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Mathematics A

  • IGCSE Edexcel
  • Revision Notes

1. Numbers & the Number System

1.1 Integers>1.2 Fractions>1.3 Decimals>1.4 Powers and Roots>1.5 Set Language and Notation>1.6 Percentages>1.7 Ratio and Proportion>1.8 Degree of Accuracy>1.9 Standard Form>1.10 Applying Numbers>1.11 Electronic Calculator>

2.1 Use of Symbols >2.2 Algebraic Manipulation >2.3 Expressions and Formulae >2.4 Linear Equations >2.5 Proportion (Higher Tier Only) >2.6 Simultaneous Linear Equations >2.7 Quadratic Equations >2.8 Inequalities >

3.1 Sequences >3.2 Function Notation (Higher Tier Only) >3.3 Graphs >3.4 Calculus (Higher Tier Only) >

4.1 Angles, Lines and Triangles >4.2 Polygons >4.3 Symmetry >4.4 Measures >4.5 Construction >4.6 Circle Properties >4.7 Geometric Reasoning >4.8 Trigonometry and Pythagoras’ Theorem >4.9 Mensuration of 2D Shapes >4.10 3D Shapes and Volumes >4.11 Similarity >

5.1 Vectors (Higher Tier Only) >5.2 Transformation Geometry >

6.1 Graphical Representation of Data >6.2 Statistical Measures >6.3 Probability >

7.1 Appendix 1: Foundation Tier Formula Sheet (Given) >7.2 Appendix 2: Foundation Tier Formula Sheet (To Memorise) >7.3 Appendix 3: Higher Tier Formula Sheet (Given) >7.4 Appendix 4: Higher Tier Formula Sheet (To Memorise) >7.5 Appendix 5: Notation >

1.4 Powers and Roots

1.4.1 Identify square numbers and cube numbers

A square number is a number that is multiplied by itself.

A cube number is a number that is multiplied by istelf and then by itself again.

1.4.2 Calculate squares, square roots, cubes and cube roots

The reverse of raising to a power is taking a root.

2² = 4

√4 = 2

∛27 = 3

1.4.3 Use index notation and index laws for multiplication and division of positive and negative integer powers including zero

  • The powers of a number is the definition of a number getting multiplied by itself again and again
    • 21 means 2
    • 22 means 2 × 2
    • 25 means 2 x 2 x 2 x 2 x 2
  • Keep in mind that any number except 0 to the power of 0 is always equal to 1

1.4.4 Express integers as a product of powers of prime factors

  • The root of a number is the opposite of a power of a number
  • A square root of 16 is a number that when squared equals 16

1.4.5 Find highest common factors (HCF) and lowest common multiples (LCM)

Type 1: Highest Common Factor (HCF)

What is HCF?

It is the highest common factor that 2 numbers share, for example 88 and 121 share the HCF of 11.

Step 1: Find the factor of A

Step 2: Find the factor of B

Step 3: Find the highest common factor

Type 2: Lowest Common Multiple (LCM)

What is LCM?

It is the lowest common multiple of 2 numbers.

Step 1: Find the multiple of A

Step 2: Find the multiple of B

Step 3: Find the lowest common multiple

1.4.6 Understand the meaning of surds (Higher Tier Only)

A surd is the square root of a number that is not a square number, for example √8 is not a square number so therefore it has to be broken down into 4 and 2. In which 4 is a square number, therefore √8 becomes 2√2

1.4.7 Manipulate surds, including rationalising a denominator (Higher Tier Only)

1.4.8 Use index laws to simplify and evaluate numerical expressions involving integer, fractional and negative powers (Higher Tier Only)

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