Download presentation

Presentation is loading. Please wait.

Published byKurt Cleaton Modified over 2 years ago

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 10 n 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 10 3 = 3.5 x 100= 3.5 x 10 2 = 6 x= 6 x 10 - 3 d.) 83700 e.) 0.00075 f.) 12.5 million = 8.37 x 10000= 8.37 x 10 4 = 7.5 x = 7.5 x 10 - 4 = 1.25 x 10 000 000 = 1.25 x 10 7 Make sure you use this notation and not calculator notation

4
Note 1: Standard Form The speed of light is 300 000 km/s. Express this speed in cm/s in standard form. Make sure you use this notation and not calculator notation xx = 30000000000 = 3 x 10 10

5
Note 1: Standard Form Given that L = 2, find the value of L in standard form when a = 4.5 x 10 12 & k = 5 x 10 7 Make sure you use appropriate brackets on your calculator = 2 = 600 = 6 x 10 2 IGCSE Ex 13 pg 13-14 odd Ex 14 pg 14-15 odd IGCSE Ex 13 pg 13-14 odd Ex 14 pg 14-15 odd

6
Note 2: Ratio and Proportion The word ‘ratio’ is used to describe a fraction. 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.) 2:5b.) 7:8c.) 33:990 1 : 1 : 30 e.g. Express the following ratios in the form n : 1 a.) 2:5b.) 3:300c.) 65:875 : 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. 3 + 4). Then John receives 3 parts and Hamish receives 4 parts. John receives of $70 = Hamish receives of $70 = $30 $40

8
His friends each get of the brothers stamps 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 IGCSE Ex 15 pg 15-16 odd IGCSE Ex 15 pg 15-16 odd = 625 stamps

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
of 3 ft is 7 ft 10 men days (3 ft) 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) 10 men x = 5 days 1 man 24 days (3 ft) = 5.6 days IGCSE Ex 16 pg 17-18 odd IGCSE Ex 16 pg 17-18 odd

11
Note 3: Approximations & Estimation Write the following correct to the nearest: Whole Number 3 sf2 dp 3.121 0.589 3.255 9.896 0.0820 3 1 3 10 0 3.12 0.589 3.26 9.90 0.0820 3.12 0.59 3.26 9.90 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 144.5 cm and 145.4999999….. 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 0.032 g. The actual weight is between and < weight < Lower bound (limit) Upper bound (limit) 0.0315 g0.0325 g 0.03150.0325 IGCSE Ex 9 pg 9 Ex 10 pg 10-11 odd Ex 11 pg 11-12 odd IGCSE Ex 9 pg 9 Ex 10 pg 10-11 odd Ex 11 pg 11-12 odd

14
Note 4: Currency Exchange An application of how we use proportion. e.g. The following are exchange rates for NZD ($). CountryExchange Rate U.K. (pounds) £0.58= $1 Canada ($)$1.276 CAD = $1 Euro (euros)€0.785 = $1 Argentina (pesos)0.897ARPO = $1 Convert $ 28.00 to euros Convert £500 to NZD $ $1 = €0.785 $28 = €0.785 x 28 $28 = €21.98 £0.58= $1 £1= £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?. S D T T = 20 s x T = 0.005556 hr D = S x T D = 108 km/hr x 0.005556 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?. S D T How far does the earthworm travel in 5 seconds? 2 x 5 s = 10 cm The ant must overtake the length and distance travelled 10 cm + 15 cm = 25 cm (in 5 seconds) The ant’s speed is = 5 IGCSE Ex 17 pg 18-19 Ex 25 pg 29-30 IGCSE Ex 17 pg 18-19 Ex 25 pg 29-30

Similar presentations

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google