Number

1. Number Language

1.1 What are Factors, Multiples, Primes, etc.
1.2 What are Square and cube roots
1.3 What are Directed numbers

2. Accuracy

2.1 How to Round whole numbers
2.2 Decimal places
2.3 What are Significant Figures
2.4 What are Upper and lower bounds

3. Calculations

3.1 How to Order numbers
3.2 Order of operations

4. Fractions and decimals

4.1 Introducing some essential language
4.2 How to find Equivalent and Simplify fractions
4.3 How to find the Fraction of an Amount
4.4 What are Improper Fractions and Mixed Numbers
4.5 Fractions and decimals
4.6 How to Add and Subtract with Fractions
4.7 How to Multiply and Divide Fractions

5. Percentages

5.1 Percentages, fractions and decimals
5.2 Calculating the percentage of a quantity
5.3 Expressing one quantity as a percentage of another
5.4 How to find Percentage Increase and Decrease
5.5 What are Reverse Percentages

6. Ratio and proportion

6.1 How to Divide a quantity in a Ratio
6.2 How to work with Direct and Inverse Proportion

7. Indices and standard form

7.1 Indices
7.2 Fractional and negative indices
7.3 How to solve Exponential Equations
7.4 How to write in Standard form

8. Interest

8.1 How to calculate Simple interest
8.2 How to calculate Compound interest

9. Venn diagrams

9.1 How to shade Venn diagrams

---

Algebra and graphs

1. Algebraic representation and manipulation

1.1 Introducing the essential language
1.2 How to Simplify Algebraic Expressions
1.3 How to Expand Algebraic Expressions
1.4 How to Factorise Algebraic Expressions
1.5 How to Evaluate Expressions by Substitution
1.6 How to Change the Subject of an Equation
1.7 How to Combine and Simplify Algebraic Fractions

2. Algebraic indices

2.1 Three laws of the indices
2.2 Zero index
2.3 Negative indices
2.4 Fractional indices
2.5 Exponential equations

3. Equations and inequalities

3.1 Solving linear equations
3.2 Constructing equations
3.3 Simultaneous equations
3.4 Solving inequalities
3.5 Solving quadratic equations
3.6 How to solve Exponential Equations

4. Linear programming

4.1 Graphing inequalities
4.2 Linear programming

5. Sequences

5.1 Finding the nth term rule

6. Variation

6.1 Direct variation
6.2 Inverse variation

7. Graphs in practical situations

7.1 Conversion graphs
7.2 Speed, distance and time
7.3 Distant-time graphs
7.4 Speed-time graphs
7.5 Acceleration and deceleration
7.6 Area under speed-time graph

8. Graphs of functions

8.1 Quadratic functions
8.2 Graphical solution of a quadratic equation
8.3 The reciprocal function
8.4 How to graph a Linear Function
8.5 How to graph Cubic and Exponential Functions
8.6 Gradients of curves
8.7 Solving equations graphically

9. Functions

9.1 Evaluating functions
9.2 Inverse functions
9.3 Composite functions

---

Geometry

1. Geometrical vocabulary

1.1 Geometrical vocabulary

2. Construction and scale drawing

2.1 Constructing polygons
2.2 Constructing bisectors
2.3 Scale drawing

3. Similarity

3.1 Similarity involving length
3.2 Similarity involving area and volume

4. Symmetry

4.1 Lines of, planes of and rotational symmetry

5. Angle properties

5.1 Basic angle properties
5.2 Sum of the interior/exterior angles
5.3 Circle properties

6. Loci

6.1 Loci

---

Mensuration

1. Measures

1.1 Converting units
1.2 Converting units involving area and volume

2. Perimeter, area and volume

2.1 Perimeter
2.2 Area of polygons
2.3 Surface area
2.4 Area and circumference of circles
2.5 Arc length and area of sector
2.6 Volume of prisms
2.7 Volume and surface area of a sphere, pyramid and cone

---

Coordinate geometry

1. Straight-line graphs

1.1 Cartesian coordinate system
1.2 Gradient of a line
1.3 Equation of a line
1.4 Horizontal and vertical lines
1.5 Parallel lines and their equations
1.6 Drawing straight-line graphs
1.7 Solving simultaneous equations graphically
1.8 Calculating length of a line segment
1.9 Midpoint of a line segment
1.10 Perpendicular lines

---

Trigonometry

1. Trigonometry

1. Pythagoras' theorem
2. Basic trigonometry
3. Trigonometry and word problems
4. 3-D trigonometry
5. Sine and Cosine rule
6. Area of any triangle
7. Bearings
8. Angles of elevation and depression

---

Vectors, matrices and transformations

1. Vectors

1.1 Translations
1.2 Addition and subtraction of vectors
1.3 Multiplying a vector by a scalar
1.4 Magnitude of a vector
1.5 Position vectors
1.6 Vector geometry

2. Matrices

2.1 Introducing matrices
2.2 Addition and subtraction of matrices
2.3 Multiplying matrices by a scalar
2.4 Multiplying a matrix by another matrix
2.5 The identity and zero matrix
2.6 The determinant and inverse of a matrix

3. Transformations

3.1 Reflection
3.2 Rotation
3.3 Translation
3.4 Enlargement
3.5 Combinations of transformations
3.6 Transformations and matrices
3.7 Shear
3.8 Stretch

---

Probablility

1. Probability

1. Basic probability
2. Further probability

---

Statistics

1. Mean, mode, median and range

1.1 Mean, mode, median and range
1.2 Mean for grouped data

2. Collecting and displaying data

2.1 Pictograms
2.2 Tally charts and frequency tables
2.3 Grouped frequency tables
2.4 Pie charts
2.5 Scatter diagrams and correlation
2.6 Histograms

3. Cumulative frequency

3.1 Introducing cumulative frequency
3.2 Quartiles and the inter-quartile range

Do you understand all these important IGCSE GCSE maths terms and expressions?  In which mathematical contexts do you use them?