Differentiation (Old Textbook)

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A2 Maths – Pure – Differentiating e^x, ln(x) and a^x

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

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9B Slides (Courtesy of Owen134866)

Dr Frost Video

• Topic Video

Bicen Maths Live Lesson

Differentiation 4 • Differentiating exponentials and logs • P2 Ex9B • 🚀

Differentiation 5 • e^x and lnx, practice and problems • P2 Ex9B • 🚀

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 11-15✦

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

• 595a: Differentiate terms given in the form a e^kx
• 595b: Differentiate terms given in the form a ln(kx)
• 595c: Differentiate a^x.
• 595d: Differentiate a mixture of e^x and ln(x) with other functions.
• 595e: Determine the rate a physical quantity is increasing/decreasing by at a particular moment in time, using an exponential model.
• 595f: Determine the turning point of a function involving e^kx
• 595g: Use a known rate of growth/decay to determine a constant or input in an exponential model.
• 595h: Determine when two exponential models are growing/decaying at the same rate.
• 595: Exam Practice: Differentiating exponential functions and ln(x)

Other Videos

Differentiation – e and ln

Courtesy of Maths Genie (note that knowledge of the chain, product and quotient rule is needed for this video)

Differentiation of a^x

Courtesy of Maths Genie

Enrichment Video

What's so special about Euler's number e? | Chapter 5, Essence of calculus

3Blue1Brown: What's so special about Euler's number e?

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Activities

• Berwick Maths Diagnostic Questions

Worksheets

• Solomon C3 Questions A and Solutions A
• Solomon C3 Questions B and Solutions B
• Solomon C4 Questions C and Solutions C (Q8-10 only)
• Jethwa Starter (p1-2)
• MadAsMaths (T. Madas)
  • Differentiation II Exam Questions Q5, 16, 22–23, 33, 40–42, 49, 54, 72, 79, 85, 90, 97, 103–104, 113, 118, 128, 143, 147–150, 156, 169, 172, 176–177, 181–183, 187, 208, 211, 218, 240 (difficulty 2–5 of 5)
  • Differentiation Practice II Q4–6 · questions only
  • Exponentials & Logarithms Exam Questions Q49, 60, 70, 86, 119 (difficulty 4–5 of 5)

A2 Maths – Pure – Chain Rule for Differentiation

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept. (All except above small section on dx/dy) Contains Trig Examples.

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9C2 Slides (Courtesy of Owen134866)

Dr Frost Video

• Topic Video (up to 10:26)

Bicen Maths Live Lesson

Differentiation 6 • Chain Rule, intro • P2 Ex9C • 🚀

Differentiation 7 • Chain Rule practice, polynomial type • P2 Ex9C • 🚀

Differentiation 8 • Chain Rule practice, mixed type • P2 Ex9C • 🚀

Differentiation 9 • Chain Rule, Powers of Trig • P2 Ex9C • 🚀

Differentiation 10 • Using the Chain Rule Twice • P2 Ex9C • 🚀

Differentiation 11 • Chain Rule – challenges • P2 Ex9C • 🚀

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 16-22✦

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

• 597a: Apply the chain rule to differentiate functions of the form f(x)=a(bx+c)ⁿ for rational n
• 597b: Apply the chain rule to differentiate functions of the form ≤ft[f(x)right]ⁿ where f(x) is a polynomial and n is rational.
• 597c: Apply the chain rule to differentiate functions of the form ln(ax+b), e^ax+b, sin(ax+b) or cos(ax+b) where the inner function is linear.
• 597d: Apply the chain rule to differentiate functions of the form ln(f(x)), e^f(x), sin(f(x)) or cos(f(x)) for more general f(x).
• 597e: Differentiate powers of sin kx and cos kx
• 597: Exam Practice: Product, quotient and chain rules

Other Videos

Differentiation – The Chain Rule

Courtesy of Maths Genie

Enrichment Video

Visualizing the chain rule and product rule | Chapter 4, Essence of calculus

3Blue1Brown: Visualizing the chain rule and product rule

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Activities

• Berwick Maths Diagnostic Questions
• Colemanweb
  • Easy Medium Hard Recap✦
  • Matching Activity✦

