Integration

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AS Maths – Pure – Intro to Integration

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

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13A/B Slides (Courtesy of Owen134866)

Dr Frost Video

• Topic Video

Bicen Maths Live Lesson

Integration 1 • Intro • P1 Ex13A • 🚀

Integration 2 • Formal Notation • P1 Ex13B • 🚀

Live Lesson 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 1-8✦ (13A)
• Dr Frost Slides 9-12✦ (13B)

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

• 521a: Integrate a collection of terms in the form ax^b
• 521b: Integrate a collection of terms in the form ax^b requiring rewriting of roots and reciprocals.
• 521c: Integrate an expression requiring bracket expansion.
• 521d: Integrate an expression written as a fraction with a single term on the denominator.
• 521: Exam Practice: Integrating xⁿ (excluding n=-1) for rational n

Further Practice

• Practise Questions

Other Videos

An Introduction to Integration

Courtesy of Maths Genie (Up to 10:13)

Enrichment Video

The essence of calculus

3Blue1Brown: The essence of calculus

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF for 13A
• Acute Learning Problem Pairs as PowerPoint or PDF for 13B

Activities

• The Chalk Face Investigating Integration
• Berwick Maths Diagnostic Questions: A · B
• Math = Love (Sarah Carter)
  • Antiderivatives Bingo
• PhET Interactive Simulations
  • PhET Calculus Grapher Interactive Simulation (embedded below)
• Transum
  • Integration
• Goal Free Problems
  • A-Level Basic Calculus set Q20, Q21
• SRWhitehouse
  • Indefinite integration activities✦
• Underground Mathematics
  • Integral chasing✦

Worksheets

• Jethwa Maths Worksheet (Part 1)
• Solomon C1 Worksheet A and Solutions A
• Rewriting to Differentiate and Integrate✦ Standard Units
• Matching Cards✦ MEI
• Mathshelper (Jon Stone)
  • Integration Indefinite
• Naiker Maths
  • Indefinite Integrals: Exam Qs 2005–11✦ · Mark scheme✦ · Exam Qs 2012–17 · Mark scheme · Extra practice · Solutions
• Physics & Maths Tutor
  • Basic Integration: Questions 2021–24 · Mark scheme · Model answers · Questions 2018–21 (with MS) · Model answers
• Dr Oliver Mathematics
  • Indefinite integration questions✦ (solutions✦)
• MadAsMaths (T. Madas)
  • Calculus Introduction Exam Questions Q4, 12, 16, 24, 44, 49, 120, 179 (difficulty 2–4 of 5)
  • Introduction to Integration Standard Integration Practice Q1–6; Various Integration Questions Q1–3, 8, 13, 22, 32
• Starting Points Maths
  • Increasingly Difficult Integration · PDF
• Pret Homework (@MissCarrollEcon)
  • Integration (@MissCarrollEcon, pdf)

AS Maths – Pure – Finding Functions using Integrating (+C)

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

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13C Slides (Courtesy of Owen134866)

Dr Frost Video

• Topic Video

Bicen Maths Live Lesson

Integration 3 • Finding Constant of Integration • P1 Ex13C • 🚀

Live Lesson 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 13-15✦

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

• 522a: Determine a function by integrating dy/dx
• 522b: Determine a function by integrating dy/dx, involving roots and brackets. (not yet active)
• 522c: Determine a function by integrating dy/dx in a modelled context.
• 522d: Determine a function by integrating dy/dx involving one or more unknown coefficients.
• 522e: Use a model obtained from a simple differential equation in the form dy/dx = f(x) to find outputs of the model.
• 522f: Determine a function by integrating d²y/dx² twice involving one or more unknown coefficients.
• 522: Exam Practice: Determining a function given its derivative and a point, for polynomials

Further Practice

• Practise Questions

Other Videos

An Introduction to Integration

Courtesy of Maths Genie (From 10:13)

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Activities

• Berwick Maths Diagnostic Questions
• Goal Free Problems
  • A-Level Basic Calculus set Q11, Q14, Q22, Q24

Worksheets

• Jethwa Maths Worksheet (Part 2)
• Solomon C1 Worksheet B and Solutions B
• MadAsMaths (T. Madas)
  • Calculus Introduction Exam Questions Q10, 17, 39, 50, 53, 55–56, 65, 68, 71, 76, 82, 86, 90, 98, 102, 109, 126, 160–161, 174, 176, 191, 232, 259 (difficulty 2–4 of 5)
  • Introduction to Integration Various Integration Questions Q4–5, 7, 9–12, 14–15, 18–21, 23, 28–30, 33, 35

AS Maths – Pure – Finding the Area Under a Curve

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept. Video Covers 13E only (Area under the curve)

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13D Slides (Courtesy of Owen134866)

13E Slides (Courtesy of Owen134866)

Dr Frost Video

• Topic Video (Examples 1 and 2 only up to 7:13)

Bicen Maths Live Lesson

Integration 4 • Definite Integration • P1 Ex13D • 🚀

Integration 5 • Area under Curves • P1 Ex13E • 🚀

Live Lesson 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 16-24✦
• Dr Frost slides 20-19✦

