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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 MEAN FROM A TABLE •Multiply frequency by the value •Divide this total by total frequency Total Mean How many ESTIMATE OF THE MEAN •2 extra columns •Use mid point of groups •Mid point x frequency •Big total divided by little total Basic Averages • Modal class is the mode group • Median is the middle one • Mean is total divided how many? Mean Total How many? 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 HISTOGRAMS •Frequency density is freq divided by class width •The area of a bar is the frequency TREE DIAGRAMS • Each V adds to 1 • Multiply alon g the branches STRATIFIED SAMPLING Eg 239 of 100 Total •Fraction of – divide by the bottom, times by the top. FREQUENCY DIAGRAMS Frequency polygon = join midpoints of bar chart Frequency diagram = bar chart Venn Diagrams 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 POWERS •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 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) (b) 32 8 4 2 10 4 2 2 60 2 5 6 2 3 2 2 ANSWER = 2 X 2 X 2 X 2 X 2 5 =2 ANSWER = 2 X 2 X 3 X 5 2 =2 X3X5 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 PERCENTAGES •1% - divide by 100 •10% - divide by 10 • % change is change / original x 100% Percentage Increase by Multiplier 100% + 1.85% = 101.85% = Multiplier 1.0185 £5600 x 1.018515 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 • 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 20% £40000 £31865 = £8135 40% 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 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 Area under a Curve Height of each bar is the y coordinate • Find the area of each triangle / trapezium, then find the total • The area under velocity time curve is the distance Plans and Elevations Nets of 3d shapes 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 VOLUME •Prisms – Area of front x length Density Formula Triangles Mass Density Population Volume Pop density Area of country ANGLES •Parallel lines- look for FUZ: Corresponding Interior Alternate •Bearings measure clockwise from North 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 •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 Speed is how far you travel in 1 hour Distance Speed Time BEARINGS ANG LE MEASURED FROM THE (North line must be on zero degrees on a protractor) NORTH LINE MEASURED IN A CLOCKWISE DIRECTION MUST BE WRITTEN AS THREE Find the bearing of B from A N A 054 ° B FIGURES Tessellations Shapes tessellate when the angles at the point they meet add to 360 deg TRIG Opp Sin Opp Adj Hyp • • • • • Cos Hyp Right angle triangle Label sides Pick correct triangle Cover up the side you want If finding angle use the 2ndF button Tan Adj 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 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, … +4 +4 +4 100th term = 4x100 -1 100th term = 399 Nth term so far = 4n Start number is Nth term 1 is 4n - 1 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 STRAIGHT LINES • Look neg at the gradient – positive or •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 x2 Circumference of Circle = pi x diameter Area of Circle = pi x radius2 Fraction of Circle = 60 / 360 Find this fraction of area for sector area and same with circumference for arc length ( divide by bottom, times by top) To find the gradient when x=4 1. Mark the point 2. Draw tangent 3. Find the gradient of the line Pick 2 points on the line Gradient = up / across Upper and Lower Bounds 100 / 2 = 50, so do 31500 + and - 50 1 / 2 = 0.5, do 46 + and – 0.5 When you add or multiply, use the 2 biggest or the 2 smallest When you subtract or divide, cross match them