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Edexcel GCSE Maths

Revision Notes

Home / GCSE / Maths / Edexcel / Revision Notes / 1. Number / 1.1 Arithmetic / 1.1.3 Mathematical Symbols


1.1.3 Mathematical Symbols


Mathematical Symbols

What mathematical symbols do I need to know?

 

  • Starting with the basic four operations

plus  Addition, plus, sum, total

minus  Subtraction, minus, difference, take away

cross times Multiplication, product, times

divided by Division, divide, share

  • Equals signs

equals Equal to e.g. 3 x plus 7 equals 19

not equal to Not equal to e.g. 2 minus 5 not equal to 5 minus 2

almost equal to Approximately equal to e.g. straight pi almost equal to 3.14

identical to Identical to e.g. 12 x plus 6 identical to 3 left parenthesis 4 x plus 2 right parenthesis

  • Inequality signs

greater than Greater than e.g. 5 greater than negative 2

less than Less than 1 half less than 2 over 3

greater or equal than Greater than or equal to 

less or equal than Less than or equal to

  • Other helpful symbols

left parenthesis space space right parenthesis  Brackets: used to group symbols e.g. left parenthesis 2 x space plus space 4 right parenthesis space – space 3 left parenthesis x space plus 7 right parenthesis

3 to the power of x   Powers (also called indices or order): repeated multiplication of the base number

   e.g. 3 to the power of 4 equals 3 cross times 3 cross times 3 cross times 3 equals 81

square root of blank end rootSquare root: opposite of squaring e.g. 9 squared equals 81 left right double arrow square root of 81 space equals space 9

plus-or-minus   Plus Minus: Used to allow for two distinct answers, often in quadratics

a plus-or-minus b is shorthand for a plus b and a minus b

   e.g. x equals 3 plus-or-minus 2.5 leading to x equals 5.5 and x equals 0.5 

straight pi   Pi: the ratio of the circumference of a circle to its diameter

What do the order of operations BIDMAS or BODMAS mean?

  • The order of operations helps when solving simple and complex mathematical problems
  • It simply tells us the order to approach a calculation
  • Each letter of BIDMAS or BODMAS stands for a different mathematical symbol or operation

Brackets left parenthesis space space right parenthesis

Indices or Order x squared

Division divided by

Multiplication cross times

Addition plus

Subtraction minus

  • If there are multiple addition and subtraction symbols these should be worked out in order left to right 

Worked Example

Work out left parenthesis 5 space – space 3 right parenthesis space plus space 2 space cross times space 7 squared

First deal with anything inside BRACKETS       2 space plus space 2 space cross times space 7 squared

Then any powers                    2 space plus space 2 space cross times space 14

