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This whole chapter is A level only (not needed for AS Further Maths).
Contents
- Whole Topic Notes
- 6A Reduction Formulae*
- 6B Arc Length*
- 6C Area of a Surface of Revolution*
- Whole Topic Summary Resources (Including Past Paper Questions)
Whole Topic Notes
Full Notes to Accompany Examples
Dr Frost
- Dr Frost Further Pure 2 Integration Techniques Section
6A Reduction Formulae*
Textbook resources
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Dr Frost resources
No Live Lesson Video Yet
Key Skills
Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost
- 822a: Prove a reduction formula from an integral (excluding hyperbolic functions).
- 822b: Use a reduction formula to integrate an expression with a high power (excluding hyperbolic functions).
- 822c: Prove a reduction formula for a definite integral (excluding hyperbolic functions).
- 822d: Use a reduction formula to calculate a definite integral.
- 822e: Prove a reduction formula from a hyperbolic integral.
- 822f: Use a reduction formula to integrate a hyperbolic expression with a high power.
- 822: Exam Practice: Reduction formulae
6B Arc Length*
Textbook resources
No Video Yet
Dr Frost resources
No Live Lesson Video Yet
Key Skills
Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost
- 823a: Determine an arc length for curve given in the form y = f(x) (excluding hyperbolics).
- 823b: Determine an arc length given parametric equations of the curve.
- 823c: Determine an arc length given a polar equation.
- 823d: Determine the length of an arc that requires a hyperbolic substitution.
- 823e: Determine the length of an arc involving a hyperbolic function.
- 823: Exam Practice: Arc length for Cartesian, parametric or polar equations
6C Area of a Surface of Revolution*
Textbook resources
No Video Yet
Dr Frost resources
No Live Lesson Video Yet
Key Skills
Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost
- 824a: Determine an expression for the surface area of the solid produced by revolving a curve with Cartesian equation around the x-axis.
- 824b: Determine the surface area of the solid produced by revolving a curve with Cartesian equation around the x-axis.
- 824c: Determine an expression for the surface area of the solid produced by revolving a curve with parametric equations around the x-axis.
- 824d: Determine the surface area of the solid produced by revolving a curve with parametric equations around the x-axis.
- 824e: Determine the surface area of the solid produced by revolving a curve with polar equation around the x-axis.
- 824f: Determine the surface area of the solid produced by revolving a curve around the x-axis, requiring a hyperbolic substitution.
- 824g: Determine the surface area of the solid produced by revolving a curve around the x-axis, given a hyperbolic function.
- 824: Exam Practice: Area of surface of revolution
Whole Topic Summary Resources (Including Past Paper Questions)
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.)