AQA Core 3
Domain and range of functions. Composition of functions. Inverse functions. Notation such as f(x)=x^{2}4 Domain and range may be expressed as x>1 for example fg(x)=f(g(x)) 
Graphs of functions and their inverses; sketching curves defined by simple equations. Geometrical interpretation of algebraic solution of equations. Use of intersection points of graphs of functions to solve equations. Inverse of f(x) written as f^{1}(x) To include reflection in y = x.

The modulus function. To include related graphs and the solution of inequalities such as x+2<3x using solutions of x+2=3x 
Knowledge of the effect of simple transformations on the graph of y = f(x) as represented by y = af(x), y = f(x) + a , y = f(x + a), y = f(ax) and combinations of these transformations. e^{x} leading to e^{2x}  1 lnx leading to 2ln(x1); secx leading to 3sec2x Transformations of functions included in modules Core 1 and Core 2 
Knowledge of secant, cosecant and cotangent and arcsin, arccos and arctan. Their relationships to sine, cosine and tangent. Understanding of their graphs and appropriate restricted domains. Knowledge that ∏/2 <arcsinx<∏ 0 <arccosx<∏, ∏/2 <arctanx<∏ The graphs of these functions as reflections of the relevant parts of the trigonometric graphs in x y plane included. The addition formulae for inverse functions are not required. The graphs of these functions as reflections of the relevant parts of the trigonometric graphs in x y plane included. The addition formulae for inverse functions are not required. 
Knowledge and use of 1 + tan^{2}x = sec^{2}x and 1 + cot^{2}x = cosec^{2}x Use in simple identities.
Solution of trigonometric equations and inequalities in a given interval. 
The function e^{x} and its graph Autograph: Describe a series of transformations which will map Y=e^{x} onto y=e^{2(x1)} 
The function lnx and its graph; lnx as the inverse function of e^{x}. 
Differentiation of e^{x}, sin x, cos x, tan x and linear combinations of these functions. To include simple composite functions.
Differentiation using the product rule, the quotient rule, the chain rule and by the use of dy/dx = 1/(dx/dy) E.g. x^{2}lnx e^{3x}sinx
(e^{2x}1)/(e^{2x}+1)
(2x+1)/(3x2) 
Integration of sinx, cosx. To include ∫cos^{2}xdx etc 
Simple cases of integration by substitution and integration by parts. Inspection ∫e^{3}xdx; ∫sin4xdx; ∫x(1+x^{2})^{0.5}dx
Substitution ∫x(2x+6)^{6}dx; ∫x(2x3)^{0.5}dx
By parts ∫xe^{2x}dx; ∫xsin3xdx; ∫xlnxdx 
These methods as the reverse processes of the chain and product rules respectively. ∫ f'(x)/f(x)dx by inspection or substitution 
Evaluation of volume of revolution. The axes of revolution will be restricted to x and y axes. 
Location of roots of f(x)=0 by considering changes of sign of f(x) in an interval of x in which f(x) is continuous. To include interval bisection and linear interpolation. Approximate solutions of equations using simple iterative methods, including Newton  Raphson. Rearrangement of equations to the form x = g(x). f(x)=6xlnx Show that f(x) has a root between 4 and 5 and determine whether the root is closer to 4 or 5. 
Staircase and cobweb diagrams. 
Numerical integration of functions using the midordinate rule and Simpson’s rule To include a geometrical determination of whether the rule over or underestimates the area and improvement of an estimate by increasing the number of steps. 