GCSE Maths practice, marked as they go.

1. 1Integer and Decimal Arithmetic+

   • Order and compare integers and decimals, including negatives
   • Use the four operations with integers, decimals and negative numbers
   • Use BIDMAS, inverse operations and place value
2. 2Factors, Multiples and Counting+

   • Identify factors, multiples and prime numbers
   • Find prime factorisations, HCF and LCM
   • Use systematic listing and the product rule for counting (Higher: harder counting problems)
3. 3Fractions, Decimals and Recurring Decimals+

   • Add, subtract, multiply and divide fractions and mixed numbers
   • Convert between fractions, decimals and percentages
   • Find fractions of amounts and use fractions in context
   • Convert recurring decimals to fractions (Higher)
4. 4Units and Conversions+

   • Use standard units of length, mass, time, money and capacity
   • Convert between metric units and between metric and common units
   • Convert units of area and volume
5. 5Indices and Roots+

   • Use the laws of indices, including negative and zero indices
   • Work with square, cube and other roots
   • Use fractional indices (Higher)
6. 6Standard Form+

   • Write numbers in standard form and convert back
   • Calculate with numbers in standard form
   • Interpret standard form on a calculator
7. 7Estimation, Rounding and Bounds+

   • Round to decimal places and significant figures
   • Estimate answers by rounding to one significant figure
   • Use upper and lower bounds and error intervals (Higher: calculate with bounds)
8. 8Algebraic Expressions and Factorisation+

   • Use algebraic notation and collect like terms
   • Expand single and double brackets
   • Factorise expressions, including quadratics and the difference of two squares
9. 9Linear Equations and Inequalities+

   • Solve linear equations with the unknown on one or both sides, including brackets and fractions
   • Form and solve equations from problems
   • Solve linear inequalities and show them on a number line
10. 10Formulae and Substitution+

    • Substitute values into expressions and formulae
    • Write formulae from descriptions
    • Change the subject of a formula
11. 11Ratio, Sharing and Fractions+

    • Simplify ratios and write them in the form 1 : n
    • Share an amount in a given ratio
    • Link ratio, fractions and scale to solve problems
12. 12Percentages and Finance+

    • Find percentages of amounts and percentage change
    • Work out reverse percentages
    • Solve problems with VAT, discounts, profit and simple interest
13. 13Straight-Line and Coordinate Graphs+

    • Plot and read coordinates in all four quadrants
    • Draw straight-line graphs and use y = mx + c
    • Find gradients, midpoints and equations of lines, including parallel and perpendicular lines (Higher)
14. 14Sequences+

    • Continue and describe number sequences
    • Find the nth term of linear sequences
    • Find the nth term of quadratic sequences and use geometric sequences (Higher)
15. 15Direct and Inverse Proportion+

    • Solve direct proportion problems using unit methods
    • Recognise and use inverse proportion
    • Write and use proportion equations (Higher)
16. 16Compound Measures and Rates+

    • Use speed, distance and time
    • Use density, pressure and other rates
    • Find rates of change from graphs and tables
17. 17Angles and Polygons+

    • Use angle facts on lines, around points and in triangles
    • Use angles in parallel lines and give reasons
    • Find interior and exterior angles of polygons
18. 18Constructions and Loci+

    • Construct triangles, bisectors and perpendiculars
    • Draw and use loci
    • Solve loci problems in context
19. 19Bearings and Scale Drawings+

    • Measure and draw bearings
    • Use scale drawings and map scales
    • Solve bearings problems
20. 20Probability and Relative Frequency+

    • Use the probability scale and calculate probabilities of single events
    • List outcomes and use sample space diagrams
    • Use relative frequency to estimate probabilities and expected outcomes
21. 21Coordinates and Transformations+

    • Reflect, rotate and translate shapes
    • Enlarge shapes by positive, fractional and negative scale factors
    • Describe single and combined transformations fully
22. 22Perimeter and Area+

    • Find perimeters and areas of triangles, quadrilaterals and compound shapes
    • Use area formulae for parallelograms and trapezia
    • Solve area problems in context
23. 23Averages and Spread+