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

• 525a: Evaluate a definite integral where the integrand is a collection of terms in the form ax^b
• 525b: Evaluate a definite integral where the integrand is a collection of terms in the form ax^b, including roots, reciprocals and where splitting of fractions is required.
• 525c: Determine definite integrals by using the areas of basic shapes.
• 525d: Determine the area enclosed between a curve, the x-axis and two given bounds.
• 525e: Determine the shaded area enclosed between a curve and the x-axis where the limits are roots.
• 525f: Determine the shaded area enclosed between a curve and the y-axis.
• 525g: Determine a definite integral in terms of an algebraic limit.
• 525h: Use a known area enclosed under a curve to determine an unknown bound or an unknown coefficient.
• 525: Exam Practice: Evaluating definite integrals for powers of x, e.g. to find an area under a curve or area between curves

Finding the Area Under a Curve using Definite Integration

Courtesy of Maths Genie (Up to 8:28)

Enrichment Video

Integration and the fundamental theorem of calculus | Chapter 8, Essence of calculus

3Blue1Brown: Integration and the fundamental theorem of calculus

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF for 13D
• Acute Learning Problem Pairs as PowerPoint or PDF for 13E

Activities

• Berwick Maths Diagnostic Questions: D · E
• Andy Lutwyche
  • Codebreaker
• Ben Sparks (GeoGebra)
  • Fundamental Theorem of Calculus: GeoGebra
• Goal Free Problems
  • A-Level Basic Calculus set Q12
• variationtheory.com
  • Definite integration✦
• Underground Mathematics
  • Meaningful areas✦

AS Maths – Pure – Area Under the x-axis

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

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13F Slides (Courtesy of Owen134866)

Dr Frost Video

• Topic Video (Example 3 only from 7:13 to 11:06)

Bicen Maths Live Lesson

Integration 6 • 'Negative' Areas • P1 Ex13F • 🚀

Live Lesson 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 25-29✦

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.
• 525: Exam Practice: Evaluating definite integrals for powers of x, e.g. to find an area under a curve or area between curves

Other Videos

Finding the Area Under a Curve using Definite Integration

Courtesy of Maths Genie (From 8:28 to 14:20)

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Activities

• Berwick Maths Diagnostic Questions
• Goal Free Problems
  • A-Level Basic Calculus set Q23, Q27

Worksheets

• Jethwa Maths Worksheet (Part 3)
• MadAsMaths (T. Madas)
  • Calculus Introduction Exam Questions Q14, 60, 72, 155 (difficulty 2–3 of 5)
  • Introductory Integration Areas Q5, 19, 39 (difficulty 2–3 of 5)

AS Maths – Pure – Finding the Area Between Two Lines Using Integration

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

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13G Slides (Courtesy of Owen134866)

Dr Frost Video

• Topic Video (Example 3 only from 11:06)

Bicen Maths Live Lesson

Integration 7 • Areas between Curves • P1 Ex13G • 🚀

Integration 8 • Tricky area questions • P1 Ex13G • 🚀

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths

Download Blank Notes

(Courtesy of King’s Chester Maths Department)

Download Slides

• Dr Frost Slides 30-33✦

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

• 525j: Determine the area of a composite shape using integration, by adding areas.
• 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

Further Practice

• Practise Questions

Other Videos

Finding the Area Under a Curve using Definite Integration

Courtesy of Maths Genie (From 14:20)

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Activities

• Berwick Maths Diagnostic Questions
• Math = Love (Sarah Carter)
  • Mystery Animal worksheet
• Goal Free Problems
  • A-Level Basic Calculus set Q25, Q26, Q28, Q29, Q30

Whole Topic Videos

Integration 9 • Challenging exam question • P1 Ex13 ExamQ • 🚀

Integration 10 • Mixed questions • P1 Ex13Mixed • 🚀

Bicen Maths Exam Questions

External Whole Topic Past Paper Style Questions

• Solomon Worksheet A and Solutions A
• Solomon Worksheet B and Solutions B
• Jethwa Maths Topic Tests and Starter Activity
• Dr Frost Topic Test✦ (Teacher Log in Required)
• PMT
  • Basic Integration 1 · 2
  • Finding Areas using Integration 1 · 2
  • Cheat Sheet
• Transum
  • Exam-style questions: Integration

Activities

• Math = Love (Sarah Carter)
  • Integrals activities collection
• NRICH (student problems)
  • Differentiation & Integration
• MEI
  • MEI teaching notes, misconceptions & prompts: Integration✦
• Underground Mathematics
  • Additional integrals✦
  • Stretching an integral✦
• Andy Lutwyche
  • (Year 1) Codebreaker

Worksheets

• Mathshelper (Jon Stone)
  • Integration FFP
  • Integration
  • Integration FFP
• MathedUp
  • Integration: Questions · Challenge · Answers
• Maths Genie
  • Integration: Questions · Solutions · Lesson · Topic page
• Jethwa Maths
  • Year 1 Integration: Worksheets · Unit Test
• Mathsaurus (Kevin Olding)
  • Integration (exam questions)
• MME
  • C1 Integration: Questions | Answers  •  C2 Calculus: Questions | Answers
• MadAsMaths (T. Madas)
  • Calculus Introduction Exam Questions Q286 (difficulty 5 of 5)