Worksheets

• Solomon C3 Questions C and Solutions C
• Solomon C3 Questions D and Solutions D
• Jethwa Starter (p7-8), Worksheet (p5-8)
• Colemanweb Practice✦
• martahidegkuti Extension Questions
• Physics & Maths Tutor
  • Chain Rule: Questions 2021–24 · Mark scheme · Model answers · Questions 2018–21 (with MS) · Model answers
• MadAsMaths (T. Madas)
  • Differentiation II Exam Questions Q2, 10–11, 13, 17, 25, 29, 64, 70, 111–112, 127, 133, 137–138, 146, 185, 188, 196, 201, 214, 216, 221, 223, 225, 231, 234, 255 (difficulty 2–5 of 5)
  • Differentiation Practice II Q1–3, 13–14 · questions only
  • Exponentials & Logarithms Exam Questions Q71 (difficulty 4 of 5)
  • Trigonometry Exam Questions Hard Questions Q92 (difficulty 4 of 5)

A2 Maths – Pure – Product Rule Differentiation

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept. Contains Trig Examples.

Download Blank Notes

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9D Slides (Courtesy of Owen134866)

Dr Frost Video

• Topic Video (from 12:30 to 22:22)

Bicen Maths Live Lesson

Differentiation 13 • The Product Rule • P2 Ex9D • 🚀

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 23-26✦

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

• 597g: Use the product rule with simple functions.
• 597h: Use the product rule and the chain rule within a single expression.
• 597k: Determine the gradient of a function at a given point, requiring use of chain, product or quotient rules.
• 597: Exam Practice: Product, quotient and chain rules

Other Videos

Differentiation – The Product Rule

Courtesy of Maths Genie

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Activities

• Berwick Maths Diagnostic Questions
• Colemanweb
  • Easy Medium Hard Recap✦
  • Matching Activity✦

Worksheets

• Solomon C3 Questions E and Solutions E
• Jethwa Starter (p9-10), Worksheet (p9-13)
• martahidegkuti Extension Questions
• Physics & Maths Tutor
  • Products and Quotients: Questions 2021–24 · Mark scheme · Model answers · Questions 2018–21 (with MS) · Model answers
• MadAsMaths (T. Madas)
  • Differentiation II Exam Questions Q6, 8–9, 14, 20–21, 27, 32, 34, 36, 43–44, 47–48, 51–53, 57, 60–61, 68, 73, 75, 81, 83, 86, 92–93, 100, 105, 107, 114–115, 117, 121–123, 126, 136, 144, 151, 153, 159, 164, 171, 173, 209 (difficulty 2–4 of 5)
  • Differentiation Practice II Q15–17 · questions only

A2 Maths – Pure – Quotient Rule for Differentiation

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept. Contains Trig Examples

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9E Slides (Courtesy of Owen134866)

Dr Frost Video

• Topic Video (from 22:22)

Bicen Maths Live Lesson

Differentiation 14 • The Quotient Rule • P2 Ex9E • 🚀

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 27-30✦

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

• 597i: Use the quotient rule with simple functions.
• 597j: Use the quotient rule and the chain rule within a single expression.
• 597l: Determine the value of a constant in a function where the gradient is given, requiring use of chain, product or quotient rules.
• 597m: Determine the second derivative or higher using the chain, product or quotient rules.
• 597: Exam Practice: Product, quotient and chain rules

Other Videos

Differentiation – The Quotient Rule

Courtesy of Maths Genie

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Activities

• Berwick Maths Diagnostic Questions
• MEI Product & Quotient Rule
  • Dominoes✦
  • Order The Steps✦
• Colemanweb
  • Easy Medium Hard Recap✦
  • Matching Activity✦

Worksheets

• Solomon C3 Questions F and Solutions F
• Solomon C3 Questions G and Solutions G (mixed product & Quotient)
• Jethwa Starter (p11-12), Worksheet (p14-17)
• martahidegkuti
  • Extension Questions
  • Mixed Extension Questions
• MadAsMaths (T. Madas)
  • Differentiation II Exam Questions Q1, 4, 12, 30, 55–56, 58, 63, 65–67, 74, 80, 82, 87, 89, 91, 94, 99, 108–110, 129, 134, 139, 142, 157–158, 170, 174–175, 200, 202, 205, 207, 210, 217, 222, 232, 256, 265 (difficulty 2–5 of 5)
  • Differentiation Practice II Q18–20 · questions only
  • Trigonometry Exam Questions Hard Questions Q48 (difficulty 4 of 5)

