The Basics: Find the distance between two points using Pythagoras' theorem. The midpoint is the average (mean) of the coordinates. The gradient = Parallel lines have the same gradient. The gradients of perpendicular lines have a product of -1. Straight Lines: Equation of a straight line is y = mx + c, where m = gradient, c = y-intercept. The equation of a line, if we know one point and the gradient is found using: (y - y1) = m(x - x1) (If given two points, find the gradient first, then use the formula.) Two lines meet at the solution to their simultaneous equations. Note: When a line meets a curve there will be 0,1, or two solutions. Use substitution to solve the simultaneous equations Rearrange them to form a quadratic equation Solve the quadratic by factorising, or by using the quadratic formula. Find the y-coordinates by substituting these values into the original equations. Other Graphs (also in Functions): Sketch the curve by finding: Where the graph crosses the y-axis. Where the graph crosses the x-axis. Where the stationary points are. Whether there are any discontinuities. What happens as Circles: Cartesian equation for a circle is (x - a)2 + (y - b)2 = r2 , where (a, b) is the centre of the circle and r is the radius. Parametric Equations: Sketch the graph by substituting in values and plotting points. Find the cartesian form by either using substitution (use t = ...), or by using the identity, . Find the gradient using the chain rule: