@Holyheadmaths GCSE METHODS REVISION- MARCH Higher Paper 1 (Non calculator)

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1 @Holyheadmaths GCSE METHODS REVISION- MARCH 201 Higher Paper 1 (Non calculator)

2 Adding Fractions To add fractions we need to multiply across the bottom and then across the fractions- flat across your bottom and cross your heart + 2 x5 + 2 x = x5 = 20 = 20 = = = = = 2 + Remember that if you have a mixed number you should change it to a top heavy fraction first. There is an example below. 2 5 = 2x5 + 5 =

3 Adding Fractions

4 Sample Space I have two spinners. Both are numbered 1 to. I spin them both and add the scores together fill out the sample space diagram to show al possible outcomes What is the probability I score: 2?? More than 5? I have two spinners. One numbered 1,,5,7, the other numbered 2,,6,8. I spin them both and multiply the scores. Fill out the sample space diagram to show al possible outcomes. + What is the probability I score: 2?? 6 or more?

5 Sample Space I have two dice. I roll them and add the scores. Create a sample space diagram. What is the probability I score 10 or more? I have a dice and a spinner labelled 2,,5,9. I spin and roll then add the scores. Create a sample space diagram. What is the probability I score less than 5?

6 Tree diagrams I have a bag with 10 red counters,6 green counters and blue counters. I pick one counter out and do not replace it, then I pick another. Draw a tree diagram. R R G Remember that the probability will change for the second pick because there are fewer counters in the bag B G B 5 19 R G R B G To find a probability multiply along the branches I.e. the probability of a blue then are green is /20 x 6/19= 2/80 If you need the probability of getting a blue and a red then you could get blue then red OR red then blue. Work out both probabilities and add them together P(RB)= 10/20 x /19= 0/80 P(BR)= /20 x 10/19= 0/80 Adding these probabilities together will give be 80/80 or /19 19 B

7 Tree diagrams I have a bag with 12 red counters,2 green counters and 6 blue counters. I pick one counter out and do not replace it, then I pick another. Draw a tree diagram and find the probability that both counters are the same colour.

8 LCM and HCF When I need to find the HCF (highest common factor) I need to list the factors of both numbers then circle the biggest numbers that s in both lists and 20 2 and 10 and and 6 2 and 18 and 12 and 9 6 The highest common factor of 20 and 6 is Find the HCF of the following pairs of numbers: 1) 2 and 0 2) 28 and 2 ) 56 and 80

9 LCM and HCF When I need the LCM (lowest common multiple ) of two numbers I need to write out the times tables of each number and find the first number that is in both lists The lowest common multiple of 20 and 6 is 180 1) 2 and 0 Find the LCM of the following pairs of numbers: 2) 16 and 2

10 Index laws The laws: If the question has.. You have to Example Multiply Add the powers a 2 xa =a 6 Divide Takeaway the powers a 6 a =a 2 Brackets Multiply the powers (a 6 ) 2 =a 12 Zero as the power Write 1 as the answer a 0 =1 Half as the power Square root the number 25 1/2 =5 A negative power Write the number as a fraction with 1 at the top (or if it was a fraction -1 =1/ (2/) -1 =/2 Sometimes you will be given a question where the numbers aren t the same but you need to change them. For example: 5 2 x x 5 5 = = = 5

11 Index laws Evaluate the following: 1) 25 ½ 2) 6 ½ ) 6 ½ ) -1 5) -2 6) 2-7) 25 -½ 8) 9 -½ 9) 81 -½ Write as a single number with a power 1) 10 x 100 2) ( x 2 ) 2 ) ) 27 2 x x ) 8 6 x 7 2 2

12 Standard form A number in standard for has to be between 1 and 10 and be multiplied by ten to the power something..5 x 10 7 = The power will tell you how many numbers come after the, we know the first one will be 5 so there must be 6 zeroes = We put a decimal place between the first two numbers to get.6, there are 8 numbers after the so it must be times ten to the power 8.6 x x 10-7 = With negative powers the number tells you how many zeroes there will be, remember that the first zero will be before the decimal point = The number will be 1. times ten to the power 6 because there are six zeroes.6 x 10 8

13 Standard form Write the following in standard form: 1) ) ) ) ) ) Write as ordinary numbers: 1). x ) 7.2 x 10 7 ) 6.5 x 10 6 ) 1.1 x ) 2.9 x ) 7.5 x 10 -

14 Standard form sums without a calculator Work out 2.5 x 10 8 x x 10-5 Multiply the numbers together 2.5 x = 7.5 Add the powers of the tens 10 8 x 10 - = = 10 5 The answer will be 7.5 x 10 5 Altering the answers Sometimes the answer will not be in standard for so you will need to change it slightly. Say our answer was 12. x We need to make 12. smaller, to 1.2, to balance that out we make 10 8 bigger to So our answer would be 1.2 x 10 9 Change these answers into standard form: 1. x 10 7=.5 x 10-7= 5.6 x 10 9= 0. x 10 5= 0.5 x 10-6= 26.8 x 10 5= Work out the following:. x 10 8 x x x 10 6 x x x 10 x 7 x 10-10

15 Similar shapes When shapes are similar, one is an enlargement of the other. To find missing lengths we need to find a scale factor. Angles in similar shapes are the same cm 25 o cm b 75 o 75 o X a 9cm.5cm Angle x will be 25, the same as the smaller shape. Here we can see that the lengths on the shape have been multiplied by. Missing length a must be 12 (x=12) and missing length b must be 1.5 (.5 =1.5).1cm 15 o 5cm b 8 o 8 o X a 20cm 15cm Scale factor= Length a= Length b= Angle x=

16 Similar shapes cm b a 17cm 82 o 2cm 25 o X 25 o 10cm Scale factor= Length a= Length b= Angle x= 6cm b a 12.5cm 6 o 80 o cm X 80 o 10cm Scale factor= Length a= Length b= Angle x=

17 Equation of a line Straight lines have the equation y=mx+c To find c we see where the line crosses the y axis To fin m we see how much the line goes up each time it goes across 1 This line has the equation y=2x+, can you see why? This line crosses the y axis at This line goes up 2 squares each time it goes across 2 What is the equation of this line?

18 Equation of a line Y= x Y= x

19 Plotting straight lines Plot the line y=2x+1 Draw a table out like this: X Y The rule tells you to multiply the x number by 2 and add 1, fill out the table X Y Now plot the point (0,1) (1,) (2,5) and (,7). Connect them with a straight line and make sure you continue the line across the whole graph.

20 Plotting straight lines Plot the line y=x+2 Plot the line y=2x+ X Y 0 1

21 Other sources of revision Here are some other places you can go for revision: Mymaths Activelearn (speak to your teacher and check your school to access) lots of great revision videos

Methods in Mathematics

Write your name here Surname Other names Pearson Edexcel GCSE Centre Number Candidate Number Methods in Mathematics Unit 1: Methods 1 For Approved Pilot Centres ONLY Foundation Tier Monday 10 November