Maths Methods Exam Cheat Sheet Simultaneous Equations Substitution method Substitute either the x value or y value in to one of the equations then solve algebraically. Elimination method

Linear graphs Parallel lines If both gradients are the same, they are parallel Perpendicular lines If m1 m2 = -1 then it is perpendicular Finding equation of straight line

  2 1Work out gradient  2 1 then substitute it into the equation along with the x and y values given to work out c Tangent of angle of slope Angle = tan-1  m Basically multiply the gradient by inverse tan. If the angle is negative add it to 180 degrees. Distance between two points AB= x  x   y y  Midpoint ( x =      ,    y = )

Angle between intersecting lines   Basically find the tangent angle of slope for both equations and subtract from each other.

Quadratics Finding Turning Points There a two very simple methods to finding the TPs. The first one is to change the formula into the turning point form: y = a(x - b)2 + c The other method is to find the x intercepts, then to find the x-value of the TP, you add the x-intercepts together and halve it. Then to find the y-intercept, substitute the x-value TP into the equation. Discriminant If: *discriminant > 0 = two solutions (x intercepts) *discriminant = 0 = 1 solution (x intercepts) *discriminant < 0 = no solutions (x intercepts) Quadratic formula in different forms: y = ax2+bx+c < use when given y-int and a point y = ax(x-b) < use when given one x-int and a point y = (x-a)(x-b) < use when give two x-ints y = a(x-b)2+c < use when given TP y = ax2+c < use when give a y and x-int Inequations If you divide or multiply negative values across, the > sign will change to < and vice versa Gallery of graphs Hyperbola y = + k a represents dilation factor h represents translation in the x-axis (positive moves left, negative moves right) k represents translation in the y-axis (positive moves up, negative moves down)

Maths Methods Exam Cheat Sheet Truncus y = + k a represents dilation factor h represents translation in the x-axis (positive moves left, negative moves right) k represents translation in the y-axis (positive moves up, negative moves down) Square root function y = a√ + k a represents dilation factor if a>1, the graph become straighter vertically 0<a<1, the graph becomes straighter horizontally h represents translation in the x-axis (positive moves left, negative moves right) k represents translation in the y-axis (positive moves left, negative moves right) If the x term is negative, than the graph becomes reflected horizontally, if the entire equation is negative, then the graph become reflected vertically. If the equation is negative as well as the x term, the graph becomes inverted both horizontally and vertically. Circles (x-h)2 + (y-k)2 = r2 The centre of the circle is the point (h, k) and the radius is r.

Semicircles

To get it back into the normal form, complete the square.