Additional Mathematics — Complete Revision Notes

Domain and range done properly for the first time, composite and inverse functions, and the modulus function — the topic that quietly decides whether the rest of this syllabus makes sense.

4 sections·~15 min·จำนวนและพีชคณิต (Number and Algebra)·CC F-IF, F-BF

Completing the square as a tool rather than a trick, the discriminant as a question about how many times a line meets a curve, and quadratic inequalities solved without guessing.

4 sections·~11 min·จำนวนและพีชคณิต (Number and Algebra)·CC A-SSE, A-REI, F-IF

Fractional and negative indices without a calculator, surds left in exact form, and the factor and remainder theorems — the tools that let you factorise a cubic.

4 sections·~12 min·จำนวนและพีชคณิต (Number and Algebra)·CC N-RN, A-APR, A-SSE

Logarithms as the inverse of a power, the three laws that do all the work, and the linear law — bending a curved relationship into a straight line so its constants can be measured.

4 sections·~12 min·จำนวนและพีชคณิต (Number and Algebra)·CC F-LE, F-BF

Gradient, midpoint and length, the perpendicular condition, and the standard 0606 question that asks you to find a fourth vertex or the area of a shape from nothing but coordinates.

3 sections·~9 min·จำนวนและพีชคณิต (Number and Algebra)·CC G-GPE, F-IF

The equation of a circle in both of its forms, how to get from one to the other by completing the square, and the tangent property that turns most circle questions into straight-line questions.

3 sections·~8 min·การวัดและเรขาคณิต (Measurement and Geometry)·CC G-GPE, G-C

Radians — what they actually are, why the arc and sector formulas become one-liners in them, and why everything in the calculus chapters depends on using them.

3 sections·~8 min·การวัดและเรขาคณิต (Measurement and Geometry)·CC F-TF, G-C

The three reciprocal ratios, the identities that connect everything, solving trigonometric equations across a stated range, and reading amplitude and period off a graph.

4 sections·~11 min·การวัดและเรขาคณิต (Measurement and Geometry)·CC F-TF, G-SRT

Counting arrangements when order matters and when it does not, and the binomial expansion — which turns out to be the same counting problem written as algebra.

3 sections·~10 min·สถิติและความน่าจะเป็น (Statistics and Probability)·CC S-CP, A-APR

Vectors as displacements rather than points, adding them by following one after another, and the relative-velocity problems that are the reason this topic is on the syllabus.

3 sections·~11 min·การวัดและเรขาคณิต (Measurement and Geometry)·CC N-VM

The gradient of a curve at a point: what a derivative means, the rules for finding one, and the three questions — tangents, stationary points and rates of change — that every calculus question on this paper reduces to.

3 sections·~12 min·แคลคูลัส (Calculus)

Integration as differentiation run backwards, definite integrals as areas, and kinematics — the one topic where the derivative and the integral both mean something you can watch happen.

3 sections·~12 min·แคลคูลัส (Calculus)