Revision Tips

Don’t leave your revision until the last minute. There is a lot to revise, and it is going to take time.

It is completely natural to forget things due to something known as the Forgetting Curve. The best way to combat this is to review things regularly as this decreases the rate at which forgetting happens. This is known as Spacing. But to do this, you need to plan ahead, not just cram the night before!

The best way to get better at solving Maths problems is to solve Maths problems. The more exam questions you answer, the better you will do in the final exam.

What is rarely helpful is rereading notes or creating summaries (see Strengthening The Student Toolbox).

But it is very easy to trick yourself that you are solving problem when you aren’t really. If you watch a video on how to solve a problem, or look through the markscheme, you develop a sense of knowing how to do it...but you didn’t actually do it. Your brain tricks you into thinking you can do it next time, but there is no evidence that this is true.

Put away the answers and try to answer each question yourself first, without looking anything up.

As mentioned in Start Early, the spacing effect is a really helpful tool to learn material better. But this means coming back to it multiple times, not just once and done.

The easiest way to do this is to do a little bit of Maths every day. About 20-30 minutes a day (throughout the course ideally, but start as soon as you can) will build up to a lot of practice in the long run, and give you a chance to review topics regularly.

In the run up to exams, do 3-4 Section A questions or 1 Section B question.

There are some topics that are assessed a lot more than others in the exams. Calculus makes up about 40% of the course, and so should be a priority.

Analysis of the A&A HL Past Papers reveals the topics that come up more regularly, based on the structure of this course. You should use this to look at the topics which are most beneficial to focus on. You can see the most common topics by looking here.

For these high leverage topics, you want to practice until you can’t get it wrong.

It is also important for you to analyse your own areas of weakness. Look at tests you have done and identify any topics that are always a problem. If these are a high leverage topic, it must be a top priority!

NB - there were 11 exam sets included in this analysis, so any topics appearing more than 11 times occur more than once per exam set on average

There are a lot of formulae given to you in the formula booklet. It is really important to know where to find these quickly, and what is there. Familiarising yourself with the formula booklet is a must.

But there are some things you need to know that are NOT in the formula booklet. You can use the Key Facts on each lesson page (and at the end each unit) to review these.

Some of these include:

• Laws of Indices

• Structure of Proof by Induction

• Definition of Conjugate

• Definition of Domain, Range, Even and Odd functions

• Perpendicular Gradients

• Finding asymptotes, roots, y-intercepts

• Graph Transformations

• Criteria for discriminant

• Remainder / Factor Theorem

• Unit Circle

• Exact Values

• Finding constants in trig functions (amplitude, principal axis, period, phase shift)

• Stationary Points, Increasing and Decreasing Functions

• \(\int \frac{f’(x)}{f(x)}dx=\ln f(x)\)

• Using GDC for Statistics Calculations

• Definition of Outlier

• Set Notation

• Mode and Median of Random Variables

• Definition of a fair game

• Indeterminate forms for l’Hopital

• l’Hopital’s Rule

• Solving Separable DEs

• Homogenous DEs

• How to use integrating factor

• Vectors are perpendicular if scalar product is 0

• \(a\cross b\) is perpendicular to both \(a\) and \(b\)

• The normal vector to a plane is the cross product of two direction vectors

• How to calculate modulus and argument of complex numbers

• Multiplication of complex numbers in polar form

You need to practise answering exam questions, as these are what you will have to answer in the exam. Textbook and ‘drill’ questions have a vital role in initial learning, but you want to move on to problem solving using this knowledge.

If you find a topic that you are really struggling with, then fall back on a textbook to get lots of practice of the basics of the idea, to really embed the concept, then move back to exam questions.