Geometry & Trigonometry
In this topic, we will look at
3D Solids- Radians, Arcs and Sectors
- Right-Angled Trigonometry
- Sine and Cosine Rule
- The Unit Circle
- Trigonometric Functions
- Pythagorean Identities
- Compound Angle Identities
- Double Angle Identities
- Solving Trigonometric Equations
- Scalar Product and Angles
- Vector Product
- Equations of Lines
- Kinematics
- Equations of Planes
- Intersections of Lines and Planes
- Vector Product
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
3-Dimensional Solids
On this page, we will look at finding the volume and surface area of three-dimensional solids. The formulae for these solids can all be found in the formula booklet. You just need to know where to...
Radians, Arcs and Sectors
On this page, we will look at another measure of angles, that is, radians. This is a far more useful measure than degrees. Formulae for calculating arcs and sectors become simpler and most importantly,...
Right-angled Trigonometry
On this page, we will learn about right-angled trigonometry. For many, this will not be a new topic, nor will it be a difficult one. However, it deserves some time, as it forms an important step towards...
Sine and Cosine Rule
On this page, we will look at the Sine Rule, the Cosine Rule and the formula for the Area of a Triangle. The formulae are fairly straightforward to use, but don't take this topic too lightly: some exam...
Unit Circle SL
The Unit Circle is probably the most important topic to understand from the whole of trigonometry. Lots of the properties of the trigonometric functions can be found from the unit circle. All the work...
Unit Circle HL
The Unit Circle is probably the most important topic to understand from the whole of trigonometry. Lots of the properties of the trigonometric functions can be found from the unit circle. All the work...
Trigonometric Graphs
On this page, we will learn about the graphs of the circular functions \sin x, \cos x and \tan x. We will link this to work that we have done on Transforming Functions to see how translating...
Pythagorean Identities HL
On this page, we will learn about the Pythagorean identities. It is actually quite rare that exam questions are solely about these identities, but it is essential that you can use and manipulate them...
Compound Angle Formulae HL
On this page, we will learn about the compound angle formulae used in trigonometry. These are really important because they open up so many other formulae in trigonometry. In particular, we can derive...
Double Angle Formulae SL
On this page, we will learn about the double angle formulae used in trigonometry. It is actually quite rare that exam questions are solely about these identities, but it is essential that you can use...
Double Angle Formulae HL
On this page, we will learn about the double angle formulae used in trigonometry. It is quite rare that exam questions are solely about these identities, but it is essential that you can use and manipulate...
Solving Trigonometric Equations
Solving trigonometric equations is a common topic in examinations. The key to solving them is a good knowledge of the trigonometric functions. Whether you prefer to use the Unit Circle or the graphs...
Vectors - Scalar Product and Angles HL
In this topic, we will look at finding the angle between vectors in different circumstances. The whole topic revolves around the scalar (or dot) product. Often we are concerned with perpendicular vectors,...
Vectors - Equation of a Line HL
You should already be familiar with the equation of a straight line in Cartesian form in 2 dimensions, y = ax + b. When we move into 3 dimensions, the Cartesian form becomes a little more awkward. Don't...
Vectors - Intersection of Lines HL
This page looks at the intersections of lines in 2 and 3 dimensions. In 2D, lines intersect or are parallel. In 3D, it is slightly more complicated: lines can intersect, be parallel, be coincident, or...
Vectors - Kinematics HL
This page is all about kinematics with vectors. You can describe the position of a moving object using vectors. This is very much like the equation of a straight line, except that the parameter is t for...
Vectors - Equations of Planes HL
This is a hugely important topic in the HL course. We can describe planes in 3D in a number of different ways. It is not enough simply to learn the different equations; it is vital that you have a strong...
Vectors - Intersection of Planes HL
This page is all about how planes meet (or not). Two distinct planes will either be parallel or meet in a line; coincident planes share the whole plane. Three planes will either 1) have no common point...
Vectors - Intersection of Line and Plane HL
For questions involving lines and planes, we are usually asked to find the point of intersection. However, when we consider a line and a plane, there are three possible situations. On this page, we will...
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