# AS-Level Mathematics: introduction

## The Cambridge International AS-Level Mathematics course (code 9709)

The Cambridge International AS-Level mathematics course provides detailed coverage of some of the key topics in mathematics. It lays a thorough foundation for the mathematical component of tertiary-level studies in science, engineering, actuarial science and other mathematically-based fields of study, and is essential for any student wishing to pursue one of these fields at university or college. In certain countries the AS-Level mathematics course will prepare you adequately for mathematics at tertiary level; in others you will be required to complete the full A-Level programme.

The AS-Level syllabus requires students to choose two out of a possible four papers:

• P1 - Pure mathematics 1 (compulsory)
• P2 - Pure mathematics 2
• M1 - Mechanics 1
• S1 - Statistics 1

As indicated above, the P1 paper is compulsory. If you are taking the AS-Level course as a stand-alone course (i.e. not as the first stage of the full A-Level programme), you may select freely from P2, M1 and S1 for the second paper. Many students find M1 less challenging than P2, and the combination of P1 and M1 generally makes for a less pressurized programme than P1 and P2, particularly if you are also studying Physics. Although some parts of the M1 syllabus require knowledge from the P1 syllabus, P1 and M1 can be taken studied simultaneously. On the other hand, it is necessary to complete P1 before starting P2. This means that if you are taking P2 as your second paper, you will have to complete the P1 syllabus more quickly so as to leave enough time to complete the P2 syllabus.

If you are looking for the most thorough preparation for mathematics at tertiary level, the combination of P1 and P2 is probably best, particularly if you are taking Physics as a separate AS-Level subject (since much of the M1 content will be covered in Physics, although from a slightly different perspective).

Statistics involves some concepts that are not dealt with directly in pure mathematics or in mechanics; these concepts are important in fields like mathematical statistics, actuarial science and statistical physics. S1 (rather than P2 or M1) is therefore a good choice for students who wish to study mathematical statistics or actuarial science. It would also be helpful for prospective physicists who will not have a dedicated statistics course in their undergraduate programme.

If the AS-Level course is being used as the first stage of the full A-Level course, then it is important to plan ahead. The Cambridge International A-Level course requires FOUR papers, chosen as follows:

• Two compulsory papers:
• P1 - Pure mathematics 1
• P3 - Pure mathematics 3 (P3 includes P2 from AS-Level plus some additional material)
• One of the following combinations:
• M1 (Mechanics 1) and M2 (Mechanics 2)
• S1 (Statistics 1) and S2 (Statistics 2)
• M1 and S1

In other words, the A-Level programme calls for:

• two full papers in pure mathematics;
• two full papers in either mechanics or statistics, or one paper in each of mechanics and statistics.

Given that the A-Level course requires P3, which includes P2, students who take the AS-Level course as the first stage of the full A-Level course should NOT take P1 and P2 for their AS-Level programme. They MUST take P1, and should choose either M1 or S1, depending on their choice for the two optional papers.

## Prerequisites

Cambridge International does not prescribe any formal prerequisite for this course. However, in order to succeed you will need an appropriate mathematical grounding. As a bare minimum, you will need to have completed the Cambridge International IG Mathematics course or an equivalent. It is highly recommended that you have some additional grounding — beyond IG Mathematics — in the following topics:

• line graphs and their equations (i.e.  $$y = mx + c$$ )
• quadratic equations and parabolas
• geometry, including triangles (congruency, similarity), circles (tangents, chords, segments), quadrilaterals
• exponents

If you do not have this grounding, or if your IG results were not good (at least above 60%; preferably above 70%), you will need to allow extra time for mastering the AS-Level curriculum.

## Imago Education's AS-Level course

Imago Education is currently offering study materials for Pure mathematics 1 (P1). For details, please see the introduction to P1.

We are also working on materials for Pure mathematics 2 (P2), which should be ready early in 2018.