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A-Level Further Maths

Further Pure Mathematics B (Unit 4)

Revision Session 1

  • De Moivre’s Theorem

Revision Session 2

  • Solving Trigonometric Equations

Revision Session 3

  • Matrices 2

Revision Session 4

  • Session Review and Polar Co-ordinates

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From the Specification and teaching guidance:

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Prove De Moivre’s Theorem using proof by induction

Prove for positive integer values of n that:

(cos(θ) + i sin(θ))n = cos(nθ) + i sin(nθ)

Solution

1. Basis step: When n = 1, LHS = (cos(θ) + i sin(θ))1 = cos(θ) + i sin(θ)

RHS = cos(1θ) + i sin(1θ) = cos(θ) + i sin(θ)

As LHS = RHS, true for n = 1

2. Assumption step: Assume true for n = k, (cos(θ) + i sin(θ))k = cos(kθ) + i sin(kθ)

3. Induction step: When n = k + 1:

4. Conclusion step: Hence true for n = k => true for k+1 and since true for n = 1, the result is proved by induction.

Formulae Booklet

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From the Specification and teaching guidance:

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Show that cos 4θ = 8cos4θ - 8cos2θ + 1

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Show that cos 4θ = 8cos4θ - 8cos2θ + 1

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Show that cos 4θ = 8cos4θ - 8cos2θ + 1

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From the Specification and teaching guidance:

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From the Specification and teaching guidance:

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https://www.geogebra.org/m/dquykuw3

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From the Specification and teaching guidance:

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A-Level Further Maths

Further Pure Mathematics B (Unit 4)

Revision Session 1

  • De Moivre’s Theorem

Revision Session 2

  • Solving Trigonometric Equations

Revision Session 3

  • Matrices 2

Revision Session 4

  • Session Review and Polar Co-ordinates

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