GCSE Maths(Higher)

Indirect Proportion

Types of proportion

Time (min)

mph

90

60

?

70More Less

MoreLess

?5

MoreLess

MoreLess

508

Direct Proportion• percentage • Conversions• Ratio• Fractions• Similar shapes• Arc & sectors• How many more can you

think of?

km

miles

Inverse Proportion

Any question where increasing one number has the effect of reducing the other

What is number?Can you think of any more?

Number

RatioPe

rcen

tage

s

Money

Numbe

r

Fractions

Time

Length

s

Weights

Standard Index Form

Below is a good rule of thumb for questions on proportion.

Number Number

Area (square number)

Area (square number)

Volume(cube number)

Volume (cube number)

Relationships that don’t fit

Number Number

Area (square number)

Area (square number)

Volume(cube number)

Volume (cube number)

No

No

No

But what do you do when you are given a questions that don’t seem to fit?

Number Number

Area (square number)

Area (square number)

Volume(cube number)

Volume (cube number)

Number

Volume (cube number)

A gift shop sells small candles that are 8cm high and cost £3.20. It sells similar candles that are 14cm high.

No

What price are the large candles, if the cost of the candle is proportional to its volume?

Strategy – extract information onto 3 lines

A gift shop sells small candles that are 8cm high and cost £3.20. It sells similar candles that are 14cm high.

Cost

Height cm

Height cm3

8

512

3.20 ?

14

274415.17?

2744512

2.3?

512

2.3

2744

?

Large candles cost £17.15 in the gift shop

What price are the large candles, if the cost of the candle is proportional to its volume (not its height)?

Number

Area (square number)

No

A gift shop sells small candles that are 8cm high and cost £3.20. It sells similar candles that are 14cm high.

It takes 144cm2 of plastic film to wrap the small candle. How much does the large candle need?

Strategy extract information onto 3 lines

A gift shop sells small candles that are 8cm high and cost £3.20. It sells similar candles that are 14cm high.

It takes 144cm2 of plastic film to wrap the small candle. How much does the large candle need?

area

Height cm

Height cm2

8

64

144 ?

14

196

441?

19664

144?

64

144

196

?

Large candles need 441cm2 of wrap

Strategy for Indirect proportion

Answer – make sure it is in context with the question

a) T in terms of L is:

T= 4

Calculation – to get method marks.

a)

Extract information from question onto lines.

QuestionA simple pendulum of length L cm,

takes T seconds to swing from A to B. T is proportional to square root of L. When T = 34 sec, L = 72.25cm

a) Express T in terms of Lb) Find T when L = 400c) Find L when T = 60

Lcm

√L

T = sec

72.25 L

√72.25 √L

34 T

LLT

L

T

425.72

3425.72

34

L

Strategy for Indirect proportion

Answer – make sure it is in context with the question

a) T in terms of L is:

T= 4

b) T=80

Calculation – to get method marks.

b) From a)

Extract information from question onto lines.

QuestionA simple pendulum of length L cm,

takes T seconds to swing from A to B. t is proportional to square root of L. When T = 34 sec, L = 72.25cm

a) Express T in terms of Lb) Find T when L = 400c) Find L when T = 60

Lcm

√l

T = sec

72.25 L

√72.25 √L

34 T

LT 4

L80204

4004

T

T

Strategy for Indirect proportion

Answer – make sure it is in context with the question

a) T in terms of L is:

T= 4

b) T=80 when L = 400

c) L = 225 when T=60

Calculation – to get method marks.

c)

Extract information from question onto lines.

QuestionA simple pendulum of length L cm,

takes T seconds to swing from A to B. T is proportional to square root of L. When T = 34 sec, L = 72.25cm

a) Express T in terms of Lb) Find T when L = 400c) Find L when T = 60

Lcm

√l

T = sec

72.25 L

√72.25 √L

34 T

L

LT

LT

LT

2

444

L

225154

60 22

Strategy for Indirect proportion

Answer – make sure it is in context with the question

Calculation – to get method marks.

Extract information from question onto lines.

Question