GCSE · Years 10 and 11
GCSE tutoring that moves grades
Our students make three times the progress of a typical year.
- Max 10 students per group
- 2-hour lesson + 1-hour clinic
- Monthly assessments
- Online or in person
- 100%
- pass rate across every exam our students have sat
- 3×
- the progress of a typical school year, on average
- 20,630+
- hours of teaching experience across our tutors
- 1,370+
- students taught
A week at TriForth
Three hours every week, plus a monthly check-in.
BeforePreparation with our resources AfterHomework that locks it in
Our programme
Mapped to your child’s exam board and split across the school year. Open any topic to see exactly what is covered.
Exam board
Science
Exam tier
Autumn
September to December
01Structure and calculation (part 1)
- Order positive and negative integers, decimals and fractions
- Use the symbols =, ≠, <, >, ≤, ≥
- Four operations with integers, decimals and fractions
- Place value with very large and very small numbers
- Inverse operations to simplify calculations
- Order of operations: brackets, powers, roots, reciprocals
- Primes, factors, multiples, HCF, LCM and prime factorisation
02Notation, vocabulary and manipulation (part 1)
- Algebraic notation: ab for a × b
- Algebraic notation: 3y, a² and a³
- Place of a × a × a, a2b in
- Place of a × a × b
- • a bin place of a ÷ b
- Fractional coefficients and brackets
- Substitute values into formulae
03Notation, vocabulary and manipulation (part 2)
- Expressions, equations, formulae, inequalities, terms and factors
- To include identities
- Simplify and manipulate algebraic expressions by:
- Collect like terms, expand, factorise and use index laws
- Simplify and manipulate algebraic expressions
- Expand double brackets; factorise x² + bx + c
- Including the difference of two squares
04Notation, vocabulary and manipulation (part 3)
- Understand and use standard mathematical formulae
- Rearrange formulae to change the subject
- Know the difference between an equation and an identity
- Prove algebraic expressions are equivalent
- Expressions as functions with inputs and outputs
05Ratio, proportion and rates of change (part 1)
- Convert standard and compound units
- Compound units (eg density, pressure)
- In numerical and algebraic contexts
- Use scale factors, scale diagrams and maps
- Express one quantity as a fraction of another
- Use ratio notation, including reduction to simplest form
- Share a quantity in a ratio
- Express the division of a quantity into two parts as a ratio
06Properties and constructions (part 1)
- Geometric terms, notation and symmetry
- Label sides and angles of triangles
- Draw diagrams from written description
- Ruler and compass constructions
- Use these to construct given figures and solve loci problems
- Shortest distance from a point to a line
- Angles at a point, on a line and vertically opposite
07Properties and constructions (part 2)
- Alternate and corresponding angles
- Angle sums in triangles and polygons
- Properties of special quadrilaterals
- Properties of triangles and other plane figures
- Congruence criteria: SSS, SAS, ASA, RHS
- Geometric proof, including Pythagoras and isosceles triangles
- Congruent and similar shapes; transformations
08Properties and constructions (part 3)
- Including fractional scale factors
- Parts of a circle: centre, radius, chord, diameter, circumference
- Including: tangent, arc, sector and segment
- Solve geometrical problems on coordinate axes
- Faces, edges and vertices of 3D shapes
- Interpret plans and elevations of 3D shapes
- Construct and interpret plans and elevations of 3D shapes
09Probability
- Frequency tables and frequency trees
- Expected outcomes from repeated trials
- Relative frequency and the 0–1 probability scale
- Probabilities of all outcomes sum to 1
- Mutually exclusive events sum to 1
- Larger samples approach theoretical probability
- Sets, grids and Venn diagrams
- Including using tree diagrams
- Sample spaces for single and combined events
- Tree diagrams for independent and dependent events
Spring
January to March
01Structure and calculation (part 2)
- Apply systematic listing strategies
- Powers and roots; powers of 2, 3, 4 and 5
- Calculate with roots, and with integer indices
- Calculate exactly with fractions
- Multiples of π calculate exactly with
- Calculate with standard form
- Integer
02Fractions, decimals and percentages
- Convert between terminating decimals and fractions
- Identify and work with fractions in ratio problems
- Interpret fractions and percentages as operators
03Graphs
- Work with coordinates in all four quadrants
- Plot straight-line graphs
