Report

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 ESTIMATE OF THE MEAN •2 extra columns •Use mid point of groups •Mid point x frequency •Big total divided by little total QUESTIONNAIRES •Look for a time limit in the question •Overlap between the choices •Any missing choices? CUMULATIVE FREQUENCY •Running total •Plot end points against cumulative frequency •Measure median and quartiles 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 FREQUENCY DIAGRAMS Frequency polygon = join midpoints of bar chart Frequency diagram = bar chart 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 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 FRACTIONS OF Eg 239 of 100 Total •Fraction of – divide by the bottom, times by the top. PERCENTAGES •1% - divide by 100 •10% - divide by 10 • % change is change / original x 100% 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 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 ANGLES •Parallel lines- look for FUZ: Corresponding Interior Alternate •Bearings measure clockwise from North CIRCLE THEOREM xo xo o DIAMETER ao o 2xo a + b = 180° x + y = 180° yo Angle at centre is twice the angle at the circumference. yo Angle made by a diameter is 90°. Opposite angles in a cyclic quadrilateral add up to 180° xo yo RADIUS xo yo xo yo Angles subtended by an arc or a chord in the same segment are equal. xo Alternate segment theorem. Angle between a tangent and a radius make 90° bo 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 TRAVEL GRAPH Away from home Journey home Stops Distance Speed Time POLYGON ANGLES Interior angle is 180 – exterior angle ENLARGEMENT Scale factor x3 Count across and up from the centre Times this by 3 from the centre Negative enlargement goes the opposite way VECTORS • Go from A to B • Only use a and b • -a+b or b-a 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 CONES AND SPHERES Everything you need to know is on the formula sheet on the paper 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 EXPANDING BRACKETS •Two brackets together – eyebrows and smiley face are 4 multiplies FACTORISING BRACKETS •Pick the x’s to times together •Pick the numbers to times to the question •Check the smiley face to see if the x term is right 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 INEQUALITIES -2 not included, empty circle 3 included, filled circle • Integer means whole number • Solve like an equation 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 TRANSFORMING GRAPHS Inside the brackets – changes x coords the opposite way Outside the brackets, changes y coords the same way TYPES OF GRAPHS Quadratic graph y = x2 Cubic graph Y = x3 x2 + y2 = r2 Reciprocal graph Y=1/x 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 1. Draw line 2x -3y = 6 by making a table 2. Pick a point not on the line Take the x and y numbers and put into the inequality. See if the inequality is true or false for that side