Exam Practice

• PMT PPQs✦

A2 Maths – Pure – Differentiating sin(x) and cos(x)

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

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9A Slides (Courtesy of Owen134866)

Dr Frost Video

• Topic Video (up to 6:23)

Bicen Maths Live Lesson

Differentiation 1 • Differentiating sinx from First Principles • P2 Ex9A • 🚀

Differentiation 2 • Visualising the derivative of sinx and cosx • P2 Ex9A • 🚀

Differentiation 3 • Differentiating sinkx and coskx • P2 Ex9A • 🚀

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 1-10✦

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

• 596a: Differentiate sin x and cos x from first principles. (not yet active)
• 596b: Differentiate expressions of the form sin(kx) and cos(kx) (not yet active)
• 596c: Differentiate a mixture of exponential, logarithmic and sinusoidal terms. (not yet active)
• 596: Exam Practice: Differentiating sin x and cos x

Other Videos

Differentiating cos and sin from First Principles

Courtesy of Maths Genie (1)

Differentiation – sin(x) and cos(x)

Courtesy of Maths Genie (2). Knowledge of Chain Rule required.

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Activities

• Berwick Maths Diagnostic Questions

Worksheets

• Jethwa Starter (p3-4)
• MadAsMaths (T. Madas)
  • Differentiation II Exam Questions Q26, 78 (difficulty 3 of 5)
  • Differentiation Practice II Q7–8 · questions only

Exam Practice

• PMT
  • OCR
    • Gradients and Differentiation of Standard Functions

A2 Maths – Pure – Differentiating tan(x), sec(x), cosec(x) and cot(x)

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

Download Blank Notes

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9F Slides (Courtesy of Owen134866)

Textbook Questions

Q1-7 – no arc functions

Dr Frost Video

• Topic Video (from 6:23)

Bicen Maths Live Lesson

Differentiation 15 • tan, sec, cot, cosec • P2 Ex9F • 🚀

Differentiation 17 • Differentiating trig in terms of y • P2 Ex9F • 🚀

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 31-37✦

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

• 598a: Differentiate expressions of the form tan (kx) and cot (kx)
• 598b: Differentiate expressions of the form sec(kx) and textrmcosec(kx)
• 598c: Use the chain rule to differentiate expressions given in the form sec(f(x)), textrmcosec(f(x)) or cot(f(x)) for more general f(x)
• 598d: Differentiate powers of tan x and reciprocal trigonometric functions.
• 598e: Use the product or quotient rule where one of the terms is tan x or a reciprocal trigonometric function.
• 598f: Determine a second derivative or higher of tan x or reciprocal trigonometric functions.
• 598g: Determine the equation of the tangent or normal to a curve, involving e^x, ln(x), sin, cos and tan (no product/quotient rule).
• 598h: Determine the equation of the tangent or normal to a curve, involving e^x, ln(x), sin, cos and tan, requiring use of the product/chain/quotient rule. (not yet active)
• 598i: Determine the stationary point for expressions involving e^x, ln(x), sin, cos and tan, requiring use of the product rule. (not yet active)
• 598j: Determine the stationary point of a fractional expression using the quotient rule. (not yet active)
• 598k: Determine the range of values for which a non-polynomial function is increasing or decreasing. (not yet active)
• 598l: Show that a non-polynomial function is increasing or decreasing. (not yet active)
• 598m: Find the value of a constant for which a non-polynomial function is increasing or decreasing. (not yet active)
• 598n: Determine the range of a non-polynomial function by use of differentiation. (not yet active)
• 598: Exam Practice: Differentiating tan x, reciprocal trigonometric functions, and powers of these

Other Videos

Differentiation – More Trigonometric Functions

Courtesy of Maths Genie

A Level Maths Differentiation Questions Video

Courtesy of Haberdashers’ Adams Maths Dept. Extra Practice at more exam style questions from the techniques we have seen to date.

