HKDSE Maths M2 study plan

Recall and apply the binomial theorem for positive integral indices, including finding a general term and a specific coefficient in an expansion of the form (a + b)^n

Compute and manipulate factorials, permutations and combinations, and solve counting problems involving arrangements with and without repetition

Expand and simplify expressions involving sigma notation, and prove simple summation identities by induction

State and apply the principle of mathematical induction to prove statements about sums, divisibility and inequalities

Perform polynomial long division and synthetic division, and state the quotient and remainder correctly

Apply the remainder theorem and factor theorem to find unknown coefficients in a polynomial

Solve polynomial equations with complex roots and use conjugate root pairs to reconstruct a polynomial

Manipulate complex numbers in rectangular and polar form, including modulus, argument and de Moivre's theorem

Solve systems of linear equations in three unknowns using Gaussian elimination and interpret the solution set geometrically

Compute 2x2 and 3x3 determinants and inverses, and use them to solve matrix equations of the form AX = B

Apply matrix operations to represent transformations and verify properties such as associativity and non-commutativity

Set up and solve word problems that reduce to a system of linear equations

Compute limits of rational, surd and trigonometric functions algebraically, including one-sided limits and limits at infinity

Determine continuity of a piecewise function at a point and find unknown constants that make a function continuous or differentiable

Differentiate from first principles and state the derivative rules for powers, products, quotients and the chain rule

Differentiate implicit and parametric functions and find second derivatives

Apply differentiation to find tangents, normals and stationary points, and classify them using the first or second derivative test

Solve rates of change and related rates problems by setting up the connecting equation before differentiating

Locate maxima and minima in applied optimisation problems and justify the answer with a derivative test

Sketch curves accurately using intercepts, asymptotes, stationary points and symmetry

Integrate standard functions and use substitution to evaluate indefinite and definite integrals

Evaluate definite integrals by parts and by partial fractions, choosing the method before starting

Apply integration to find areas between curves and volumes of revolution about the x-axis

Use the fundamental theorem of calculus to differentiate integrals with variable limits

Solve first-order separable differential equations and apply an initial condition to find the particular solution

Model and solve simple growth, decay and cooling problems using differential equations

Evaluate limits using L'Hopital's rule where appropriate and recognise when it does not apply

Combine calculus techniques to answer multi-step examination-style questions under time pressure

Re-solve every question previously logged as an error until each is correct without notes

Complete a full-length timed mock under examination conditions and manage time allocation across both domains

State and apply the key formulas for binomial expansion, matrices, differentiation and integration from memory in a rapid recall drill

Identify and fix the two highest-frequency remaining error types from the mock analysis