Rectangular Cartesian co-ordinate systems; distance between two points; gradient of a line; co-ordinates of a point dividing a line segment in a given ratio; equation of a circle in the form (x-a) 2 + (y-b) 2 = r2; x2+ y2+2gx + 2fy+c.
Points of intersection of lines and circles; limit of a function of one variable at a point; continuous functions; derivatives of a function and its interpretation as the rate of change; higher order derivatives; differentiation of algebraic, circular exponential functions; sum, product and quotient rules; differentiation of composite, absolute value and implicit function; small increments and calculation of approximate values; application of derivative to increasing and decreasing of functions; maxima and minima; curve sketching; integration as the inverse of differentiation; integration of simple continuous functions and rational functions by substitution; parametric representation of loci; the parabola, ellipse and rectangular hyperbola; chords, tangents and normals; circular functions of angles of any magnitude and their graphs; trigonometric formula including multiple angles, half angles and identities; solutions to trigonometric equations.