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Activities

• Berwick Maths Diagnostic Questions
• Underground Maths Trig Gradient Match✦
• WW Kahoot Quiz 1
• WW Kahoot Quiz 2 – With Chain Rule

Worksheets

• Solomon C3 Questions H and Solutions H
• Jethwa Starter (p5-6)
• MadAsMaths (T. Madas)
  • Differentiation II Exam Questions Q15, 38, 46, 62, 77, 116, 140–141, 160, 178, 204 (difficulty 3–4 of 5)
  • Differentiation Practice II Q9–12 · questions only
  • Trigonometry Exam Questions Enrichment Questions Q72 (difficulty 5 of 5)

A2 Maths – Pure – Chain Rule for Differentiation

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept. (From 6:09 to examples – very short)

Download Blank Notes

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9C1 Slides (Courtesy of Owen134866)

Textbook Questions

Q6-10

Dr Frost Video

Topic Video (from 4:28)

Bicen Maths Live Lesson

Differentiation 12 • dx/dy • P2 Ex9C • 🚀

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 21✦

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

• 597f: Determine fractextrmdytextrmdx for a function x=f(y)
• 607a: Determine dy/dx where x = sin(ky) or x = cos(ky) (not yet active)
• 607b: Determine dy/dx where x = tan(ky) or x = cot(ky) (not yet active)
• 607c: Determine dy/dx where x = sec(ky) or x = textrmcosec(ky) (not yet active)
• 607d: Determine dy/dx where x is a power of a trigonometric function in terms of y (not yet active)
• 607e: Determine dy/dx where x = ln(f(y)) or x = e^f(y) for some trigonometric function. (not yet active)
• 607f: Determine the equation of the tangent or normal to a curve when x = f(y) (not yet active)
• 597: Exam Practice: Product, quotient and chain rules
• 607: Exam Practice: Differentiating expressions given in the form x = f(y) for trigonometric functions

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

A2 Maths – Pure – Parametric Differentiation

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

Download Blank Notes

Download Slides

9G Slides (Courtesy of Owen134866)

Dr Frost Video

• Topic Video

Bicen Maths Live Lesson

Differentiation 18 • Parametric • P2 Ex9G • 🚀

Differentiation 19 • Parametric Exam Q • P2 Ex9G • 🚀

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 38-40✦

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

• 604a: Determine dy/dx for parametric equations involving powers of t
• 604b: Determine dy/dx for parametric equations involving reciprocals.
• 604c: Determine dy/dx for parametric equations involving e^t and ln(t)
• 604d: Determine dy/dx for parametric equations involving sin, cos and tan and their powers.
• 604e: Determine dy/dx for parametric equations involving sec, textrmcosec and cot and their powers.
• 604f: Use parametric equations for a displacement (x,y) to find the speed of a particle.
• 604g: Determine the equation of a tangent or normal to a parametric curve.
• 604h: Determine the stationary point for a curve expressed using parametric equations. (not yet active)
• 604: Exam Practice: Differentiating parametric equations

Further Practice

• Practise Questions

Other Videos

Differentiation of Parametric Equations

Courtesy of Maths Genie

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Activities

• Berwick Maths Diagnostic Questions
• MEI Matching Activity✦

Worksheets

• Solomon C4 Questions B and Solutions B
• Jethwa Starter (p15-16), Worksheet (p18-22)
• Naiker Maths
  • Parametric Differentiation: Exam Qs 2005–11 · Mark scheme · Exam Qs 2012–17 · Mark scheme
• Physics & Maths Tutor
  • Parametric Differentiation: Questions 2021–24 · Mark scheme · Model answers
• MadAsMaths (T. Madas)
  • Parametric Equations Parametric Differentiation Q1–7
  • Parametric Equations Exam Questions Q1, 3, 5–6, 9–11, 13, 16, 18, 23, 25, 27, 31, 35, 37–40, 44, 46–47, 49–50, 52, 57–58, 60, 63–66, 68–69, 76–77, 79–84, 86–88, 90–101, 104, 106–108, 111, 114, 116–129, 132, 141 (difficulty 2–5 of 5)

Exam Practice

• PMT
  • Edexcel
    • Parametric Differentiation

A2 Maths – Pure – Implicit Differentiation

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

Download Blank Notes

Download Slides

9H Slides (Courtesy of Owen134866)

