Prior Content: Solving Simple Equations, Substitution, Forming Simple Equations, Manipulating Formulae/ Changing the Subject, Drawing & Using Graphs, Simplifying Basic Expressions, Solving Quadratics
Possible Next Steps: Graphical Transformations, Algebraic Proof
Contents
- 1.1 Function Machines
- 2.1 Domains & Ranges
- 2.2 Limited Domains
- 2.3 Piecewise Functions
- 3.1 Compound Functions
- 4.1 Inverse Functions
- 5.1 Functions as Graphs
- Whole Topic Summary Resources (Including Past Paper Questions)
1.1 Function Machines
Teaching Videos, Exercises & Activities
Tutorial Videos
Corbett Maths Function Machines
Online Platforms (with Videos & Exercises)
- Khan Academy
- Function inputs & outputs: Videos & practice
Activities & Resources
- Pixi Maths
- Function Machines ppt
- Introduction to Functions ppt (Slides 1-7) Remainder of ppt can be used before introducing Compound Functions or Graphical Transformations
- Andy Lutwyche
- Miss Konstantine (MathsHKO)
- Math = Love (Sarah Carter)
- Silent Board Game for function rules
- Function Notation Puzzler
- Evaluating from a Table Notes
- Evaluating from an Equation Notes
- Evaluating Functions Spider Puzzles
- Function Machines Activity (CPM)
- Evaluating Functions Puzzle
- Evaluating Functions War
- Evaluating Functions Notes
- Flip Chutes Function Machines
- Function Machines & Notation Foldable
- CPM
- TES
- Don Steward
- The Chalkface
- Guess the Rule: Excel (if macros are blocked: right-click the file › Properties › tick Unblock)
- PhET Interactive Simulations
- PhET Function Builder Interactive Simulation (embedded below)
- Transum
- Access Maths
- Interactive Maths
- Functions Introduction: Video
- Goal Free Problems
- Go Teach Maths
- thewessens.net Classroom Apps
- Function Pyramids (test inputs to crack the hidden function)
- Jo Morgan
- Polypad (Amplify)
Worksheets
- Dr Austin Maths
- Corbettmaths
- Number & Function Machines Practice Questions, Solutions & Video Solutions
- Function Machines Worksheet✦ & Solutions
- Functions Worksheet (Q1-7) & Solutions
- Pixi Maths
- CIMT MEP (online self-checking)
- Miss Konstantine (MathsHKO)
- Maths Genie
- Function Machines: Booklet · Worksheet · Solutions · Lesson · Topic page
- MME
- OCR
- Mr Thompson Maths
- Mr Morley Maths
- Function Machines: Notes jotter/worksheet
Dr Frost Resources
Dr Frost Video
K365: Find the Output of a Function Machine.
K366: Find the Input of a Function Machine.
K590: Find the Output of a Function, Given the Input.
K591: Find the Input of a Function, Given the Output.
Dr Frost Slides & Activities
- All in one summary sheet
Extra Questions
- Dr Frost Questions
Key Skills
Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost
- 133d: Calculate the output of a two-step function machine.
- 133e: Calculate the input of a two-step function machine.
- 133f: Determine a missing operation in a two-step function machine.
- 195a: Calculate the input or output of a function machine involving a negative value.
- 195b: Calculate the input or output of a function machine involving a decimal value.
- 195c: Calculate the input or output of a function machine involving a fractional value.
- 195d: Determine an algebraic expression for the output of a function machine.
- 195e: Determine the missing operation in a function machine given a single variable as the input and an algebraic expression as the output.
- 432a: Calculate the output of a function, given the input.
- 432b: Determine an output for a given scenario modelled as a quadratic function.
- 432c: Write a function that represents a function machine.
- 432d: Determine the input of a linear function, given the output.
- 432e: Determine the input of a non-linear function, given the output.
- 432f: Determine an expression using transformations of a function with a single variable input.
- 432g: Determine an expression for f(…) with more general algebraic inputs.
- 432h: Determine an expression for a combination of f(…) with different inputs.
- 432i: Solve equations given in the form f(…) = k for more general algebraic inputs.
- 432j: Determine an input for a given scenario modelled as a quadratic function.
- 432k: Solve equations where the output of two functions is equated, leading to a linear equation.
- 432l: Solve equations where the output of two functions is equated, leading to a quadratic equation.
