For Students
For Teachers
For Parents

Join class Login Sign up

For Students
For Teachers
For Parents
For Schools
Resources

Join class
Login

Revision notes
KS3
Maths
Maths: KS3
Substituting into Real-Life Expressions

Substituting into Real-Life Expressions

Maths: KS3, topic 2.2.3

Test yourself on Substituting into Real-Life Expressions

Practise this topic for free

Previous topic2.2.2 Substituting into Algebraic Expressions Next topic2.2.4 Simplifying Expressions by Collecting Like Terms

Maths: KS3 contents

1 Number
- 1.1 Place Value & Ordering
  1.1.1 Ordering Integers
  1.1.2 Ordering Decimals
  1.1.3 Equal Symbols
  1.1.4 Place Value
- 1.2 Numerical Operations
  1.2.1 Adding Integers
  1.2.2 Subtracting Integers
  1.2.3 Multiplying Integers
  1.2.4 Dividing Integers
  1.2.5 Dividing with a Remainder
  1.2.6 Adding & Subtracting Decimals
  1.2.7 Multiplying Decimals
  1.2.8 Dividing Decimals
  1.2.9 Adding & Subtracting Negative Numbers
  1.2.10 Multiplying & Dividing Negative Numbers
  1.2.11 Multiplying by Powers of Ten
  1.2.12 Dividing by Powers of Ten
- 1.3 Fractions
  1.3.1 Writing Fractions
  1.3.2 Simplifying Fractions
  1.3.3 Equivalent Fractions
  1.3.4 Constructing Fractions
  1.3.5 Ordering Fractions
  1.3.6 Recurring Decimal Notation
  1.3.7 Mixed Numbers & Improper Fractions
- 1.4 Numerical Operations (Fractions)
  1.4.1 Adding & Subtracting Fractions
  1.4.2 Add & Subtract Mixed Numbers & Improper Fractions
  1.4.3 Multiplying Fractions
  1.4.4 Multiplying Mixed Numbers
  1.4.5 Reciprocals
  1.4.6 Dividing Fractions
  1.4.7 Dividing Mixed Numbers
- 1.5 Roots & Powers
  1.5.1 Roots
  1.5.2 Integer Powers
  1.5.3 Estimating Powers & Roots
  1.5.4 Laws of Indicies (Multiplication)
- 1.6 Structure of Calculations
  1.6.1 Order of Operations (BIDMAS)
- 1.7 Numerical Skills
  1.7.1 Using a Calculator - Powers, Roots & Fractions
- 1.8 Factors & Multiples
  1.8.1 Divisibility Rules
  1.8.2 Finding Multiples
  1.8.3 Finding Factors
  1.8.4 Finding Prime Numbers
- 1.9 Systematic Listing
  1.9.1 Systematic Listing
- 1.10 Standard Form
  1.10.1 Reading Standard Form
  1.10.2 Converting to Standard Form (Positive Powers)
  1.10.3 Converting to Standard Form (Negative Powers)
  1.10.4 Converting Form Standard Form (Positive Powers)
  1.10.5 Converting From Standard Form (Negative Powers)
  1.10.6 Adding & Subtracting Standard Form
  1.10.7 Standard Form on a Calculator
- 1.11 Fractions, Decimals & Percentages
  1.11.1 Converting Fractions, Decimals & Percentages
  1.11.2 Numbers as Percentages
  1.11.3 Fractions of Amounts
- 1.12 Percentage Change
  1.12.1 Percentages of Amounts (Calculator)
  1.12.2 Percentages of Amounts (No Calculator)
  1.12.3 Percentage Change
- 1.13 Rounding & Estimation
  1.13.1 Rounding Integers
  1.13.2 Estimating Calculations
  1.13.3 Rounding Decimals
  1.13.4 Rounding With Significant Figures
- 1.14 Bounds & Accuracy
  1.14.1 Finding Error Intervals
2 Algebra
- 2.1 Algebraic Notation
  2.1.1 Function Machines
  2.1.2 Using Algebraic Notation
- 2.2 Substitution & Simplification
  2.2.1 Substituting into Expressions with Operations
  2.2.2 Substituting into Algebraic Expressions
  2.2.3 Substituting into Real-Life Expressions
  2.2.4 Simplifying Expressions by Collecting Like Terms
- 2.3 Brackets
  2.3.1 Expanding Single Brackets
  2.3.2 Expanding & Simplifying with Single Brackets
  2.3.3 Expanding Double Brackets
  2.3.4 Factorising Into One Bracket
- 2.4 Algebraic Fractions
  2.4.1 Operations with Algebraic Fractions
- 2.5 Rearranging
  2.5.1 Changing the Subject
- 2.6 Functions
  2.6.1 Finding the Input of a Function
- 2.7 Solving Linear Equations
  2.7.1 Solving Linear Equations (One Step)
  2.7.2 Solving Linear Equations (Multi-Step)
  2.7.3 Solving Linear Equations (Unknown Both Sides)
  2.7.4 Solving Equations (Unknown in Denominator)
  2.7.5 Forming & Solving Linear Equations
- 2.8 Inequalities