    • Calculate the mean, median, mode and range
    • Estimate the mean from grouped data
    • Compare distributions using averages and spread
24. 24Frequency Tables and Charts+

    • Draw and interpret bar charts, pie charts, pictograms and frequency polygons
    • Use frequency tables and stem-and-leaf diagrams
    • Interpret charts and spot misleading displays
25. 25Surds and Exact Calculation+

    • Simplify surds and calculate with them (Higher)
    • Rationalise denominators (Higher)
    • Give exact answers using surds, fractions and π (Higher)
26. 26Quadratic Equations and Inequalities+

    • Solve quadratic equations by factorising
    • Use the quadratic formula and completing the square (Higher)
    • Solve quadratic inequalities (Higher)
27. 27Simultaneous Equations+

    • Solve two linear simultaneous equations by elimination or substitution
    • Form simultaneous equations from a problem
    • Solve a linear and a quadratic equation together (Higher)
28. 28Circles, Arcs and Sectors+

    • Find the circumference and area of circles
    • Find arc lengths and sector areas
    • Give answers in terms of π
29. 29Surface Area and Volume+

    • Find volumes and surface areas of prisms and cylinders
    • Find volumes and surface areas of cones, spheres and pyramids
    • Solve problems with units of volume and capacity
30. 30Pythagoras and Right-Angle Trigonometry+

    • Use Pythagoras' theorem to find missing sides
    • Use sine, cosine and tangent to find sides and angles
    • Know exact trigonometric values and solve problems in context
31. 31Algebraic Fractions+

    • Simplify algebraic fractions by factorising (Higher)
    • Add, subtract, multiply and divide algebraic fractions (Higher)
    • Solve equations that contain algebraic fractions (Higher)
32. 32Functions and Non-Linear Graphs+

    • Plot and sketch quadratic, cubic and reciprocal graphs
    • Identify roots, intercepts and turning points
    • Use function notation, composite and inverse functions (Higher)
    • Recognise exponential and trigonometric graphs and the equation of a circle (Higher)
33. 33Congruence and Similarity+

    • Identify congruent and similar shapes
    • Use scale factors for lengths
    • Relate length, area and volume scale factors (Higher)
34. 34Algebraic Reasoning and Proof+

    • Know the difference between an equation and an identity
    • Show that statements are true by algebraic argument
    • Prove simple results about numbers algebraically
35. 35Growth and Decay+

    • Calculate compound interest and repeated percentage change
    • Solve growth and decay problems
    • Use exponential growth and decay models (Higher)
36. 36Circle Theorems+

    • Name the parts of a circle and use the circle theorems (Higher)
    • Find angles and give reasons using the theorems (Higher)
    • Use tangent and alternate segment properties (Higher)
37. 37Vectors+

    • Use vector notation and column vectors
    • Add, subtract and scale vectors
    • Use vectors in geometric arguments (Higher)
38. 38Non-Right-Angle and 3D Trigonometry+

    • Use the sine and cosine rules (Higher)
    • Find the area of a triangle using ½ab sin C (Higher)
    • Use trigonometry and Pythagoras in three dimensions (Higher)
39. 39Combined and Conditional Probability+

    • Use the addition and multiplication rules for probability
    • Use tree diagrams, with and without replacement
    • Calculate conditional probability (Higher)
40. 40Sets, Venn Diagrams and Tables+

    • Use set notation and Venn diagrams
    • Use two-way tables to find probabilities
    • Calculate probabilities from Venn diagrams (Higher: conditional)
41. 41Histograms, Cumulative Frequency and Box Plots+

    • Draw and interpret cumulative frequency graphs (Higher)
    • Draw and interpret box plots and the interquartile range (Higher)
    • Draw and interpret histograms using frequency density (Higher)
42. 42Scatter Graphs and Time Series+

    • Draw scatter graphs and describe correlation
    • Draw and use a line of best fit
    • Interpret time series graphs
43. 43Sampling and Populations+

    • Understand populations and samples
    • Compare sampling methods and spot bias
    • Use capture-recapture to estimate a population (Higher)

Topics follow the AQA 8300 specification. PrepAcer is independent and not affiliated with the exam board.