Integration

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A2 Maths – Pure – Integration

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

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11A Slides (Courtesy of Owen134866)

Bicen Maths Live Lesson

Integration 1 • Standard Functions • P2 Ex11A • 🎲

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths

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• Dr Frost Slides 5-10✦

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

• 617a: Integrate trigonometric functions of the form k sin x
• 617b: Integrate other standard functions (no chain rule).
• 617c: Integrate standard functions first requiring bracket expansion (no chain rule).
• 617d: Determine a definite integral using trigonometric functions of the form k sin x
• 617e: Determine a definite integral using other standard functions (no chain rule).
• 617f: Use a known definite integral value to determine an unknown constant or bound, involving standard functions (no chain rule).
• 617: Exam Practice: Integrating exponential, trigonometric functions and 1/x

Other Videos

Trigonometric Integration 1

Courtesy of Maths Genie (1)

Exponential Integration

Courtesy of Maths Genie (2)

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Activities

• WW Kahoot Basic A2 integrals
• Berwick Maths Diagnostic Questions
• SRWhitehouse
  • Standard Integrals✦
• Ticktock Maths
  • Integrating Standard Functions lesson (slides)

Worksheets

• Solomon Integration A (exponentials and 1/x only) Questions and Solutions
• Dr Oliver Mathematics
  • Integrating e and ln exam questions✦ (solutions✦)
• MadAsMaths (T. Madas)
  • Integration Basics Q11–18 · questions only

A2 Maths – Pure – Integration f(ax+b)

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

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11B Slides (Courtesy of Owen134866)

Dr Frost Video

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Bicen Maths Live Lesson

Integration 2 • f(ax+b) type • P2 Ex11B • 🎲

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths

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• Dr Frost Slides 11-13✦

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

• 618a: Integrate expressions given in the form (x + b)ⁿ
• 618b: Integrate expressions given in the form (ax + b)ⁿ
• 618c: Integrate expressions given in the form a/(bx+c)ⁿ
• 618d: Integrate other standard functions given in the form f(ax+b), including 1/ax+b
• 618i: Calculate a definite integral involving integration by inspection.
• 618: Exam Practice: Integration by inspection

Other Videos

Integration by Reversing the Chain Rule

Courtesy of Maths Genie

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Activities

• WW Kahoot Basic A2 Integrals with Chain Rule
• Berwick Maths Diagnostic Questions
• Ticktock Maths
  • Integrating f(ax+b) lesson (slides)

Worksheets

• Solomon Integration B (exponentials and 1/x only) Questions and Solutions
• Solomon Integration D (Q 1& 2 only, rest Trig Identities) Questions and Solutions
• Mathshelper (Jon Stone)
  • Integration By Reverse Chain Rule
• MadAsMaths (T. Madas)
  • Integration Basics Q1–20 · questions only
  • Integration Exam Questions Part I Q1, 5, 10, 13, 15, 20, 26, 40–41, 56 (difficulty 2–3 of 5)

A2 Maths – Pure – Integrating using the ln(f(x)) rule

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

Reverse chain rule integration

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11D Slides (Courtesy of Owen134866)

Dr Frost Video

• Topic Video (up to 4:28)

Bicen Maths Live Lesson

Integration 4 • Reverse Chain Rule pt. 1 • P2 Ex11D • 🎲

Integration 5 • Reverse Chain Rule pt. 2 • P2 Ex11D • 🎲

Integration 6 • Reverse Chain Rule (with trig) pt. 3 • P2 Ex11D • 🎲

Integration 7 • More Reverse Chain examples pt. 4 • P2 Ex11D • 🎲

Live Lessons Using Dr Frost Based Slides Courtesy of Bicen Maths

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• Dr Frost slides 17-22✦

Exam Practice

• Exam Practice

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

• 618e: Integrate expressions given in the form kf'(x)≤ft[ f(x) right]ⁿ by inspection.
• 618f: Integrate expressions given in the form kf'(x)/≤ft[ f(x) right]ⁿ by inspection.
• 618g: Integrate expressions given in the form k f'(x)/f(x)
• 618j: Calculate a definite integral involving integration by inspection that includes a tangent or normal.
• 618: Exam Practice: Integration by inspection

Further Practice

• Practise Questions

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Activities

• Berwick Maths Diagnostic Questions
• SRWhitehouse
  • Integration by recognition matching activity✦
• Ticktock Maths
  • Reverse Chain Rule lesson (slides)