  2.8.1 Representing Inequalities on a Number Line
  2.8.2 Solving Linear Inequalities
  2.8.3 Linear Inequalities with Unknowns on Both Sides
- 2.9 Simultaneous Equations
  2.9.1 Solving Simultaneous Equations Graphically
  2.9.2 Solving Simultaneous Equations by Elimination
- 2.10 Sequences
  2.10.1 Term-to-Term Rules (Patterns)
  2.10.2 Term-to-Term Rules (Numerical)
  2.10.3 Substituting into a Given Rule
  2.10.4 Position-to-Term Rules
  2.10.5 Finding the Nth Term (Linear Sequences)
  2.10.6 Simple Geometric Progressions
- 2.11 Coordinates
  2.11.1 Midpoints of Line Segments
- 2.12 Linear Graphs
  2.12.1 Equations of Straight Lines
  2.12.2 Finding Line Equation from Point & Gradient
  2.12.3 Finding Line Equations from Two Points
  2.12.4 Parallel Line Equations
- 2.13 Quadratic Graphs
  2.13.1 Interpreting Quadratics
3 Ratio, Proportion & Rates of Change
- 3.1 Unit Conversion
  3.1.1 Using Clocks
  3.1.2 Calculating with Time
  3.1.3 Using Timetables
  3.1.4 Using Calendars
  3.1.5 Converting Units of Length
  3.1.6 Converting Units of Mass
  3.1.7 Converting Units of Capacity
  3.1.8 Metric Conversions
  3.1.9 Converting Units of Area & Volume
- 3.2 Compound Units
  3.2.1 Estimating & Measuring
  3.2.2 Calculating Speed
  3.2.3 Best Buy & Unit Pricing
  3.2.4 Density, Mass & Volume
- 3.3 Ratio Fundamentals
  3.3.1 Ratio Notation & Simplification
  3.3.2 Ratios as Fractions and Linear Equations
  3.3.3 Sharing in a Ratio
  3.3.4 Proportion Problems
- 3.4 Advanced Ratio and Scale
  3.4.1 Map Scales & Real Distances
- 3.5 Proportion
  3.5.1 Currency Conversion
  3.5.2 Direct Proportion
  3.5.3 Inverse Proportion
- 3.6 Algebraic Proportion
  3.6.1 Direct Proportion
  3.6.2 Inverse Proportion
4 Geometry & Measures
- 4.1 Area & Perimeter
  4.1.1 Perimeter of Simple Shapes
  4.1.2 Perimeter of Compound Shapes
  4.1.3 Area of Triangles
  4.1.4 Area of Rectangles & Parallelograms
  4.1.5 Area of Trapezia
  4.1.6 Area of Compound Shapes
  4.1.7 Area of Compound Shapes with Triangles
- 4.2 Properties of Shapes
  4.2.1 Naming & Classifying Triangles
  4.2.2 Naming & Classifying Quadrilaterals
  4.2.3 Properties of Lines
  4.2.4 Shortest Distance from a Point to a Line
  4.2.5 Properties of 3D Shapes
- 4.3 Angles
  4.3.1 Classification of Angles
  4.3.2 Angles on a Line & Around a Point
  4.3.3 Combining Angle Facts in Triangles
  4.3.4 Angles on Parallel Lines
  4.3.5 Interior & Exterior Angles in Polygons
- 4.4 Trigonometry
  4.4.1 Pythagoras' Theorem
  4.4.2 Sides in Right-Angles Triangles
  4.4.3 Angles in Right-Angled Triangles
- 4.5 Similarity & Congruence
  4.5.1 Congruent Shapes
  4.5.2 Length Scale Factors in Similar Shapes
- 4.6 Circle Geometry
  4.6.1 Identifying Parts of a Circle
  4.6.2 Calculating Circumference
  4.6.3 Calculating Area of a Circle
  4.6.4 Calculating Arc Lengths
  4.6.5 Calculating Area of Sectors
- 4.7 3D Representations
  4.7.1 Nets of 3D Shapes
- 4.8 Surface Area
  4.8.1 Surface Area of Cubes & Cuboids
  4.8.2 Surface Area of Prisms
  4.8.3 Surface Area of Cylinders
- 4.9 Volume
  4.9.1 Volume of Prisms
  4.9.2 Volume of Cylinders
- 4.10 Transformations
  4.10.1 Translation using Vectors
  4.10.2 Rotations
  4.10.3 Enlargements & Positive Scale Factors
- 4.11 Scale Drawings
  4.11.1 Scale Drawings
- 4.12 Bearings
  4.12.1 Bearings
5 Probability
- 5.1 Single Events
  5.1.1 Writing Probabilities as Fractions
  5.1.2 Mutually Exclusive Events
  5.1.3 Expected Results
- 5.2 Combined Events
  5.2.1 Reading Venn Diagrams
  5.2.2 Venn Diagrams (Set Notation)
  5.2.3 Independent & Mutually Exclusive Events
- 5.3 Experimental Probability
  5.3.1 Relative Frequency & Convergence
6 Statistics
- 6.1 Averages & Range
  6.1.1 Range
  6.1.2 Median
  6.1.3 Mode
  6.1.4 Mean
  6.1.5 Interpreting Two-Way Tables
- 6.2 Scatter Graphs
  6.2.1 Lines of Best Fit
- 6.3 Collecting & Presenting Data
  6.3.1 Types of Data

