@Holyheadmaths GCSE METHODS REVISION- MARCH 201 Higher Paper 1 (Non calculator)
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 15 + 8 2 5 = x5 = 20 = 20 = 1 20 2 + = = = = 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 = 1 5 2 + 2 1
Adding Fractions 2 + 2 1 1 + 2 5 10 + 2 1 2
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. + 1 2 1 2 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?
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?
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 9 19 6 19 R G Remember that the probability will change for the second pick because there are fewer counters in the bag 10 20 20 6 20 B G 19 10 19 10 19 19 6 19 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
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.
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. 20 1 and 20 2 and 10 and 5 6 1 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
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 20 20 0 60 80 100 120 10 160 180 6 6 72 108 1 180 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
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 125 25 5 2 x 5 5 = = 5 5 2 5 2 = 5
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 9 2 25 6 x 5 7 125 2 5) 8 6 x 7 2 2
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 5 000 000 6 000 000= 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 10 8.5 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 0.0000005 0.000001= The number will be 1. times ten to the power 6 because there are six zeroes.6 x 10 8
Standard form Write the following in standard form: 1) 50000 2) 50000 ) 12000000 ) 0.0005 5) 0.005 6) 0.000005 Write as ordinary numbers: 1). x 10 5 2) 7.2 x 10 7 ) 6.5 x 10 6 ) 1.1 x 10-6 5) 2.9 x 10-5 6) 7.5 x 10 -
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 - = 108 - = 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 10 8. We need to make 12. smaller, to 1.2, to balance that out we make 10 8 bigger to 10 9. 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 10-5 5.1 x 10 6 x x 10 1.5 x 10 x 7 x 10-10
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=
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=
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?
Equation of a line Y= x Y= x
Plotting straight lines Plot the line y=2x+1 Draw a table out like this: X Y 0 1 2 The rule tells you to multiply the x number by 2 and add 1, fill out the table X Y 0 1 2 1 5 7 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.
Plotting straight lines Plot the line y=x+2 Plot the line y=2x+ X Y 0 1 2 @Holyheadmaths
Other sources of revision Here are some other places you can go for revision: Mymaths Activelearn (speak to your teacher and check your school email to access) www.hegartymaths.com- lots of great revision videos