Prior content: A2 Integration (See Modelling with Integration),
Previous Section: Differential Equations
Next Section: Core Pure 1 & 2 General Support
Contents
- Whole Topic Notes
- 8A Modelling with First Order Differentials
- 8B Simple Harmonic Motion
- 8C Part 1 Damped Harmonic Motion
- 8C Part 2 Forced Harmonic Motion
- 8D Coupled Differential Equations
- 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 A2 Core Pure Modelling with Differential Equations Section
- Dr Frost A2 Core Pure Modelling with Differential Equations Slides
- Blank Notes to Follow Slides Word Doc or PDF (Courtesy of King’s Chester Maths Department)
Acute Learning Whole Chapter Problem Pairs
Notes
- Physics & Maths Tutor
- CP2 Ch.8 Modelling with Differential Equations: Cheat sheet
8A Modelling with First Order Differentials
Textbook resources
Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.
Dr Frost resources
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
- 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
Other resources
3Blue1Brown Linear transformations and matrices | Chapter 3, Essence of linear algebra
Alternative Handouts
- Acute Learning Problem Pairs as PowerPoint or PDF
Online Platform
- Bossmaths interactive 2×2 transformations and questions
Online Platforms
- Khan Academy
- Exponential models & differential equations: Videos & practice
- The logistic differential equation: Videos & practice
Worksheets
- MadAsMaths (T. Madas)
- First Order Differential Equations Exam Questions Q3, 8 (difficulty 2–3 of 5)
- Differential Equations in Context With Modelling Q45 (difficulty 5 of 5)
- Dynamics with Harder ODEs (M4/M6) Q1–3, 6–8, 10–12, 16, 18, 19 (difficulty 2–4 of 5)
8B Simple Harmonic Motion
Textbook resources
Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.
Dr Frost resources
Download Blank Notes
(Courtesy of King’s Chester Maths Department)
Download Slides
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
- 741a: Determine the period of oscillation of a particle with SHM given the amplitude and maximum speed. (not yet active)
- 741b: Determine the speed of a particle with SHM at a particular displacement, given the amplitude and maximum speed. (not yet active)
- 741c: Determine the time taken for a particle with SHM to move between different displacements, given the amplitude and maximum speed. (not yet active)
- 741d: Determine the period of oscillation of a particle with SHM given the the mass of a particle and a force in the form kx (not yet active)
- 741e: Determine the period of oscillation of a particle with SHM given the maximum acceleration and maximum speed. (not yet active)
- 741f: Determine the amplitude of oscillation of a particle with SHM given the maximum acceleration and maximum speed. (not yet active)
- 741g: Determine the time taken for a particle with SHM to move between different displacements given the maximum acceleration and maximum speed. (not yet active)
- 741h: Determine the amplitude of motion of a particle with SHM given the period and maximum speed. (not yet active)
- 741: Exam Practice: Simple Harmonic Motion (excluding springs) (not yet active)
Other resources
Alternative Handouts
- Acute Learning Problem Pairs as PowerPoint or PDF
Online Platform
- Bossmaths interactive 2×2 transformations and questions
Activities
- PhET Interactive Simulations
- PhET Masses and Springs Interactive Simulation (embedded below)
8C Part 1 Damped Harmonic Motion
Textbook resources
Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept. Up to 17:03
Dr Frost resources
Download Blank Notes
(Courtesy of King’s Chester Maths Department)
Download Slides
Extra Questions
- Dr Frost Questions (very short)
Key Skills
Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost
- 742a: Form a second-order differential equation involving a damping force on an oscillation. (not yet active)
- 742b: Determine whether damped motion is heavy damping, critical damping or light damping using its second-order differential equation. (not yet active)
- 742c: Determine the equation of motion for damped oscillations. (not yet active)
- 742d: Determine the period of the motion of damped oscillations. (not yet active)
- 742: Exam Practice: Modelling damped oscillations using second order differential equations (not yet active)
Other resources
Alternative Handouts
- Acute Learning Problem Pairs as PowerPoint or PDF
Online Platform
- Bossmaths interactive 3×3 transformations and questions
Worksheets
- MadAsMaths (T. Madas)
- Dynamics with Harder ODEs (M4/M6) Q4, 5, 9, 13–15 (difficulty 3–4 of 5)
8C Part 2 Forced Harmonic Motion
Textbook resources
Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept. From 17:03
Dr Frost resources
Download Blank Notes
(Courtesy of King’s Chester Maths Department)
Download Slides
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
- 743a: Form a second-order differential equation involving forced harmonic motion. (not yet active)
- 743b: Determine the equation of motion for forced harmonic motion. (not yet active)
- 743: Exam Practice: Modelling forced harmonic motion using non-homogeneous second order differential equations (not yet active)
Other resources
Alternative Handouts
- Acute Learning Problem Pairs as PowerPoint or PDF
Online Platform
- Bossmaths interactive 2×2 transformations and questions
Worksheet & Activities
- MEI activities from old FP1
Worksheets
- MadAsMaths (T. Madas)
- Second Order Differential Equations Exam Questions Standard Questions Q6 (difficulty 3 of 5)
- Dynamics with Harder ODEs (M4/M6) Q17 (difficulty 4 of 5)
8D Coupled Differential Equations
Textbook resources
Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.
Dr Frost resources
Download Blank Notes
(Courtesy of King’s Chester Maths Department)
Download Slides
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
- 744a: Understand and form Lotka-Volterra (predator-prey) equations. (not yet active)
- 744b: Use homogeneous coupled differential equations to form a single second order differential equation. (not yet active)
- 744c: Find a general solution for x in terms of t for homogeneous coupled differential equations. (not yet active)
- 744d: Find a general solution for y in terms of t for homogeneous coupled differential equations, given the solution for x (not yet active)
- 744e: Use non-homogeneous coupled differential equations to form a single second order differential equation. (not yet active)
- 744f: Find a general solution for x in terms of t for non-homogeneous coupled differential equations. (not yet active)
- 744g: Find a general solution for y in terms of t for non-homogeneous coupled differential equations, given the solution for x (not yet active)
- 744h: Determine particular solutions to non-homogenous coupled differential equations and find the output for a given input. (not yet active)
- 744i: Suggest limitations of the solutions to Lotka-Volterra equations. (not yet active)
- 744: Exam Practice: Coupled first order linear differential equations (no use of eigenvalues)
Other resources
Alternative Handouts
- Acute Learning Problem Pairs as PowerPoint or PDF
Activities
- Ben Sparks (GeoGebra)
- Coupled Differential Equations: GeoGebra
Worksheets
- MadAsMaths (T. Madas)
- Second Order Differential Equations Exam Questions Standard Questions Q8–11 (difficulty 3–4 of 5)
Whole Topic Summary Resources (Including Past Paper Questions)
External whole topic past paper style questions
- WW Dr Frost Style QQQs (Version 1) Word Doc, PDF (Q’s Only) or PDF (Q’s & Sol.)
- WW Dr Frost Style QQQs (Version 2) Word Doc, PDF (Q’s Only) or PDF (Q’s & Sol.)
- Advanced Highers Matrices Exam Questions & Answers
Activities
- NRICH (student problems)
Worksheets
- Jethwa Maths
- 10 Minute Starters: Modelling with Differential Equations
- Physics & Maths Tutor
- CP2 Ch.8 Modelling with Differential Equations: Questions by topic