Foundations · GCSE · Grade 8/9
Mathematics
Mathematics tuition can start with basic number confidence and progress all the way through the supplied GCSE Grade 8/9 topic map, with support tailored around gaps, targets and future technical ambitions.
What we teach
Learn from your current level.
This is not a fixed pre-recorded course. Usavir Academy can teach the subject around what the student already knows, what they are struggling with and what they want to achieve. Lessons can focus on one topic or grow into a wider subject pathway over time.
Foundation building
Rebuild arithmetic, fractions, place value, percentages and core skills until the basics feel reliable.
GCSE progression
Develop algebra, graphs, geometry, ratio, probability, statistics and exam-focused problem solving.
Higher GCSE / advanced topics
Work through Grade 7–9 areas such as surds, algebraic fractions, functions, circle theorems, vectors, proof and harder probability.
Number & arithmeticFractions, decimals & percentagesRatio & proportionAlgebraEquations & inequalitiesGraphs & functionsGeometry & measuresProbabilityStatisticsTrigonometryVectorsProofHigher GCSE techniques
Full GCSE Mathematics topic map · 134 areas
Grade 113 topics
Addition and SubtractionMultiplication and DivisionTimeMetric ConversionsWriting, Simplifying and Ordering FractionsPlace ValueRoundingNegative NumbersPowers and RootsBIDMASFactors and MultiplesCoordinatesPictograms
Grade 217 topics
Calculation ProblemsUsing a CalculatorSystematic ListingFractions of an AmountFractions, Decimals and PercentagesSimplifying AlgebraWriting an ExpressionFunction MachinesSolving One Step EquationsAnglesArea and PerimeterProbabilityFrequency PolygonsAveragesBar ChartsStem and LeafPie Charts
Grade 320 topics
Error IntervalsFractionsEstimatingWriting and Simplifying RatioRatioProportionPercentagesPercentage ChangeExchange RatesConversions and UnitsScale DrawingsBest Buy QuestionsSubstitutionSolving EquationsDrawing Linear GraphsArea and Circumference of CirclesTransformationsArea of Compound ShapesFrequency TreesTwo Way Tables
Grade 420 topics
Compound Interest and DepreciationIndicesPrime Factors, HCF and LCMReal Life and Distance Time GraphsInequalitiesForming and Solving EquationsSequences (Nth Term)Expanding and FactorisingPythagorasAngles in Parallel LinesAngles in PolygonsSurface AreaVolume of a PrismCylindersLoci and ConstructionBearingsPlans and ElevationsAverages from Frequency TablesProbabilityScatter Graphs
Grade 523 topics
Writing a Ratio as a Fraction or Linear FunctionDirect and Inverse ProportionReverse PercentagesStandard FormSpeed and DensityChanging the Subject of a FormulaExpanding and Factorising QuadraticsSolving QuadraticsDrawing Quadratic GraphsDrawing Other Graphs: Cubic/ReciprocalSimultaneous EquationsSolving Simultaneous Equations GraphicallyMidpoint of a Line SegmentGradient of a LineEquation of a LineSpheres and ConesSector Areas and Arc LengthsSimilar Shapes (Lengths)SOHCAHTOA (Trigonometry)Exact trig valuesVectorsProbability TreesVenn Diagrams
Grade 613 topics
Recurring Decimals to FractionsFractional and Negative IndicesThe Product Rule for CountingRepeated Percentage ChangeExpanding Triple BracketsParallel and Perpendicular LinesInequalities on GraphsSimilar Shapes (Area and Volume)Enlarging with Negative Scale FactorsCircle TheoremsCumulative FrequencyBox PlotsCapture Recapture
Grade 717 topics
SurdsBoundsDirect and Inverse ProportionQuadratic FormulaFactorising Harder QuadraticsAlgebraic FractionsRearranging Harder FormulaeTrigonometric and Exponential GraphsInverse and Composite FunctionsIterationFinding the Area of Any TriangleThe Sine RuleThe Cosine RuleCongruent Triangles3d Pythagoras and TrigonometryHistogramsConditional Probability
Grade 8/911 topics
Quadratic Simultaneous EquationsTransforming Graphs y=f(x)ProofCompleting the SquareThe Nth Term of a Quadratic SequenceQuadratic InequalitiesVelocity Time GraphsProof of the Circle TheoremsPerpendicular Lines and the equation of a tangentVectors Proof QuestionsProbability Equation Questions
Practical outcomes
What could this help you build or achieve?
Learning matters more when students can see where it leads. These are examples of the skills and outcomes the subject can support as knowledge develops over time.
Stronger GCSE performance
Target weak areas, rebuild foundations and progress through the full range from basic arithmetic to Grade 8/9 topics.
Programming & Computer Science
Algebra, logic, functions and problem solving directly support coding and technical learning.
AI & Machine Learning foundations
Probability, statistics, algebra and functions are central to understanding AI at a deeper level.
Engineering problem solving
Geometry, trigonometry, algebra and modelling are heavily used across engineering pathways.
Finance & economics
Percentages, statistics, modelling and quantitative reasoning support financial and economic subjects.
Confident quantitative thinking
Build the habit of breaking complex problems into clear steps — useful far beyond an exam paper.
Future pathways
Fields the subject can help unlock.
Indicative UK salary ranges below are drawn from National Careers Service profiles checked in August 2026. They are career examples, not promises of future earnings; pay varies by experience, employer, region and specialism.
Actuary
£32,000–£70,000Uses mathematics and statistics to assess long-term financial costs and risk.
National Careers Service ↗Data Scientist / ML pathway
£32,000–£83,000Maths and statistics are explicitly listed as key knowledge and common degree routes.
National Careers Service ↗Aerospace Engineer
£30,000–£70,000Uses mathematics alongside physics and engineering science to design and test aircraft and spacecraft.
National Careers Service ↗Civil Engineer
£29,000–£63,000Uses mathematical modelling and problem solving in major construction and infrastructure projects.
National Careers Service ↗Management Accountant
£30,000–£60,000Maths is listed among relevant degree routes into finance and management accounting.
National Careers Service ↗Software Developer
£30,000–£75,000Mathematics is one of the degree routes listed by the National Careers Service for software development.
National Careers Service ↗Study combinations
Subjects that can strengthen the pathway.
Students do not need every subject below. The point is to show which combinations can become especially useful depending on future goals.
Computer Science
A powerful pairing for programming, algorithms, technical university routes and digital careers.
Artificial Intelligence
AI increasingly rewards strong mathematical thinking. Learning AI alongside Maths can turn abstract ideas into a modern technical advantage.
Physics
One of the classic combinations for engineering, mechanics, modelling and scientific study.
Further Mathematics
A strong route for students progressing towards highly mathematical A levels or university subjects.
Economics
Uses quantitative reasoning, graphs, modelling and statistics in real economic problems.
Business / Finance
Useful for accounting, investment, commercial analysis and entrepreneurship.
Consider AI alongside Mathematics.
Algebra, probability, statistics, functions and optimisation sit underneath many Machine Learning ideas. Combining Mathematics with AI knowledge can be especially valuable for future study in computing, engineering, data science and other technical fields.
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Get ready for your first live Mathematics class.
Tell us the student's current level, target and the areas they want help with. Send the enquiry once, then WhatsApp opens with the same information ready to send. Pick a suitable time and join the lesson live on Google Meet.