1. 14. Mathematics and driving
Study guide
14. Mathematics and driving

2. Cost of purchase
Cost of a purchasing a motor vehicle depends on many factors such as whether it is new or used, make, model.
A motor vehicle is not an investment. It decreases in value immediately.
Buying a motor vehicle on finance requires you to pay a deposit and then make a large number of repayments.
HSC Hint – Total cost of purchasing a motor vehicle using finance is greater than the sale price for cash.

3. Insurance
Insurance is a major cost in keeping a motor vehicle on the road. There are three main types of insurance:
Green slip or compulsory third party
Third party property insurance
Comprehensive insurance
Insurance premium is determined by the make/model of car, your age, driving history, finance, modifications, accessories and location.
Cost of insurance is affected by: No-claim bonus and excess amount.
HSC Hint – No-claim bonus is the percentage decrease in the cost of the premium.

4. Stamp duty
Stamp duty is the tax you pay to the government when registering or transferring a motor vehicle.
To calculate the stamp duty on vehicles:
Round the cost of the vehicle up to the nearest $100, $200, etc. (as required)
Express the stamp duty as a fraction or decimal.
Multiple the answer in step 1 by the answer in step 2.
HSC Hint – Stamp duty increases when the price of the vehicle increases.

5. Running costs
Fuel consumption is the number of litres of fuel a vehicle uses to travel 100 kilometres.
Fuel consumption is calculated by filling the motor vehicle with fuel and recording the kilometres travelled from the odometer.
HSC Hint – Vehicles with a lower fuel consumption have lower petrol costs.

6. Straight line depreciation
Straight line depreciation occurs when the value of the item decreases by the same amount each time period.
S – Salvage value or current value of an item.
V0 – Purchase price of the item. Value of item when n = 0
D – Depreciated amount per time period.
n – Number of time periods.
HSC Hint – Straight line depreciation has a constant depreciation irrespective of the current value.

7. Declining balance depreciation
Declining balance depreciation occurs when the value of the item decreases by a fixed percentage each time period.
S – Salvage value or current value of an item.
V0 – Purchase price of the item. Value of item when n = 0
r – Rate of interest per time period expressed as a decimal.
n – Number of time periods.
HSC Hint – Declining balance formula is the compound interest formula with a minus instead of a plus.

8. Safety
Speed is a rate that compares the distance travelled to the time taken. The speed of a car is measured in kilometres per hour (km/h).
Stopping distance is the distance a vehicle travels from the time a driver sees an event occurring to the time the vehicle is brought to a stop.
HSC Hint – Braking distance is quadrupled if the speed of the car is doubled.

9. Blood alcohol content
Blood Alcohol Content (BAC) is a measure of the amount of alcohol in your blood. The measurement is the number of grams of alcohol in 100 millilitres of blood.
BAC – Blood alcohol content.
N – Number of standard drinks consumed.
H – Hours drinking.
M – Mass in kilograms.
HSC Hint – Show the substitution of values into the BAC formulas.

10. Driving statistics
A distance-time graph describes a journey involving different events. It is a line graph with time on the horizontal axis and distance on the vertical axis.
Summary statistics are used to measure accident data that resulted in death, injury and damage.
HSC Hint – Distance-time graph with a horizontal line indicates that the object is not moving or is at rest.