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

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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.

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Note 1: Standard Form Write the following in standard form. a.) 9000 b.) 350 c.) = 9 x 1000 = 9 x 10 3 = 3.5 x 100= 3.5 x 10 2 = 6 x= 6 x d.) e.) f.) 12.5 million = 8.37 x 10000= 8.37 x 10 4 = 7.5 x = 7.5 x = 1.25 x = 1.25 x 10 7 Make sure you use this notation and not calculator notation

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

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

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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

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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

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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 odd IGCSE Ex 15 pg odd = 625 stamps

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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

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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 odd IGCSE Ex 16 pg odd

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Note 3: Approximations & Estimation Write the following correct to the nearest: Whole Number 3 sf2 dp

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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 … < length < Lower bound (limit) Upper bound (limit)

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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 < weight < Lower bound (limit) Upper bound (limit) g g IGCSE Ex 9 pg 9 Ex 10 pg odd Ex 11 pg odd IGCSE Ex 9 pg 9 Ex 10 pg odd Ex 11 pg odd

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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 $ to euros Convert £500 to NZD $ $1 = €0.785 $28 = €0.785 x 28 $28 = €21.98 £0.58= $1 £1= £500=$862.07

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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 = hr D = S x T D = 108 km/hr x hr D = 0.6 km D = 600 m

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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 Ex 25 pg IGCSE Ex 17 pg Ex 25 pg 29-30

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