In this post, we will look at top 10 hardest GCSE maths questions that Studyply found in the past papers. The ranks are based on the examiner reports. These questions are extremely tough with different topics involved. Circle equations, trigonometry, simultaneous equations, just to name a few. Make sure to try each of them yourself before looking at the answers, but don't worry if you get it wrong. You can only become good in maths through practice and many mistakes. All answers are attached for each question. If you manage to solve all of these questions however... well done you are officially in the top 1% of the country :)
10. June 2017 AQA GCSE Paper 1 - Q27
Let's see if you are an expert when it comes to algebra and circle equations. A quick tip: make sure to recite the definition for a tangent to a circle before starting the question. Good luck!
From the examiners report: "This question was not well answered, with many students not using the gradient of OP as the starting point of their working. It was common to see sqrt(17), either from the equation of the circle or from the application of Pythagoras’ Theorem." Indeed the crucial step that many students missed out was realizing that finding the gradient of line PO would them gradient of the tangent (using negative reciprocal). A tangent to a circle is perpendicular to its gradient and touches the circle at one point only. So finding gradient of PO and using negative reciprocal would be the correct approach:
9. June 2019 Edexcel GCSE Paper 3 - Q22
A similar question, so if you finished the previous question and understood it then this one should not be a problem. Just a few extra steps and details:
As the examiners noted: "Fully correct answers to this question were seen only rarely. It was found to be the most challenging question on the paper. Having said that, a significant proportion of students were able to score at least one mark for a successful start by identifying that angle OAB is a right angle or for a correct process to find the radius of the circle. Few students could see how to use the coordinates of P in order to derive an equation by either using the equation of the circle or by using Pythagoras’s Theorem. The evidence from students’ scripts showed that more students took the former approach, quoting x 2 + y 2 = r 2 and then substituting x = 3p, y = p, r = 8 to get an equation in p. Unfortunately, the lack of of use of correct notation, that is a pair of brackets, meant that many students wrote 3p 2 + p 2 = 82 instead of (3p)² + p 2 = 8². These students usually went on to simplify their equation to 4p 2 = 82 . " A similar question to the first one, but with some extra steps. Here is the mark scheme:
8. June 2017 AQA GCSE Paper 2 - Q24
According to the examiners report: "Many students found this question to be one of the most challenging on the paper. Quite a lot of students could work out the frequencies but very few were able to use them to deduce the quartiles. Those who could correctly work out one of the quartiles usually found the lower quartile. Often 45, instead of 48, was divided by 4 when attempting to work out the lower quartile. Working was often difficult to follow. "
Histograms are one of the hardest topics in maths, particularly when it comes to finding the mean, interquartile range and estimating for some value. Here is how to do this question:
7. November 2018 AQA GCSE Paper 3 - Q20:
As challenging maths questions go, this algebra questions can prove to be a difficult one. Let's see how good you are with algebra.
The examiners mentioned: "This question was not well answered, with a high number of non-attempts and very few students having any success. Almost all students did not know the correct method to proceed with this question. A few students expanded the brackets correctly. The common error was to change the sign of the right hand side of the equation. " Indeed a very difficult maths question, here are the answers:
6. November 2013 Edexcel GCSE Paper 1 - Q24
This question will definitely test your skills in vectors. Proving is perhaps the most challenging part of vectors. Don't worry if you find this easy, harder vectors are coming.
Quite a challenge? Wait until you reach Questions 3 and 2! Here are the answers:
5. June 2015 Edexcel GCSE Paper 1 - Q23
This semi algebra question will put your logical abilities up to test. Will you be able to solve this one? Comment below or on my YouTube: https://www.youtube.com/channel/UCNESUWAws9YlyVwkuXqWh8Q
This will make many students scratch their heads. Here are the answers:
4. November 2014 Edexcel GCSE Paper 1 - Q23
A very hard probability question. Like I promised there will be difficult questions from a range of topics. Try it!
Probabilities can be very difficult. This challenging question definitely made you think. Here are the answers for it:
3. May 2019 AQA GCSE Paper 1 - Q22
As promised, here is a harder vector question. Enjoy!
As the examiners report states: "The majority of students were successful in part (a), although some failed to actually show the required calculation, stating only that AC was –3b and AD was 6a + 7.5b Little accurate working was seen in part (b), although a reasonable number of students picked up one mark for stating that BC was ka + 3b or that BD was ka + 6a + 7.5b". This definitely is a difficult vector question, so here are the answers:
2. November 2017 Edexcel GCSE Paper 3 - Q21
One more vector question but even harder. Can you solve this super challenging and confusing vector question?
This is perhaps the most difficult vector question I've seen in GCSEs. Here is the mark scheme for it:
1. May 2022 Edexcel GCSE Paper 1
The infamous summer 2022 GCSE math question that shocked every student. I am sure you have already seen and attempted it, but in case if you missed it or would like to do it again, here you go..
Here is a hint:
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