Preliminaries: how to study for AS-Level Mathematics, P1

maths p1 preliminariesWelcome to the Pure Maths 1 (P1 from now on!) component of the AS-Level mathematics course. This is a challenging course, but we do hope that you will find it stimulating and interesting; it certainly will develop your analytical, mathematical, and problem-solving abilities!


Please read these guidelines carefully; they explain what materials you need for this course, how to plan your schedule, how to organize yourself, and how to approach each lesson. These are relatively straightforward matters, but if you don't approach them in a disciplined way you will make your task significantly more difficult and reduce your chances of success.

Make sure that you work out a plan to implement these guidelines, and come back to them periodically — especially in the early stages of this course — to make sure that you are following them. If at some stage you seem to be stuck, or feel that you are not in control of your work, review these guidelines to see if there is something you are not doing.

Text book and other materials

pure maths 1 textYour text book for this course is Pure Mathematics 1: Coursebook by Hugh Neill, Douglas Quadling and Julian Gilbey, revised edition (Cambridge University Press, 2016, ISBN 9781316600207). This book is endorsed by Cambridge Assessment International Education (Cambridge International). Even if you already have an older edition of the book, it is better to buy the revised edition, as some of the exercises have changed. The layout also makes the revised edition easier to read.

The text book can be purchased from your local Cambridge University Press branch, or from online bookshops like You need to obtain the text book before you can start the course.

In addition to the text book you will need a thick, hard-covered A4 exercise book (you might need more than one, but that will become evident in due course!) and an A5 notebook (hard- or soft-covered). The exercise book is for your daily exercises (called 'weight lifting' in this course), and the A5 notebook is for you to compile a summary of definitions, formulae, etc.

Most of the time you will simply write with a pen (blue or black), but you should also have a ruler and pencil on hand for drawing sketch-graphs. A red pen will be helpful for marking your work.

Organizing your schedule

It is critically important that you plan your schedule properly from the beginning. You need to ensure that you finish working through all the material early enough to leave time for exam preparation. It is a serious mistake to think that you can finish the chapter-by-chapter exercises at the last minute, go and write your exam without any additional preparation, and still do well. After you have completed the chapter-by-chapter exercises, you need to work through past exam papers. This will give you the opportunity of revising concepts and skills that you did not master in your initial exposure to them, and will help you to integrate the separate skills in your understanding so that you are able to combine and apply them to solving problems you haven't seen before. You should allow at least four weeks for this revision.

Most students will need to allow one-and-a-half to two hours per day, five days per week, for a period of 22 weeks, to complete this course successfully (excluding time for practising past papers). If your prior knowledge or ability are a little weaker, you will probably need a bit more time than that. Please don't make the mistake of trying to skimp on the work, or fall into the trap of putting off the day's scheduled work because you think you still have plenty of time before the exam. Discipline yourself to keep to your schedule and you will be rewarded with a sense of confidence that you have prepared yourself adequately for the exam. Please see the My downloads area of the 'My account' menu item for a sample schedule as well as one that you can complete according to your own programme.

Tackling the lessons

Most lessons begin with an explanation of some key concepts. This is usually done by means of videos. Watch the videos and make sure that you understand the concepts being explained. It may help you to take notes while the video plays. Note that you can pause the video at any point; this can be useful if you want to review an extended calculation that has been written out on the whiteboard, or if you want to make a note of a formula or calculation that has been done on the board.

Tip for saving time and bandwidth: If you keep your browser window and tab open on the lesson you are busy with, you can play the videos over and over without having to download them again. If you close your browser or tab, or move to a different web page in that same tab, you may have to download the video again.

Where applicable, you will be directed to make a note of an important formula, definition, procedure, etc. Write this down in your A5 notebook. It is probably easiest if you write all the notes for each chapter together, in the order in which they appear. You should not have much more than one or two pages of notes per chapter. In this way, your notebook will provide you with a summary of nearly all the concepts and principles that are needed for solving the problems. As you tackle the problems, you can look over these notes to see which ones might be applicable for the problem at hand. If you get stuck, this approach will often give you an idea of where to start looking for a solution to the problem.

Most important, each lesson includes a section called 'Weight lifting', in which you are assigned exercises to work through. It cannot be emphasized enough that you must work through these exercises yourself, in writing, in your exercise book. You must guard against the idea that, just because you think you understood the explanation, you have mastered the concept under discussion. At this point I like to use the analogy of weight lifting. If you want to bench-press 80 kg by the end of the year, it is not enough to listen to your coach explaining the procedure and then watch him demonstrating it. You can do that the whole year long, but when you get to the end of the year you will be no more able than you were at the beginning of the year to bench-press the 80 kg. What is required is for you to develop your own muscles, and the only way to do that is to get on the bench and start lifting weights. Moreover, you have to start with a weight you can manage and increase it gradually, in accordance with your increasing strength, until you reach your target. Intellectual learning works just like this. You have to actually engage with the work yourself, starting with simple exercises which increase gradually in complexity until you acquire the requisite skill. Do not try to short-circuit this process; you will pay the price! The exercises are appropriately graded, and if you answer the questions as assigned you should be able to develop the necessary level of skill. If you are really stuck in trying to solve a problem you may look at one or two of the worked solutions to get yourself started. But if you do this you must make sure that you practise enough examples of the particular type of problem without looking at the solution.

Once you have completed the exercises, download the worked solutions and mark/correct your work. This is very important! It will help you to see how much you really understand, and where you may be going wrong. Where you find mistakes in your work, make a note of what kind of mistake you made. Here are some possibilities:

  • copy error (either in copying from the question itself, or in copying from one line to another of your own work)
  • arithmetical/calculation error (e.g. you calculated 12 x7 as 96 instead of 84)
  • conceptual error (misunderstanding of the problem)

Of course, the most serious kind of error is a misunderstanding of the problem. If you make such an error, read the solution carefully to see what it is that you don't understand. If necessary, watch the videos again to clarify the concepts in your mind.

If you find that you are really not able to complete all the exercises in the time available for your lesson, don't simply do the earlier ones and neglect the later ones. Make sure that you select exercises evenly over the full range so that you practise all the required skills.

A note to parents

Naturally, you want to help your child as much as you can with his/her studies. When it comes to a subject like mathematics, parents who are not trained in the subject can feel quite out of their depth and at a loss to know how best to help. The good news is that, even if you know very little maths, there is quite a lot you can do to help your child. Here are some suggestions:

  • Work through the guidelines on this page with your child.
  • Help your child to set up the right environment and make sure that he/she has both the place and time to work; see that the place and time are protected from interruptions.
  • Help your child to set up a study programme for the year that fits in with your family's overall plans (travelling, visits from extended family, holidays, etc.).
  • Discuss your child's work with him/her on a regular basis; give him/her guidance on the implementation of these guidelines. Keep coming back to the guidelines and make sure that your child knows how to implement them and is actually doing so.


If you get stuck at some point, please send us a message via the contact form (see top menu) so that we can attempt to help you. We cannot help with every individual exercise question, but, especially if you have more overarching challenges, we will try to give you some guidance. If there are particular problems that you find especially difficult, please send us a note. If there are a number of students with the same difficulties we can perhaps add a video or some notes that will address those issues.

We wish you every success and trust that you will enjoy studying mathematics through Imago Education!