000 4 Rover 21,000 142,000 2.3 29 6,495 2 Ford 8,800 23,000 1.3 30 4,050 4 Ford 8,400 48,000 1.3 31 6,300 2 Ford 10,300 26,000 1.3 32 4,100 4 Vauxhall 8,900 37,000 1.3 33 6,600 1 Vauxhall 8,500 9,000 1.3 34 7,800 1 Peugeot 10,500 13,000 1.4 35 8,700 3 Vauxhall 16,000 42,000 2.0 36 2,000 7 Peugeot 8,300 65,000 1.4

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Using the table I have drawn 4 graphs for age against second hand price.

Middle

Vauxhall

Say you wanted to find out how much the Vauxhall will be worth after 8 years.

Because the Vauxhall starts at £8,200 and the gradient is 750 the formula would be shown as:

Page 3

Y = 8200 - (750 x 8)

Y = 8200 - 6000

Y = 2200

Therefore the value of the car after 8 years would be £2,200.

Rover

Say you wanted to find out how much the Rover will be worth after 8 years.

Because the Rover starts at £5, from 800 and the gradient is 450 the formula would be shown as:

Y = 5800 - (450 x 8)

Y = 5800 - 3600

Y = 2200

Therefore the value of the car after 8 years would be £2,200

Car Manufacturer

Value after:

Ford

Vauxhall

Rover

Cost when new

£7,900

£8,200

£5,800

2 Years

£6,450

£6,700

£4,900

4 Years

£5,000

£5,200

£4,000

6 Years

£3,550

£3,700

£3,100

8 Years

£2,100

£2,200

£2,200

10 Years

£650

£700

£1,300

This table shows that after 10 years the Rover is valued the highest, despite being the cheapest to start with. So far this investigation  is in Rovers favour showing that it is the best value car.

For mileage against price I have drawn another 4 graphs. 1 for each manufacturer as before.

The gradients for these graphs are:

Ford

The graph for Ford is a strong, negative correlation. The Ford becomes worthless when it reaches 126,000 miles.

Conclusion

Because the Rover starts at £5,800 and the gradient is 400 the formula would be shown as:

Y = 5800 - (400 x 8)

Y = 5800 - 4000

Y = 2600

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Therefore the value of the car after 80,000 miles would be £2,600.

The table below shows the value of each make of car after various mileages using the formula.

Car Manufacturer

Value after:

Ford

Vauxhall

Rover

0 Miles (Cost when new)

£7,900

£8,200

£5,800

20,000 Miles

£6,600

£6,600

£5,000

40,000 Miles

£5,300

£5,000

£4,200

60,000 Miles

£4,000

£3,400

£3,400

80,000 Miles

£2,700

£1,800

£2,600

100,000 Miles

£1,400

£200

£1,800

Looking at this table Rover is the best value car as it loses the least amount of money after every 10,000 miles. After starting off the costliest the Vauxhall is only worth £200 after 100,000 miles, which makes it the car that loses the highest value by far. Whereas the Rover starts off the cheapest and finishes the highest priced of the three manufacturers after 100,000 miles.

In this experiment I discovered that Rover is the best value car out of the three that I chose to investigate. Vauxhall was the worst value car because it lost the most money on age and mileage. Ford was almost as bad value for money as the Vauxhall. My investigation could be improved by including more manufacturers and their cars. Also because the graphs are not 100% accurate. In real life as soon as you drive a new car off the forecourt it drops in value instantly. This means the graphs should have looked more like

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