Prior Content: IGCSE Differentiation, AS Co-Ordinate Geometry
Previous Section: Vectors
Next Section: Integration
Contents
- Whole Topic Notes
- 12B First Principles
- 12C General Rules
- 12D Multiple Terms
- 12E Preparing for Calculus
- 12F Tangents & Normals
- 12G Increasing & Decreasing Functions
- 12J Graphing the Gradient Function
- 12H Second Derivatives
- 12I Stationary Points
- 12K Differentiation in Context
- Whole Topic Summary Resources (Including Past Paper Questions)
Whole Topic Notes
Download Full Topic Slides
- Textbook Notes as PPTs (Courtesy of Owen134866)
Full Notes to Accompany Slides
Dr Frost
- Dr Frost Differentiation Section
- Dr Frost Differentiation Slides
- Blank Notes to Follow Slides Word Doc or PDF (Courtesy of King’s Chester Maths Department)
Acute Learning Whole Chapter Problem Pairs
12B First Principles
Textbook resources
Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.
Dr Frost resources
Dr Frost Video
Bicen Maths Live Lesson
Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths
Download Blank Notes
(Courtesy of King’s Chester Maths Department)
Download Slides
Extra Resources
- Just for your Interest: Why can’t we immediately make h zero in differentiation by first principles?
Topic Tests
Extra Questions
Key Skills
- No Key Skills Yet
Further Practice
Other resources
Other Videos
Courtesy of Maths Genie
Khan Academy introducing Differentiation
Alternative Handouts
- Acute Learning Problem Pairs as PowerPoint or PDF
Activities
- WW First Principles Scaffolding Word Doc & PDF
- MEI Geogebra Resource Introducing Concept Through Secants
- Applications on wyzant
Worksheets
- Jethwa Maths Worksheet (p1-2)
- Maths Genie Worksheet & Solutions
- Mathsaurus Mixed Exam Board Questions (no solutions)
- RIMT Worked Examples and Questions
12C General Rules
Textbook resources
Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.
Dr Frost resources
Dr Frost Video
- Topic Video (Some elements of 12D too)
Bicen Maths Live Lesson
Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths
Download Blank Notes
(Courtesy of King’s Chester Maths Department)
Download Slides
Extra Questions
Key Skills
Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost
- 585 Differentiate a single term in the form axb.
Differentiation Key Skills Section (for selecting more than one)
Other resources
Other Videos
Courtesy of Maths Genie (Up to 3:00)
Alternative Handouts
- Acute Learning Problem Pairs as PowerPoint or PDF
Note: a lot of activities for this section can be taken from the start of worksheets/ activities from the next section: 12D Multiple terms
12D Multiple Terms
Textbook resources
Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept. (Up to 4:14)
Dr Frost resources
Dr Frost Video
Bicen Maths Live Lesson
Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths
Download Blank Notes
(Courtesy of King’s Chester Maths Department)
Download Slides
Topic Tests
Extra Questions
Key Skills
Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost
- 586 Differentiate a collection of terms in the form axb.
- 593 Differentiate an expression requiring bracket expansion.
- Combination of all
Differentiation Key Skills Section (for selecting more than one)
Further Practice
Other resources
Other Videos
Alternative Handouts
- Acute Learning Problem Pairs as PowerPoint or PDF
Online Platforms (with Videos & Exercises)
- Khan Academy Lesson (Extends Into Tangents)
Activities
- Standards Unit Matching Functions and Derivatives (Finding Gradients at Certain Points)
Worksheets
- Dr Austin Maths
- Differentiation by Rule Practice Strips (Editable Word | PDF | Answers)
- Jethwa Maths Starter Activities (p1-6 & 17-18) some of 12E included
- kutasoftware Power, Constant, and Sum Rules 1
12E Preparing for Calculus
Textbook resources
Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept. (From 4:14)
Dr Frost resources
Dr Frost Video
- Topic Video (from 8:35)
Bicen Maths Live Lesson
Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths
Download Blank Notes
(Courtesy of King’s Chester Maths Department)
Download Slides
Topic Tests
Extra Questions
Key Skills
Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost
- 762 Write a Collection of Terms in the Form axb.
- K207d Write a Fraction With an Algebraic Term on the Denominator as a Power of x.
- 587 Differentiate a collection of terms in the form axb that may require rearrangement.
- 593 Differentiate an expression requiring bracket expansion.
- 594 Differentiate an expression written as a fraction with a single term on the denominator.
- K338e: Differentiate xn to find the gradient of a curve at a given point.
- Combination of all
Differentiation Key Skills Section (for selecting more than one)
Further Practice
Other resources
Other Videos
Alternative Handouts
- Acute Learning Problem Pairs as PowerPoint or PDF
Activities
- Matching Cards MEI
- Rewriting to Differentiate and Integrate Standard Units
Worksheets
- Dr Austin Maths
- Harder Differentiation by Rule Practice Strips (Editable Word | PDF | Answers)
- Harder Differentiation Match-Up (Editable Word | PDF | Answers)
- Maths4Everyone Differentiation of Polynomials (TES Account Required)
- martahidegkuti.com Differentiation Practice
- WW Rewriting Word Doc, PDF & Answers
- karel Writing Exponential Equations in the Form ax^n (TES Account Required)
- Solomon C1 Differentiation B (Covering Sections C, D, E & H) & Solutions
- kutasoftware Power, Constant and Sum Rules 2
- PMT PPQs
- Edexcel C1
- Edexcel C2
- OCR MEI C2 and Answers (1)
- OCR MEI C2 and Answers (2)
- OCR MEI C2 and Answers (3)
12F Tangents & Normals
Textbook resources
Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.
