Higher Maths Course - Key Facts

Introduction

I’ve taught many hundreds of Higher Maths students and have seen many successes and failures along the way. Higher Maths is a significant step up from National 5 Maths. I’m often asked by parents and students if they should take Higher Maths. This post aims to give you key information about the Higher Maths course to help you answer that, and other, common questions.

What is the Higher Maths Course?

Higher Mathematics has SQA course code C847 76 and is suitable for learners who have performed well in the National 5 Maths course and either wish to study Maths further or are required to study Maths further for their future plans – for example, to meet university entry requirements. Higher Maths is often a necessary requirement for students following technical careers and further education courses. Otherwise, students only need general Maths skills and numeracy. These are fulfilled by either National 5 Maths or National 5 Applications of Maths. Very few university courses, or careers, require Advanced Higher Maths (some exceptions do exist). So, for most students, Higher Maths is the pinnacle of their high school Maths education. Higher Maths is where students start to ‘specialise’ in Maths to some extent, studying challenging topics beyond ‘general’ Mathematics.

Who is the Higher Maths Course for?

The SQA state in the Higher Maths SPECIFICATION that the course is ‘particularly for students who have demonstrated an aptitude for National 5 Mathematics’ and who ‘are interested in developing Mathematical techniques to use in further study or in the workplace.’ From my experience I only recommend Higher Maths to students who need the qualification for their future, or who are really really up for it. Higher Maths is challenging and a significant step up from National 5 Maths. Students often take Higher Maths without a strong enough motivation and get caught out by the increase in course sophistication. Many technical further education courses require students to have completed Higher Maths, often at an A or B grade. Students don’t have to be ‘into’ Maths to do well at Higher, but all students have to be committed and practice the techniques.

What is Taught in the Higher Maths Course?

Higher Maths has traditionally been taught in three units – Expressions & Functions, Relationships & Calculus, and Applications. However, some teachers now prefer to order the course in their own way. There are many sub-topics but primarily the course centers around functions, which is odd since the preparatory course, National 5 Maths, barely mentions functions. The big topics in the Higher Maths course are Polynomials, Trigonometry, Straight Lines, and Differential & Integral Calculus. In fact, students could ignore the other topics and still do very well, not that I’m recommending that! You can view the full course syllabus HERE and read more about the course content in the SQA Higher Maths SPECIFICATION.

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Is the Higher Maths Course Difficult?

Higher Maths is a challenging course with a range of topics, techniques and skills. In my experience of working with Higher students of various abilities, commitment and diligence are the keys. If students make a strong start to the course and work diligently to practice the techniques throughout the year, they tend to do well. If they don’t, even if they have a lot of natural ability, they tend to struggle. Cramming Higher just before the final exam usually ends badly. Students should only take Higher Maths if they have an A or strong B grade from National 5 Maths. Even then I’ve seen many students get caught out and go from an A at National 5 Maths to a D at Higher. This is not because the course is beyond them, it’s just that they don’t adapt to the increased level and, therefore, aren’t as ‘on it’ as they need to be.

What are the Easiest Topics?

Easy is, of course, a subjective term but there are certainly topics that students tend to do well in or struggle with. Polynomials is one of the more manageable topics. So much so, that students who practice should expect to get most, if not all, of the marks. Straight Lines tend to be done quite well because students have experience of it from National 5 Maths. Recurrence Relations, which was removed from the 2022 final exams, is a small and straight-forward topic. The topics that students find easiest are those with procedural question types which can be anticipated and practiced.

What are the Most Challenging Topics?

There are two reasons why students tend to find particular topics challenging. Firstly, it’s technically demanding and they struggle to really understand it. Secondly, the question types may involve an element of problem-solving where memorising a procedure isn’t enough to get all, or sometimes any, of the marks. Trigonometry is challenging for many students because there are a range of techniques and some are very similar but answer different question types. Students often get them muddled. Differentiation and Integration, collectively the Calculus topics, are new types of Mathematics for students and can be technically challenging at first. Even when the techniques are mastered students will sometimes use them to answer the wrong question. Trigonometry and Calculus together account for at least 25% of the marks on the final paper. In some years, possibly way more.

How Does Higher Maths Compare to National 5 Maths?

National 5 Maths has a diverse curriculum with a focus on developing key algebra skills. However, Higher Maths assumes those algebra skills and focuses on more advanced skills such as Trigonometry, Functions and Calculus. You can view the National 5 Maths syllabus HERE. The two courses are very different in nature and Higher is not really the continuation from National 5 Maths that a lot of students expect. Rather, it’s a significant step-change in level with a focus on very different topics. That said, students who do not pick up key skills and techniques from National 5 Maths (in particular Algebra and Trigonometry) face the challenge of improving those skills while learning new topics at Higher. This is a very common scenario that I see a lot. It’s made worse since students tend to forget those skills over the summer holidays and it takes time to recall them again.

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How is the Higher Maths Course Assessed?

Higher Maths, like National 5 Maths, is assessed by two final exam papers – one non-calculator paper and one calculator paper. For the 2022 final exams paper 1, the non-calculator paper, lasted 75 minutes and paper 2, the calculator paper, lasted 90 minutes. Maths students at all levels often assume calculator papers will be easier but that is generally not the case. In fact, they often contain longer, more strenuous and time-consuming questions. Furthermore, there are actually not many questions where a calculator helps. Students can get caught out by the use of the calculator which is, in itself, a skill to be developed and practiced. You can view the past exam papers and marking guides HERE.

Do I Need Higher Maths for University or College?

Students should check the entry requirements for their chosen course as they are subject to change. In general, Higher Maths is only required for courses of a technical nature or which contains a Mathematical element. As you’d expect courses such as engineering, sciences, accountancy, architecture and others of a technical nature, will require Higher Maths. Some may require Advanced Higher Maths or, at least, it would be an advantage. If a student plans to take a higher education course which does not require Higher Maths then I would not recommend they take it as an elective. I’ve seen many students do that and run out of steam because it is a demanding course and, therefore, detracts from time and energy for their other courses. That said, if a student is particularly motivated to achieve Higher Maths, even if they don’t require it, it will look good on their record.