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 o o o xo xo ao 2xo bo yo yo xo xo yo DIAMETER RADIUS 8 a + b = 180° x + y = 180° Angle at centre is twice the angle at the circumference. Angle made by a diameter is 90°. Opposite angles in a cyclic quadrilateral add up to 180° xo yo o RADIUS xo yo Angles subtended by an arc or a chord in the same segment are equal. Alternate segment theorem. Angle between a tangent and a radius make 90° 8

TREE DIAGRAMS Each V adds to 1 Multiply alon g the branches

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

Two brackets together – eyebrows and smiley face are 4 multiplies EXPANDING BRACKETS Two brackets together – eyebrows and smiley face are 4 multiplies 11

Pick the x’s to times together 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 12

INEQUALITIES 3 included, filled circle -2 not included, empty 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

TRANSFORMING GRAPHS Inside the brackets – changes x cords 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

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 19

Draw line 2x -3y = 6 by making a table 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