A Level Maths — How to prep after a summer off

Getting back into the swing of things after a nice summer break can be difficult at the best of times, but unfortunately you don’t get much slack when jumping in with A Levels.

What if I’ve forgotten everything?

The short answer here is simply “You haven’t!”
Let’s face it, you’re not going to remember everything you stressed over 3 months ago, but when starting new topics in A Level there is some groundwork that comes from your GCSE. Remember that GCSE is broad, whereas A Level is far more refined, so you’ve got to start somewhere.

Where do I start though?!

As it’s still early in the term there are plenty of opportunities you can take to get the ball rolling. Algebra’s going to be a key focus here and love it or hate it, you better get used to it as it’s going to underpin and tie together topics to help you get that top grade you’re after. Here’s a few points to get you started:

• Rearranging equations is vital at this point, so make sure you can pick out that 𝒙, and make it the subject.
• Quadratic equations play an important role with so many applications. Ensure you can spot, sketch, solve, complete the square and find the maxima / minima. I can’t stress how important it is to be able rattle through these questions.
• Simultaneous equations. You’re at the stage now where you’re not going to be handed a step-by-step manual of how to solve a question. You will often see this in context of a bigger problem where at the end you are left with two simultaneous equations to solve. You don’t want to have done all the hard work and then be caught out on the algebra at the end!
• Indices. Know all of the laws of indices like the back of your hand. This is an easy one to tick off and practice!
• Surds. If you’re comfortable with the GCSE surds content you will be in safe hands for AS. Another easy one to keep practicing and set that foundation for.
• Sketching graphs. A vital skill for A Level and one which will really help your understanding when dealing with some dreaded modelling problems. You should have a good grip on the shape of a graph, now its time to really look at the important coordinates to nail a rough sketch. We’re not looking for perfection in the sketch itself, but if you’ve got a wobbly cubic with the desired roots, 𝒚-intercept and minima/maxima you’re doing good! (not to mention using those quadratic equations skills mentioned earlier)

These skills are topics in themselves, but their applicability to other regions of the syllabus makes them so important. Being comfortable here will not only allow you to unlock more marks in the exams, but also give you more time in the exam, taking the edge off a bit.

Extra Steps

There are plenty of things you can do to focus your understanding of a problem. At the risk of sounding like a broken record, consolidation and repetition are essential to giving you a good base level. Know the tools you can use (and know them well) then apply them as necessary. I’ve listed a few additional opportunities you can take advantage of to push this:

• Think you understand something? Teach it to someone else! This is a great way to validate your mathematical reasoning skills if you can clearly communicate it to someone else.
• Find similar questions to show you understand the methodology. Remember, we don’t just want to memorise the answer! No two modelling problems are going to be the same!
• Share your knowledge. As well as teach an interesting question to someone else, if you’re able to help younger students revise it’s a great learning tool for you too. Consolidate that GCSE Maths and you’re helping yourself just as much as them, especially if it’s algebra!
• Read around the topic. There are plenty of great books out there to inspire you and help build a connection with how maths can model the world around us, from the trajectory of a football to the probability it goes in the back of the goal.