# Algebra

- Comparison of syllabus content between HL and SL
- Discussion of ways to approach the teaching of the Algebra topic - HL and SL considered separately
- Connections between Algebra topic and other parts of the syllabus
- Thorough discussion on helpful ways to introduce and teach proof by mathematical induction (HL only)
- Potential ideas for student Explorations involving concepts in the Algebra topic
- Exercise sets (including answers) and student activities (including teacher's notes)
- Unit tests and quizzes (with solution keys)

#### Comparison of syllabus content between HL & SL - Algebra topic

There is a significant difference in syllabus content between the Algebra topic in Maths HL and the Algebra topic in SL. The number of recommended **teaching hours** for the Algebra topic in **HL is 30 hours** but only **9 hours in SL**. That is the biggest difference for any of the six syllabus topics. This is primarily due to the fact that **mathematical induction** and **complex numbers** are in HL but not in SL. Take a look at the **Algebra syllabus content for HL** in the Syllabus Content sub-section of the Basics section on this site where you can see that most of the content in the Algebra topic for HL is __not__ in the Algebra topic for SL.

Although the number of instructional hours recommended for the Algebra topic differs significantly between SL (9 hours) and HL (30 hours), there are several syllabus content items that are in both the SL Algebra topic and the HL Algebra topic. These items include:

♦ arithmetic sequences & series

♦ geometric sequences & series (including infinite geometric series)

♦ sigma notation

♦ working with relevant laws for exponents & logarithms

♦ expansion of binomials (a+b)^{n}

♦ binomial theorem

♦ binomial coefficients / Pascal's triangle / combinations _{n}*C*_{r}

#### Teaching Approaches / Points to Consider

## Selected Pages

### exponents & logarithms 10 December 2018

Quick links:► downloadable teaching materials for exponents & logarithms► syllabus content for the Algebra Topic: SL...

more

### sequences & series 6 December 2018

Quick links:► downloadable teaching materials for sequences & series► syllabus content for the Algebra Topic: SL syllabus...

more

### proof by induction (HL) 28 March 2016

Proof by mathematical induction is only in the HL course (not in SL) - and is the only formal proof method in the HL syllabus....

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### complex numbers (HL) 16 November 2018

Quick links:► downloadable teaching materials for complex numbers► syllabus content for the Algebra Topic: HL syllabus...

more

### binomial theorem 7 November 2018

Quick links:► downloadable teaching materials for binomial theorem► syllabus content for the Algebra Topic: SL syllabus...

more

### Euler's identity 11 January 2018

Although time for teaching Maths HL is very precious and a teacher should endeavour to not use up valuable class time for...

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