Seneca

Teachers
Parents
Students
Your school
Join class
Get mobile app
Evidence Seneca works

Resources

Revision Notes
International A Level
IGCSE
IB Diploma
Maths
Teacher CPD
Resource Hub
Blog
Free CPD courses
Definitions
Mental health & wellbeing
Find tutors
Become a tutor

Legal

Terms
Privacy - UK
GDPR
Cookies
Privacy - DE + AT
Privacy - ES
Privacy - FR
Privacy - IT

Contact us

learnmore@seneca.io
Instagram
Facebook
YouTube
X
TikTok
Help & FAQs
Press kit

A Level Courses

A Level Biology Revision
A Level Business Revision
A Level Chemistry Revision
A Level Physics Revision
A Level Economics Revision
A Level English Language Revision
A Level English Literature Revision
A Level Geography Revision
A Level History Revision
A Level Political Studies Revision
A Level Psychology Revision
A Level Sociology Revision
A Level Maths Revision

GCSE Courses

GCSE Biology Revision
GCSE Business Revision
GCSE Chemistry Revision
GCSE Physics Revision
GCSE Computer Science Revision
GCSE Design Technology Revision
GCSE English Language Revision
GCSE English Literature Revision
GCSE Food Preparation & Nutrition Revision
GCSE French Revision
GCSE Geography Revision
GCSE German Revision
GCSE History Revision
GCSE Maths Revision
GCSE Media Studies Revision
GCSE Music Revision
GCSE Physical Education Revision
GCSE Religious Studies Revision
GCSE Sociology Revision
GCSE Spanish Revision

International A Level

International A Level Biology Revision
International A Level Chemistry Revision
International A Level Physics Revision

IGCSE

IGCSE Biology Revision
IGCSE Chemistry Revision
IGCSE Physics Revision
IGCSE Geography Revision
IGCSE English Language Revision
IGCSE Computer Science Revision

IB Diploma

IB Biology Revision
IB Physics Revision
IB Chemistry Revision
IB Business Revision
IB Economics Revision

KS3 Courses

KS3 English Revision
KS3 French Revision
KS3 Spanish Revision
KS3 Geography Revision
KS3 History Revision
KS3 Maths Revision
KS3 Science Revision

KS2 Courses

KS2 Computing
KS2 English
KS2 French
KS2 Geography
KS2 History
KS2 Maths
KS2 Science