Followed by any multiplication or division       2 plus 28

Finally dealing with any addition or subtraction  bold 30



  • 1. Number
    • 1.1 Arithmetic
      • 1.1.1 Multiplication (non-Calc)
        • 1.1.2 Division (non-Calc)
          • 1.1.3 Mathematical Symbols
            • 1.1.4 Negative Numbers
              • 1.1.5 Order By Size
                • 1.1.6 Time
                • 1.2 Fractions
                  • 1.2.1 Mixed Numbers & Top Heavy Fractions
                    • 1.2.2 Adding & Subtracting Fractions
                      • 1.2.3 Multiplying & Dividing Fractions
                      • 1.3 Basic Percentages
                        • 1.3.1 Basic Percentages
                          • 1.3.2 Percentage Increases & Decreases
                          • 1.4 Reverse Percentages
                            • 1.4.1 Reverse Percentages
                            • 1.5 Compound Interest
                              • 1.5.1 Compound Interest
                                • 1.5.2 Depreciation
                                • 1.6 LCM / HCF / Prime Factors
                                  • 1.6.1 Prime Factors
                                    • 1.6.2 HCFs & LCMs
                                    • 1.7 Roots & Indices
                                      • 1.7.1 Roots & Indices - Basics
                                        • 1.7.2 Roots & Indices - Harder
                                        • 1.8 Rounding & Estimation
                                          • 1.8.1 Rounding & Estimation
                                          • 1.9 Standard Form
                                            • 1.9.1 Standard Form - Basics
                                              • 1.9.2 Standard Form - Harder
                                              • 1.10 Bounds & Error Intervals
                                                • 1.10.1 Bounds & Error Intervals - Basics
                                                  • 1.10.2 Calculations using Bounds
                                                  • 1.11 Recurring Decimals
                                                    • 1.11.1 Recurring Decimals
                                                    • 1.12 Surds
                                                      • 1.12.1 Surds - Basics
                                                        • 1.12.2 Surds - Rationalising Denominators
                                                        • 1.13 Using a Calculator
                                                          • 1.13.1 Using a Calculator
                                                          • 1.14 Counting
                                                            • 1.14.1 Counting
                                                            • 1.15 Best Buy
                                                              • 1.15.1 Best Buy
                                                              • 1.16 Exchange Rates
                                                                • 1.16.1 Exchange Rates
                                                              • 2. Algebra Basics
                                                                • 2.1 Expanding One Bracket
                                                                  • 2.1.1 Expanding One Bracket
                                                                  • 2.2 Simple Factorisation
                                                                    • 2.2.1 Simple Factorisation
                                                                    • 2.3 Expanding Quadratics
                                                                      • 2.3.1 Expanding Two Brackets - Basics
                                                                        • 2.3.2 Expanding Two Brackets - Harder
                                                                          • 2.3.3 Expanding Three Brackets
                                                                          • 2.4 Factorising Quadratics
                                                                            • 2.4.1 Factorising Quadratics - Basics
                                                                              • 2.4.2 Factorising Quadratics - Harder
                                                                                • 2.4.3 Difference of Two Squares
                                                                                  • 2.4.4 Factorising Quadratics - General
                                                                                  • 2.5 Rearranging Formulae
                                                                                    • 2.5.1 Rearranging Formulae - Basics
                                                                                      • 2.5.2 Rearranging Formulae - Harder
                                                                                      • 2.6 Solving Linear Equations
                                                                                        • 2.6.1 Collecting Like Terms
                                                                                          • 2.6.2 Solving Linear Equations
                                                                                            • 2.6.3 Forming Expressions & Equations
                                                                                            • 2.7 Substitution
                                                                                              • 2.7.1 Substitution
                                                                                              • 2.8 Proof/Reasoning
                                                                                                • 2.8.1 Proof/Reasoning - Algebraic
                                                                                                • 2.9 Functions
                                                                                                  • 2.9.1 Functions - Basics
                                                                                                    • 2.9.2 Compound Functions
                                                                                                      • 2.9.3 Inverse Functions
                                                                                                      • 2.10 Algebraic Fractions
                                                                                                        • 2.10.1 Algebraic Fractions - Adding & Subtracting
                                                                                                          • 2.10.2 Algebraic Fractions - Simplifying Fractions
                                                                                                            • 2.10.3 Algebraic Fractions - Multiplying & Dividing
                                                                                                          • 3. Solving Equations & Inequalities
                                                                                                            • 3.1 Quadratic Formula
                                                                                                              • 3.1.1 Quadratic Formula
                                                                                                              • 3.2 Completing the Square
                                                                                                                • 3.2.1 Completing the Square
                                                                                                                • 3.3 Linear Simultaneous Equations
                                                                                                                  • 3.3.1 Linear Simultaneous Equations
                                                                                                                  • 3.4 Quadratic Simultaneous Equations
                                                                                                                    • 3.4.1 Quadratic Simultaneous Equations
                                                                                                                    • 3.5 Inequalities
                                                                                                                      • 3.5.1 Solving Inequalities - Linear
                                                                                                                        • 3.5.2 Solving Inequalities - Quadratic
                                                                                                                        • 3.6 Inequalities on a Graph
                                                                                                                          • 3.6.1 Inequalities on Graphs - Drawing
                                                                                                                            • 3.6.2 Inequalities on Graphs - Interpreting
                                                                                                                            • 3.7 Iteration
                                                                                                                              • 3.7.1 Iteration - Using a Calculator
                                                                                                                                • 3.7.2 Iteration - Applications
                                                                                                                                • 3.8 Equations & Problem Solving
                                                                                                                                  • 3.8.1 Equations & Problem Solving
                                                                                                                                • 4. Sequences
                                                                                                                                  • 4.1 Sequences - Linear
                                                                                                                                    • 4.1.1 Sequences - Linear
                                                                                                                                    • 4.2 Sequences - Quadratic
                                                                                                                                      • 4.2.1 Sequences - Quadratic
