Learning paths
- Lessons
- 121
- Topics
- 120
Free, no account neededA tour of GCSE Maths14 short steps.
Start lessonLosing marks to careless slips?Six quick questions find your slip, then fix it.
Start the clinicThe course, in test order
Number
14 lessons
- 2 lessonsFreePlace value, ordering and decimal operations
- Signed arithmetic and number lines
- Operation order, inverses and reciprocals
- Primes, factor trees, HCF and LCM
- Systematic lists and combinations
- Integer powers and roots
- Equivalent fractions and mixed numbers
- Fraction arithmetic and exact answers
- Decimals, fractions and percentages
- Metric units, money and dimensional conversion
- Estimation and sense checks
- Rounding, significant figures and error intervals
- Standard form and calculator entry
Ratio, proportion and rates of change
10 lessons
- Ratio notation and multiplicative comparison
- Fractions within ratio problems
- Sharing quantities and equivalent ratios
- Scale factors, scale drawings and maps
- Percentages, changes and multipliers
- Original values, profit and simple interest
- Compound growth and decay
- Direct and inverse proportion: tables and relationships
- Speed, density, pressure and unit pricing
- Proportional graphs and rates of change
Algebra
21 lessons
- Algebraic language and notation
- Substitution and calculator brackets
- Like terms and algebraic index rules
- Single brackets and common factors
- Expanding two binomials
- Monic quadratics and difference of squares
- Formulae and changing the subject
- Identities and algebraic reasoning
- Input/output and inverse number machines
- Linear equations, including both sides
- Forming equations from situations
- One-variable linear inequalities
- Two linear simultaneous equations
- Solving monic quadratics by factorisation
- Coordinates and geometric problems on axes
- Plotting lines, gradient and intercept
- Equations of lines and parallel lines
- Quadratic graphs, roots and turning points
- Cubic, reciprocal and contextual graphs
- Term rules, special and geometric sequences
- The nth term of a linear sequence
Geometry and measures
19 lessons
- Shape vocabulary, symmetry and quadrilaterals
- Angles at points, lines and parallel lines
- Triangles, interior and exterior polygon angles
- Congruence criteria and geometric deductions
- Compass constructions and loci
- Reflections, rotations and translations
- Positive and fractional enlargements
- Column vectors and vector arithmetic
- Solids, plans and elevations
- Circle vocabulary and perimeter
- Areas of triangles, quadrilaterals and composites
- Prisms, cylinders and surface area
- Pyramids, cones, spheres and composite solids
- Arc lengths and sectors
- Similar figures and length ratios
- Pythagoras in two dimensions
- Right-triangle trigonometry in two dimensions
- Exact trigonometric values
- Bearings and geometric modelling
Probability and statistics
9 lessons
- Probability language, frequency trees and expectation
- Exhaustive outcomes and experimental probability
- Sets, Venn diagrams and sample spaces
- Independent and dependent event trees
- Samples, populations and statistical claims
- Data tables, bar/pie/time-series charts and frequency polygons
- Ordered stem-and-leaf, averages, spread and grouped means
- Scatter graphs and predictions
- Linked representations and multistep reasoning
Foundation tier: clinics and exam repair
8 lessons
- Foundation numerical fluency clinic
- Foundation ratio and percentage problems
- Foundation algebra and graph clinic
- Foundation geometry and equipment clinic
- Foundation statistics and probability clinic
- Foundation non-calculator assessment and repair
- Foundation calculator assessment and repair
- Foundation readiness and tier-transition review
Higher tier: number, algebra and proportion
23 lessons
- Product counting and estimating powers/roots
- Fractional and negative indices
- Surds, exact calculations and rationalising
- Recurring decimals as fractions
- Upper/lower bounds in calculations
- Algebraic fractions and rational equations
- Three binomials and non-monic factorisation
- General algebraic proofs
- Formal, inverse and composite functions
- Translations and reflections of function graphs
- Perpendicular gradients and line equations
- Origin-centred circles and tangents
- Completing the square and turning points
- Quadratic formula and rearranged quadratics
- Linear/quadratic simultaneous equations
- Quadratic and two-variable inequalities
- Exponential and trigonometric graphs
- Graph gradients and areas
- Average and instantaneous rates of change
- Iterative formulae, roots and growth models
- Quadratic sequence nth terms
- Geometric sequences with surds and other patterns
- Constructing direct/inverse proportional equations
Higher tier: geometry and measures
10 lessons
- Negative-scale-factor enlargement
- Combined transformations and invariance
- Area and volume in similar figures
- Circle theorems and angle chains
- Circle theorem proofs and linked geometry
- Three-dimensional Pythagoras and trigonometry
- Sine rule and the ambiguous case
- Cosine rule for sides and angles
- Area of any triangle and mixed trigonometry
- Vector geometric arguments and proofs
Higher tier: probability, statistics and readiness
7 lessons