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Mathematics Intermediate Tier

Number

GCSE Revision

Intermediate Tier - Number revision

Contents Calculator questions Best buy

questions Long multiplication Long

division Simple fractions questions Negative

numbers Rounding Estimating Percentages Ty

pes of number Products of primes HCF and

LCM Indices Simplifying roots Standard

Form Ratio Fractions with the four

rules Recurring decimals as fractions Units

Distance, Speed, Time questions Density, Mass,

Volume questions

Calculator questions

Which buttons would you press to do these on a

calculator ?

2.5 4.1 3.5

1.7 2.8 2.3 0.2

1.56

Best buy questions

Always divide by the price to see how much 1

pence will buy you

Beans Large? 400?87 4.598g/p Small? 150?34

4.412g/p Large is better value (more grams for

every penny spent)

Milk Large? 2.1?78 0.0269L/p Small? 0.95?32

0.0297L/p Small is better value OR (looking at it

differently) Large? 78?2.1 37.14p/L Small?

32?0.95 33.68p/L

Long multiplication

Use the method that gives you the correct answer

!!

Question 78 x 59

70

8

50

3500

400

9

630

72

Total 3500 400 630 72

Answer 4602

Now try 84 x 46 and 137 x 23 and check on your

calculator !!

Long division

Again use the method that gives you the correct

answer !!

Question 2987 ? 23

1

2

9

6

22

20

Answer 129 r 20

Now try 1254 ? 17 and check on your calculator

Why is the remainder different?

Simple fractions questions

Equivalent fractions

Fractions into decimals

Divide top by bottom

Fractions of amounts

Divide by the bottom then times by the top

Negative numbers

Put these in order - smallest first

- 4 , - 3.6 , - 0.4 , - 0.36 , - 1 , 0 , 2 , - 1.4

Up and down the scale

Two signs next to each other

- 3 - 1

- 4 2

Multiplication and Division

Signs same ? ve answer Signs different ? -ve

answer

4715.692803 cm

Rounding

- Round this number off to
- 1 decimal place
- (b) 1 significant figure
- 2 decimal places
- (d) 2 significant figures
- the nearest centimetre
- (f) the nearest metre
- 3 decimal places
- (h) 3 significant figures

- 4715.7 cm
- (b) 5000 cm
- 4715.69 cm
- (d) 4700 cm
- 4716 cm
- (f) 47 m
- 4715.692 cm
- (h) 4720 cm

But there is always a trickier one

14.9999

- Round this number off to
- the nearest whole number
- (b) 3 significant figures
- 2 decimal places

- 15
- (b) 15.0
- 15.00

If you are asked to estimate an answer to a

calculation Round all the numbers off to 1 s.f.

and do the calculation in your head. DO NOT USE

A CALCULATOR !!

Estimating

e.g. Estimate the answer to 4.12 x 5.98 ? 4

x 6 24

Always remember to write down the numbers you

have rounded off

Estimate the answer to these calculations

Percentages

Percentage increase and decrease

A womans wage increases by 13.7 from 240 a

week. What does she now earn ?

Increase

New amount

13.17 of 240

240 31.608

271.608

Her new wage is 271.61 a week

13.17 100

x

240

31.608

30

75

10

1

Percentages of amounts

25

45

5

(Do these without a calculator)

85

20

50

2

Percentages

Fractions, decimals and percentages

50

Copy and complete

0.5

Reverse

e.g. A womans wage increases by 5 to 660 a

week. What was her original wage to the nearest

penny?

Original amount 660 1.05 628.57

e.g. A hippo loses 17 of its weight during a

diet. She now weighs 6 tonnes. What was her

former weight to 3 sig. figs. ?

Original weight 6 0.83 7.23 tonnes

Repeated

This is not the correct method 12000 x 0.065

780 780 x 5 3900 12000 3900 15900

e.g. A building society gives 6.5 interest p.a.

on all money invested there. If John pays in

12000, how much will he have in his account at

the end of 5 years.

He will have 12000 x (1.065)5 16441.04

This is not the correct method 40000 x 0.23

9200 9200 x 4 36800 40000 36800 3200

e.g. A car loses value at a rate of approximately

23 each year. Estimate how much a 40000 car be

worth in four years ?