Worksheets

• Solomon Integration E Q7 only Questions and Solutions (Mainly Substitution, but Mainly Can be Done by Spotting Derivatives Instead)
• Mathshelper (Jon Stone)
  • Integration By Inspection
• MadAsMaths (T. Madas)
  • Integration by Reverse Chain Rule Q1–9 · questions only
  • Integration Exam Questions Part I Q120, 143–144, 147, 184, 191, 209, 215, 304, 308 (difficulty 4–5 of 5)

A2 Maths – Pure – Integrating using Trig Identities

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

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11C Slides (Courtesy of Owen134866)

Bicen Maths Live Lesson

Integration 3 • Using Trigonometric Identities • P2 Ex11C • 🎲

Live Lessons Using Dr Frost Based Slides Courtesy of Bicen Maths

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• Dr Frost Slides 14-16✦

Extra Questions

• Dr Frost Questions (Short)

Key Skills

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 618h: Integrate sin² x, cos² x, tan² x, cot² x
• 618: Exam Practice: Integration by inspection

Other Videos

Integration by Reversing the Chain Rule

Courtesy of Maths Genie (1)

The Integration of sin^2 x and cos^2 x

Courtesy of Maths Genie (2)

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Activities

• Berwick Maths Diagnostic Questions
• SRWhitehouse
  • Further trig integration✦
• Underground Mathematics
  • Trigsy integrals✦
  • Two for one✦
• Ticktock Maths
  • Using Trigonometric Identities lesson (slides)

Worksheets

• Solomon Integration D (Q 3 onwards) Questions and Solutions
• Unknown Author, good selection of Questions
• Mathshelper (Jon Stone)
  • Trigonometric Integration
  • Integrating Squares Of Trig Functions
• MadAsMaths (T. Madas)
  • Integration by Trigonometric Identities Q1–9 · questions only
  • Integration Exam Questions Part I Q11, 52, 59, 63, 78, 82, 90, 95, 109, 114, 127, 137, 171, 174, 203, 205, 207–208, 223, 230, 232, 241, 245, 252, 300, 302 (difficulty 2–5 of 5)

A2 Maths – Pure – Integration with Partial Fractions

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

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11G Slides (Courtesy of Owen134866)

Dr Frost Video

• Topic Video

Bicen Maths Live Lesson

Integration 18 • Using Partial Fractions • P2 Ex11G • 🎲

Integration 19 • Algebraic Division & Partial Fractions • P2 Ex11G • 🎲

Live Lessons Using Dr Frost Based Slides Courtesy of Bicen Maths

Download Blank Notes

(Courtesy of King’s Chester Maths Department)

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• Dr Frost Slides 40-45✦

Exam Practice

• Exam Practice

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

• 621a: Determine an integral involving partial fractions.
• 621b: Determine an integral involving partial fractions where a factor in the denominator is in the form ax² + c.
• 621c: Determine a definite integral involving partial fractions.
• 621d: Determine an indefinite or definite integral by use of a substitution followed by splitting into partial fractions.
• 621: Exam Practice: Integration using partial fractions

Further Practice

• Practise Questions

Other Videos

Integration Using Partial Fractions

Courtesy of Maths Genie

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Activities

• Berwick Maths Diagnostic Questions

Worksheets

• Solomon Integration C Questions and Solutions
• Naiker Maths
  • Partial Fractions in Integration: Exam Qs 2005–11 · Mark scheme · Exam Qs 2012–17 · Mark scheme
• MadAsMaths (T. Madas)
  • Integration by Partial Fractions Q1–5 · questions only
  • Integration Exam Questions Part I Q4, 6, 12, 17, 22, 29, 34–35, 37, 43, 47, 58, 60, 62, 69, 77, 81, 94, 97–98, 103, 111, 124, 160–161, 169, 179, 182, 190, 195, 212, 217, 234, 325 (difficulty 2–5 of 5)
  • Integration by a Special Manipulation · questions only

Past Paper Questions

• PMT
  • Edexcel
    • Integration using Partial Fractions
  • OCR
    • Integration by Partial Fractions

A2 Maths – Pure – Integrating by Parts

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

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11F Slides (Courtesy of Owen134866)