- Use the form y = mx + c to identify parallel lines
- Equation of a line through two points
- Gradients and intercepts of linear functions
- Roots, intercepts and turning points of quadratics
- Deduce roots algebraically
- Sketch and interpret linear and quadratic graphs
- Cubic and reciprocal graphs
- Real-life graphs: distance, speed and acceleration
- Including reciprocal graphs
04Ratio, proportion and rates of change (part 2)
- Ratio in real contexts: scaling, mixing, conversion
- Ratios and fractions as multiplicative relationships
- Understand and use proportion as equality of ratios
- Relate ratios to fractions and to linear functions
- Define percentage as ‘number of parts per hundred’
- Percentages and percentage change as multipliers
- Express one quantity as a percentage of another
- Compare two quantities using percentages
05Ratio, proportion and rates of change (part 3)
- Work with percentages greater than 100%
- Percentage change, reverse percentages and simple interest
- Direct and inverse proportion
- Use compound units such as speed, rates of pay, unit pricing
- Use compound units such as density and pressure
- Compare lengths, areas and volumes using ratio notation
- Scale factors
- Make links to similarity (including trigonometric ratios)
06Mensuration and calculation (part 1)
- Standard units of measure
- Scale drawings, maps and bearings
- Area of triangles, parallelograms and trapezia
- Volume of cuboids, prisms and cylinders
- Circumference and area of a circle
- Calculate perimeters of 2D shapes, including circles
- Areas of circles and composite shapes
- Give answers in terms of π
- Surface area and volume of spheres, pyramids and cones
07Statistics (part 1)
- Sampling and its limitations
- Draw and interpret tables, bar charts, pie charts and pictograms
- Including tables and line graphs for time series data
- Compare distributions of data
- Represent discrete, continuous and grouped data
- Mean, median, mode and range; outliers
- Apply statistics to describe a population
Summer
April to July
01Measures and accuracy
- Standard and compound measures with decimals
- Estimate answers
- Check calculations by estimating
- Round to decimal places and significant figures
- Error intervals from rounding and truncation
02Number
- Apply and interpret limits of accuracy
03Solving equations and inequalities
- Solve linear equations in one unknown algebraically
- Find approximate solutions using a graph
- Solve equations with unknowns on both sides
- Solve quadratic equations algebraically by factorising
- Solve linear simultaneous equations
- Form expressions and formulae from situations
- Form and solve equations from problems
- Solve linear inequalities in one variable
- Represent the solution set on a number line
04Sequences
- Term-to-term and position-to-term sequence rules
- Triangular, square and cube numbers; arithmetic sequences
- Fibonacci, quadratic and geometric sequences
- Where n is an integer and r is a rational number > 0)
05Algebra
- nth term of linear sequences
06Ratio, proportion and rates of change (part 4)
- Inverse proportion as proportional to 1/x
- Equations of direct and inverse proportion
- Gradient as a rate of change
- Graphs of direct and inverse proportion
- Growth, decay and compound interest
07Mensuration and calculation (part 2)
- Arc length and sector area
- Lengths in similar figures
- Pythagoras' theorem and SOH CAH TOA
- Adjacent
- Find lengths and angles in right-angled triangles
- Sin θ and cos θ for θ = 0°, know the exact values of
- Exact trig values for 0°, 30°, 45°, 60° and 90°
- 60°
08Vectors
- Describe translations as 2D vectors
09Geometry and measures
- Add, subtract and scale vectors
10Statistics (part 2)
- Use and interpret scatter graphs of bivariate data
- Recognise correlation
- Know that it does not indicate causation
- Draw estimated lines of best fit
- Make predictions
- Interpolation, extrapolation and their risks
Autumn
September to December
01Notation, vocabulary and manipulation
- Simplify expressions with surds and algebraic fractionsHigher
- Expand multiple brackets; factorise ax² + bx + cHigher
- To include proofsHigher
- Interpret the reverse process as the ‘inverse function’Higher
- Composite functionsHigher
02Graphs
- Use the form y = mx + c to identify perpendicular linesHigher
- Deduce turning points by completing the squareHigher
- Exponential graphsHigher
- Graphs of sin, cos and tanHigher
- Sketch translations and reflections of a given functionHigher
- Including exponential graphsHigher
- Gradients and areas under graphsHigher
- Equation of a circle centred at the originHigher
