3.1Algebra
Modulus, polynomial division, the factor and remainder theorems, partial fractions and the binomial series for rational n.
5 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, equations with the unknown in the index, and reduction to linear form.
4 sub-topics · Laws of logarithms and relationship with indices · Properties and graphs of e^x and ln x as inverse functions …
Trigonometry
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) …
Differentiation
Derivatives of the standard functions including tan⁻¹, the product and quotient rules, and parametric and implicit differentiation.
3 sub-topics · Derivatives of e^x, ln x, sin x, cos x, tan x, tan^-1(x) and composites · Product rule and quotient rule …
Integration
The standard integrals, partial fractions, the f′/f form, by parts and by substitution.
6 sub-topics · Integration of e^(ax+b), 1/(ax+b), sin(ax+b), cos(ax+b), sec^2(ax+b), 1/(x^2+a^2) · Using trigonometric identities in integration …
Numerical Solution of Equations
Locating roots by sign change or sketch, 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 …
Vectors
Vector notation in 2D and 3D, lines in the form r = a + tb, parallel/intersecting/skew, and the scalar product.
6 sub-topics · Vector notation in 2D and 3D · Addition, subtraction of vectors and multiplication by a scalar …
Differential Equations
Turning a rate-of-change sentence into an equation, separating the variables, and interpreting the answer.
4 sub-topics · Formulating differential equations from rate-of-change statements · Solving first-order separable differential equations by integration …
Complex Numbers
Cartesian and polar form, the Argand diagram, conjugate root pairs, square roots and loci.
8 sub-topics · Terminology: real part, imaginary part, modulus, argument, conjugate · Arithmetic of complex numbers in Cartesian form (x + iy) …