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Algebraic manipulation

Algebraic notation

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Calculating probability

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Venn diagrams

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Pythagoras’ theorem

Trigonometric ratios: SOH CAH TOA

Finding missing lengths in a triangle

Finding missing angles in a triangle

Drawing shapes

Transformations

Constructions

Constructing triangles

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Types of angles

Angle rules

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Area and perimeter: Triangles and quadrilaterals

Area of compound shapes

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Properties of shapes

Symmetrical shapes and rotational symmetry

Congruent shapes

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Shapes

Quadrilaterals: Types and properties

Triangles and regular polygons: Types and properties

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3D shapes: Identification and properties

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Solving simultaneous equations using graphs

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Travel graphs: Distance-time graphs

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X and Y coordinates

Straight line graphs

Drawing straight line graphs

Finding the gradient

Equation of a straight line: y = mx + c

Drawing a graph of a linear equation

Estimating values using linear graphs

Formulae and equations

Substituting numbers into an expression

Writing and using formulae

Solving equations

Rearranging formulae

Number patterns and sequences

The nth term

Inequalities: Greater than or less than

Simultaneous equations

Algebraic manipulation

Algebraic notation

Algebraic terms

Simplifying algebraic expressions

Multiplying and dividing algebraic expressions

Single brackets: Expanding and factorising

Expanding double brackets: FOIL and multiplication grid

Fractions, decimals and percentages

Converting between fractions, decimals and percentages

Fractions

Fraction operations: Add, subtract, multiply, divide

Percentages

Rounding: Decimal places and significant figures

Rounding errors and estimating

Number calculations

Ordering numbers: Whole numbers and decimals

Addition and subtraction using the column method

Multiplying and dividing by powers of 10

Adding and subtracting decimals

Methods for multiplication and division

Order of operations: BIDMAS

Types of numbers

Understanding place value

Negative numbers: Add, subtract, multiply, divide

Special types of numbers

Multiples, factors and prime factors

Lowest common multiple and highest common factor

Square roots and cube roots

Writing indices and index laws

Standard form

Explainer Video

Tutor: Meera

Summary

Algebraic notation

In a nutshell

Algebra uses letters called 'variables' to represent unknown quantities. The basic rules for algebraic notation help write terms in a concise way. These terms can then be used in expressions, formulae or equations.

Example 1

The letter 'a' could represent an apple. Two apples could be described by $\underline{2a}$ .

Basic rules

Adding equal variables

Add the numbers and copy the variable. If there is no number with the variable, it means $1$ . For example, $x$ means $1x$

Example

$x+x=2x$

Subtracting equal variables

Subtract the numbers and copy the variable.

Example

$7x-5x=2x$

Multiplying same variables

Multiplying the same variables changes the power. When multiplying, add the powers. If there is no number with the variable, it means $1$ .

Example

$x \times x = x^2$

Multiplying different variables

Write the letters without the multiplication sign. Multiplying different variables will not change their powers.

Example

$x \times y = xy$

Adding/subtracting different variables

These cannot be added or subtracted so they will remain the same.

Example

$a+b=a+b$ 

Formulae

Formulae help find quantities.

Examples

$F=ma$

Calculate the force ( $F$ ) on an object from its mass ( $m$ ) and acceleration ( $a$ ).

$P = 2(l+w)$

Calculate the perimeter ( $P$ ) of a rectangle from its length ( $l$ ) and width ( $w$ ).

$A=\frac{1}{2} bh$

Calculate the area ( $A$ ) of a triangle from its base ( $b$ ) and its height ( $h$ ).

Equations

An equation is formed when two expressions equal each other.

Examples

\frac x 2 =5

2x-3=7

x^2 -2x-8=0

Learn with Basics

Length:

Unit 1

Algebraic terms

Jump Ahead

Optional

Unit 2

Algebraic notation

Final Test

Create an account to complete the exercises

FAQs - Frequently Asked Questions

What is algebraic notation?

Algebraic notation involves writing algebraic terms, with a combination of numbers and letters. These terms can then be used further in expressions and equations.

What are variables?

Variables are a short hand way to name a quantity. The letter variable can then be used in an expression.

What is algebra?

Algebra uses letters called variables to represent unknown quantities.

