Maths T3 Revision

Question 1

What is the formula for calculating percentage change?

Answer 1

difference / original number x 100

e.g. The population of a school increased from 500 to 650. What was the percentage increase?

1. 650 - 500
   = 150
2. 150 / 500 x 100
   = 30% increase
3. Therefore, there is a 30% increase

Question 2

How do I get a percentage of a number?

Answer 2

e.g. 30% of 400
1. Convert percentage to a decimal (divide by 100)

2. Multiply the decimal by the number you are finding the percent of (in this case, 400)

ANSWER:
0.3 x 400
= 120

Question 3

How do I increase/decrease an amount by a percentage?

Answer 3

1. The original amount = 100%
2. Add or subtract the percentage you are increasing/decreasing by from the 100%
3. Convert the new percentage to a decimal (divide by 100)
4. Multiply the original amount by this decimal

EXAMPLE QUESTION:
A top is usually sold for $20. They have increased the prices by 20%. Calculate the new price.

1. $20 = 100%
   100% + 20% = 120%
2. 120% -> decimal = 1.2
3. $20 x 1.2
   = $24
   Therefore the new cost is $24

Question 4

Solve: A TV is usually sold for $1300, but in a sale it is discounted by 20%. Calculate the discount.

Answer 4

Working:
1. Discount (converted to a decimal) x original price

20% = 0.2
0.2 x 1300
= $260
Therefore, the discount is $260

*note, the discount is not the new sale price. To get the new sale price, I need to subtract the discount from the original price.

Question 5

What is the formula for calculating distance when you are given the speed and time?

Answer 5

Distance = speed x time

e.g. Maria goes for a walk. She walks 8km/h for 2 hours. How far does she walk?

Distance = 8 x 2
= 16 km

Question 6

What is the formula for calculating speed when you are given distance and time?

Answer 6

Speed = distance / time

e.g. Lucas has swam 50m in 30.58 seconds. What is his speed in m/s?

Speed = 50 / 30.58
= 1.635…
= 1.6m/s (1dp)

Question 7

What is the formula for calculating time when you have been given the distance and speed?

Answer 7

Time = distance / speed

e.g. Ronald runs at 16km/h for 30km. How long in hours has he ran?

Time = 30 / 16
= 1.875
= 1.88 (2dp)
Therefore he runs for 1.88 hours

Question 8

Solve:
Gemma drives at an average speed of 85km/h for 2 hours. How far does she travel?

Answer 8

Distance = speed x time

Distance = 85 x 2
= 170km
Therefore she drives for 170km

Question 9

Calculate the speed:
A truck travels 240km in 3hours

Answer 9

Speed = distance / time

Speed = 240 / 3
= 80km/h

Question 10

Solve:
A truck is travelling at 90km/h. How long would it take the truck to drive 36km? Give your answer in the most appropriate units

Answer 10

1. Find the time it takes for 1km
   -> 90km / 60mins
   divide both sides by 90
   -> 1km / 0.67 mins
   times both by 36
   -> 36km / 24mins

Therefore it takes 24 mins for the truck to travel 36km