IGCSE Mathematics for Edexcel

Theme

1. Working with whole numbers

2. Fraction and Decimals

3. Ratios and percentages

4. Powers, roots and reciprocals

5. Working with Algebra

5. Working with Algebra

6. Algebraic equations

7. Graph of straight lines

8. simultaneous equations

9. Inequalities

10. Number Sequences

11. Travel and other graphs

12. Working with shape and space

13. Circles and cylinders

14. Geometric constructions

15. Transformation and similiarity

16. Pythagoras' theorem

17. Introducing trigonometry

17. Introducing trigonometry

18. 2D and 3D Objects

19. Circle theorems

20. Sets

21. Working with data

22. Probability

23. Using a calculator efficiently

24.Direct and inverse proportion

25. Quadratic equations

26. Advanced algebra

27. Functions and function notation

28. Futher trigonometry

29. Graphs of curves

30. Vectors

31. Mathematical proofs

32. Calculus

32. Calculus

33. Further probability and statistics

IGCSE Mathematics for Edexcel

Sub Theme Added

Addition and Subraction without a calculator

multiplication without a calculator

division without a calculator

positive and negative integers

factor, multiples, and primes

Highest common factor

Lowest common Multiple

Equivalent Fraction

Multiplying and Dividing with Fraction

Arithmetic with Decimals

Decimals and Factions

Rounding and approximation

Working with ratios

Simple percentages

Percentages increase and decrease

reverse percentage problems

simple and compound interest

Roman Numeral

Basic Power and Roots

Higher Power and Roots

Fractional (rational) indicies

Negative Powers and reciprocals

The Laws of Indices

Standard Index form

calculating with number in standard form

Subsituting number into formulae and expressions

working with indices

Expanding brackets

multiplying two brackets together

Factorising - Common Factor

Factorising - Quadratic Expression

Factorising - harder Quadratic expression

Factorising - difference of two squares

Generating formulae

changing the subject of formula

Expression, equations and identities

simple equations

harder linear equations

equations and bracket

equations with fractional coefficients

coordinates in all four quadrants

graph of linear functions

gradient and intercept of linear functions

equations and graph

parallel lines

solver simultaneos equations by inspection

solver simultaneos equations by algebraic elimination

solver simultaneos equations by a graphical method

setting up and solving problems using simultaneous equations

Whole number solutions to inequalities

using algebra to solve linear inequalities

illustrating inequalities on a number line

graph of linear inequalities in two variables

Number sequences

describing number sequences with rules

arithmetic sequences

Modelling with straight line graph

Distance-Time graphs

Velocity-Time Graphs

Corresponding and alternate angles

Angles in triangles and quadrilaterals

Angles in polygons

areas and perimeters of simple shapes

surfaces area and volume

Circumference and area of a circle

Sectors of a circle

circumference and area in reverse

Surface area and volume of a cylinder

Exact calculations using pi

Constructing triangles from given information

Constructions with line segments

Bearings

Reflections

Rotations

Combining transformations

Enlargements

Similar shapes and solids

Introducing Pythagoras' theorem

Using Pythagoras' theorem to find a hypotenuse

Using Pythagoras' theorem to find one of the shorter sides

Pythagoras' theorem in three dimensions

Pythagoras' theorem on a coordinate grid

The sine ratio

The cosine ratio

The tangent ratio

Choosing the right trigonometrical function

Finding an unknown angle

Multi-stage problems

Drawing and constructing 3D objects

Coordinates in 3D

Volume and surface area of pyramids, cones and spheres

Converting between units

Tangents, chords and circles

Angle properties inside a circle

Further circle theorems

Intersecting chords

Introducing set notation

Venn diagrams

Further Venn diagrams

Calculations with frequency tables

Frequensy polygons and histograms

Cumulative frequency

Theorotical and experimental probability

Mutually exclusive outcomes

Independent events

Tree diagrams

Power, roots and reciprocals

Using bracket

Using the fraction key

Using the ANS key

Upper and lower bonds

Direct proportion

Inverse proportion

Graphical representation of direct and inverse proportion

Solving quadratic equations-factorising

Solving quadratic equations-formula

Problems leading to quadratic equations

Working with surds

Algebraic fractions

Cancelling common factors in rational expressions

Simultaneous equations, one linear and one quadratic

Changing the subject of an equation where the symbol occurs twice

Intoducing functions and function notation

Domain and range

Inverse functions

The sine rule

The ambiguous case of sine rule

The cosine rule

Area of a triangle using 1/2 ab sin C, and segments of circles

Trigonometry in 3D

Table of functions

Plotting and using graphs of curves

Graph of sine, cosine and tangent fuctions

Introducing vectors

Adding and subsracting vectors

Multiplying and substracting vectors

Multiplying a vector by a number (scalar multiplication)

Using vectors

Algebraic proofs

Use of counter-examples

Gradient of a curve

Gradient of a curve-differentiation

Harder differentiation

Maximum and minimum points on curves

Futher problems on maximum and minimum

Distance, velocity and acceleration

The combined mean of two groups

Conditional probability

IGCSE Mathematics for Edexcel

Applies the LCM using unit multipliers (level 8)

calculates gross pay vs. nett pay ( level 8 no.16 and 17 )

use proportion to solve percent problems greater than 100

multiplies, divides, and perform the proper order with sign number (level 8 no.9)

add, substract, multiplies, and divides rational and common irrational number forms (level 8 no 23)

multiplies, divides, and perform the proper order with sign number (level 8 no.8)

convert between equivalent fractions, percents, proportion of number (level 8 no.25 and 26)

multiplies, divides, and perform the proper order with sign number (level 8 no.7)

multiplies, divides, and perform the proper order with sign number (level 8 no.10 and 11)

recognizes, evaluates, and graph inequalities and functions

generalizes numeric and geometric patterns and sequences

translates word into symbolic expressions, equations, or inequalities and solves (level 8 no. 31 and 32)

uses inverse operation and the properties of 1 and 0 to solve rational number problems ( level 8 no. 30 )

uses tables of ordered pairs, graphs, and linear equations to analyze patterns (level 8 no.34)

calculates volume of simple geometric solid and area of complex figures ( level 8 no.15 )

uses similiarity and congruence to find missing angles or sides of figures (level 8 no. 36)

identities and describes a variety of 3D figures

calculates volume of simple geometric solid and area of complex figures ( level 8 no.14 ) + Estimates and calculates volume and surface area of solids ( level 8 no.40 )

add, substract, multiplies, and divides rational and common irrational number forms (level 8 no 24)