Written by Steve
Having finished GCSE Maths or equivalent before the summer began and deciding that you want to study A Level Maths, you may think that you have done all of the ground work and that the transition to A Level will be easy. It is true that many people can begin the A Level course without any work during the summer, but the truth is that the step up is big and preparation early on can make the course a lot easier once you are trying to do it alongside other new subjects in September. So spend some time now making sure that you are confident with the prerequisite knowledge and have the correct equipment to hand before you start.
Regardless of which exam board you are going to work with the first thing that you need to do is ensure that your algebraic skills are strong. Make sure that you can do all of the basic skills from GCSE i.e. use laws of indices; solve linear, quadratic and simultaneous equations; simplify surds by rationalising; recall the values of sine, cosine and tangent of 30, 60 and 90 degrees; plot graphs of linear, quadratic, cubic, exponential and reciprocal functions; and understand how functions are transformed using the appropriate notation. There are a variety of textbooks for example the ‘CGP Head Start’ guides or the ‘Collins: Bridging the Gap between GCSE and A Level’ (which can be purchased on Amazon or at Collins.co.uk) or online resources that you can use to practise these. For example you might like to try studymaths or BBC.
The new A Level Maths has changed form recently to reflect a greater focus on applications, in addition to enjoying quite a few syllabus changes. To address these considerations, once you have a good review of your algebra skills, you want to look at how your algebra skills link together. For example knowing that the solutions to simultaneous equations can be illustrated using graphs to show the coordinates of intersections or understanding that by combining ‘solving’ and ‘completing the square’ you can sketch a reliable graph by finding the minimum point. Make sure that you can prove the laws of indices for multiplication, division and raising to powers and that you understand how this links to surds and their rules. Draw yourself a mind map of the key topics and find questions from your previous notes/textbooks etc. that show the topics combined. For example:
‘The length of a rectangle exceeds its width by 4cm. The area of the rectangle is 96cm2. Find the dimensions of the rectangle.’
This question links together area, solving quadratics and validity. Link together topics that are inverses of each other. For example, link together solving equations with substitution, as the solution can be verified by substituting it into the original equation. This will allow you to show an understanding of how they can be used to verify solutions and may prove useful come September, and throughout the year.
You should also be aware that the new A Level Maths requires you to study both Mechanics and Statistics and in particular that you will have to work with a large data set. This means that you will need to recall how to calculate summary statistics such as mean, median, mode, range and quartiles from both lists and grouped frequency tables. Any of the GCSE revision textbooks or online resources will be able to help you with this if you have forgotten.
Finally make sure that you have a calculator that is going to satisfy the criteria for your exam board and begin to familiarise yourself with it. Your school/college may have already specified which type of calculator they would like you to use. If not, Innovators in Mathematics Education has information about the different types of calculators and a few activities that you can use to start familiarising yourself with them.
The new A Level is an exciting opportunity to learn how Maths can be applied to real life situations, and makes you aware of possibilities for further study. When you arrive in September and your mathematical adventure continues, be sure to question why techniques work and how they link to your current knowledge. The best results will be seen from those students who are inquisitive, can understand how topics relate and who can explain why techniques and solutions work. Remember that you will be completing the same qualification as thousands of others and to be successful, you must be able to explain why your answer is valid. Most importantly of all, enjoy the course, Mathematics at A Level is interesting, useful and offers you the opportunity to develop and understand a large variety of transferable skills. You will open up enormous possibilities for yourself at the end.
Be sure to give us a shout if you have any questions!