                                                                                                                                      • 4.3 Fibonacci & Geometric
                                                                                                                                        • 4.3.1 Sequences - Basics
                                                                                                                                          • 4.3.2 Sequences - Identifying
                                                                                                                                            • 4.3.3 Sequences - Others
                                                                                                                                          • 5. Graphs
                                                                                                                                            • 5.1 Coordinates
                                                                                                                                              • 5.1.1 Coordinates
                                                                                                                                              • 5.2 Drawing Graphs
                                                                                                                                                • 5.2.1 Drawing Graphs - Shapes
                                                                                                                                                  • 5.2.2 Drawing Graphs - Using a Table
                                                                                                                                                    • 5.2.3 Drawing Graphs - Trig Graphs
                                                                                                                                                    • 5.3 Equations of a Line / y = mx + c
                                                                                                                                                      • 5.3.1 Straight Lines - Finding Equations
                                                                                                                                                        • 5.3.2 Straight Lines - Drawing Graphs
                                                                                                                                                        • 5.4 Perpendicular Lines
                                                                                                                                                          • 5.4.1 Perpendicular Lines
                                                                                                                                                          • 5.5 Transformations of Graphs
                                                                                                                                                            • 5.5.1 Transformations of Graphs
                                                                                                                                                            • 5.6 D-T / V-T Graphs
                                                                                                                                                              • 5.6.1 Distance - Time Graphs
                                                                                                                                                                • 5.6.2 Speed-Time Graphs
                                                                                                                                                                • 5.7 Solving Equations using Graphs
                                                                                                                                                                  • 5.7.1 Solving Equations using Graphs
                                                                                                                                                                  • 5.8 Equation of a Circle
                                                                                                                                                                    • 5.8.1 Circles - Equation & Graphs
                                                                                                                                                                      • 5.8.2 Circles - Finding Tangents
                                                                                                                                                                      • 5.9 Estimating Areas & Gradients of Graphs
                                                                                                                                                                        • 5.9.1 Estimating Areas & Gradients of Graphs
                                                                                                                                                                      • 6. Ratios, Proportion & Rate of Change
                                                                                                                                                                        • 6.1 Ratios
                                                                                                                                                                          • 6.1.1 Ratios
                                                                                                                                                                          • 6.2 Direct & Inverse Proportion
                                                                                                                                                                            • 6.2.1 Direct & Inverse Proportion
                                                                                                                                                                            • 6.3 Speed, Density & Pressure
                                                                                                                                                                              • 6.3.1 Speed, Density & Pressure
                                                                                                                                                                                • 6.3.2 Speed, Density & Pressure - Harder
                                                                                                                                                                              • 7. Geometry & Measures
                                                                                                                                                                                • 7.1 Angles in Parallel Lines
                                                                                                                                                                                  • 7.1.1 Angles in Parallel Lines
                                                                                                                                                                                  • 7.2 Angles in Polygons
                                                                                                                                                                                    • 7.2.1 Angles in Polygons
                                                                                                                                                                                    • 7.3 Similarity - Lengths
                                                                                                                                                                                      • 7.3.1 Similarity - Lengths
                                                                                                                                                                                      • 7.4 Similarity - Areas & Volumes
                                                                                                                                                                                        • 7.4.1 Similarity - Areas & Volumes
                                                                                                                                                                                        • 7.5 Congruent Triangles
                                                                                                                                                                                          • 7.5.1 Congruent Triangles
                                                                                                                                                                                          • 7.6 Transformations
                                                                                                                                                                                            • 7.6.1 Transformations - Rotation
                                                                                                                                                                                              • 7.6.2 Transformations - Reflection
                                                                                                                                                                                                • 7.6.3 Transformations - Translation
                                                                                                                                                                                                  • 7.6.4 Transformations - Enlargement
                                                                                                                                                                                                    • 7.6.5 Combined Transformations
                                                                                                                                                                                                    • 7.7 Transformations - Enlargement (Negative Scale Factor)