- Find the equation of a tangent to a circle at a given pointHigher
03Structure and calculation
- Including use of the product rule for countingHigher
- Estimate powers and roots of any given positive numberHigher
- Calculate with fractional indicesHigher
- Calculate exactly with surdsHigher
- Simplify surds and rationalise denominatorsHigher
04Ratio, proportion and rates of change
- Form equations for direct and inverse proportionHigher
- Gradient at a point as instantaneous rate of changeHigher
- Average and instantaneous rates of changeHigher
- And work with general iterative processesHigher
05Properties and constructions
- Including negative scale factorsHigher
- Combined transformations and invarianceHigher
- Prove and apply circle theoremsHigher
06Probability
- Conditional probability with tables, trees and Venn diagramsHigher
07Statistics
- Histograms and cumulative frequency graphsHigher
- • including box plotsHigher
- • including quartiles and inter-quartile rangeHigher
Spring
January to March
01Solving equations and inequalities
- Including those that require rearrangementHigher
- Completing the square and the quadratic formulaHigher
- Including linear/quadraticHigher
- Solve equations by iterationHigher
- Linear and quadratic inequalitiesHigher
- Show inequality solutions on number lines and graphsHigher
02Sequences
- Including other sequencesHigher
- Including where r is a surdHigher
03Fractions, decimals and percentages
- Convert recurring decimals to fractionsHigher
04Mensuration and calculation
- Lengths, areas and volumes in similar figuresHigher
- Trigonometry in 2D and 3DHigher
- Sine rule and cosine ruleHigher
- To find unknown lengths and anglesHigher
- Know and applyHigher
- Area = 1 2absinCHigher
- To calculate the area, sides or angles of any triangleHigher
Summer
April to July
01Algebra
- Including quadratic sequencesHigher
02Number
- Including upper and lower boundsHigher
03Geometry and measures
- Use vectors to construct geometric arguments and proofsHigher
04Revision and final exams
- Full mock exams for every paper under timed conditions
- Gap review: re-teaching topics flagged by monthly assessments
- Past papers marked against official mark schemes
- Exam technique: command words, timing and marks
Built from the full exam board specifications (AQA, Pearson Edexcel and OCR). Boards update their specifications from time to time, so we always check the latest version.
Taught to your exam board
Every lesson is matched to your child’s specification, so they’re taught everything the exam can ask.
- Mapped to the full specification
- Every required topic covered
- Past papers from your board
Exam boardAQA
Exam boardEdexcel
Exam boardOCR
The TriForth Method
A proven cycle that turns every lesson into lasting progress.
- 01PrepareA head start on every topic, before the lesson.
- 02LearnClear teaching that checks understanding as it goes.
- 03PractiseGuided first, then on their own, until it sticks.
- 04ReviewMistakes found, fixed and followed up.
What your child walks away with
Everything they need to walk into the exam ready.
- 01
Exam technique that earns marks
They learn how questions are marked and how to pick up every mark.
- 02
Constant exam practice
The real paper feels familiar, not frightening.
- 03
Revision that starts early
Topics come back again and again, so revision is review, not panic.
- 04
The grade they’re capable of
A target grade agreed with you, and a clear plan to reach it.
You’ll always know how they’re doing
Live updates, monthly results and a parents’ evening every term.
Mock exam · MathsGrade 7Up from grade 5
Homework this month6 of 6 completed
Parents’ evening bookedAutumn term review
Which exam board do you follow?
Your child’s. Tell us which board at the free assessment and we teach to that specification.
Do you teach Foundation and Higher tier?
Yes. Groups are set by tier, so every student works at the right level.
Is it too late to start in Year 11?
No. We focus on the topics that move grades most and build exam technique from the first week.
How will I know it is working?
Monthly assessments, a live parent dashboard and a parents’ evening every term.
Do you teach both Combined and Triple Science?
Yes. Tell us which your child sits and we’ll teach to that route.
Do you use past papers?
Constantly. Exam-style questions end every lesson, and monthly assessments use past-paper style questions.
What grade can my child expect?
We agree a realistic target grade after the assessment and show you progress towards it every month.
Do you run mock exams?
Monthly assessments work like mini mocks, and our winter booster prepares students for January mocks.