# Revision Exercise for MATH Freshmen 2017-18

1. Revision Exercise (pdf, 47kb)
2. Numerical Answer for the Revision Exercise (pdf, 36kb)

After you have completed the exericse, please see the follow-up advice below (click to expand):

Question 1:
Are you a local JUPAS student?

Question 2:
Are you a Mainland student who did Gaokao?

We suppose you went through the most most difficult mathematics syllabus in one of GCE A-levels, IB, SAT, or something equivalent. Very likely you have had an exposure in most of the topics that this Revision Exercise covers. (It is even better than the most difficult syllabus for local students.)

However, if you feel that you were struggling in the Revision Exercise, it is most likely because the syllabus you went through might put less emphasis on ‘drilling of techniques’. As a consequence you have difficulty when you run into questions which are not straightforward. Such a question tends to involve complicated calculation and combination of skills.

Please be reminded that being able to do complicated calculation and to combine various skills in handling a problem is an integral part of mathematical training at the university level. We urge you to spend the next few weeks to do some self-study, so that you are better prepared when the semester begins.

Question 3:
Did you do ‘Module 2’ at school?

If you did ‘Module 1’ or neither module at school, it is natural that you are unfamiliar with some of the questions in the Revision Exercise.

We urge you to spend the next few weeks to do some self-study on ‘Module 2’.

The questions in the Revision Exercise suggest which area you should focus on.

These books below, which are available at http://archive.org for free, may serve as reference:

1. C. J. Tranter: Advanced Level Pure Mathematics
2. F. Gerrish: Pure Mathematics Volumes 1, 2
3. B. D. Bunday, H. Mulholland: Pure Mathematics for Advanced Level

Alternatively you may try to find additional maths and pure maths textbooks of the ‘old curriculum’ for self study.

Question 4:
How much time on average does it take you to get the answer of one question in the revision exercise?

Congratulations. You have learnt school mathematics well and have not forgotten it after the summer vacation. We believe that you will encounter very few problems in our level-1000 courses, as long as you treat the coursework seriously.

You may proceed cautiously to do some self-study on multi-variable calculus, and perhaps beyond. A good textbook is Fitzpatrick’s Advanced Calculus.

You may also be interested in the challenges offered by the First-Year Honours Scheme in summer 2018. For detail, please visit the webpage: First-Year Mathematics Honours Scheme 2017

This will help you prepare for the level-2000 courses, probably in the second year.

We suggest you spend some time over the next weeks to recall what you might have forgotten in school mathematics; this may help you a lot when the first semester begins. (At which questions in the revision exercise do you struggle? This suggests where you need do revision.)

You will not encounter too many problems in our level-1000 courses, provided you remember that as a full-time student, your priority is to study.

You may also be interested in the challenges offered by the First-Year Honours Scheme in summer 2018. For detail, please visit the webpage: First-Year Mathematics Honours Scheme 2017

We are concerned that one or both of the things below has happened:

• You have forgotten some important mathematics over the summer.
• You may have missed out altogether some important mathematics that your school teacher should have covered.
• You have missed out nothing, but you did not have, or were not expected to have, the kind of training that this level requires.

You urge you to do some serious revision on school mathematics over the next few weeks, and pay attention in the level-1000 courses; otherwise you will have a lot of struggles.