Multiply frequency by the value Divide this total by total frequency MEAN FROM A TABLE Multiply frequency by the value Divide this total by total frequency Total How many Mean

ESTIMATE OF THE MEAN 2 extra columns Use mid point of groups Mid point x frequency Big total divided by little total

Modal class is the mode group Basic Averages Modal class is the mode group Median is the middle one Mean is total divided how many? Total How many? Mean

Fraction of – divide by the bottom, times by the top. STRATIFIED SAMPLING Eg 239 of 100 Total Fraction of – divide by the bottom, times by the top. 4

FREQUENCY DIAGRAMS Frequency polygon = join midpoints of bar chart Frequency diagram = bar chart

Venn Diagrams AI means not A Everything in the rectangle is part of the universal set AuB is everything in either A, B or both AI means not A

STANDARD FORM It’s a number between 1 and 10 times by a power of 10. e.g. 450 is 4.5 x 102 Use the exp button on the calculator 7

When multiplying times the numbers and add the powers When dividing divide the numbers and take away the powers Power of 0 is 1 Fraction powers: ½ is square root, 1/3 is cube root Negative powers – work out + power and turn upside down 8

PRIME FACTOR TREES PRIME NUMBERS 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, … EXAMPLES Find the product of prime factors for the following numbers: (a) 32 (b) 60 8 4 10 6 4 2 2 2 5 2 3 2 2 2 ANSWER = 2 X 2 X 3 X 5 ANSWER = 2 X 2 X 2 X 2 X 2 = = X 3 X 5 9

LCM is a multiple, so is bigger than the start numbers LCM and HCF LCM is a multiple, so is bigger than the start numbers HCF is a factor, so is smaller than the start numbers 10

PERCENTAGES 1% - divide by 100 10% - divide by 10 % change is change / original x 100%

£5600 x 1.018515 Percentage Increase by Multiplier

Currency exchange

AER Percentage Rate As a decimal number eg 15% as 0.15 Per day, week, month etc With AER you can compare rates over different times as if they were one year

Income tax Example Income is £50000 Taxable Income = £40000 Taxable pay = salary – allowance Put as much as you can into each “piggy bank” tax rate Example Income is £50000 Taxable Income = £40000 Split this into 2 parts £31865 £40000 - £31865 = £8135 40% 20%

CALCULATOR WORK + ESTIMATION Work out the top Work out the bottom Top divided by the bottom Estimate means round the numbers first

Surds

Recurring decimal to fraction Write x out as a long decimal Keep working 10x, 100x etc until they are the same after the decimal point

Plans and Elevations

Nets of 3d shapes

Rectangle is length x width Triangle is height x base / 2 AREA Rectangle is length x width Triangle is height x base / 2 Trapezium is (add parallel sides) x height /2 Compound shapes – split into easier shapes then add together 21

Prisms – Area of front x length VOLUME Prisms – Area of front x length 22

Density Formula Triangles Mass Volume Density Population Area of country Pop density

Parallel lines- look for FUZ: Corresponding Interior Alternate ANGLES Parallel lines- look for FUZ: Corresponding Interior Alternate Bearings measure clockwise from North 24

SIMILAR SHAPES Congruent means exactly the same Length scale factor = x Area scale factor = x2 Volume scale factor = x3

PYTHAGORAS TAKE THE 2 NUMBERS SQUARE ADD OR SUBTRACT SQUARE ROOT

Area of Isosceles Triangle Use Pythagoras to find the height Then use base x height / 2 for the area

TRAVEL GRAPH Away from home Journey home Stops Distance Speed Time Speed is how far you travel in 1 hour Distance Speed Time

MEASURED FROM THE NORTH LINE BEARINGS ANGLE MEASURED FROM THE NORTH LINE (North line must be on zero degrees on a protractor) MEASURED IN A CLOCKWISE DIRECTION MUST BE WRITTEN AS THREE FIGURES Find the bearing of B from A N 054° B A 29

Tessellations Shapes tessellate when the angles at the point they meet add to 360 deg

TRIG Right angle triangle Label sides Opp Adj Tan Opp Hyp Sin Adj Hyp Cos Right angle triangle Label sides Pick correct triangle Cover up the side you want If finding angle use the 2ndF button Write SOHCAHTOA on the formula page of the paper

CIRCLES Area = pi x rad2 Circumference = pi x diameter Leave in terms of pi means treat pi as a letter

Circle Area – Work backwards We are given the area, find the radius

CONES AND SPHERES Everything you need to know is on the formula sheet on the paper

Volume of a sphere – find the radius

1 kg is 2.2 lbs 5 miles is 8 Km 1 litre is 1.75 pints Conversion Units to Learn 1 kg is 2.2 lbs 5 miles is 8 Km 1 litre is 1.75 pints 1 litre is 1000 cm3

Collect like terms Don’t forget that you cannot add an x2 term and an x term

Nth Term Find the nth term of the following sequences and then calculate the 100th term. a) 3, 7, 11, 15, … Nth term so far = 4n +4 Start number is -1 Nth term is 4n - 1 Worksheet needs printing 100th term = 4x100 -1 100th term = 399 38

PROPORTION Bring in k Y = k x2 Work out k If inverse proportion, Y = k