We’ve looked at the hardest GCSE Maths questions, so it only makes sense to look at the next level up and assess the hardest A-Level Maths questions. A-Level Maths is one of the most popular subject choices for students, as suitable maths qualifications are useful for many future degrees and careers. However, it is also notorious for being one of the most difficult A-Level subjects available. There are plenty of past paper questions that students have struggled with, and some of the hardest have been collated here. Whether you want some challenging practice questions to aim for the highest grades, or are simply curious about the difficulty of the current A-Level Maths, this article contains ten of the hardest past exam questions we could find.
Disclaimer: Of course, everyone’s mathematical ability is different. Some people will find a particular topic really easy, even if others struggle with it. Therefore, not every single question on this list will be hard for everyone. Instead, this list uses information from examiner reports to find out which questions the cohort as a whole found really difficult to score highly on. If you have come across a particular A-Level Maths question you found really difficult that you think should be included on this list, feel free to vote for it in the poll below!#
The three most common exam boards are AQA, Pearson Edexcel and OCR. All the questions included here are from one of these exam boards, from the most recent specification (which first came into use in 2017). Keep reading for the most difficult A-Level Maths questions we found!
Table of Contents
1. OCR June 2018 – Paper 2, Question 13
This question, found on OCR’s Pure Mathematics and Statistics paper in 2018, was found to be really challenging for students. Click here for the full paper that contained this question, but a screenshot is included below.
The main reason this was seen to be a difficult question was the combination of topics involved. Although the paper as a whole contained both pure and statistical work, they were both included in the same question here. Many people found it difficult to combine different topics involved – probability, as well as binomial expansion.
According to the examiners’ report, which can be found here, very few students were able to link the different parts of the question together. In fact, for the last part of the question, it states that ‘Almost no candidates gave a correct solution based on their answer to part (iii)(a)’.
This question was so contentious that there is a long forum thread discussing it, which can be found here on The Student Room. Alternatively, check out this link for the mark scheme to the paper. This has the correct answers, as well as a step-by-step demonstration of different methods that can be used to complete this question.
2. Edexcel June 2019 – Paper 1, Question 10
Although there were not a huge number of marks available for this next question, the students taking the exam found it difficult to score highly. Have a look at the question, shown below, or in the exam paper here.
According to the examiners’ report, the mean mark for this question was just 1.7 out of 6. For this statistic, as well as other official comments on the question, you can find the examiners’ report on this link.
The main difficulty with this problem was that many students were unfamiliar with methods of proof, which is essential for the first part of the question. The official report says that a surprising number of candidates left this question blank or found it difficult to make a significant attempt at it.
Potentially, A-Level Maths students think that proof is a smaller topic, and they would rather focus on more common areas of the specification, such as calculus. This would suggest that it is not the question itself that is hard, but that students put less focus on this topic area.
Click here for the mark scheme to this particular question. Alternatively, for some useful revision resources on proof, have a look at this link from Physics and Maths Tutor. It is designed specifically for Edexcel – the exam board this question was taken from.
3. Edexcel June 2019 – Paper 2, Question 8
This next question, from this Edexcel exam paper, focuses on the A-Level Maths topic of sequences and series. However, it also incorporates aspects of other topics, such as logarithms.
While both parts of this question may seem daunting at first glance, they are actually not worth very many marks. This suggests there is not as much working out needed as you might think.
In fact, the examiners’ report seems to find that many students were able to attempt this question, or start promisingly. However, it was more difficult to arrive at the final answer, with various common mistakes made.
Nevertheless, this emphasises the importance of having a go at a question, even if you aren’t sure how to finish it. There are almost always marks available for the first steps to the right answer. For example, in this question, the report says more successful candidates began by writing out the terms of the series.
4. Edexcel June 2019 – Paper 2, Question 10
Have a look at this next question, which is centred on the topic of vectors, found in this Edexcel paper from 2019.
A range of marks were achieved for this question. The examiners’ report tells us that this question was able to distinguish between students of different abilities, because it began with more straightforward maths, and gradually got more difficult. Overall, very few students managed to get full marks.
This report can be found here. It also contains explanations of common mistakes made when candidates attempted this question. It is helpful to look at this alongside the mark scheme, linked here. You can see the mistakes to avoid, as well as the correct answer and methods to reach it.
Vectors is actually a topic at A-Level that uses many skills from GCSE. However, many students still struggled with this question. Have a look at this Think Student article for plenty more information on how hard A-Level Maths is in comparison to the GCSE.
5. AQA June 2019 – Paper 2, Question 6
Just 12% of students were able to get all the marks available for this next question, according to the examiners’ report, which can be found here.
The main problem students had with this question was getting started. The trick is to notice that the equation of the curve can be rewritten in the form R cos ( x ± α ) or R sin ( x ± α ).
This conversion is usually taught as part of the A-Level specification. Often, it can be difficult to take a step back from a question and make connections to things you have learned in class. This is particularly hard in the heat of an exam situation.
