Hyperbolic Functions

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A2 Further Maths – Core – Introduction to Hyperbolic Functions

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

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6A Slides (Courtesy of Owen134866)

Hyperbolic Functions 1 • Definitions and Graphs • CP2 Ex6A • 🎯

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 1-13

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

• 733a: Calculate sinh, cosh, tanh, textrmsech, textrmcosech and coth of an integer value.
• 733b: Calculate sinh, cosh, tanh, textrmsech, textrmcosech and coth of a logarithmic value. (not yet active)
• 733c: Recognise graphs of y = sinh x, y = cosh x and y = tanh x (not yet active)
• 733d: Recognise graphs of y = textrmsech x, y = textrmcosech x and y = coth x (not yet active)
• 733: Exam Practice: Definitions and graphs of hyperbolic functions

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

A2 Further Maths – Core – Inverse Hyperbolic Functions

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

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6B Slides (Courtesy of Owen134866)

Hyperbolic Functions 2 • Inverse Functions • CP2 Ex6B • 🎯

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 14-19

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

• 734b: Recognise graphs of y = mathrmarsinh x, y = mathrmarcosh x and y = mathrmartanh x (not yet active)
• 734c: Use formulae to calculate the output of inverse hyperbolic values. (not yet active)
• 734: Exam Practice: Inverse hyperbolic functions and solving hyperbolic equations

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Online Platform

• Bossmaths interactive 2×2 transformations and questions

A2 Further Maths – Core – Hyperbolic Equations and Identities

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

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6C Slides (Courtesy of Owen134866)

Hyperbolic Functions 3 • Hyperbolic Identities • CP2 Ex6C • 🎯

Hyperbolic Functions 4 • Osborn's Rule • CP2 Ex6C • 🎯

Hyperbolic Functions 5 • Solving Equations • CP2 Ex6C • 🎯

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 20-26

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

• 734a: Solve a simple hyperbolic equation given in the form sinh x = k (not yet active)
• 734d: Determine the hyperbolic counterpart to a trigonometric identity using Osborn’s rule. (not yet active)
• 734e: Solve an equation with a mixture of hyperbolic functions, without squares. (not yet active)
• 734f: Solve an equation involving a mixture of hyperbolic and exponential terms. (not yet active)
• 734g: Solve an equation using a hyperbolic identity. (not yet active)
• 734h: Determine the output of a hyperbolic function given the output of another. (not yet active)
• 734i: Solve a more complex equation by using the definition of a inverse hyperbolic term. (not yet active)
• 734: Exam Practice: Inverse hyperbolic functions and solving hyperbolic equations

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Online Platform

• Bossmaths interactive 3×3 transformations and questions

A2 Further Maths – Core – Differentiating Hyperbolics

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

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6D Slides (Courtesy of Owen134866)

Hyperbolic Calculus 1 • Differentiating Hyperbolic Functions • CP2 Ex6D • 🏆

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 27-32

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

• 735a: Differentiate a simple hyperbolic term. (not yet active)
• 735b: Differentiate a hyperbolic expression using the chain rule. (not yet active)
• 735c: Differentiate a simple inverse hyperbolic term. (not yet active)
• 735d: Differentiate a inverse hyperbolic expression using the chain rule. (not yet active)
• 735e: Differentiate a product involving an inverse hyperbolic term. (not yet active)
• 735f: Obtain a first order differential equation from an inverse hyperbolic function. (not yet active)
• 735g: Obtain a second order differential equation from an inverse hyperbolic function. (not yet active)
• 735: Exam Practice: Differentiating hyperbolic and inverse hyperbolic functions

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

A2 Further Maths – Core – Integration of Hyperbolics

A2 Further Maths – Core – Integration using Hyperbolic Substitutions

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

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6E Slides (Courtesy of Owen134866)

Hyperbolic Calculus 2 • Integrating with Hyperbolic Functions • CP2 Ex6E • 🏆

Hyperbolic Calculus 3 • Substitutions for Hyperbolic Integration • CP2 Ex6E • 🏆

Hyperbolic Calculus 4 • Using Completing the Square • CP2 Ex6E • 🏆

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 33-46

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

• 736a: Integrate standard results to yield a hyperbolic expression. (not yet active)
• 736b: Integrate functions to yield a hyperbolic expression that first requires splitting a fraction. (not yet active)
• 736c: Integrate a product of two hyperbolic terms where one has a power. (not yet active)
• 736d: Integrate expressions involving sinh² or cosh² (not yet active)
• 736e: Integrate expressions involving sinh³ or cosh³ (not yet active)
• 736f: Integrate expressions involving a product of an exponential and hyperbolic term. (not yet active)
• 737a: Integrate expressions given in the form frac1√x² + a² (not yet active)
• 737b: Find the definite integral of expressions given in the form frac1√x² + a² (not yet active)
• 737c: Integrate expressions given in the form frac1√x² – a² (not yet active)
• 737d: Calculate a definite integral for expressions given in the form frac1√x² – a² (not yet active)
• 737e: Integrate √x² + a² using a hyperbolic substitution. (not yet active)
• 737f: Integrate expressions given in the form frac1√a² x² + b² (not yet active)
• 737g: Calculate a definite integral for expressions given in the form frac1√a² x² + b² (not yet active)
• 737h: Integrate an expression given in the form fracf(x)√x² + a² and fracg(x)√x² – a² using a hyperbolic substitution. (not yet active)
• 737i: Integrate an expression given in the form 1/x² + bx + c by completing the square. (not yet active)
• 737j: Calculate a definite integral for expressions given in the form 1/x² + bx + c (not yet active)
• 737k: Integrate an expression given in the form frac1√x² + bx + c by completing the square. (not yet active)
• 737l: Calculate a definite integral for expressions given in the form frac1√x² + bx + c (not yet active)
• 737m: Integrate an expression given in the form 1/ax² + bx + c by completing the square. (not yet active)
• 737n: Integrate an expression given in the form frac1√ax² + bx + c by completing the square. (not yet active)
• 736: Exam Practice: Integrating hyperbolic functions
• 737: Exam Practice: Integrating functions given in the form frac1√x² + a² and frac1√x² – a²

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Whole Topic Videos

A2 Further Maths – Core – Hyperbolics – Just for fun

Haberdashers’ Adams Maths Department “Hyperbolics just for fun!”

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

Worksheets

• Mathshelper (Jon Stone)
  • Hyperbolic Functions
• MathedUp
  • Hyperbolic functions: Questions · Challenge · Answers
• Jethwa Maths
  • 10 Minute Starters: Hyperbolic Functions
• Physics & Maths Tutor
  • CP2 Ch.6 Hyperbolic Functions: Questions by topic
• MadAsMaths (T. Madas)
  • Hyperbolic Functions Q73, 74, 86, 87 (difficulty 4–5 of 5)
• Dr Austin Maths
  • Proof Cards (Word | PDF | Answers)
  • Plotting Graphs Practice Grid (Word | PDF | Answers)
  • Solving Equations Crack the Code (Word | PDF | Answers)