Integers, Powers & Roots
Rational and irrational numbers, estimating roots, the index laws and fractional indices.
The Thai Guy · Mathematics
16 topics across the three strands, 69 lessons with step-by-step worked solutions, and hundreds of practice questions that mark themselves and explain where you went wrong.
Working with numbers in every form, then letting letters stand in for them: indices, standard form, fractions, equations, sequences, proportion and percentages.
Rational and irrational numbers, estimating roots, the index laws and fractional indices.
Simplifying, algebraic fractions, expanding brackets, substitution and rearranging formulae.
Multiplying and dividing by powers of ten, standard form, and upper and lower bounds — including bounds in calculations.
Factors, multiplying and dividing fractions, order of operations, and recurring decimals — including the algebraic method.
Building and solving linear equations, inequalities, gradients and simultaneous equations.
Solving ratio problems, direct proportion and inverse proportion.
Term-to-term and nth term rules, functions, straight-line graphs and reading real-life graphs.
Estimation, multiplying and dividing decimals, compound percentage change, reverse percentages and percentage error.
Expanding, factorising and solving quadratics, sketching their graphs, and where a line meets a curve.
Shape, space and size: circles, Pythagoras, surface area and volume, angles in polygons, constructions and transformations.
Inscribed polygons, ruler-and-compass constructions, scales, bearings, and symmetry in 3D.
Circles, Pythagoras’ theorem, surface area and volume, units of area and volume, similar solids, and compound units.
Angles in polygons, tessellations, multi-step angle problems and coordinates on a line segment.
Enlargement, describing single transformations, and combining them.
Collecting and summarising data, choosing the right graph to tell its story, and measuring how likely things are to happen.
Averages and range from grouped frequency tables, and how to take a fair sample.
Frequency polygons, back-to-back stem-and-leaf diagrams, scatter graphs and choosing the right chart.
Combined events, sample space diagrams, tree diagrams and experimental probability.
What the idea is, why it matters, and the rules and formulas you need.
Try it yourself, then reveal the solution one step at a time — not all at once.
Fourteen kinds of question, marked instantly, with a hint when you are stuck.
A scored paper that mixes question types, then a full review of every answer.