Dr Frost Video

• Topic Video

Bicen Maths Live Lesson

Integration 13 • By Parts pt. 1 • P2 Ex11F • 🎲

Integration 14 • By Parts (twice) pt. 2 • P2 Ex11F • 🎲

Integration 15 • By Parts (twice, second example) pt. 3 • P2 Ex11F • 🎲

Integration 16 • By Parts (lnx, definite) pt. 4 • P2 Ex11F • 🎲

Integration 17 • By Parts (weird question!) pt. 5 • P2 Ex11F • 🎲

Live Lessons Using Dr Frost Based Slides Courtesy of Bicen Maths

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(Courtesy of King’s Chester Maths Department)

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• Dr Frost Slides 31-39✦

Exam Practice

• Exam Practice

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

• 620a: Determine an integral using integration by parts (excluding ln(x)).
• 620b: Determine an integral involving ln(x)
• 620c: Determine an integral using integration by parts twice.
• 620d: Determine a definite integral or area under a graph using integration by parts.
• 620e: Determine an integral involving (ln(x))²
• 620f: Determine the area formed by a curve and a normal to the curve.
• 620g: Use a substitution to obtain an expression which can be integrated by parts.
• 620h: Determine a definite integral by use of a substitution followed by integration by parts.
• 620i: Determine an integral involving ln(x+k) (not yet active)
• 620: Exam Practice: Integration by parts

Further Practice

• Practise Questions

Other Videos

Integration by Parts

Courtesy of Maths Genie

I Integrate By Parts (Total Eclipse of the Heart Parody)

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Activities

• Berwick Maths Diagnostic Questions
• Underground Mathematics
  • Integral chasing II✦

Worksheets

• Solomon Integration F Questions and Solutions
• Jethwa Maths Worksheet (p10-13)
• Mathshelper (Jon Stone)
  • Integration By Parts
• Naiker Maths
  • Integration by Parts: Exam Qs 2005–11 · Mark scheme · Exam Qs 2012–17 · Mark scheme
• Physics & Maths Tutor
  • Integration by Parts: Questions 2021–24 · Mark scheme · Model answers · Questions 2018–21 (with MS) · Model answers
• Colemanweb
  • Integration by parts concept questions✦
• SRWhitehouse
  • Integration by parts worksheet✦
• MadAsMaths (T. Madas)
  • Integration Areas Q7, 11 (difficulty 3 of 5)
  • Integration by Parts Q1–9 · questions only
  • Integration Exam Questions Part I Q3, 8, 18–19, 32, 39, 55, 61, 64, 67, 71, 74–75, 79, 83, 99, 113, 119, 122–123, 126, 130, 132, 156, 173, 177, 189, 204, 207, 259, 267, 293, 299, 311 (difficulty 2–5 of 5)
  • Integration Exam Questions Part II Q90, 106 (difficulty 5 of 5)

Past Paper Questions

• PMT
  • Edexcel
    • Integration by Parts 1 · 2
  • OCR
    • Integration by Parts
  • OCR MEI
    • Integration by Parts

A2 Maths – Pure – Integrating by Substitution (Beginner)

A2 Maths – Pure – Integrating by Substitution (Advanced)

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

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11E Slides (Courtesy of Owen134866)

Dr Frost Video

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Bicen Maths Live Lesson

Integration 8 • By Substitution pt. 1• P2 Ex11E • 🎲

Integration 9 • By substitution (using implicit differentiation) pt. 2 • P2 Ex11E • 🎲

Integration 10 • By Substitution (with trig, with limits) pt. 3 • P2 Ex11E • 🎲

Integration 11 • By Substitution (difficult question) pt. 4 • P2 Ex11E • 🎲

Integration 12 • By Substitution (exam questions) pt. 5 • P2 Ex11E • 🎲

Live Lessons Using Dr Frost Based Slides Courtesy of Bicen Maths

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• Dr Frost Slides 23-30✦

Exam Practice

• Exam Practice

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

• 619a: Integrate expressions given in the form x(ax+b)ⁿ using a substitution.
• 619b: Integrate expressions given in the form sinⁿ(x) cos(x) using a substitution.
• 619c: Use a (non-trigonometric) substitution to integrate more general expressions.
• 619d: Determine a definite integral involving a (non-trigonometric) substitution.
• 619e: Use a trigonometric substitution to integrate more general expressions.
• 619f: Determine a definite integral involving a trigonometric substitution.
• 619g: Use a substitution u² = … to integrate an expression.
• 619: Exam Practice: Integration by substitution

