Prior content: A2 Integration
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Contents
- Whole Topic Notes
- 3A Improper Integrals
- 3B Mean Value of a Function
- 3C Differentiating Inverse Trig Functions
- 3D Integrating with Trig Substitutions
- 3E Integrating with Partial Fractions
- 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 AS Core Pure Methods in Calculus Section
- Dr Frost AS Core Pure Methods in Calculus 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.3 Methods in Calculus: Cheat sheet
3A Improper Integrals
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
- 726a: Determine an improper integral where one of the bounds is infinity. (not yet active)
- 726b: Determine an improper integral for a finite range that extends over a discontinuity. (not yet active)
- 726c: Determine an improper integral from negative infinity to positive infinity. (not yet active)
- 726d: Determine an improper integral that requires splitting into partial fractions. (not yet active)
- 726: Exam Practice: Improper integrals where one of the limits extends to infinity
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
- Improper integrals: Videos & practice
Worksheets
- MadAsMaths (T. Madas)
- Integration Exam Questions Part I Q249, 292, 310, 332 (difficulty 5 of 5)
- Improper Integrals Q1–12 (difficulty 3–5 of 5)
- Integration Exam Questions Part II Q70, 81, 109, 135 (difficulty 4–5 of 5)
- Reduction Formulae Q15 (difficulty 3 of 5)
3B Mean Value of a Function
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
- 728a: Determine the mean value of a function involving simple polynomials or expressions given in the form (ax + b)n (not yet active)
- 728b: Determine the mean value of more general functions. (not yet active)
- 728c: Determine the mean value of a function requiring integration by substitution. (not yet active)
- 728d: Determine the mean value of a function involving functions given in the form 1/a2 – x2 and 1/a2 + x2 (not yet active)
- 728: Exam Practice: Mean value of a function
Other resources
Alternative Handouts
- Acute Learning Problem Pairs as PowerPoint or PDF
Online Platform
- Bossmaths interactive 2×2 transformations and questions
Online Platforms
- Khan Academy
- Average (mean) value of a function: Videos & practice
Worksheets
- MadAsMaths (T. Madas)
- Improper Integrals Q6–7 (difficulty 3 of 5)
- Integration Exam Questions Part II Q8 (difficulty 2 of 5)
3C Differentiating Inverse Trig Functions
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 (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
- 608a: Differentiate inverse trigonometric functions directly. (not yet active)
- 608b: Differentiate a product or quotient involving an inverse trigonometric function. (not yet active)
- 608c: Differentiate composite functions using standard results for inverse trigonometric functions. (not yet active)
- 608d: Determine the equation of a tangent or normal to an inverse trigonometric curve. (not yet active)
- 608: Exam Practice: Differentiating inverse trigonometric functions
Other resources
Alternative Handouts
- Acute Learning Problem Pairs as PowerPoint or PDF
Online Platform
- Bossmaths interactive 3×3 transformations and questions
Online Platforms
- Khan Academy
- Derivatives of inverse trig functions: Videos & practice
Worksheets
- MadAsMaths (T. Madas)
- Integration Areas Q23 (difficulty 4 of 5)
- Integration Exam Questions Part I Q254, 313 (difficulty 5 of 5)
- Integration Exam Questions Part II Q12, 26, 37, 41, 58, 63, 66, 75, 104, 110, 118, 122, 129 (difficulty 2–5 of 5)
- Differentiation II Exam Questions Q131, 154, 162–163, 165, 168, 179, 184, 192, 212, 228, 230, 244 (difficulty 4–5 of 5)
- Implicit Equations Exam Questions Q59, 64 (difficulty 4 of 5)
- Trigonometric Inverse Functions Basic Questions Q21–22; Standard Questions Q2, 11, 13–15, 17–18; Hard Questions Q1, 8, 12–13, 15–16; Enrichment Questions Q3–4, 28–29 (difficulty 3–5 of 5)
- Differentiation Practice III (Hyperbolic & Inverse Functions) Q3
3D Integrating with Trig Substitutions
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
- 727a: Integrate functions given in the form 1/a2 + x2
- 727b: Integrate functions given in the form frac1√a2 – x2 (not yet active)
- 727c: Integrate functions given in the form 1/a2 – x2 (not yet active)
- 727d: Integrate functions given in the form 1/a2 – b2 x2 and frac1√a2 – b2 x2
- 727e: Integrate functions given in the form 1/a2 – b2 x2 and frac1√a2 – b2 x2 that first requires splitting a fraction. (not yet active)
- 727g: Integration functions using a substitution with subsequent inverse trigonometric results. (not yet active)
- 727: Exam Practice: Integrating functions given in the form 1/a2 – x2 and 1/a2 + x2
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
- Mathshelper (Jon Stone)
- MadAsMaths (T. Madas)
- Integration by Substitution Q12 · questions only
- Integration Exam Questions Part I Q244, 250–251, 256, 271, 276, 284, 291, 295, 297, 307, 321, 328 (difficulty 5 of 5)
- Integration Exam Questions Part II Q2–4, 6, 9–10, 16–19, 21, 25, 27–28, 32–33, 36, 38, 42–43, 47–51, 53, 56–57, 60, 67–68, 70, 73, 87, 91, 93, 111, 115–117, 120, 125–126 (difficulty 2–5 of 5)
- Definite Integration Megamix Part 2 · questions only
3E Integrating with Partial Fractions
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
- 621b: Determine an integral involving partial fractions where a factor in the denominator is in the form ax2 + c.
- 727f: Integrate functions requiring a split into partial fractions with subsequent inverse trigonometric results. (not yet active)
- 621: Exam Practice: Integration using partial fractions
- 727: Exam Practice: Integrating functions given in the form 1/a2 – x2 and 1/a2 + x2
Other resources
Alternative Handouts
- Acute Learning Problem Pairs as PowerPoint or PDF
Worksheets
- Mathshelper (Jon Stone)
- MadAsMaths (T. Madas)
- Algebraic Fractions Exam Questions Q15 (difficulty 3 of 5)
- Algebraic Fractions Partial Fractions Q13–16
- Integration Exam Questions Part II Q1, 5, 13, 24, 30, 40, 45, 65, 77–78, 80, 83, 96 (difficulty 2–5 of 5)
Online Platforms
- Khan Academy
- Integration with partial fractions: Videos & practice
Whole Topic Summary Resources (Including Past Paper Questions)
Download PPQs as WW Powerpoint for Core Pure Integration
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
- MathedUp
- Jethwa Maths
- 10 Minute Starters: Methods in Calculus
- Physics & Maths Tutor
- CP2 Ch.3 Methods in Calculus: Questions by topic
- MadAsMaths (T. Madas)
- Dr Austin Maths