1. Standard Form, Ratio, Rates & Proportion
IGCSE – Chapter 1
Number

2. Note 1: Standard Form
We use standard form when dealing with very large or very small numbers. a x 10n is in standard form when 1 < a < 10 and n is a positive or negative number.

3. Note 1: Standard Form
Write the following in standard form. a.) 9000 b.) 350 c.) 0.006
= 9 x 1000
= 9 x 103
Make sure you use this notation and not calculator notation
= 3.5 x 100
= 3.5 x 102
= 6 x
= 6 x 10- 3
d.)
e.)
f.) million
= 8.37 x 10000
= 8.37 x 104
= 7.5 x
= 7.5 x 10- 4
= 1.25 x
= 1.25 x 107

4. Note 1: Standard Form
The speed of light is km/s. Express this speed in cm/s in standard form. x x =
= 3 x 1010
Make sure you use this notation and not calculator notation

5. Note 1: Standard Form
Given that L = 2 , find the value of L in standard form when a = 4.5 x 1012 & k = 5 x 107
Make sure you use appropriate brackets on your calculator
= 2
= 600
= 6 x 102
IGCSE
Ex 13 pg odd
Ex 14 pg odd

6. Note 2: Ratio and Proportion
The word ‘ratio’ is used to describe a fraction.
e.g.
If the ratio of your height to your fathers height is 4:5, then you
are of your fathers height.
e.g.
Express the following ratios in the form 1 : n
a.) 2:5 b.) 7:8 c.) 33:990
1 :
1 : 30
1 :
e.g.
Express the following ratios in the form n : 1
a.) 2:5 b.) 3:300 c.) 65:875
: 1
: 1
: 1

7. Note 2: Ratio and Proportion
Divide $70 between John and Hamish in the ratio of 3:4
Consider that $70 has 7 equal parts(i.e ). Then John receives 3 parts and Hamish receives 4 parts.
John receives of $70 =
Hamish receives of $70 =
$30
$40

8. Note 2: Ratio and Proportion
A brother and sister share out their collection of 5000 stamps in the ratio 5:3. The brother then shares his stamps with two friends in the ratio 3:1:1, keeping the most for himself. How many stamps do each of his friends receive?
Brother receives of 5000 =
3125 stamps
His friends each get of the brothers stamps
= 625 stamps
IGCSE
Ex 15 pg odd

9. Note 2: Ratio and Proportion
Proportion – Finding a unit quantity
If a wire of length 5 metres costs $35, find the cost of a wire of length 75 cm
500 cm costs 3500 cents
1 cm costs
= 7 cents
75 cm costs 7 x 75 = 525 cents
= $5.25

10. Note 2: Ratio and Proportion
If it takes 6 men 4 days to dig a hole 3 feet deep, how long will it take 10 men to dig a hole 7 feet deep?
6 men 4 days (3 ft)
of 3 ft is 7 ft
1 man 24 days (3 ft)
10 men days (3 ft)
10 men x
= days
= 5.6 days
IGCSE
Ex 16 pg odd

11. Note 3: Approximations & Estimation
Write the following correct to the nearest:
Whole Number
3 sf
2 dp
3.121
0.589
3.255
9.896
0.0820 3
3.12
3.12 1
0.589
0.59 3
3.26
3.26
9.90 10
9.90
0.0820
0.08

12. Note 3: Measurements & Bounds (Limits of accuracy)
Remember that measurements are approximate.
e.g. The length of a fabric is measured to 145 cm to the nearest cm.
The actual length is between cm and …..
144.5 < length < 145.5
Lower bound
(limit)
Upper bound
(limit)

13. Note 3: Measurements & Bounds (Limits of accuracy)
Remember that measurements are approximate.
e.g. The weight of a butterfly is given as g.
The actual weight is between and g g
< weight <
0.0315
0.0325
Upper bound
(limit)
Lower bound
(limit)
IGCSE
Ex pg 9
Ex 10 pg odd
Ex 11 pg odd

14. Note 4: Currency Exchange
An application of how we use proportion.
e.g. The following are exchange rates for NZD ($).
Country
Exchange Rate
U.K. (pounds)
£0.58= $1
Canada ($)
$1.276 CAD = $1
Euro (euros)
€0.785 = $1
Argentina (pesos)
0.897ARPO = $1
Convert $ to euros Convert £500 to NZD $
$1 = €0.785
£0.58= $1
$28 = €0.785 x 28
£1=
$28 = €21.98
£500=$862.07

15. Note 5: Speed, distance & time
Great care must be taken with units in these problems.
e.g. How long is a train which passes a signal in twenty seconds at a speed of 108 km/hr?.
T = 20 s x
T = hr
D = S x T
D = 108 km/hr x hr
D = 0.6 km
D = 600 m

16. Note 5: Speed, distance & time
Great care must be taken with units in these problems.
e.g. An earthworm of length 15cm is crawling along at 2 cm/s. An ant overtakes the worm in 5 seconds. How fast is the ant walking?.
How far does the earthworm travel in 5 seconds?
x 5 s = 10 cm
The ant must overtake the length and distance travelled
10 cm + 15 cm = 25 cm
(in 5 seconds)
IGCSE
Ex pg 18-19
Ex pg 29-30
The ant’s speed is
= 5