Further Practice

• Practise Questions

Other Videos

Integration by u Substitution

Courtesy of Maths Genie (1)

Integration by u Substitution 2

Courtesy of Maths Genie (2)

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Activities

• Berwick Maths Diagnostic Questions
• Underground Mathematics
  • Integral sorting✦
  • Slippery areas✦

Worksheets

• Solomon Integration E Questions and Solutions
• Jethwa Maths Worksheet (p7-9)
• Naiker Maths
  • Integration by Substitution: Exam Qs 2005–11 · Mark scheme · Exam Qs 2012–17 · Mark scheme
• Physics & Maths Tutor
  • Integration by Substitution: Questions 2021–24 · Mark scheme · Model answers · Questions 2018–21 (with MS) · Model answers
• SRWhitehouse
  • Integration by substitution worksheet✦
  • Parts, substitution, recognition✦
• Colemanweb
  • How to get exam marks✦ (parts✦)
• MadAsMaths (T. Madas)
  • Integration Areas Q12, 20 (difficulty 3–4 of 5)
  • Integration by Substitution Q1–12 · questions only
  • Integration Exam Questions Part I Q2, 7, 9, 14, 16, 21, 23–24, 28, 30–31, 33, 36, 38, 42, 44–46, 49–51, 53–55, 57, 65–66, 70, 72, 74, 76, 84–88, 91–94, 96–97, 100–102, 104–107, 110, 112, 115–118, 121–122, 125–126, 128–130, 133–136, 138–141, 145–146, 148–151, 153–157, 160, 162–163, 165, 167–170, 172, 175–181, 183, 185–188, 190, 192–195, 197–202, 206, 208, 210–212, 214, 216–221, 226, 229, 234–235, 237–238, 243, 260, 263, 265, 267, 273, 278, 280–281, 285, 288–290, 330 (difficulty 2–5 of 5)

Past Paper Questions

• PMT
  • Edexcel
    • Integration by Substitution 1 · 2
  • OCR
    • Integration by Substitution
  • OCR MEI
    • Integration by Substitution

A2 Maths – Pure – Areas under a Parametric Curve

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

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*note some examples from notes come from old course textbook and are not covered in the video

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*note this was initially left out the textbook so the slides below are from the old course. These accompany the above notes handout (after Q1)

11H Slides (Courtesy of Owen134866)

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Bicen Maths Live Lesson

Integration 23 • Parametric • P2 Ex11 in slides • 🎲

Live Lessons Using Dr Frost Based Slides Courtesy of Bicen Maths

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• Dr Frost Slides 56-59✦

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

• 624a: Determine an indefinite integral using parametric equations.
• 624b: Determine the area between a parametric curve and the x-axis.
• 624c: Determine the area between a parametric curve and the y-axis. (not yet active)
• 624: Exam Practice: Integrating parametric equations

Further Practice

• Practise Questions

Other Videos

Parametric Integration – Finding the Area Under a Curve

Courtesy of Maths Genie

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Activities

• Berwick Maths Diagnostic Questions (Only 1 Q)
• SRWhitehouse
  • Parametric integration✦

Worksheets

• Solomon Integration G Questions and Solutions
• Edited PMT Edexcel PPQs from C4 Set Integration – Area with MS at end
• Madas Maths 68 Exam Questions
• Some extra questions are also in the old P3 textbooks, but contain volumes of revolutions as a part b, which should be ignored.
• Mathshelper (Jon Stone)
  • Parametric Integration
• Naiker Maths
  • Areas Under Parametric Curves: Exam Qs 2005–11 · Mark scheme · Exam Qs 2012–17 · Mark scheme
• Physics & Maths Tutor
  • Parametric Integration: Questions 2021–24 · Mark scheme · Model answers

A2 Maths – Pure – Integration to Calculate the Area Under a Curve

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

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11H Slides (Courtesy of Owen134866)

Bicen Maths Live Lesson

Integration 20 • Finding Areas • P2 Ex11H • 🎲

Live Lessons Using Dr Frost Based Slides Courtesy of Bicen Maths

Download Blank Notes

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• Dr Frost Slides 46-49✦

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

• 525i: Determine an area enclosed between a curve and the x-axis where the curve goes both above and below the axis.
• 525k: Determine the area between a curve and a line by subtraction of areas.
• 525l: Determine the area enclosed between two curves, where the bounds are given.
• 525m: Determine the area enclosed between two curves, where the bounds need to be determined.
• 525: Exam Practice: Evaluating definite integrals for powers of x, e.g. to find an area under a curve or area between curves

