A level Further Maths, Maths and Physics, worked through step by step.

Matched topic by topic to your AQA, OCR or Pearson Edexcel specification.

  • Animated lessons
  • Exam questions
  • Worksheets
  • Weekly Challenge
  • Revision Journal
Create a free account Watch a free lesson

Free, and about a minute to set up. Or try a practice question first.

Watch the free lessonDe Moivre's theorem, the whole lesson, no account neededFree A worked example from the lesson on De Moivre's theorem: expressing cos 3θ in powers of cos θ.

Choose your subject

Further MathsComplex numbers, matrices, proof by induction, further calculus, and optional modules in mechanics, statistics and decision maths.AQA 7367 and Pearson Edexcel 9FM0 MathsAlgebra and functions, calculus, trigonometry and vectors, with the statistics and mechanics every student sits.AQA 7357 and Pearson Edexcel 9MA0 PhysicsMechanics, electricity, waves, fields and particles, with the required practicals you are examined on.AQA 7408 and Pearson Edexcel 9PH0

What's inside

Lessons

A short animated lesson for each sub-topic, in five parts: what it's for, why it works, a worked example, one for you to try, and a summary. Watch it, or read it as text.

New words are explained on screen, and the lesson starts again where you stopped.

Go to Lessons

Practice questions

Exam-style questions at three levels for every sub-topic. Each one has a worked solution laid out like a mark scheme, so you see which step earns which mark.

M1 Method A1 Accuracy B1 Independent

Try practice questions

Complex numbers

Not needed for Year 12Hard

Multiple angles · Year 13 · 4 marks

  1. Use de Moivre's theorem to show that cos⁡3θ\cos 3\theta=4cos3⁡θ{}= 4\cos^{3}\theta−3cos⁡θ{}- 3\cos \theta.
    (4)
Show worked solutionHide worked solution
  1. (cos⁡θ+isin⁡θ)3(\cos\theta + \mathrm{i}\sin\theta)^3=cos⁡3θ{}= \cos 3\theta+isin⁡3θ{}+ \mathrm{i}\sin 3\theta
  2. Binomial expansion, real part.Re:cos3⁡θ\text{Re}: \cos^3\theta−3cos⁡θsin2⁡θ{}- 3\cos\theta\sin^2\theta
  3. Use sin2⁡θ\sin^{2}\theta=1−cos2⁡θ{}= 1 - \cos^{2}\theta.=4cos3⁡θ−3cos⁡θ= 4\cos^3\theta - 3\cos\theta

Total4

  • M
  • A
  • B

Worksheets

Printable PDFs for almost every sub-topic, and a longer test for most topics. There is space for working on the page, and the mark scheme is at the back.

Go to Worksheets

Challenge

Harder questions that mix the sub-topics of a topic. You type the answer, and the fewer tries you need, the more points you score. A new set every week.

Go to the Challenge

Journal

Rate each sub-topic from Not yet to Strong. Every topic gets a level, the weakest come first, and your lesson history sits alongside.

Go to the Journal

Profile

A page of your own, with a picture, banner and style you choose, the badges you earn, and friends to follow. You decide what it shows.

Start with one sub-topic.

An account is free and takes about a minute. Your lessons, ratings and Challenge points are then saved on every device.

Create a free account