Algebra
In this topic, we will look at
Arithmetic and Geometric Sequences and Series- Exponents and Logarithms
- The Binomial Theorem
- Deductive Proofs
- Permutations and Combinations
- Proof by Contradiction
- Proof by Induction
- Complex Numbers
On each page, you will find
- Video tutorials explaining key concepts.
- Concise revision notes providing you with reminders of all the key content you need
- Onscreen quizzes giving you instant feedback
- Exam style questions with hints, detailed solutions and explanation
Arithmetic Sequences
An arithmetic sequence is a sequence in which the same value, called the common difference, is added to each term to obtain the next term. For example, the sequence \(1,5,9,\ldots\) has common difference \(4\)....
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...
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....
Counting Principles HL
This page deals with all the counting principles in the HL course: Arrangements, Permutations and Combinations. You need to be familiar with combinations for the Binomial Theorem, but it is also useful...
Binomial Theorem SL
The following page will help you with questions about the Binomial Theorem (or Binomial Expansion). The Binomial Theorem is used for expanding brackets in the form (a+b)^n. Questions on this topic...
Binomial Theorem HL
The following page will help you with questions about the Binomial Theorem (or Binomial Expansion). The Binomial Theorem is used for expanding brackets in the form (a+b)^n. Questions on this topic...
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...
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...
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...
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...
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...
Complex Numbers HL - Roots of Polynomials
The Conjugate Root Theorem states that if the complex number a + ib is a root of a polynomial in one variable with real coefficients, then the complex conjugate a - bi is also a root of that...
Navigating the pages
Each of the topic pages is designed in the same way:
Had an explanation in class that you didn't quite understand? The short, high quality videos in this section will help you understand all the key concepts from each topic. Some are designed to explain concepts from the beginning and others are focussed on very specific skills and typical exam questions. All videos come with a set of notes that you can keep.
This section is all about getting practice. Before you try any exam-style questions, you will need a quick check to see if you have understood all the concepts from the page. These onscreen quizzes allow you to get just that. You can get instant feedback on your answers including advice about how to tackle the question and worked solutions.
This is the section where you can practise questions just like you the ones that you will get in the exam. If you need some help getting started, there are hints. Each question has a full solution with explanation
Each of the questions is marked by difficulty level
Easy
Medium
Hard