                                                                                                                                                                                                      • 7.7.1 Transformations - Enlargement (Negative Scale Factor)
                                                                                                                                                                                                      • 7.8 Area - Triangles & Quadrilaterals
                                                                                                                                                                                                        • 7.8.1 Area - Formulae
                                                                                                                                                                                                          • 7.8.2 Area - Adding & Subtracting
                                                                                                                                                                                                          • 7.9 Circles - Area & Circumference
                                                                                                                                                                                                            • 7.9.1 Circles - Area & Circumference
                                                                                                                                                                                                            • 7.10 Circles - Sector & Arcs
                                                                                                                                                                                                              • 7.10.1 Circles - Sector Areas & Arc Lengths
                                                                                                                                                                                                              • 7.11 Problem Solving with Areas
                                                                                                                                                                                                                • 7.11.1 Problem Solving with Areas
                                                                                                                                                                                                                  • 7.11.2 Converting Lengths & Areas
                                                                                                                                                                                                                  • 7.12 3D - Shapes
                                                                                                                                                                                                                    • 7.12.1 3D Shapes - Surface Area
                                                                                                                                                                                                                      • 7.12.2 3D Shapes - Volume
                                                                                                                                                                                                                      • 7.13 Pythagoras
                                                                                                                                                                                                                        • 7.13.1 Pythagoras Theorem
                                                                                                                                                                                                                        • 7.14 SOHCAHTOA
                                                                                                                                                                                                                          • 7.14.1 SOHCAHTOA
                                                                                                                                                                                                                            • 7.14.2 3D Pythagoras & SOHCAHTOA
                                                                                                                                                                                                                            • 7.15 Sine/Cos Rules & Area of a Triangle
                                                                                                                                                                                                                              • 7.15.1 Sine & Cosine Rules, Area of a Triangle - Basics
                                                                                                                                                                                                                                • 7.15.2 Sine & Cosine Rules, Area of a Triangle - Harder
                                                                                                                                                                                                                                • 7.16 Circle Theorems
                                                                                                                                                                                                                                  • 7.16.1 Circle Theorems - Angles at Centre & Circumference
                                                                                                                                                                                                                                    • 7.16.2 Circle Theorems - Tangents
                                                                                                                                                                                                                                      • 7.16.3 Circle Theorems - Cyclic Quadrilaterals
                                                                                                                                                                                                                                        • 7.16.4 Circle Theorems - Alternative Segment
                                                                                                                                                                                                                                        • 7.17 Loci & Construction
                                                                                                                                                                                                                                          • 7.17.1 Loci & Construction
                                                                                                                                                                                                                                          • 7.18 Bearings & Scale
                                                                                                                                                                                                                                            • 7.18.1 Bearings & Scale
                                                                                                                                                                                                                                            • 7.19 Vectors
                                                                                                                                                                                                                                              • 7.19.1 Vectors - Basics
                                                                                                                                                                                                                                                • 7.19.2 Vectors - Finding Paths
                                                                                                                                                                                                                                                  • 7.19.3 Vectors - Proving Things
                                                                                                                                                                                                                                                  • 7.20 Drawing Plans & Elevations
                                                                                                                                                                                                                                                    • 7.20.1 Drawing Plans & Elevations
                                                                                                                                                                                                                                                    • 7.21 Trigonometry - Exact Values
                                                                                                                                                                                                                                                      • 7.21.1 Trigonometry - Exact Values
                                                                                                                                                                                                                                                    • 8. Probability
                                                                                                                                                                                                                                                      • 8.1 Basic Probability
                                                                                                                                                                                                                                                        • 8.1.1 Basic Probability
