Proofs SL

" To divide a cube into two other cubes, a fourth power, or in general any power whatever into two powers of the same denomination above the second is impossible, and I have assuredly found an admirable proof of this, but the margin is too narrow to contain it. "

Pierre de Fermat

Direct Proofs

Prior Knowledge

Recognize all the basic functions
You must be able to manipulate algebraic expressions.
(If not, check this lesson)
You must be able to manipulate exponential expressions.
(If not, check this lesson)
You must be able to manipulate logarithmic expressions.
(If not, check this lesson)

Key Points

1. Watch the video:

2. Read this presentation
3. Watch this solved problem

Extra

Material and references:

Hodder Book SL(ISBN: 9781510462359) :
11A

Key Points

1. You should be able to work with and understand the notation for identities. An identity occurs when two expressions always take the same value for all allowed values of the variable; when this is emphasized, the symbol \( \equiv \) is used in place of the equals sign; and if two polynomials are identical, you can compare coefficients.
1. You should also be able to construct simple deductive proofs, usually by starting from one side and showing through a series of identities that it is equivalent to the other side.

IB Past Paper Problems

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