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Activities

• Berwick Maths Diagnostic Questions

Worksheets

• Solomon Integration H (mixed) Questions and Solutions
• Naiker Maths
  • Finding Areas Using Integration: Exam Qs 2005–11 · Mark scheme · Exam Qs 2012–17 · Mark scheme
• Physics & Maths Tutor
  • Finding Area using Integration: Questions 2021–24 · Mark scheme · Model answers · Questions 2018–21 (with MS) · Model answers
• MadAsMaths (T. Madas)
  • Integration Areas Q1–13, 15–22, 24–35 (difficulty 2–5 of 5)
  • Integration Exam Questions Part I Q83, 239, 257 (difficulty 3–5 of 5)

Past Paper Questions

• PMT
  • Edexcel
    • Finding Areas using Integration 1 · 2
  • OCR
    • Definite Integrals and Areas
  • OCR MEI
    • Integration as Inverse of Differentiation and to Find Area Under a Curve (Yr. 2)

A2 Maths – Pure – Trapezium Rule

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

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11I Slides (Courtesy of Owen134866)

Bicen Maths Live Lesson

Integration 22 • Trapezium Rule • P2 Ex11I • 🎲

Live Lessons Using Dr Frost Based Slides Courtesy of Bicen Maths

Download Blank Notes

(Courtesy of King’s Chester Maths Department)

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• Dr Frost Slides 50-55✦

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

• 625a: Use the trapezium rule (trapezoidal rule) with a given table of values. (not yet active)
• 625b: Use the trapezium rule (trapezoidal rule) where a table of values is first required. (not yet active)
• 625c: Determine when the trapezium rule (trapezoidal rule) will underestimate or overestimate an area under the graph. (not yet active)
• 625d: Explain how an estimate for the area using the trapezium rule (trapezoidal rule) could be made more accurate. (not yet active)
• 625e: Use an estimate for an area under a graph to estimate the area of a transformed function. (not yet active)
• 625: Exam Practice: The trapezium rule (trapezoidal rule)

Other Videos

The Trapezium Rule

Courtesy of Maths Genie

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Activities

• Berwick Maths Diagnostic Questions
• The Chalkface
  • Numerical Integration: Excel (if macros are blocked: right-click the file › Properties › tick Unblock)
• Ben Sparks (GeoGebra)
  • Numerical Integration Options: GeoGebra
• Transum
  • Trapezium Rule
• Underground Mathematics
  • Is the Serpentine Lake really 40 acres?✦
  • Underneath the arches✦

Worksheets

• Solomon Integration C (AS) Questions and Solutions
• Solomon Integration M (not Q5) Questions and Solutions
• PMT
  • Edexcel
    • Trapezium Rule 1 · 2
  • OCR
    • Numerical Integration
  • OCR MEI
    • Numerical Integration
• Mathshelper (Jon Stone)
  • Numerical Integration
• MathedUp
  • Trapezium rule: Questions · Challenge · Answers
• Naiker Maths
  • Trapezium Rule: Exam Qs 2005–11 · Mark scheme · Exam Qs 2012–17 · Mark scheme
• Physics & Maths Tutor
  • Trapezium Rule: Questions 2021–24 · Mark scheme · Model answers · Questions 2018–21 (with MS) · Model answers
• SRWhitehouse
  • Trapezium rule examples✦ (worksheet✦)
• phildb
  • Trapezium rule worksheet✦
• MadAsMaths (T. Madas)
  • Integration Exam Questions Part I Q27, 48, 80, 89, 131, 139, 142, 152, 158, 164 (difficulty 3–4 of 5)
  • Numerical Integration Trapezium Rule Q1–22 (difficulty 2–5 of 5)
• Pret Homework (@MissCarrollEcon)
  • Trapezium Rule (@MissCarrollEcon, pdf)

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

Tutorial Videos

A-Level Maths: H4-01 Integration: Integration as the Limit of a Sum

A-Level Maths: H4-01 Integration: Integration as the Limit of a Sum by TLMaths

Edexcel A level Maths: Areas as a Limit of a Summation

Edexcel A level Maths: Areas as a Limit of a Summation by Zeeshan Zamurred

Definite integral as the limit of a Riemann sum | AP Calculus AB | Khan Academy

Definite integral as the limit of a Riemann sum by Khan Academy

Download Blank Notes

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11L Slides (Courtesy of Owen134866)

