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Trial and Improvement Venn Diagrams Reflect a shape Rotate a shape Translate a shape Across Up or Down ENLARGEMENT Scale factor x3 Count across and up from the centre Times this by 3 from the centre Negative enlargement goes the opposite way POLYGON ANGLES Interior angle is 180 – exterior angle 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 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 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 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 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 ESTIMATE OF THE MEAN •2 extra columns •Use mid point of groups •Mid point x frequency •Big total divided by little total 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 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 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