**1. Number**
- Fractions, decimals and percentages
- Powers, roots, and index laws (including fractional and negative indices)
- Standard form
- Surds and rationalising the denominator
- Recurring decimals to fractions
- Bounds, estimation, and accuracy
- HCF, LCM, and prime factors
**2. Algebra**
- Expanding and factorising (including quadratics)
- Solving linear and quadratic equations
- Simultaneous equations (linear and non-linear)
- Inequalities
- Sequences (linear, quadratic, geometric)
- Straight-line graphs and gradients
- Quadratic, cubic, reciprocal, and exponential graphs
- Function notation, composite and inverse functions
- Algebraic proof
- Iteration
- Transformations of graphs
- Equation of a circle and tangents
- Algebraic fractions
**3. Ratio, proportion and rates of change**
- Ratio and sharing
- Direct and inverse proportion
- Compound measures (speed, density, pressure)
- Percentage change, growth and decay
- Compound interest and reverse percentages
- Rates of change from graphs
**4. Geometry and measures**
- Angle facts and polygons
- Circle theorems
- Pythagoras' theorem
- Trigonometry (including sine rule, cosine rule, and area of a triangle)
- Exact trigonometric values
- Vectors
- Similarity and congruence
- Transformations (reflection, rotation, translation, enlargement)
- Perimeter, area, volume, and surface area
- Arc length and sector area
- Constructions, loci, and bearings
- Plans and elevations
**5. Probability**
- Basic probability and expected outcomes
- Sample spaces
- Venn diagrams and set notation
- Tree diagrams
- Independent and conditional probability
**6. Statistics**
- Averages and range
- Frequency tables and grouped data
- Histograms
- Cumulative frequency and box plots
- Scatter graphs and lines of best fit
- Sampling methods
- Comparing distributions
Mohamed Ali Abualhawa.