Have a look at this article from Think Student for a range of tips on time management in exams. This can help to make sure you are focussed on the question itself and what you can do to solve it, rather than the stress of the exam setting.
6. AQA June 2019 – Paper 3, Question 15
The next question, from this AQA paper, is part of the statistics section of the A-Level Maths course. It mainly requires skills and knowledge about hypothesis testing, but also needs students to have an awareness of correlation.
The examiners’ report suggests that it was not the content of this question that students struggled with. Instead, they found it hard to know exactly what the question was asking, and therefore lost marks or had working out that gained no credit. Check out the mark scheme here for a guide to what, exactly, the marks were awarded for.
For example, although they could compare the necessary values, very few students gained the final mark for the actual inference statement. You can read more about this in the report here.
This is more of an issue with exam technique, and how familiar you are with question styles, than a difficulty with the maths skills involved to answer this question and get full marks. Therefore, it emphasises how important it is to practise exam questions, under exam conditions if you can. This makes sure that when the real exams come, you are not held back because you do not know what to expect from the questions’ format or wording.
7. AQA November 2021 – Paper 1, Question 11
According to the examiners’ report for this paper, less than a third of students were able to make any progress on this next question, from this 2021 paper.
With 8 marks available, this is clearly a long question that will require a lot of working and mathematical skills. While many other questions are broken down step by step, you do not get the same guidance through this problem.
The general topic tested here is calculus, specifically, forming and solving differential equations. This is an area many students find difficult when learning it in lessons, so it is no wonder this lengthy question proved so difficult in the exam itself.
Indeed, it was the fact that a differential equation is involved that tripped up many students. Without this key step, they found it difficult to make a good attempt at this question. For more on this, have a look at the examiners’ report here.
However, it is also worth noting that this was from November 2021 exams. Autumn exams are usually resits, so fewer people are taking them. In addition, disruption to education from COVID-19 that year may mean students found the exams harder than they would have otherwise.
The solution to this question, along with the steps along the way that would get you credit in an exam, can be found in the mark scheme here.
8. AQA November 2021 – Paper 2, Question 9
The next question posed a real challenge for students sitting the exam. The examiners’ report, which you can have a look at here, says that many students left parts of the question blank, unable to attempt to solve the problem.
The full question can be seen below. Alternatively, the full exam paper is available here.
This is clearly a long question, with lots of information to read at the beginning, and lots of different stages. However, it has been broken down into different sections, which can be helpful to guide you through, rather than one large question worth all 9 marks.
If you want to have a go at this question, check out the mark scheme here for step by step solutions to each part.
One bit of advice the examiners’ report had was for students to make use of any diagrams given to them. Diagrams are really helpful in A-Level Maths. They often help you to visualise what the question is asking, and it can be helpful to annotate them as you work through the question.
For more tips specific to A-Level Maths to help you get the top grades, have a look at this article from Think Student.
9. AQA November 2021 – Paper 2, Question 18
Next on the list is a question about the mechanics content of the A-Level Maths specification. The examiners’ report, which you can access here, shows that candidates struggled with all three parts of this question.
It can be daunting to see a lot of information to read, followed by questions worth a lot of marks. As with the previous question, it can be helpful to use a diagram to make sense of what is involved in the problem.
Ultimately, as mentioned, it is always useful to have a go at the question, even if you don’t understand it. The examiners’ report for this question said that many students left parts blank, so could not get any marks. Making a start might be worth credit in the mark scheme, but it can also make next steps for solving the question clearer.
10. Edexcel June 2022 – Paper 1, Question 16
The final question on this list was the final question on this Edexcel paper from 2022. The examiners’ report says that the mean mark was just 1.9, out of 9 total marks available.
As the last question on the exam, you may expect it to be difficult. Indeed, students struggled with this, many leaving it blank. There were also a range of common mistakes made, which are outlined in the examiners’ report here.
It requires calculus skills of both differentiation and integration, as well as knowledge of how parametric equations fit into this. This is not the only calculus-based question featured on this list, reinforcing the idea that this is one of the hardest areas of A-Level Maths.
These pages of Physics and Maths Tutor may be useful to revise A-Level calculus: click here for differentiation, and here for integration. Alternatively, if you are ready to attempt the question above, you can find the mark scheme here.
Where can you find more difficult A-Level Maths questions?
Hopefully, this article has given you an idea of some of the hardest A-Level Maths questions available. If you think these are incredibly difficult, you are not alone.
If you are looking to improve your maths skills to prepare for the final A-Level exams, the best way to do this is to practise. There are a huge number of past papers available on official exam board websites. Make sure to enter the correct qualification – you don’t want to accidentally practise with nothing but GCSE Maths papers!
While past questions aren’t the most fun thing to do, it really works! The more practice you get, the better prepared you will be for your final exams, and to tackle questions as hard as the ones in this article.