                                                                                                                                                                                                                                                        • 8.2 Venn Diagrams & Two Way Tables
                                                                                                                                                                                                                                                          • 8.2.1 Probability - Venn Diagrams
                                                                                                                                                                                                                                                            • 8.2.2 Probability - Two Way Tables
                                                                                                                                                                                                                                                              • 8.2.3 Set Notation & Venn Diagrams
                                                                                                                                                                                                                                                              • 8.3 Combined Probability
                                                                                                                                                                                                                                                                • 8.3.1 Combined Probability - Basics
                                                                                                                                                                                                                                                                  • 8.3.2 Combined Probability - Harder
                                                                                                                                                                                                                                                                • 9. Statistics
                                                                                                                                                                                                                                                                  • 9.1 Mean, Median & Mode
                                                                                                                                                                                                                                                                    • 9.1.1 Mean, Median & Mode
                                                                                                                                                                                                                                                                      • 9.1.2 Averages from Tables & Charts
                                                                                                                                                                                                                                                                        • 9.1.3 Averages from Grouped Data
                                                                                                                                                                                                                                                                          • 9.1.4 Calculations with the Mean
                                                                                                                                                                                                                                                                            • 9.1.5 IQR & Range
                                                                                                                                                                                                                                                                            • 9.2 Box Plots
                                                                                                                                                                                                                                                                              • 9.2.1 Box Plots
                                                                                                                                                                                                                                                                              • 9.3 Stem & Leaf Diagrams
                                                                                                                                                                                                                                                                                • 9.3.1 Stem & Leaf Diagrams
                                                                                                                                                                                                                                                                                • 9.4 Frequency Polygons
                                                                                                                                                                                                                                                                                  • 9.4.1 Frequency Polygons
                                                                                                                                                                                                                                                                                  • 9.5 Scatter Graphs (inc. Time Series)
                                                                                                                                                                                                                                                                                    • 9.5.1 Scatter Graphs
                                                                                                                                                                                                                                                                                      • 9.5.2 Time Series Graphs
                                                                                                                                                                                                                                                                                      • 9.6 Histograms
                                                                                                                                                                                                                                                                                        • 9.6.1 Histograms
                                                                                                                                                                                                                                                                                        • 9.7 Cumulative Frequency Graphs
                                                                                                                                                                                                                                                                                          • 9.7.1 Cumulative Frequency
                                                                                                                                                                                                                                                                                          • 9.8 Bar Charts
                                                                                                                                                                                                                                                                                            • 9.8.1 Bar Charts
                                                                                                                                                                                                                                                                                            • 9.9 Population & Samples
                                                                                                                                                                                                                                                                                              • 9.9.1 Comparing Distributions
                                                                                                                                                                                                                                                                                                • 9.9.2 Capture - Recapture


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                                                                                                                                                                                                                                                                                              Author: Lucy

                                                                                                                                                                                                                                                                                              Lucy has been a passionate Maths teacher for over 12 years, helping to engage interest and develop confidence in the subject at all levels. As Head of Department and Director of Maths, Lucy has advised schools across both academy trusts and an entire city, where her role was to support and coach teachers to improve Maths teaching for all.


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