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UK GCSE Mathematics · independent study
Independent myAudience subject study using references for England. Published readings cover selected topics; full curriculum, assessment and practical coverage are not verified. No awarding-body affiliation, endorsement, qualification or grade guarantee is offered. Check the source specification and your centre for the requirements of your chosen course.
Put numbers in order
Calculate with signed numbers and decimals
Operate with fractions and mixed numbers
Use inverses and operation priority
Use primes to find common factors and multiples
List possibilities without missing or repeating them
Understand powers and real roots
Calculate with integer indices
Keep fractions and multiples of pi exact
Use powers of ten to represent scale
Move between terminating decimals and fractions
Connect ratios with fractions of a whole
Apply a fraction or percentage to a quantity
Convert units without changing the quantity
Read rates and compound measures
Use estimates to catch implausible answers
Round values and describe their intervals
Interpret the precision of a reported measurement
Count linked choices with a product
Locate a root between familiar powers
Read fractional powers as roots
Simplify roots without approximating them
Convert a recurring decimal to an exact fraction
Bound a calculation from rounded measurements
Read the shorthand of algebra
Replace variables and keep the operations
Distinguish expressions, equations and identities
Combine terms with matching variable structure
Distribute a factor and reverse the operation
Expand and factorise simple quadratics
Change the subject of a formula
Show why a relationship holds
Treat an expression as an input-output rule
Factorise a quadratic with a non-unit leading coefficient
Multiply more than two brackets in stages
Simplify rational expressions while keeping restrictions
Reverse and combine function rules
Locate points in all four quadrants
Build a line from a gradient and an intercept
Interpret a gradient as a rate of change
Read roots, intercepts and turning points
Recognise linear, quadratic and cubic shapes
Understand the gap in a reciprocal graph
Use a graph to estimate a solution in context
Distinguish position-time and velocity-time graphs
Find a perpendicular line using reciprocal gradients
Complete the square to locate a turning point
Recognise exponential growth and decay
Read sine, cosine and tangent graphs in degrees
Translate and reflect a whole function graph
Interpret an exponential graph in a real context
Estimate the gradient of a curve with a tangent
Calculate and estimate area under a graph
Use the equation of a circle centred at the origin
Find a tangent at a point on an origin circle
Solve a linear equation without breaking equality
Use factors to solve a quadratic equation
Find values satisfying two equations together
Translate a situation into equations and interpret the result
Solve an inequality and represent its solution set
Find roots using the quadratic formula
Solve by completing the square
Solve a line and a quadratic together
Use iteration to approximate a root
Represent two-variable inequalities as regions
Find intervals where a quadratic has the required sign
Generate terms from recurrence and position rules
Recognise square, cube, triangular and Fibonacci-type patterns
Recognise a constant multiplicative step
Deduce the position rule of a linear sequence
Generate a geometric sequence with a surd ratio
Deduce a quadratic position rule from differences
Convert quantities without changing what they measure
Use a scale only after matching the units
Express one quantity as a fraction of another
Reduce a ratio while preserving the comparison
Divide a total into part-to-part shares
Distinguish a part-to-whole ratio from a part-to-part ratio
Explain how many times one quantity is another
Recognise proportion as equality of ratios
Connect a ratio, a fraction and a linear rule
Choose the reference amount for a percentage
Apply a percentage change to the current amount
Recover an original value by undoing its multiplier
Calculate interest from the original principal
Identify a constant ratio and its proportionality coefficient
Identify a constant product in inverse proportion
Use compound units to compare rates fairly
Connect mass, volume and density
Interpret force per unit area
Apply the correct scale factor to length, area and volume
Interpret equations involving a reciprocal
Recognise proportional graphs and their rate meaning
Build a model for repeated percentage changes
Construct a direct or inverse proportional model
Separate interval averages from a rate at one point
Model a repeated multiplier and fixed addition
Read the language of a diagram
Separate reflection from rotation
Construct an equal-distance boundary
Bisect an angle and interpret a locus
Use angle facts rather than appearances
Recognise angles on parallel lines
Build polygon angle sums from triangles
Classify quadrilaterals by their properties
Use equal sides to deduce angles
Prove triangles have the same size and shape
Why the squares on a right triangle balance
Translate every vertex by the same vector
Rotate about a specified centre
Reflect in a horizontal or vertical line
Reflect in a diagonal mirror
Enlarge from a centre, not from the origin by habit
Use fractional scale factors without losing the centre
Negative scale sends vertices through the centre
Recover a centre and verify the whole correspondence
Translations: follow the journey, then combine the movement
Two mirrors: why parallel reflections slide and crossing mirrors turn
A turn followed by a translation: order changes the destination
Three transformations: reverse the route and check what survives
Define a circle by its fixed distance, not its appearance
Chord, diameter and tangent: count the boundary contacts
An arc is a boundary; a sector and segment are regions
Central and circumference angles: prove the relationship with the right arc
Chord bisection and tangent lengths: identify the congruent triangles
Recover a missing vertex from geometry, not the outline of the sketch