– Simplification of rational expressions including
factorizing and cancelling, and algebraic division definition of a function.
Domain and range of functions. Composition of functions. Inverse functions and
their graphs, the modulus function, and Combinations of the transformations

– Knowledge of secant, cosecant and cotangent and of arc sin,
arc cos and arctan. Their relationships to sine, cosine and tangent.
Understanding of their graphs and appropriate restricted domains, Knowledge and
use of sec2 θ = 1 + tan2 θ and cosec2 θ = 1 + cot2 θ, Knowledge and use of
double angle formulae; use of formulae for sin (A ± B), cos(A ± B) and tan (A ±
B) and of expressions for a cos θ + b sin θ in the equivalent forms of r cos(θ
± a) or rsin (θ ± a).

– The function ex and its graph, The function ln x and its
graph; ln x as the inverse function of e^x, and Use logarithmic
graphs to estimate parameters in relationships of the form y = axⁿ
and y = kb^x

– Differentiation of e^kx, ln kx, sin kx, cos kx,
tan kx and their sums and differences

– Differentiation using the product rule, the quotient rule
and the chain rule, and understand and use exponential growth and decay

– Integration of e^kx, 1 / x , sin kx, cos kx and
their sums and differences, in addition to Integration by recognition of known
derivatives.

– 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, and Approximate
solution of equations using simple iterative methods, including recurrence
relations of the form xⁿ + 1 = f(xⁿ)