IGCSE Mathematics — Complete Revision Notes

Everything the rest of the syllabus assumes you can already do — index laws, standard form, surds, bounds, ratio, and the percentage questions that come back in every exam.

4 sections·~14 min·จำนวนและพีชคณิต (Number and Algebra)·CC 8.NS, 8.EE, N-RN, 7.RP

Expanding, factorising in every form the syllabus asks for, algebraic fractions, and rearranging a formula when the letter you want appears twice.

3 sections·~9 min·จำนวนและพีชคณิต (Number and Algebra)·CC A-SSE, A-APR

Linear and quadratic equations by every method the syllabus allows, simultaneous equations including the linear-and-quadratic case, and inequalities on a number line.

3 sections·~10 min·จำนวนและพีชคณิต (Number and Algebra)·CC A-REI, 8.EE

Finding the rule behind a list of numbers — linear on both tiers, quadratic and geometric on Extended — and using it to answer questions listing cannot.

3 sections·~9 min·จำนวนและพีชคณิต (Number and Algebra)·CC F-BF, F-LE

Function notation, the shapes of the standard graphs, and reading solutions off a curve — plus composite and inverse functions on Extended.

3 sections·~11 min·จำนวนและพีชคณิต (Number and Algebra)·CC F-IF, F-BF

Gradient, midpoint and length from coordinates, and the equations of lines that are parallel or perpendicular to a given one.

3 sections·~9 min·การวัดและเรขาคณิต (Geometry and Measure)·CC G-GPE, 8.EE

Angle facts, polygon angles, similarity and congruence, and the circle theorems — each with the reason it holds rather than as a list to memorise.

3 sections·~11 min·การวัดและเรขาคณิต (Geometry and Measure)·CC 8.G, G-C, G-SRT

Perimeter, area, surface area and volume for every shape on the syllabus, including arcs, sectors and the solids that taper.

3 sections·~10 min·การวัดและเรขาคณิต (Geometry and Measure)·CC 7.G, G-GMD

Right-angled triangles first, then the sine and cosine rules that handle every other triangle — plus bearings, three-dimensional problems and the trigonometric graphs.

3 sections·~12 min·การวัดและเรขาคณิต (Geometry and Measure)·CC G-SRT, F-TF

Describing a transformation completely enough to earn the marks, and the column-vector arithmetic that turns geometry into calculation.

3 sections·~12 min·การวัดและเรขาคณิต (Geometry and Measure)·CC 8.G, N-VM

Single events, combined events, tree diagrams and Venn diagrams — with the with-and-without-replacement distinction that most of these questions turn on.

3 sections·~10 min·สถิติและความน่าจะเป็น (Statistics and Probability)·CC S-CP, 7.SP

Averages from grouped data, the charts this syllabus is particular about — histograms with unequal widths and cumulative frequency — and what a scatter graph can and cannot prove.

3 sections·~11 min·สถิติและความน่าจะเป็น (Statistics and Probability)·CC S-ID, 8.SP