Even though everyone learns mathematics at school, it is difficult to define exactly what mathematics is. Clearly numbers, shapes and equations form part of it, but only a small part compared to the vast space of mathematical concepts and ideas. The best way to understand what mathematics is and what mathematicians work on – is to do mathematics.
Application Of Mathematics
Despite being so abstract and theoretical, Mathematics has countless applications in every possible aspect of life. Without mathematics our civilization would be little more advanced than the ancient Egyptians: we wouldn’t have governments funded by a tax system, no phones, no television, no computers, no internet and no satellite navigation. The cultural value and the monetary economic value of mathematics are too large to
measure.
Language Of The Universe
Mathematics is also the language of the universe, from the electrochemical signals in our brain to the equations of General Relativity which govern the motion of stars and galaxies everywhere in the universe. It is one of humanity’s most noble endeavors to understand the universe we live in, and that would not be possible without mathematics.
Fundamental Ideas
One idea that appears everywhere in mathematics is abstraction. Instead of thinking about particular numbers, shapes, equations or any other objects, mathematicians tend to think about their underlying structures and patterns. This means that the results, called Theorems, are more general and provide deeper insight.
Another fundamental idea in mathematics is proof. Mathematicians can’t just say that an idea is true, or test it in a few cases. They need a rigorous and watertight argument to
deduce that it is always true. Maybe this makes mathematics more difficult than other
sciences, but it also means that mathematicians can obtain absolute and definitive
knowledge – which is impossible in any other discipline.
Syllabus Outline
| Syllabus Component | Suggested teaching hours – SL | Suggested teaching hours – HL |
|---|---|---|
| Topic 1 – Number and algebra | 16 | 29 |
| Topic 2 – Functions | 31 | 42 |
| Topic 3 – Geometry and trigonometry | 18 | 46 |
| Topic 4 – Statistics and probability | 36 | 52 |
| Topic 5 – Calculus | 19 | 41 |
| The “toolkit” and Mathematical exploration Investigative, problem-solving and modelling skills development leading to an individual exploration. The exploration is a piece of written work that involves investigating an area of mathematics. | 30 | 30 |
| Total teaching hours | 150 | 240 |
Assessment outline
For Standard Level
| Assessment component | Weighting |
|---|---|
| External Assessment (3 hours) Paper 1 (90 minutes) Technology required (80 marks) Compulsory short-response questions based on the syllabus (80 marks) | 80% 40% |
| Paper 2 (90 minutes) Technology required (80 marks) Compulsory extended-response questions based on the syllabus (80 marks) | 40% |
| Internal Assessment: This component is internally assessed by the teacher and externally moderated by the IB at the end of the course. Mathematical Exploration: Internal assessment in mathematics is an individual exploration. This is a piece of written work that involves investigating an area of mathematics.(20 marks) | 20% |
For Higher Level
| Internal assessment task | Weighting |
|---|---|
| External assessment (5 hours) Paper 1(120 minutes) Technology required (110 marks) Compulsory short response questions based on the syllabus. | 80% 30% |
| Paper 2 (120 minutes) Technology required (110 marks) Compulsory extended response questions based on the syllabus | 30% |
| Paper 3 (60 minutes) Technology required (55 marks) Two compulsory extended response problem-solving questions. | 20% |
| Internal assessment: This component is internally assessed by the teacher and externally moderated by IB at the end of the course. Mathematical Exploration: Internal assessment in mathematics is an individual exploration. This is a piece of written work that involves investigating an area of mathematics (20 marks) | 20% |