Should I take Maths for A Level?
Mathematics has been the most popular A Level choice for some time now. This is due to Maths being a highly applicable subject in a range of professions, and is often a requirement for some university degrees. While it is a popular choice, it is also a challenging subject that will require a lot of work to get top marks.
After completing GCSEs, students will have to make the important decision of choosing which subjects they will continue to study for the next two years. Most people do only 3 or 4 subjects for A Level, so choosing subjects that you are eager to study in depth is vital, as you will spend a lot more time with each of these subjects. With this in mind, students should consider whether Maths is the right choice for them from the perspective of ability and interest.
Many schools will only let students take A Level Maths if they achieved a 6 or higher in their GCSE Maths exam, though this may vary at different institutions. If you are on track for a 7,8, or 9 at GCSE, then A Level Maths will likely be within your ability.
Finally, students that are aiming for a certain degree should confirm whether Maths is a required or suggested subject for their course. Potential Maths or Physics students should certainly be taking Maths (and often Further Maths) at A Level, but many other STEM subjects also ask for a strong grade in Maths. For example, courses in Medicine, Psychology, and Computer Science may require students to take Maths or a similar subject for A Level.
What is the difference between Maths and Further Maths?
Further Maths is a whole additional A Level, so completing Maths and Further Maths will account for two separate qualifications. Further Maths explores the topics from the Maths course in more detail, as well as introducing more sophisticated ideas such as complex numbers or proof by induction.
Should I take Further Maths for A Level?
Further Maths is an excellent choice for students looking to study a STEM subject, particularly when applying for competitive courses. Many university courses recommend that applicants take Further Maths, so make sure to check university websites for their entry requirements. As some schools do not offer Further Maths, it is often not a strict requirement for entry - that said, if it is a recommended subject then it will likely be almost essential for easing the transition to higher education. For example, Mathematics degrees usually only list Further Maths as a recommended subject, not a required course. However, plenty of material from Further Maths appears at degree level, so applicants are given a big head start if they took this course at A Level. Some other courses that can recommend Further Maths are Computer Science, Engineering, or Biochemistry.
Further Maths is a popular course, with over 15,000 students studying the subject, but this is only a fraction of the students that take Mathematics. This is due to Further Maths having a less broad appeal in university application, as well as the fact that Further Maths is much harder than the straight Maths course. Schools will ask that students achieve at least a 7 (but usually an 8 or 9) at GCSE to take Further Maths at A Level, and since these courses are worth two A Level qualifications, students will find that about half (or more!) of their A Level work is centred on Mathematics.
Students should consider whether Further Maths will be useful in their future studies, as well as whether they enjoy Mathematics enough to complete two full A Levels in the subject. A prospective Maths student will likely relish the opportunity to focus a large portion of their time on Mathematics, while a student hoping to study a course that doesn’t require Further Maths, like Psychology or Law, may decide that the regular Maths qualification would be enough for them. There is no one-size-fits-all approach, so having a conversation with teachers or career advisors will be greatly beneficial in finalising your decisions.
Does Further Maths help with A Level Maths?
Completing the Further Maths course will help students to consolidate their knowledge from A Level Maths, and as a result, students that take Further Maths will often achieve some excellent results in the straight Maths course. That said, success in Further Maths is built on the foundation of the Maths course, so students that have had a lot of difficulties with Maths will likely have a lot more trouble in the Further Maths course.
How to get an A* in A Level Maths
Independent Review - A Level Maths is a broad subject that many students find highly challenging, and a likely problem will be older topics getting forgotten as students move on to the next part of the course, particularly when moving between Pure Maths, Mechanics, and Statistics. Hopefully, teachers will set their students regular tests on this past material to keep it fresh, but students can take this into their own hands as well. Frequently looking back over the past month’s work will boost recollection and reduce the revision workload for the end of the year significantly.
Calculator Skills - While students will likely be very comfortable with the standard functions on a calculator by the time they take their A Levels, there are plenty of additional techniques that can boost their score. For example, many exam-approved calculators have an integral calculator, and while this cannot be used to solve the question (showing your work is necessary!) it can definitely be used to check your answer at the end.
Time Management - Maths exams are often quite time pressured, so being able to cope with these conditions will help students to achieve the highest mark possible. An excellent technique is to work through the paper from start to finish, and skip any questions that you are unable to solve. This guarantees that you will complete every question that you are capable of finishing, and you won’t waste time on a question that you won’t be able to figure out. After finishing the easier questions, you can go back to the difficult questions and hopefully scoop up a few extra marks before the end of the test.
Past Paper Practice - Understanding the course material is essential for Maths, but putting that knowledge into practice is what will earn the best grades in the exam. Regular practice with past paper questions will develop student’s problem solving techniques, and timed practice without notes will acclimate students to the style of examinations.
Common Pitfalls
We have gone through a range of examiner’s reports from the new A Level exams, and picked out a few common errors that arise across the years, as well as some personal tips from tuition experience. This is by no means an exhaustive list, but focussing on some of these areas may help to boost your mark from an A to an A*.