Home

Maths

Algebraic manipulation

Algebraic notation

Videos

Summary

Exercises

Select Lesson

Statistics

Qualitative and quantitative data

Representing data: Graphs and charts

Mean, median, mode and range

Frequency tables

Averages from frequency tables

Averages from grouped frequency tables

Scatter graphs

Probability

Calculating probability

Equal and unequal probabilities

Relative frequency

Listing outcomes

Venn diagrams

Trigonometry

Pythagoras’ theorem

Trigonometric ratios: SOH CAH TOA

Finding missing lengths in a triangle

Finding missing angles in a triangle

Drawing shapes

Transformations

Constructions

Constructing triangles

Lines and angles

Types of angles

Angle rules

Interior and exterior angles

Parallel lines

Measures

Area and perimeter: Triangles and quadrilaterals

Area of compound shapes

Volume of prisms

Properties of shapes

Symmetrical shapes and rotational symmetry

Congruent shapes

Similar shapes

Nets and surface area

Shapes

Quadrilaterals: Types and properties

Triangles and regular polygons: Types and properties

Circles: Area and circumference

3D shapes: Identification and properties

Rates of change

Percentage change

Conversion factors

Imperial units

Solving best buy problems

Reading timetables

Maps and scale drawings

Speed: Formula and units

Density: Formula and units

Proportion

Ratio

Other graphs

Interpreting graphs

Solving simultaneous equations using graphs

Quadratic graphs

Travel graphs: Distance-time graphs

Conversion graphs

Straight line graphs

X and Y coordinates

Straight line graphs

Drawing straight line graphs

Finding the gradient

Equation of a straight line: y = mx + c

Drawing a graph of a linear equation

Estimating values using linear graphs

Formulae and equations

Substituting numbers into an expression

Writing and using formulae

Solving equations

Rearranging formulae

Number patterns and sequences

The nth term

Inequalities: Greater than or less than

Simultaneous equations

Algebraic manipulation

Algebraic notation

Algebraic terms

Simplifying algebraic expressions

Multiplying and dividing algebraic expressions

Single brackets: Expanding and factorising

Expanding double brackets: FOIL and multiplication grid

Fractions, decimals and percentages

Converting between fractions, decimals and percentages

Fractions

Fraction operations: Add, subtract, multiply, divide

Percentages

Rounding: Decimal places and significant figures

Rounding errors and estimating

Number calculations

Ordering numbers: Whole numbers and decimals

Addition and subtraction using the column method

Multiplying and dividing by powers of 10

Adding and subtracting decimals

Methods for multiplication and division

Order of operations: BIDMAS

Types of numbers

Understanding place value

Negative numbers: Add, subtract, multiply, divide

Special types of numbers

Multiples, factors and prime factors

Lowest common multiple and highest common factor

Square roots and cube roots

Writing indices and index laws

Standard form

Explainer Video

Tutor: Meera

Summary

Algebraic notation

In a nutshell

Example 1

The letter 'a' could represent an apple. Two apples could be described by $\underline{2a}$ .

Basic rules

Adding equal variables

Add the numbers and copy the variable. If there is no number with the variable, it means $1$ . For example, $x$ means $1x$

Example

$x+x=2x$

Subtracting equal variables

Subtract the numbers and copy the variable.

Example

$7x-5x=2x$

Multiplying same variables

Multiplying the same variables changes the power. When multiplying, add the powers. If there is no number with the variable, it means $1$ .

Example

$x \times x = x^2$

Multiplying different variables

Write the letters without the multiplication sign. Multiplying different variables will not change their powers.

Example

$x \times y = xy$

Adding/subtracting different variables

These cannot be added or subtracted so they will remain the same.

Example

$a+b=a+b$ 

Formulae

Formulae help find quantities.

Examples

$F=ma$

Calculate the force ( $F$ ) on an object from its mass ( $m$ ) and acceleration ( $a$ ).

$P = 2(l+w)$

Calculate the perimeter ( $P$ ) of a rectangle from its length ( $l$ ) and width ( $w$ ).

$A=\frac{1}{2} bh$

Calculate the area ( $A$ ) of a triangle from its base ( $b$ ) and its height ( $h$ ).

Equations

An equation is formed when two expressions equal each other.

Examples

\frac x 2 =5

2x-3=7

x^2 -2x-8=0

Learn with Basics

Length:

Unit 1

Algebraic terms

Jump Ahead

Optional

Unit 2

Algebraic notation

Final Test

Create an account to complete the exercises

FAQs - Frequently Asked Questions

What is algebraic notation?

Algebraic notation involves writing algebraic terms, with a combination of numbers and letters. These terms can then be used further in expressions and equations.

What are variables?

Variables are a short hand way to name a quantity. The letter variable can then be used in an expression.

What is algebra?

Algebra uses letters called variables to represent unknown quantities.

Algebraic notation

Videos

Summary

Exercises

Select Lesson

Statistics

Probability

Trigonometry

Drawing shapes

Lines and angles

Measures

Properties of shapes

Shapes

Rates of change

Proportion

Ratio

Other graphs

Straight line graphs

Formulae and equations

Algebraic manipulation

Fractions, decimals and percentages

Number calculations

Types of numbers

Explainer Video

Summary

Algebraic notation

In a nutshell

Example 1

Basic rules

​​Adding equal variables

Example

Subtracting equal variables

Example

Multiplying same variables

Example

​x×x=x2x \times x = x^2x×x=x2Multiplying different variables

Example

Adding/subtracting different variables

Example

Formulae

Examples

Equations

Examples

Learn with Basics

Unit 1

Algebraic terms

Jump Ahead

Unit 2

Algebraic notation

Final Test

FAQs - Frequently Asked Questions

What is algebraic notation?

What are variables?

What is algebra?

Algebraic notation

Videos

Summary

Exercises

Select Lesson

Statistics

Probability

Trigonometry

Drawing shapes

Lines and angles

Measures

Properties of shapes

Shapes

Rates of change

Proportion

Ratio

Other graphs

Straight line graphs

Formulae and equations

Algebraic manipulation

Fractions, decimals and percentages

Number calculations

Types of numbers

Explainer Video

Summary

Algebraic notation

Adding equal variables

$x \times x = x^2$

Multiplying different variables

Adding equal variables

$x \times x = x^2$

Multiplying different variables