2.1Algebra
The modulus function, polynomial division, and the factor and remainder theorems.
3 sub-topics · Modulus function: graph of y = |ax + b| and solving modulus equations/inequalities · Polynomial division by linear or quadratic polynomial …
Logarithmic and Exponential Functions
Laws of logarithms, e^x and ln x, and turning curved data into straight lines.
4 sub-topics · Laws of logarithms and relationship with indices · Properties and graphs of e^x and ln x as inverse functions …
sec, cosec and cot, the Pythagorean identities, compound and double angles, and the R-form.
5 sub-topics · Secant, cosecant and cotangent functions and their graphs · Pythagorean identities (sec^2 = 1 + tan^2, cosec^2 = 1 + cot^2) …
Derivatives of e^x, ln x and the trig functions; product, quotient, parametric and implicit.
3 sub-topics · Derivatives of e^x, ln x, sin x, cos x, tan x and composites · Product rule and quotient rule …
Integrating the standard functions, using identities, and the trapezium rule.
3 sub-topics · Integration of e^(ax+b), 1/(ax+b), sin(ax+b), cos(ax+b), sec^2(ax+b) · Using trigonometric identities (e.g. double-angle formulae) in integration …
Numerical Solution of Equations
Locating roots by sign change, and iterating to a root to a required accuracy.
3 sub-topics · Locating roots by sign change or graphical methods · Convergent sequences of approximations to a root …