Bicen Maths Live Lesson

Live Lessons Using Dr Frost Based Slides Courtesy of Bicen Maths

Download Blank Notes

(Courtesy of King’s Chester Maths Department)

Download Slides

• Dr Frost Slides 50-55

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

• 523a: Calculate the left Riemann sum of a given function with uniform partitions. (not yet active)
• 523b: Calculate the right Riemann sum of a given function with uniform partitions. (not yet active)
• 523c: Calculate the middle Riemann sum of a given function using the midpoint rule. (not yet active)
• 523d: Understand a definite integral as a Riemann sum in the limit where the rectangles become infinitely small. (not yet active)
• 523: Exam Practice: Riemann sums (not yet active)

Other Videos

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Past Paper Resources

• PMT
  • OCR MEI
    • Integration as the Limit of a Sum

A2 Maths – Pure – Solving Differential Equations

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

Download Blank Notes

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11J Slides (Courtesy of Owen134866)

Dr Frost Video

• Topic Video (examples 1 and 2 only from the video)

Bicen Maths Live Lesson

Integration 24 • Differential Equations • P2 Ex11J • 🎲

Live Lessons Using Dr Frost Based Slides Courtesy of Bicen Maths

Download Blank Notes

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• Dr Frost Slides 60-65✦

Exam Practice

• Exam Practice

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

• 622b: Solve differential equations given in the form dy/dx propto x and dy/dx propto y and appreciate their significance in modelling.
• 622c: Determine general solutions to differential equations involving general polynomial expressions in x and y, including roots and reciprocals
• 622d: Determine particular solutions to differential equations involving general polynomial expressions in x and y, including roots and reciprocals
• 622e: Solve a differential equation involving exponential functions.
• 622f: Solve a differential equation involving trigonometric functions.
• 622g: Solve a differential equation involving partial fractions.
• 622h: Solve a differential equation where factorisation is required to make the variables linearly separable.
• 622: Exam Practice: Solving linearly separable first order differential equations

Other Videos

Differential Equations

Courtesy of Maths Genie

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Activities

• Berwick Maths Diagnostic Questions
• Goal Free Problems
  • A-Level Algebra & Coordinate Geometry set Q25 | A-Level Basic Calculus set Q17
• MEI
  • The world population✦
• SRWhitehouse
  • Differential equations (SRWhitehouse on TES)✦

Worksheets

• Solomon Integration K Questions and Solutions
• Mathshelper (Jon Stone)
  • Differential Equations Worksheet
• MathedUp
  • Differential equations: Questions
• Mathsaurus (Kevin Olding)
  • Differential equations (exam questions)
• Naiker Maths
  • Differential Equations: Exam Qs 2005–11 · Mark scheme · Exam Qs 2012–17 · Mark scheme
• Physics & Maths Tutor
  • Solving Differential Equations: Questions 2021–24 · Mark scheme · Model answers
• Colemanweb
  • How to get exam marks✦
• MadAsMaths (T. Madas)
  • Differential Equations in Context Without Modelling Q1; With Modelling Q46, 48 (difficulty 2–5 of 5)
  • Separable Differential Equations General Solutions Q1–14; Specific Solutions Q1–78, 82 (difficulty 2–5 of 5)

A2 Maths – Pure – Differential Equations in Context

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

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11K Slides (Courtesy of Owen134866)

Dr Frost Video

• Topic Video (examples 3)

Bicen Maths Live Lesson

Integration 25 • Forming Differential Equations • P2 Ex11K • 🎲

Integration 26 • Further Differential Equation example • P2 Ex11K • 🎲

Live Lessons Using Dr Frost Based Slides Courtesy of Bicen Maths

Download Blank Notes

(Courtesy of King’s Chester Maths Department)