Careless errors - Whether looking at students in Year 7 or Year 13, one of the most common places that students lose marks is in simple mistakes like misreading the question, failing to put the correct units in their answer, or forgetting to check their negative signs in an expansion. Improving this skill comes with practice, but picking up some techniques for checking your work (such as calculator functions) can help eliminate these mistakes.
Calculus - This is a notoriously challenging topic which is usually new for students in Year 12. Making sure to understand the process used in Differentiation and Integration fully will help secure top marks, as harder A Level questions will demand deeper knowledge of these topics.
Trigonometric - Identities Using these identities is not that difficult in a vacuum, but it can be difficult for students to notice when they can be used in more open ended questions. Being confident with these identities will help to avoid getting lost in these complex questions.
Modelling - A focus in the new specification is applying mathematical ideas to real life scenarios, and usually constructing or explaining a model for these situations. Generally, students have struggled with questions that require an explanation, so becoming familiar with these questions is a must.
Large Data Set - This was a new addition to the Statistics paper, and has been generally poorly attempted in papers since. Taking some time to get familiar with the data set would help candidates aim for the very top marks.
Resultant Forces - This is a very common Mechanics topic that is usually not too difficult for most students, but there are occasional questions that ask students to find more difficult forces, such as resultant forces acting on a pulley, or questions involving scale pans.
How to get an A* in Further Maths
All of the A Level Maths advice above applies to Further Maths, and perhaps to a higher degree: independent review will help students stay on top of the large and varied workload, calculator aptitude will help with checking answers and avoiding computational errors, and Further Maths exams tend to be even more time pressured than the Maths course so good exam technique and plenty of practice are essential.
Don’t neglect the basics - Further Maths is an extension of the Maths A Level, and so strong fundamentals are necessary when tackling harder content. Taking some time to revisit the material from the previous year’s work will help to build a full picture of the course, and ensuring mastery of core A Level skills will make it easy to transfer those skills to difficult Further Maths topics.
Ask for help - While this advice is true for any A level subject, Further Maths is an especially difficult course to grasp conceptually. Individual students will find different areas of the course particularly challenging, and trying to keep up with the increased workload of A Levels can often lead to these difficult topics remaining a mystery throughout the year. When a topic doesn’t make sense, talking to a friend, teacher, or tutor can help clear up any misconceptions. You might find Collisions from Further Mechanics challenging, while your neighbour may struggle with the Geometric Distribution from Further Statistics, so having a chat about these areas together will likely help to address any concerns and strengthen your knowledge.
Common Pitfalls
As stated above, this list is based on information from examiners reports as well as personal tutoring experience. There are plenty of other tricky points in the Further Maths course, but these are a few of the common areas that students find difficult.
Many of the usual errors made in the regular Maths course also apply to Further Maths, particularly careless errors as many Further Maths questions require a lot of work which raises the chance of small arithmetic or typographic errors.
Induction - These questions are usually quite varied, and there is not a single approach that works for every type of question. Broad practice of this technique is key, especially as induction questions can include algebra, series, matrices, and other topics.
Probability Generating Functions and Distributions - One of the most difficult Statistics topics, understanding the harder variants of PGF questions is likely to make a candidate stand out. Being able to recognise when to use different distributions and knowing the conditions for when a distribution is applicable are also common areas for losing marks.
Significant Figures - In Mechanics papers, it is stated that the acceleration from gravity g is 9.8, while many candidates use the (more accurate) g value 9.81, which loses an accuracy mark. Similarly, answers should be rounded to the number of significant figures given by data in the questions (which includes g = 9.8). These are very small errors that could make students narrowly miss grade boundaries.
Open-ended Questions - A new focus of the curriculum is questions that have less structure, and the results so far have shown that students find these questions difficult to complete. Be prepared to tackle questions that don’t guide you towards a given answer or, for example, ask you to calculate an integral without telling you which method to use. A lot of varied practice questions will be key to mastering this idea.
What are the best universities for Mathematics?
The Complete University Guide ranks the best UK universities for Maths as follows:
- Cambridge University
- Oxford University
- University of Warwick
- Durham University
- Imperial College London
- University College London
- London School of Economics and Political Science
- University of Bristol
- University of Bath
- University of St Andrews
These rankings should not be taken as gospel however, as there are many other factors to consider when applying to a Maths course at university. Some universities will offer different joint courses with Maths, such as the Mathematics and Philosophy course at Oxford, and the materials covered by the course will vary in different institutions, particularly in the later years of the course. Overall ranking is a fairly good judge of a course’s quality, but taking a student’s individual interests and needs into account will be more beneficial than simply choosing the ‘best’ university!
Recommended resources for A Level Maths
A collection of practice papers and focussed exercises for A Level Maths and Further Maths.
A huge database of powerpoints and worksheets for all of the A Level papers.
Questions separated into each topics
Recommended Youtube Channels for A Level Maths and Further Maths
Tutors for A Level Maths and Further Maths
With tutors based in London and available online to families around the world, Keystone is one of the UK’s leading private tutoring organisations. We have a range of specialist A Level Maths and Further Maths tutors who can assist students approaching A Levels and university admissions tests for Maths.