Number

1. Number Operations and Integers

   • Four operations (addition, subtraction, multiplication, division)

   • Negative numbers, place value, and ordering

2. Fractions, Decimals, and Percentages

   • Converting between fractions, decimals, and percentages

   • Calculating percentages, percentage change

3. Factors, Multiples, and Primes

   • Prime numbers, prime factorization, HCF, LCM

4. Indices and Standard Form

   • Laws of indices, calculations with standard form

5. Rounding and Estimation

   • Rounding to significant figures and decimal places, estimation

6. Surds (Higher Tier)

   • Simplifying surds, rationalizing the denominator

Algebra

1. Expressions, Equations, and Formulae

   • Simplifying expressions, solving linear equations, forming equations

2. Quadratics

   • Expanding, factorizing, solving quadratic equations

3. Simultaneous Equations

   • Solving linear simultaneous equations algebraically and graphically

4. Inequalities

   • Solving and representing linear inequalities on a number line

5. Sequences

   • Generating sequences, finding nth terms for arithmetic sequences

6. Graphs

   • Plotting linear, quadratic, and other function graphs

Ratio, Proportion, and Rates of Change

1. Ratios

   • Simplifying ratios, sharing in a given ratio

2. Proportion

   • Direct and inverse proportion

3. Rates of Change

   • Speed, density, and other rates

Geometry and Measures

1. Properties of Shapes

   • Types of angles, properties of polygons, circles

2. Geometric Constructions

   • Constructing triangles, bisectors, and loci

3. Transformations

   • Translations, rotations, reflections, and enlargements

4. Congruence and Similarity

   • Conditions for congruence, similar shapes and scale factors

5. Perimeter, Area, and Volume

   • Calculating perimeter, area of 2D shapes, surface area and volume of 3D shapes

6. Trigonometry

   • Trigonometric ratios (sine, cosine, tangent), solving right-angled triangles

   • Sine and cosine rules (Higher Tier)

Probability

1. Basic Probability

   • Probability scales, theoretical and experimental probability

2. Combined Events

   • Calculating probabilities of combined events using tree diagrams and Venn diagrams

Statistics

1. Data Collection

   • Types of data, methods of data collection

2. Data Representation

   • Constructing and interpreting bar charts, histograms, pie charts, and scatter graphs

3. Measures of Central Tendency and Spread

   • Mean, median, mode, range, interquartile range, and standard deviation (Higher Tier)

Additional Topics (Higher Tier Only)

1. Algebraic Manipulation

   • Advanced algebraic fractions, rearranging complex formulae

2. Further Graphs

   • Exponential, reciprocal graphs, transformations of functions

3. Advanced Trigonometry

   • Trigonometric graphs, solving trigonometric equations

4. Vectors

   • Vector notation, vector addition and subtraction, scalar multiplication