Download Slides

• Dr Frost Slides 66-69✦

Exam Practice

• Exam Practice

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

• 622a: Form a differential equation using provided relationships between variables/quantities.
• 622i: Use a model obtained from a first-order differential equation to find inputs, outputs and long-term behaviour.
• 622j: Use connected rates of change to form and solve a linear separable first-order differential equation. (not yet active)
• 623a: Understand the properties of logistic growth and how it forms the differential equation dP/dt = kP(a – P), and recognise the shape of the graph. (not yet active)
• 623b: Solve a logistic growth differential equation to obtain a logistic equation. (not yet active)
• 623c: Determine an output of a logistic model. (not yet active)
• 623d: Determine an input of a logistic model given the output. (not yet active)
• 623e: Determine the horizontal asymptote (carrying capacity) of a logistic model. (not yet active)
• 622: Exam Practice: Solving linearly separable first order differential equations
• 623: Exam Practice: Logistic models f(x) = fracL1 + Ce^-kx

Further Practice

• Practise Questions

Other Videos

Differential Equations

Courtesy of Maths Genie

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Activities

• Berwick Maths Diagnostic Questions
• CHar293 Matching Activity (TES Account Required)

Worksheets

• Solomon Integration L Questions and Solutions
• Jethwa Maths Worksheet (p17-21)
• MadAsMaths (T. Madas)
  • Differential Equations in Context Without Modelling Q2–29; With Modelling Q1–41, 43–44, 47; Related Variables Q1–22 (difficulty 2–5 of 5)

Past Paper Questions

• PMT
  • OCR
    • Differential Equations
  • OCR MEI
    • Differential Equations

A2 Maths – Integration Questions Video 1

A2 Maths – Integration Questions Video 2

Courtesy of Haberdashers’ Adams Maths Dept.

No Textbook Resources

This is not a section in the textbook (unless you include the mixed exercise), but is worth spending time on. The videos are a mass collection of questions. Try to think about what method is required for each before having a go at the question. Note there are no separating the variables questions in these particular videos.

Bicen Maths Live Lesson

Integration 21 • Which technique should I use? • P2 Ex11 all • 🎲

Live Lessons Using Dr Frost Based Slides Courtesy of Bicen Maths

Download Blank Notes

(Courtesy of King’s Chester Maths Department)

Download Slides

• Dr Frost Slides 70-72✦

Extra Questions

• Dr Frost Questions Select Integration in KS5 and Go

Key Skills

No Key Skills Yet

Flowcharts & Mixed Questions

• WW How do I integrate that? Presentation

and Accompanying Flowchart:

Activities

• WW Kahoot Integration Methods
• MEI Methods of Integration✦

Whole Topic Videos

How to integrate ANYTHING • Part 1: Techniques ✍️ [A-Level Maths]

How to integrate ANYTHING • Part 2: Examples ✍️ [A-Level Maths]

External Whole Topic Past Paper Style Questions

• Jethwa Maths Worksheet, Topic Tests and Starter Activity
• Dr Frost Topic Test✦ (Teacher Login Required)
• PMT
  • AQA
    • Calculus
    • Integration
  • Edexcel
    • Basic Integration 1 · 2
  • OCR
    • Indefinite Integrals
  • Cheat Sheet

Activities

• NRICH (student problems)
  • Differentiation & Integration
  • Differential Equations
• MEI
  • MEI teaching notes, misconceptions & prompts: Integration✦
  • MEI teaching notes, misconceptions & prompts: Differential equations✦
  • Integration activities✦ (original by MEI; by Susan Wall, MEI; copy hosted on Jo Morgan’s Drive)
• Colemanweb
  • Methods for integration✦ (info sheet✦)
• @fortunatesums
  • Integration looky-likeys✦
• Andy Lutwyche
  • Erica’s Errors
  • Erica's Errors On Integration 2, 3, 5
  • (Year 2) Codebreaker

Worksheets

• MathedUp
  • Integration 2: Questions · Challenge · Answers
  • Integration 3: Questions
• Maths Genie
  • Integration: Questions · Solutions · Lesson · Topic page
• Jethwa Maths
  • Year 2 Integration: Worksheets · Unit Test
• Mathsaurus (Kevin Olding)
  • Integration (exam questions)
• Physics & Maths Tutor
  • Definite Integration: Questions 2021–24 · Mark scheme · Model answers · Questions 2018–21 (with MS) · Model answers
• MME
  • C3 Integration: Questions | Answers  •  C4 Calculus: Questions | Answers
• SRWhitehouse
  • Integration worksheets✦ (solutions✦)
  • Integration revision✦
• Dr Oliver Mathematics
  • Integration exam questions✦ (solutions✦)