SCATTER DIAGRAMS Plot the points Line of best fit Positive and negative correlation

SIMPLE PROBABILITY Probabilities add to 1 Multiply the probability by the number of times

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

QUESTIONNAIRES Look for a time limit in the question Overlap between the choices Any missing choices?

Cumulative Frequency I Running total Plot end points against cumulative frequency Measure median and quartiles

Cumulative Frequency II Three quarters way Half way Quarter way

BOX PLOTS Plot 5 measures to draw it. Lowest value, lower quartile, median, upper quartile, highest value To compare, 1 comment on the median, 1 comment on the interquartile range (the width of the box) Remember that there is 25% of the data between each point

TREE DIAGRAMS Each V adds to 1 Multiply along the branches

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 13

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 14

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 15

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 16

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

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

RATIO RATIO 2:3 MEANS 2+3 = 5 PARTS FIND THE VALUE OF 1 PART

BEST VALUE Change £ into pence by x 100 Work out the cost of each per unit Show all your working out State the answer at the end

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 26

Prisms – Area of front x length VOLUME Prisms – Area of front x length 27

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 29

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

Locus This traces the path of a point as it moves From one point it is a circle From two points it is the perpendicular bisector of the line joining them From one line it is a parallel line either side From 2 lines it is the angle bisector

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 35

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

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

Conversion Graph Plot points from a table Join to make a straight line Be prepared to be taken off the graph

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

SIMULTANEOUS EQUATIONS Criss cross the numbers in front of x Times the equation by that number Change the sign of all the bottom equation Work out y Use y to work out x

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 44

STRAIGHT LINES Form is y=mx+c To plot the line, take 3 x values and find out the y values that go with them

Gradient is up divided by the across STRAIGHT LINES Look at the gradient – positive or neg Gradient is up divided by the across Line is y=mx+c, where m is the gradient and c the intercept

FORM AND SOLVE EQUATION This one is about angles, so add algebra together and put equal to 360. If perimeter, do the same but put = perimeter. Solve by simplifying and solving

PLOTTING GRAPHS Complete table of values Plot points on grid Join points together to make a graph

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

Upper and Lower Bounds 100 / 2 = 50, so do 31500 + and - 50 When you add or multiply, use the 2 biggest or the 2 smallest When you subtract or divide, cross match them