- 133: Exam Practice: Function machines
- 195: Exam Practice: Function machines involving decimals, negative numbers and algebraic inputs
- 432: Exam Practice: Function notation and calculating outputs or inputs or a function
Extension Materials
Activities
- Sarah Carter Functions Puzzle
2.1 Domains & Ranges
Teaching Videos, Exercises & Activities
Tutorial Videos
Domain and Range (1 of 2: Introduction) by Eddie Woo
How to find the domain and the range of a function given its graph (example) by Khan Academy
Corbett Maths Domains & Ranges
Online Platforms (with Videos & Exercises)
- Khan Academy
- Intro to domain & range: Videos & practice
Activities & Resources
- Pixi Maths
- IGCSE Introduction to Functions ppt (Slides 1-9)
- Andy Lutwyche
- Math = Love (Sarah Carter)
- Set & Interval Notation template
- Build a Function activity
- Domain & Range Challenge
- Find the Flubs activity
- Domain & Range Foldables
- Domain & Range Organiser (DIXI ROYD)
- Domain & Range Foldables
- Boxes for Domain & Range
- Domain & Range Organiser
- Interactive Domain & Range Foldable
- DIX ROY Acronym
- Domain & Range Pictionary
- Domain & Range Notation Foldable
- Ben Sparks (GeoGebra)
- Domain and Range: GeoGebra
- Acute Learning Problem Pairs
- Level 2 FM: Functions: Domain, Range, Composite & Inverse as PowerPoint or PDF
- Transum
- Desmos
- Domain and Range Introduction (find domains and ranges from graphs, including piecewise functions)
- Free-Range Functions (challenges common misconceptions about range)
Worksheets
- Dr Austin Maths
- Corbettmaths
- Domains & Ranges Sketching Functions Practice Questions & Solutions
- Mathshelper (Jon Stone)
Dr Frost Resources
Dr Frost Slides & Activities
- Dr Frost Slides (4)
Key Skills
Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost
- 437b: Determine the range of values that should be excluded from the domain of a reciprocal function or root function. (not yet active)
- 437c: Determine the range of a quadratic function in completed square form. (not yet active)
- 437e: Determine the domain or range of a function in graph form. (not yet active)
- 437: Exam Practice: Domain and range of simple functions
Extension Materials
Videos & Other Multimedia
2.2 Limited Domains
TEACHING VIDEOS, EXERCISES & ACTIVITIES
Tutorial Videos
Domain and Range by 1st Class Maths
How To Find The Domain and Range of a Quadratic Function by The Organic Chemistry Tutor
Online Platforms (with Videos & Exercises)
Activities & Resources
- Andy Lutwyche
- Math = Love (Sarah Carter)
Worksheets
Dr Frost resources
Dr Frost Video
Dr Frost Slides & Activities
- All in one summary sheet
Extra Questions
- Dr Frost Questions
Key Skills
Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost
- 437a: Determine the range of a linear function for a given domain. (not yet active)
- 437d: Determine the range of a quadratic function with a given domain. (not yet active)
- 437f: Determine the domain of a function for a given range. (not yet active)
- 437: Exam Practice: Domain and range of simple functions
Further Practice
- Practise Questions (may include angles in a triangle and on a straight line)
EXTENSION MATERIALS
Online Platforms
- Khan Academy
- Determining the domain of a function: Videos & practice
2.3 Piecewise Functions
TEACHING VIDEOS, EXERCISES & ACTIVITIES
Tutorial Videos
Evaluating Piecewise Functions | PreCalculus by The Organic Chemistry Tutor
Graphing Piecewise Functions – Precalculus by The Organic Chemistry Tutor
Piecewise function formula from graph by Khan Academy
Corbett Maths Drawing Functions
Online Platforms (with Videos & Exercises)
Activities & Resources
- Andy Lutwyche
- Ben Sparks (GeoGebra)
- Batman Piecewise Plot: GeoGebra
- Acute Learning Problem Pairs
- Level 2 FM: Sketching Graphs & Piecewise Functions as PowerPoint or PDF
Worksheets
- Dr Austin Maths
- Corbett Maths
- Domain & Ranges and Sketching Functions Practice Questions & Solutions
Dr Frost resources
Dr Frost Video
Dr Frost Slides & Activities
- All in one summary sheet
Extra Questions
- Dr Frost Questions
Key Skills
Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost
- 487a: Use a piecewise function to find an output for a specific input.
- 487b: Sketch a piecewise function involving linear segments.
- 487c: Sketch a piecewise function that includes non-linear segments. (not yet active)
- 487d: Determine the component functions of a sketched piecewise function.
- 487e: Determine the number of solutions to f(x) = k where the function is piecewise.
- 487f: Solve equations given in the form f(x) = k when the function is piecewise.
