Prior Content: GCSE Iterations
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Next Section: Integration
Contents
- Whole Topic Notes
- 10A Roots within Intervals
- 10B Iterations
- 10C Newton Raphson
- 10D 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 Numerical Methods Section
- Dr Frost Numerical Methods 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
- Ch.10 Numerical Methods: Cheat sheet
10A Roots within Intervals
Textbook resources
Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.
Dr Frost resources
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
Exam Practice
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
- 441b: Appreciate the significance of a sign change in identifying an interval for the root of an equation.
- 609a: Appreciate the significance of a sign change in identifying an interval for the root of a more advanced equation. (not yet active)
- 441: Exam Practice: Fixed point iteration to approximate a solution to an equation
- 609: Exam Practice: (Fixed point) iteration on more advanced functions and use of cobweb and staircase diagrams
Further Practice
Other resources
Other Videos
Courtesy of Maths Genie
Alternative Handouts
Activities
Worksheets
- Jethwamaths Starter Activity (P3-4)
- Solomon Numerical Methods A Questions✦ & Solutions✦
- Physics & Maths Tutor
- Location of Roots: Questions 2021–24 · Mark scheme · Model answers · Questions 2018–21 (with MS) · Model answers
- MadAsMaths (T. Madas)
- Numerical Solutions Of Equations Iterative Methods Q30 (difficulty 4 of 5)
Online Platforms
- Khan Academy
- The intermediate value theorem: Videos & practice
10B Iterations
Textbook resources
Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.
Dr Frost resources
Dr Frost Video
- Topic Video (up to 4:28)
Bicen Maths Live Lesson
Download Blank Notes
(Courtesy of King’s Chester Maths Department)
Download Slides
Exam Practice
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
- 441a: Rearrange an equation into the form x = g(x) (‘fixed point iteration’) for subsequent use in an iterative method.
- 441c: Approximate a solution to an equation using (fixed point) iteration.
- 609b: Form an iterative formula that would enable the root of the function to be found. (not yet active)
- 609c: Use an iterative formula involving ln(x), ex, sec, textrmcosec, cot or inverse trigonometric functions. (not yet active)
- 609d: Form an iterative formula to that would enable a point of intersection of two curves to be found. (not yet active)
- 609e: Form an iterative formula to determine a turning point or where the gradient is a given value. (not yet active)
- 609f: Justify that a solution found from iteration is correct to a given number of decimal places. (not yet active)
- 609g: Use a cobweb or staircase diagram to determine whether an iterative formula will converge to the root. (not yet active)
- 609h: Use ≤ft|f'(a)right| < 1 to determine whether an iterative formula will converge to the root. (not yet active)
- 441: Exam Practice: Fixed point iteration to approximate a solution to an equation
- 609: Exam Practice: (Fixed point) iteration on more advanced functions and use of cobweb and staircase diagrams
Further Practice
Other resources
Other Videos
Courtesy of Maths Genie
Alternative Handouts
Activities
- Berwick Maths Diagnostic Questions
- MEI Investigating Iterative Formulae✦
- whitwortht89 Cobweb Diagrams✦ (TES Account Required)
- Transum
- Goal Free Problems
Worksheets
- Jethwamaths Starter Activity (P1-2) & Topic Test (p1-2)
- Solomon Numerical Methods B Questions✦ & Solutions✦
- Solomon Numerical Methods C Questions✦ & Solutions✦
- Solomon Numerical Methods D Questions✦ & Solutions✦
- PMT PPQs Location of Roots & Iterations✦
- Mathshelper (Jon Stone)
- Naiker Maths
- Locating Roots & Iteration: Exam Qs 2005–11 · Exam Qs 2012–17 · Mark scheme
- Physics & Maths Tutor
- Iterative Equations: Questions 2021–24 · Mark scheme · Model answers · Questions 2018–21 (with MS) · Model answers
- MadAsMaths (T. Madas)
- Numerical Solutions Of Equations Iterative Methods Q1–29, 31–33, 35 (difficulty 2–5 of 5)
10C Newton Raphson
Textbook resources
Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.
Dr Frost resources
Dr Frost Video
- Topic Video (up to 4:28)
Bicen Maths Live Lesson
Download Blank Notes
(Courtesy of King’s Chester Maths Department)
Download Slides
Exam Practice
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
- 611a: Use a given point and given gradient to perform one iteration of the Newton-Raphson method. (not yet active)
- 611b: Understand the conditions under which the Newton-Raphson method fails. (not yet active)
- 611c: Form an iterative formula using the Newton-Raphson method. (not yet active)
- 611d: Use the Newton-Raphson method to find the root of a function. (not yet active)
- 611e: Use the Newton-Raphson method to find the solution of an equation given in the form f(x) = g(x) (not yet active)
- 611f: Use the Newton-Raphson method to find the turning point of a graph. (not yet active)
- 611: Exam Practice: Solving equations using the Newton-Raphson method (Newton’s method)
Further Practice
Other resources
Other Videos
Courtesy of Maths Genie
Alternative Handouts
Activities
Worksheets
- Jethwamaths Starter Activity (P7-8) & Topic Test (p3-4)
- Naiker Maths
- Newton-Raphson Method: Exam Qs 2005–11 · Mark scheme
- Physics & Maths Tutor
- Newton Raphson: Questions 2021–24 · Mark scheme · Model answers · Questions 2018–21 (with MS) · Model answers
- MadAsMaths (T. Madas)
- Differentiation II Exam Questions Q247 (difficulty 5 of 5)
- Numerical Solutions Of Equations Newton–Raphson Method Q1–13 (difficulty 2–4 of 5)
- Advanced Mensuration Q9 (difficulty 5 of 5)
10D Context
Textbook resources
Tutorial Videos
Edexcel A level Maths: 10.4 Numerical Methods Application to Modelling by Zeeshan Zamurred
Dr Frost resources
Bicen Maths Live Lesson
Download Blank Notes
(Courtesy of King’s Chester Maths Department)
Download Slides
Key Skills
No Key Skills Yet
Other resources
Whole Topic Summary Resources (Including Past Paper Questions)
Download PPQs as WW Powerpoint for A2 Numerical Methods
External Whole Topic Past Paper Style Questions
- Jethwa Maths Topic Tests & Starter Activities
- OCR
- Dr Frost Topic Test✦ (Teacher Login Required)
- PMT
- Pret Homework (@DrBennison)
- Numerical Methods (@DrBennison, docx)
Activities
- NRICH (student problems)
- The Chalkface
- Numerical Methods Gun Running: PDF
- MEI
- SRWhitehouse
- Andy Lutwyche
Worksheets
- MathedUp
- Maths Genie
- Numerical Methods: Questions · Solutions · Lesson · Topic page
- Jethwa Maths
- Year 2 Numerical Methods: Worksheets · Unit Test
- Mathsaurus (Kevin Olding)
- MME
- Dr Oliver Mathematics
- Dr Austin Maths
✦ Links marked ✦ are also featured and recommended by Jo Morgan on Resourceaholic.