Dr Frost Video

• Topic Video

Bicen Maths Live Lesson

Differentiation 20 • Implicit Differentiation • P2 Ex9H • 🚀

Differentiation 21 • Implicit with Product Rule • P2 Ex9H • 🚀

Differentiation 22 • Implicit – problems • P2 Ex9H • 🚀

Differentiation 23 • Implicit – with simultaneous equations • P2 Ex9H • 🚀

Differentiation 24 • Implicit – Parallel/Perpendicular to Axes • P2 Ex9H • 🚀

Differentiation 25 • Implicit – Exam Question • P2 Ex9 ExamQ • 🚀

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 41-45✦

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

• 600a: Differentiate a single term in terms of x and y
• 600b: Determine the gradient function for a polynomial in x and y
• 600c: Determine the gradient for a polynomial in x and y at a specific point.
• 600d: Determine dy/dx for more general implicit relationships, including trigonometric, logarithmic and exponential terms.
• 600e: Determine dy/dx for more general implicit relationships, where x or y is given.
• 600f: Determine the stationary points for an implicit polynomial relationship between x and y (not yet active)
• 600g: Determine the stationary points for an implicit non-polynomial relationship between x and y (not yet active)
• 600h: Determine the coordinates of critical points where the tangent of a curve, defined by an implicit equation, is parallel to the y-axis. (not yet active)
• 600i: Determine the coordinates of points on a circle, with given equation, where the tangent has given gradient. (not yet active)
• 600j: Determine the coordinates of critical points where the tangent of a curve, defined by an implicit equation, is parallel to a non-vertical/horizontal line. (not yet active)
• 600k: Determine the equation of the tangent or normal to a curve using implicit differentiation. (not yet active)
• 601a: Prove that the derivative of a^x is a^x ln a (not yet active)
• 601b: Differentiate functions of the form ≤ft[f(x)right]^x (not yet active)
• 601c: Differentiate functions of the form ≤ft[f(x)right]^g(x) (not yet active)
• 601d: Determine the stationary point for a function of the form ≤ft[f(x)right]^x (not yet active)
• 600: Exam Practice: Implicit differentiation
• 601: Exam Practice: Logarithmic differentiation

Further Practice

• Practise Questions

Other Videos

Implicit Differentiation

Courtesy of Maths Genie

Enrichment Video

Implicit differentiation, what's going on here? | Chapter 6, Essence of calculus

3Blue1Brown: Implicit differentiation, what's going on here?

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Activities

• Berwick Maths Diagnostic Questions

Worksheets

• Solomon C4 Questions C and Solutions C
• Jethwa Starter (p17-18), Worksheet (p23-26)
• Naiker Maths
  • Implicit Differentiation: Exam Qs 2005–11 · Mark scheme · Exam Qs 2012–17 · Mark scheme
• Physics & Maths Tutor
  • Implicit Differentiation: Questions 2021–24 · Mark scheme · Model answers · Questions 2018–21 (with MS) · Model answers
• MadAsMaths (T. Madas)
  • Differentiation II Exam Questions Q45, 50, 124–125, 130, 166, 186, 189–191, 193–195, 203, 213, 215, 220, 224, 268 (difficulty 3–5 of 5)
  • Implicit Differentiation Basic Differentiation Q1–5; Tangents and Normals Q1–10; Turning Points Q1–6
  • Implicit Equations Exam Questions Q1–58, 60–63, 65–75, 77–78, 80–82 (difficulty 2–5 of 5)

Exam Practice

• PMT
  • Edexcel
    • Implicit Differentiation 1 · 2
  • OCR
    • Implicit Differentiation
  • OCR MEI
    • Implicit Differentiation

A2 Maths – Pure – Concave and Convex Regions

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

Download Blank Notes

Download Slides

9I Slides (Courtesy of Owen134866)

Bicen Maths Live Lesson

Differentiation 26 • Second Derivative – concave/convex/inflection • P2 Ex9I • 🚀

Differentiation 27 • Concave/Convex/Inflection problems • P2 Ex9I • 🚀

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 45-48✦

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

• 602a: Determine whether a curve is convex (concave-up) or concave (concave-down) at a specific point. (not yet active)
• 602b: Reason about the shape of a drawn graph at a specific point by using the second derivative. (not yet active)
• 602c: Determine the interval for which a curve is convex (concave-up) or concave (concave-down). (not yet active)
• 602d: Show that function is convex or concave for all real values of x (not yet active)
• 602e: Determine a non-stationary point of inflection of a cubic function. (not yet active)
• 602f: Determine a non-stationary point of inflection for a more complex function. (not yet active)
• 602: Exam Practice: Concavity and points of inflection