- 487g: Determine the range of a piecewise function.
- 487h: Determine a piecewise function given knowledge of its range.
- 487i: Determine the area enclosed under a piecewise function with linear segments.
- 488a: Determine an output of a step function using a graph. (not yet active)
- 488b: Determine an output of a step function defined algebraically piecewise. (not yet active)
- 488c: Determine the range of a step function defined algebraically piecewise. (not yet active)
- 488d: Sketch a step function using a single algebraic expression that makes use of the floor function (greatest integer function) or ceiling functions. (not yet active)
- 487: Exam Practice: Piecewise functions
- 488: Exam Practice: Stepwise functions
Further Practice
- Practise Questions (may include angles in a triangle and on a straight line)
EXTENSION MATERIALS
Online Platforms
- Khan Academy
- Piecewise functions: Videos & practice
3.1 Compound Functions
TEACHING VIDEOS, EXERCISES & ACTIVITIES
Tutorial Videos
Corbett Maths Composite Functions
Online Platforms (with Videos & Exercises)
- Khan Academy
- Composite functions: Videos & practice
Activities
- Maths 4 Everyone (Good Introductory Task)
- Pixi Maths
- Introduction to Functions ppt (Slides 8-11) can be used before introducing Compound Functions
- Composite Functions ppt
- Andy Lutwyche
- Math = Love (Sarah Carter)
- Don Steward
- Interactive Maths
- Composite Functions: Video
- Go Teach Maths
- BossMaths
- MathsPad
- MathsBot
Worksheets
- Dr Austin Maths
- Composite One-Step Fill in the Blanks (Word | PDF | Answers)
- Composite Two-Step Fill in the Blanks (Word | PDF | Answers)
- Evaluating Composite One-Step Fill in the Blanks (Word | PDF | Answers)
- Evaluating Composite Two-Step Fill in the Blanks (Word | PDF | Answers)
- Composite Practice Strips (Word | PDF | Answers)
- Composite Match-Up (Word | PDF✦ | Answers✦)
- Evaluating Composite Practice Strips (Word | PDF | Answers)
- Composite Fill in the Blanks (Word | PDF | Answers)
- Corbettmaths
- Maths 4 Everyone
- Pixi Maths
- Maths Genie
- Inverse and Composite Functions: Booklet · Worksheet · Solutions · Lesson · Topic page
- Naiker Maths
- Composite & Inverse Functions: Worksheet
- Access Maths
- MME
- 1st Class Maths
- Starting Points Maths
- Mr Morley Maths
- Functions (with Composite and Inverse): Notes jotter/worksheet · How-to sheet · Exam questions · Mark scheme
Dr Frost resources
Dr Frost Video
K595: Find the Numerical Output of a Composite Function.
Dr Frost Slides & Activities
- Slides & Worksheet
Topic Test
- Standard Test
Extra Questions
- Dr Frost Questions
Key Skills
Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost
- 435a: Calculate the numeric output of a composite function.
- 435b: Determine the algebraic output of a composite function where both functions are linear.
- 435c: Determine the algebraic output of a composite function where at least one function is quadratic.
- 435d: Determine the algebraic output of a composite function for more general functions. (not yet active)
- 435e: Identify the constituent functions that make up a composite function. (not yet active)
- 435f: Solve an equation involving a composite function, leading to a linear equation. (not yet active)
- 435g: Solve an equation involving a composite function, leading to a quadratic equation. (not yet active)
- 435h: Determine ff(x) for functions given in the form f(x) = ax+b/cx+d
- 435i: Determine the output of a composite function where at least one the functions are in graph form. (not yet active)
- 435: Exam Practice: Composite functions (excluding exponentials and modulus)
Further Practice
- Practise Questions
EXTENSION MATERIALS
4.1 Inverse Functions
TEACHING VIDEOS, EXERCISES & ACTIVITIES
Tutorial Videos
Corbett Maths Inverse Functions
Online Platforms (with Videos & Exercises)
- Khan Academy
- Intro to inverse functions: Videos & practice
Activities
- Pixi Maths
- Math = Love (Sarah Carter)
- Don Steward
- Interactive Maths
- Inverse Functions: Video
- Go Teach Maths
- BossMaths
- MathsPad
Worksheets
- Dr Austin Maths
- Corbettmaths
- Composite & Inverse Functions Practice Questions & Solutions
- Functions Worksheet (Q13-17) & Solutions
- Maths 4 Everyone
- Pixi Maths
- 1st Class Maths
Dr Frost resources
Dr Frost Video
K592: Find the Inverse Function for a Linear Expression.
