Maths with Lemon

Exponential Functions

"Mathematics compares the most diverse phenomena and discovers the secret analogies that unite them. "

Joseph Fourier

Properties of the exponents

What you have to know:

Key Points

  • 1. Watch the video:

Exponential Equations

What you have to know:

  • You must be able to manipulate algebraic equations.

Key Points

  • 1. Watch the video:

Logarithms

What you have to know:

Key Points

  • 1. Watch the video:

  • 3. Watch this video how to solve logarithmic equations.

  • 4. Check these notes as a revision for arithmetic sequences

Logistic models

What you have to know:

Key Points

  • 1. Watch the video:

Extra

Material and references:

  • Hodder Book SL(ISBN: 9781510462359) :
    1A, 1B, 12A, 12B

Key Points

  • You should know how to use the laws of exponents with integer exponents:
    \( a^m \times a^n = a^{m+n} \),
    \( \frac{a^m}{a^n} = a^{m-n} \),
    \( (a^m)^n = a^{mn} \),
    \( a^{-n} = \frac{1}{a^n} \),
    \( (ab)^n = a^n b^n \),
    \( \left(\frac{a}{b}\right)^n = \frac{a^n}{b^n} \).

  • You should be able to extend the laws of exponents to general rational exponents:
    \( a^{\frac{1}{n}} = \sqrt[n]{a} \).

IB Past Paper Problems

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