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Number

26 units
  1. Counting
  2. Place Value (Including Decimals)
  3. Number Properties
  4. Addition & Subtraction
  5. Times Tables
  6. Multiplication & Division
  7. Factors, Multiples, Primes & Divisibility
  8. Roman Numerals
  9. Rounding
  10. Estimation
  11. Money
  12. Fractions
  13. Decimal Arithmetic
  14. Negative Numbers
  15. Powers & Roots
  16. Order of Operations
  17. Calculator Use
  18. Fraction, Decimal & Percentage Equivalence
  19. Percentages
  20. Standard Form
  21. Bases
  22. Surds
  23. Venn Diagrams & Sets
  24. Combinations & Permutations
  25. Number Theory (Advanced)
  26. Group Theory

Ratio & Proportion

5 units
  1. Multiplicative Reasoning
  2. Ratio
  3. Similarity & Congruence
  4. Compound Measures
  5. Algebraic Proportion

Geometry & Measures

26 units
  1. Directional Language & Grid References
  2. Units of Measurement
  3. Time
  4. Properties of 2D Shapes
  5. Properties of 3D Shapes
  6. Area & Perimeter (Excluding Circles)
  7. Geometric Notation
  8. Angles & Bearings
  9. Transformations of Shapes
  10. Coordinates
  11. Scale Drawings & Isometric Drawings
  12. Surface Area & Volume
  13. Circles, Arcs & Sectors
  14. Constructions & Loci
  15. Pythagoras' Theorem
  16. Circle Theorems
  17. Trigonometry of Right-Angled Triangles
  18. Vector Expressions
  19. Trigonometric Graphs, Expressions & Equations in Degrees
  20. Trigonometry of Non-Right-Angled Triangles
  21. Trigonometry in Radians
  22. Vector Equations of Lines & Planes
  23. Polar Coordinates
  24. Fractals
  25. Advanced Geometric Theorems
  26. Non-Euclidean Geometry

Algebra

33 units
  1. Algebraic Notation & Manipulation
  2. Substitution
  3. Sequences (Fundamentals)
  4. Laws of Indices
  5. Expanding Brackets
  6. Factorising Expressions
  7. Solving Linear Equations
  8. Solving Quadratic Equations
  9. Linear Graphs
  10. Systems of Equations (Simultaneous Equations)
  11. Inequalities
  12. Changing the Subject
  13. Graph Plotting & Recognition
  14. Graphs of Quadratic & Polynomial Functions
  15. Algebraic Fractions
  16. Functions
  17. Graphs of Exponential Functions
  18. Graphs of Circles
  19. Graphs of Reciprocal Functions
  20. Transformations of Curves
  21. Algebraic Proof
  22. Estimating Gradient and Area Under a Curve
  23. Polynomials (Division, Roots & Factor Theorem)
  24. Partial Fractions
  25. Boolean Algebra & Logic
  26. Binomial Expansion
  27. Logarithms & Solving Exponential Equations
  28. Numerical Methods
  29. Modulus Function
  30. Sequences & Series (Advanced)
  31. Parametric Equations
  32. Conics
  33. Hyperbolic Functions

Statistics & Probability

33 units
  1. Tabulated Data & Frequency Tables (Reading & Forming)
  2. Averages & Range for Listed Data
  3. Averages & Range for Tabulated Data
  4. Two-Way Tables & Frequency Trees
  5. Representations of Discrete Data
  6. Representations of Continuous Data
  7. Probability Scale
  8. Theoretical Probabilities & Mutually Exclusive Events
  9. Experimental Probability (Relative Frequency) & Bias
  10. Correlation & Regression
  11. Time Series & Moving Averages
  12. Quartiles & Percentiles
  13. Standard Deviation & Variance
  14. Skewness
  15. Probability from Venn Diagrams
  16. Probability of Independent, Dependent & Conditional Events
  17. Data Collection & Sampling
  18. Summary Statistics
  19. Risk Calculations & Risk Analysis
  20. Quality Assurance
  21. Index Numbers
  22. Coding of Data
  23. Probability Distributions (Discrete)
  24. Probability Distributions (Normal)
  25. Probability Distributions (Other Continuous)
  26. Hypothesis Tests (Correlation)
  27. Hypothesis Tests (z-tests for Mean & Proportion)
  28. Hypothesis Tests (Goodness of Fit χ2)
  29. Probability Generating Functions
  30. Quality of Tests
  31. Estimators, Bias & Sampling Distributions
  32. Hypothesis Tests (Non-Parametric, t-tests, F-distribution & ANOVA)
  33. Markov Chains

Calculus

8 units
  1. Limits
  2. Differentiation of Polynomials
  3. Integration of Polynomials
  4. Differentiation of Non-Polynomials
  5. Integration of Non-Polynomials
  6. Differential Equations
  7. Numerical Methods for Differential Equations
  8. Partial Differentiation & Surfaces

Complex Numbers

3 units
  1. Cartesian Form
  2. Modulus-Argument Form, Argand Diagrams & Loci
  3. Exponential Form & De Moivre's Theorem

Matrix Algebra

6 units
  1. Matrix Operations
  2. Inverse Matrices & Determinants
  3. Solving Systems of Linear Equations Using Matrices
  4. Linear Transformations with Matrices
  5. Eigenvectors
  6. Vectors Spaces, Kernels & Images

Mechanics

13 units
  1. Kinematics in 1D
  2. Single Particles in Equilibrium (N1L)
  3. Single Particles with Acceleration (N2L)
  4. Connected Particles with Acceleration (N3L)
  5. Moments
  6. Kinematics in 2D
  7. Momentum and Impulse
  8. Work, Energy & Power
  9. Elastic Springs and Strings & Elastic Energy
  10. Elastic Collisions
  11. Circular Motion
  12. Centres of Mass
  13. Dynamics

Discrete Maths

7 units
  1. Algorithms
  2. Graph Theory
  3. Linear Programming
  4. Critical Path Analysis
  5. Optimising Costs in Transportation & Allocation
  6. Flows in Networks
  7. Game Theory & Making Decisions

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