K593: Find the Inverse Function of f(x)=(ax+b)/(cx+d).
Dr Frost Slides & Activities
- Slides & Worksheet
Topic Test
- Standard Test
Extra Questions
- Dr Frost Questions
Key Skills
Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost
- 436a: Determine the inverse function for an expression with one operation. (not yet active)
- 436b: Determine the inverse function for a linear expression.
- 436c: Determine the inverse function for a expression containing a power or root of x (not yet active)
- 436d: Determine the value of inverse function for a given input. (not yet active)
- 436e: Use a graph to determine the inverse function for a given input. (not yet active)
- 436f: Determine the inverse function where f(x) = ax+b/cx+d
- 436g: Determine the inverse function for a quadratic expression by completing the square.
- 436h: Solve equations of the form f-1(x) = k (not yet active)
- 436i: Determine the inverse function of a composite function. (not yet active)
- 436j: Solve an equation involving both a composite and inverse function. (not yet active)
- 436k: Simplify f-1 f(x) and understand self-inverse functions. (not yet active)
- 436: Exam Practice: Inverse functions (excluding exponentials and modulus)
Further Practice
- Practise Questions
EXTENSION MATERIALS
Other Videos & Multimedia
How all Calculators should look
5.1 Functions as Graphs
TEACHING VIDEOS, EXERCISES & ACTIVITIES
Tutorial Videos
Functions and Graphs | Precalculus by The Organic Chemistry Tutor
Evaluating with function notation by Khan Academy
Corbett Maths Drawing Functions
Online Platforms (with Videos & Exercises)
- Khan Academy
- Evaluating functions: Videos & practice
Activities
- WW Functions as Graphs ppt (see Worksheets for accompanying worksheets)
- Math = Love (Sarah Carter)
- Interactive Maths
- Function Graphs & Important Points: Video
- Go Teach Maths
- Desmos
- Function Carnival (watch a video and graph what you see)
Worksheets
Dr Frost resources
Dr Frost Video
Dr Frost Slides & Activities
- Slides & Worksheet
Topic Test
- Standard Test
Extra Questions
- Dr Frost Questions
Key Skills
Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost
- 433a: Determine the output of a function using a graph. (not yet active)
- 433b: Determine the roots of a function using a graph. (not yet active)
- 433c: Solve f(x) = k, for some fixed k, using a graph.
- 433d: Solve f(x) = k, using a graph, where k must be calculated. (not yet active)
- 433e: Solve f(x) = g(x), using a graph, where y=g(x) must be drawn. (not yet active)
- 433f: Determine the range of values of k for which f(x) = k has a particular number of solutions. (not yet active)
- 438a: Recognise odd functions and even functions from their graphs. (not yet active)
- 438b: Determine if a function is odd, even or neither from its algebraic definition. (not yet active)
- 438c: Recognise periodic functions from their graphs. (not yet active)
- 433: Exam Practice: Graph representation of functions
- 438: Exam Practice: Properties of functions
Further Practice
- Practise Questions
EXTENSION MATERIALS
Whole Topic Summary Resources (Including Past Paper Questions)
Download Functions PPQs as WW Powerpoint for Edexcel IGCSE, AQA GCSE, Edexcel GCSE or OCR GCSE (or all GCSE together)
Other Whole Topic Resources
Acute Learning Problem Pairs
- Functions as PowerPoint or PDF
Worksheets
- Dr Austin Maths
- Corbettmaths
- Function Notation Practice Questions & Solutions
- Maths 4 Everyone
- Andy Lutwyche
- Mathshelper (Jon Stone)
- MathedUp
- Functions: Worksheet · Practice · Quiz · Exam · Question Gallery
- Function Machines: Worksheet · Practice · Quiz · Question Gallery
- Functions, Domain & Range: Worksheet · Practice · Quiz · Question Gallery
- Composite & Inverse Functions: Worksheet · Practice · Quiz · Question Gallery
- Mathsaurus (Kevin Olding)
- Physics & Maths Tutor
- MME
- @taylorda01
- transfinite
- 1st Class Maths
Activities
- Don Steward
- Transum
- Interactive Maths
- Function Notation Revision: Video
- Go Teach Maths
- Johnathan Byrne
- Tristan Jones
- Dr Austin Maths
External
- NCETM
- AQA (All About Maths)
- Bridging the Gap Pocket 2: Function Notation (AQA KS3-4 Bridging the Gap)
✦ Links marked ✦ are also featured and recommended by Jo Morgan on Resourceaholic.