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Complex Numbers HL - de Moivre's Theorem
De Moivre's Theorem gives a formula for calculating complex numbers. It enables us to connect complex numbers and trigonometry. Most importantly, it is incredibly useful for finding powers and roots of...
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Complex Numbers HL - The Basics
This page will allow you to become confident in the basic principles of complex numbers. It is important to understand, and be able to use, the three different forms of a complex number: Cartesian, Polar...
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Proof by Induction HL
Proof by Induction is a method of proof commonly used in HL mathematics. The method is always the same and questions are worth a good deal of marks in an exam. Therefore, it is really worth investing...
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Proof by Contradiction HL
"...when you have eliminated the impossible, whatever remains, however improbable, must be the truth?" Sherlock Holmes in The Sign of the Four by Sir Arthur Conan Doyle. Holmes was a wonderful detective...
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Deductive Proofs
On this page, we will look at deductive reasoning in order to be able to make direct proofs. This is a hugely important topic in mathematics, since we like to be absolutely sure of the results we have...
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Indices and Logarithms
Logarithms are useful for solving problems involving indices (or exponents). In fact, logarithms are indices written in another form. The definition a^x=b\Longleftrightarrow x=\log_a b is valid when a>0, a\neq1 and b>0....
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Geometric Sequences
These are sequences where you go from term to term by multiplying by a common ratio. The sequence in the image 1, 2 , 4 , 8 has a common ratio of 2 since we multiply the previous term by 2. There are...
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Graphs and Derivatives
On this page, we will look at graphs and derivatives. We will practise sketching derivative functions and carefully consider stationary points (local maxima, local minima and stationary points of inflexion),...
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Introducing Derivatives
Differentiation allows us to determine rates of change. When we differentiate a function \(f\), we obtain its derivative function \(f'\). The value \(f'(x)\) gives the instantaneous rate of change of \(f\),...
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Which type of Differential Equation Quiz
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