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Activities

• Berwick Maths Diagnostic Questions

Worksheets

• Jethwa Starter (p21 & 22)
• MadAsMaths (T. Madas)
  • Calculus Introduction Exam Questions Q80, 186, 189, 200, 228, 230 (difficulty 3–4 of 5)
  • Differentiation II Exam Questions Q88, 96, 98 (difficulty 3–4 of 5)

A2 Maths – Pure – Connected Rates of Change

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

Download Blank Notes

Download Slides

9J Slides (Courtesy of Owen134866)

Dr Frost Video

• Topic Video

Bicen Maths Live Lesson

Differentiation 28 • Connected Rates of Change pt. 1 • P2 Ex9J • 🎲

Differentiation 29 • Connected Rates of Change pt. 2 • P2 Ex9J • 🎲

Differentiation 30 • Connected Rates of Change, exam question pt. 3 • P2 Ex9J • 🎲

Differentiation 31 • Connected Rates of Change pt. 4 (triple) • P2 Ex9J • 🎲

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 49-52✦

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

• 603a: Determine the rate of change of a volume or surface area of a cube, given the rate of change of the height, or vice versa.
• 603b: Determine the rate of change of the volume, area or surface area of a curved shape or solid, given the rate of change of a length, or vice versa.
• 603c: Determine the rate of change of a volume, surface area or length given an arbitrary formula. (not yet active)
• 603d: Determine the rate of change of a volume, surface area or length where the formula must be derived. (not yet active)
• 603e: Use the chain rule twice to determine the rate at which the volume or surface area of a solid is increasing given the rate of the other. (not yet active)
• 603: Exam Practice: Connected rates of change

Further Practice

• Practise Questions

Other Videos

Connected Rates of Change

Courtesy of Maths Genie

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Activities

• Berwick Maths Diagnostic Questions
• Desmos Forming Differential Equations 1 Card Sort by Laura Kavalier

Worksheets

• Solomon C4 Questions D and Solutions D
• Jethwa Starter (p19-20), Worksheet (p27-29)
• Naiker Maths
  • Connected Rates of Change: Exam Qs 2005–11 · Mark scheme · Exam Qs 2012–17 · Mark scheme
• Physics & Maths Tutor
  • Rates of Change: Questions 2021–24 · Mark scheme · Model answers
• MadAsMaths (T. Madas)
  • Related Rates Of Change Q1–56 (difficulty 2–5 of 5)

Exam Practice

• PMT
  • Edexcel
    • First Order Differential Equations
    • Rates of Change

External Whole Topic Past Paper Style Questions

• Jethwa Maths Worksheets, Topic Test and Starter Activities
• Dr Frost Topic Test 1✦ (Teacher Login Required)
• Topic Test 2 (WW but in style of Dr Frost – I use this for resit purposes)
• PMT
  • AQA
    • Calculus
    • Differentiation
  • Edexcel (Most Covered in Broken Down Sub-Topics Above)
    • Basic Differentiation
    • Chain Rule
    • Products and Quotients 1 · 2
    • Rates of Change
    • Stationary Points 1 · 2
    • Tangents and Normals 1 · 2
  • OCR
    • Differentiation from First Principles
    • Tangents, Normals, Stationary Points and Increasing and Decreasing Functions
    • Techniques of Differentiation
  • OCR MEI
    • Applications of Differentiation to Functions and Graphs (Yr. 2)
    • Product, Quotient and Chain Rules
  • Cheat Sheet

Worksheets

• Maths Genie
  • Differentiation: Questions · Solutions · Lesson · Topic page
• Mathsaurus (Kevin Olding)
  • Differentiation (exam questions)
  • Further differentiation (exam questions)
• Naiker Maths
  • Differentiating Functions & Expressions: Exam Qs 2005–11 · Mark scheme · Exam Qs 2012–17 · Mark scheme
• Physics & Maths Tutor
  • Stationary Points: Questions 2018–21 (with MS) · Model answers
  • Tangents and Normals: Questions 2018–21 (with MS) · Model answers
• MME
  • C3 Differentiation: Questions | Answers
• MadAsMaths (T. Madas)
  • Differentiation II Exam Questions Q3, 7, 18, 28, 31, 35, 59, 71, 76, 102, 106, 120, 145, 155, 180, 199, 227, 237, 241–242 (difficulty 2–5 of 5)
  • Differentiation Practice II Q21 · questions only
  • Differentiation Practice II Exam Questions Q1–15 (difficulty 2–5 of 5)