Dr Frost resources
Dr Frost Video
Bicen Maths Live Lesson
Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths
Download Blank Notes
(Courtesy of King’s Chester Maths Department)
Download Slides
Topic Tests
Extra Questions
Key Skills
Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost
- 596 Find an equation of a tangent to a curve.
- 597 Find an equation of a normal to a curve.
- Combination of all
Differentiation Key Skills Section (for selecting more than one)
Further Practice
Other resources
Alternative Handouts
- Acute Learning Problem Pairs as PowerPoint or PDF
Activities
- Desmos Tangents and Normals Lesson by Jo Hill
Worksheets
- Jethwa Maths Starter Activities (p7-10)
- Solomon C1 Differentiation C & Solutions
- naikermaths PPQ Booklet & Solutions
- PMT PPQs
- Edexcel C1
- Edexcel C2
- OCR MEI C2 and Answers (1)
- OCR MEI C2 and Answers (2)
- OCR MEI C2 and Answers (3)
- OCR MEI C2 and Answers (4)
12G Increasing & Decreasing Functions
Textbook resources
Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.
Dr Frost resources
Dr Frost Video
Bicen Maths Live Lesson
Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths
Download Blank Notes
(Courtesy of King’s Chester Maths Department)
Download Slides
Topic Tests
Extra Questions
Key Skills
Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost
- 620 Increasing and decreasing cubic functions.
Differentiation Key Skills Section (for selecting more than one)
Further Practice
Other resources
Other Videos
Alternative Handouts
- Acute Learning Problem Pairs as PowerPoint or PDF
Activities
- undergroundmathematics.org Increasing and Decreasing Functions Activity
Worksheets
- Jethwa Maths Starter Activities (p11-12)
Extension/ Further Interest
- kutasoftware Intervals of Increase and Decrease (Ignore Q4 and 7)
12J Graphing the Gradient Function
Textbook resources
Dr Frost resources
Other resources
12H Second Derivatives
Textbook resources
Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.
Dr Frost resources
Dr Frost Video
- Topic Video (up to 3:43)
Bicen Maths Live Lesson
Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths
Download Blank Notes
(Courtesy of King’s Chester Maths Department)
Download Slides
Extra Resources
- Just for your Interest: Why do we put the squareds where they are in the second derivative, d2y/dx2?
Extra Questions
Key Skills
Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost
- 621 Find the second derivative of a function.
Differentiation Key Skills Section (for selecting more than one)
Other resources
Alternative Handouts
- Acute Learning Problem Pairs as PowerPoint or PDF
Worksheets
- kutasoftware Higher Order Derivatives
12I Stationary Points
Textbook resources
Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.
Dr Frost resources
Dr Frost Video
Whole Topic Video (from 3:43) Second Derivatives
Whole Topic Video (up to 7:48) Maxima & Minima
Bicen Maths Live Lesson
Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths
Download Blank Notes
(Courtesy of King’s Chester Maths Department)
Download Slides
Topic Tests
- Standard Test (Understand and use the second derivative of a function.)
- Advanced Test (Understand and use the second derivative of a function.)
- Standard Test (Maxima and minima and stationary points.)
- Advanced Test – NOT Q4, 6, 7 (Maxima and minima and stationary points.)
Extra Questions
Key Skills
Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost
- 715 Find Coefficients of a Cubic Equation Given a Turning Point.
- 814 Determine Whether a Stationary Point is a Maximum or a Minimum.
- 811 Determine the Interval for Which a Cubic function is Increasing or Decreasing.
- Combination of All
- K341a Determine the Stationary Points of a Curve.
Differentiation Key Skills Section (for selecting more than one)
Further Practice
- Practise Questions (Understand and use the second derivative of a function.)
- Practise Questions (Maxima and minima and stationary points.)
Other resources
Other Videos
Alternative Handouts
- Acute Learning Problem Pairs as PowerPoint or PDF
Activities
- Underground Maths: Floppy Hair
Worksheets
- Dr Austin Maths
- Stationary Points Practice Strips (Editable Word | PDF | Answers)
- Stationary Points Fill In The Blanks (Editable Word | PDF | Answers)
- Jethwa Maths Starter Activities (p15-16 & 19-20)
- Solomon C2 Differentiation A & Solutions
- PMT PPQs
- Edexcel C1
- Edexcel C2
- OCR MEI C2 and Answers (1)
- OCR MEI C2 and Answers (2)
- OCR MEI C2 and Answers (3)
12K Differentiation in Context
Textbook resources
Dr Frost resources
Other resources
Alternative Handouts
- Acute Learning Problem Pairs as PowerPoint or PDF
Activities
- thechalkface Baked Beans Optimisation ppt and Worksheet for Tins in General, Oil Drum
Worksheets
- Dr Austin Maths
- Applied Calculus Problems Practice Strips (Editable Word | PDF | Answers)
- Jethwa Maths Starter Activities (p13-14)
- naikermaths PPQ Booklet and Solutions
- Mathsaurus Mixed Exam Board Questions (No Solutions)
- Solomon C2 Differentiation B and Solutions
Whole Topic Summary Resources (Including Past Paper Questions)
Download PPQs as WW Powerpoint for AS Differentiation
Whole Topic Videos
Bicen Maths Exam Questions
External Whole Topic Past Paper Style Questions
- Jethwa Maths Worksheet & Topic Test
- Maths Genie Worksheet & Solutions
- Dr Frost Topic Test (Teacher Login Required)
- Dr Frost Full coverage (Year 1)
- Mathsaurus Mixed Exam Board Questions (No Solutions), Covers All Except Modelling and First Principles
- Solomon C2 Differentiation C and Solutions
- PMT C1 PPQ by Topic
- PMT C2 PPQ by Topic