The cars new value 40000 x (0.77)4 14061

(nearest )

Types of number

- From this set of numbers
- list the
- Odd numbers
- Even numbers
- Multiples of 8
- Factors of 12
- Prime numbers
- Square numbers
- Cube numbers

- Some useful words to know the meaning of
- Sum add together
- Product multiply together
- Difference subtract one number from another
- Reciprocal of a number 1 divided by the number

- (e.g. Reciprocal of 4 ¼ or 0.25)

40

Products of primes

Express 40 as a product of primes

40 2 x 2 x 2 x 5 (or 23 x 5)

630

Express 630 as a product of primes

Now do the same for 100 , 30 , 29 , 144

630 2 x 3 x 3 x 5 x 7 (or 2 x 32 x 5 x 7)

Finding the HCF and LCM of a pair of numbers

HCF stands for the Highest Common Factor (the

biggest number that will go into both

numbers) LCM stands for Lowest Common Multiple

(the first number to appear in both numbers

times table)

e.g. Find the HCF and LCM of the two numbers 140

and 112

Write both numbers as a product of primes

140 2 x 2 x 5 x 7 and 112 2 x 2 x 2 x 2 x

7

For the HCF write out all the primes that appear

in both answers

HCF 2 x 2 x 7 28

For the LCM write out the largest number of each

prime that exists in either number

LCM 2 x 2 x 2 x 2 x 5 x 7 560

104

Indices

52

91

32

102

75 ? 73

23

190

26

53

171

25

Simplifying roots

Tip Always look for square numbered

factors (4, 9, 16, 25, 36 etc)

e.g. Simplify the following into the form a ? b

?12

?4 x ?3

2 ?3

?8

?4 x ?2

2 ?2

?45

?9 x ?5

3 ?5

?72

?36 x ?2

6 ?2

?700

?100 x ?7

10 ?7

Standard form

Write in Standard Form

Write as an ordinary number

0.0001

9.6

4.7 x 109

8 x 10-3

3 600

0.041

1 x 102

5.1 x 104

23 600

0.2

8.6 x 10-1

7 x 10-2

8 900 000 000

9.2 x 103

3.5 x 10-3

46.7

0.003

2 x 100

6 x 106

Do 3 x 104 x 7 x 105 with and without a calculator

Ratio

Equivalent Ratios

Splitting in a given ratio

Total parts 12

Anne gets 2 of 600 100 12

600 is split between Anne, Bill and Claire

in the ratio 273. How much does each receive?

Basil gets 7 of 600 350 12

Claire gets 3 of 600 150 12

Fractions with the four rules

Learn these steps to complete all fractions

questions

- Always convert mixed fractions into top heavy

fractions before you start - When adding or subtracting the bottoms need to

be made the same - When multiplying two fractions, multiply the

tops together and the bottoms together to get

your final fraction - When dividing one fraction by another, turn the

second fraction on its head and then treat it as

a multiplication

Fractions with the four rules

4? 1½

4? ? 1½

Recurring decimals as fractions

Learn this technique which changes recurring

decimals into fractions

Express 0.77777777.. as a fraction.

Let n 0.77777777.. so 10n

7.77777777.. so 9n 7

so n 7/9

Express 2.34343434.. as a fraction.

Let n 2.34343434.. so 100n

234.34343434.. so 99n 232

so n 232/99

Express 0.13213213.. as a fraction.

Let n 0.132132132.. so

1000n 132.132132132.. so 999n 132

so n 132/999 n 44/333

Units

1 inch ? 2.5 cm 1 yard ? 0.9 m 5 miles ?

8 km 2.2 lbs ? 1 kg 1 gallon ? 4.5 litres

Learn these rough conversions between imperial

and metric units

Learn this pattern for converting between the

various metric units

Metric length conversions

Metric weight conversions

Metric capacity conversions

Speed, Distance, Time questions

Speed, Distance and Time are linked by this

formula

To complete questions check that all units are

compatible, substitute your values in and

rearrange if necessary.

- Speed 45 m/s
- Time 2 minutes
- Distance ?

2. Distance 17 miles Time 25 minutes Speed

?

3. Speed 65 km/h Distance 600km Time ?

45 m/s and 120 secs

17 miles and 0.417 hours

45 x 120 D

S 40.8 mph

T 9.23 hours

D 5400 m

Density, Mass, Volume questions

Density, Mass and Volume are linked by this

formula

To complete questions check that all units are

compatible, substitute your values in and

rearrange if necessary.

- Density 8 g/cm3
- Volume 6 litres
- Mass ?

2. Mass 5 tonnes Volume 800 m3 Density ?

3. Density 12 kg/m3 Mass 564 kg Volume ?

8 g/cm3 and 6000 cm3

800 m3 and 5000 kg

8 x 6000 M

D 6.25 kg/m3

V 47 m3

M 48000 g

( or M 48 kg)

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