Maths muddles

A question that was in a recent GCSE maths exam has sparked outrage among the thousands of pupils who sat the paper this past week. By the afternoon the issue was trending on Twitter, highlighting the difficultly of one particular question.

The question that drew all the attention was: “Hannah has 6 orange sweets and some yellow sweets. Overall, she has n sweets. The probability of her taking 2 orange sweets is 1/3. Prove that: n^2-n-90=0.” (^ means “to the power of”.)

Not only was the question trending on Twitter, an online petition has been set up calling for the board to lower the grade boundaries when marking the paper. The student behind the petition explained that “thousands of young people who sat the exam today found the paper disastrously hard and this is especially unfair considering how reasonable papers were during the previous years. This isn’t because of lack of revision, but because of the sheer difficulty of the paper. Fair enough the first half was alright, however after that it goes quite downhill, proving impossible for even the most able students”.

When asked about the question under the scrutiny, a Pearson spokesperson said that the question was aimed at students aiming for A and A* grades and that it would ensure students were “treated fairly” when the papers were marked.

In May, exam boards had been asked to rewrite questions for the GCSE maths papers, after being told they were too tough for even the brightest students. Pearson, who created the Edexcel paper that is causing the uproar, were one of the boards asked to revise their papers. A representative of Pearson stated that “our exam papers are designed by an experienced team of expert teachers with a deep understanding of the subject matter; in the event that any one paper turns out to be more or indeed less challenging than usual, our marking and grading process always ensures students are awarded the grades they deserve”.

But what do you think? Could you work out the answer? Have the questions become too challenging? Or were previous papers too easy and needed to be made harder to prepare the future generation? Have your say here..

29 thoughts on “Maths muddles”

1. Marion says:

Hi what is the answer I worked it out as ten sweets in total meaning four yellow

2. pbingwa says:

Hannah has 6 orange sweets +some yellow sweets.
Total number of sweets is n.
P (2 orange sweets) is 1/3
Proving that n^2-n-90=0 :
P (1st orange sweet)= 6/n
P (2nd orange sweet)=5/(n-1)
P (1st and 2nd orange sweet) is
6/n × 5/(n-1) = 1/3
30/n(n-1) = 1/3
30/(n^2 – n) = 1/3 {cross multiply}
90 = n^2 – n
0= n^2 – n-90
n^2 – n -90 =0…….I have done this by considering the information given in the question bit by bit. All students can do it in the future if we encourage them to be reflective thinkers, who are confident to tackle any question, and don’t put up mental blocks when they meet unfamiliar questions.

3. K Rowan says:

My mum got an O-level grade 6. After nearly 45 years since taking it, she came to the answer in her head in 2 minutes. I don’t think the question in the paper is the concern. I think it is the standard of students today.

4. Peter Brodie says:

Set towards the end of the paper for A and A* candidates, I don’t see it as unreasonable if they’ve been trained to answer questions of this sort. It wouldn’t have been considered at all out of place fifty years ago in O Level papers. A quick factorisation produces the two factors of n= -9 or +10. Since possessing a negative number of sweets is a material impossibility, the total number of sweets must be 10, six of which we’re told are orange, leaving the remaining four to be yellow. Unless the reference to the probability was intended for use in a further part of the question, it was an irrelevance except for its potential as a check on the answer of 10, for which it works.

5. Wanda says:

Re-calibrating the grades could be seen as unfair to all the students who were able to solve this problem.

6. Timothy Skinner says:

Factorise it first just to see what is going on. Get (n-10) (n+9). So n=10.
What have we got? First “event” is 6 /n, second will be 5/n-1.
Multiplying them gives 30/n2-n. This =1/3.
Multiply both sides by 3. Get 90/n2-n = 1.
I did these simple quadratics in the 3rd form at my grammar school in 1965.
The whole school did O level Math and English Language at the end of the 4th year and Additional Math O level along with 7 other subjects at the end of the 5th year and you had to get grades 1 to 3 of 6 pass grades to get onto an A level in any subject.
Saying this simple quadratic is A level standard is absurd.
No wonder UK is now way down the international league table behind such as Singapore.
The future of UK in the data age will be bleak, one of the first post-industrial societies with regression back to pre-industrial times.

7. Anna Max says:

As a maths teacher whose subject knowledge peaks at GCSE A* topics and whose school teaches a different exam board, I was disappointed when I tried the question and got the answer easily straight away. I was very amused and intrigued by all the tweets and buzzfeeds previous to trying the question and expected to be stumped. Mathematics is meant to teach problem solving skills and the maths in life needed isn’t always prescribed to us to say what method to use. I enjoyed doing the question but expect that only those that get an A* will have got marks on the question whereas sometimes my students manage to gain marks on A* questions despite being on a C/B border line. Sadly I’m not familiar enough with the boards papers to know how unusual that question was from previous papers. It seems in line with what I expect to see on OCR though. I think however partly the fuss here has happened because our students now have a voice via social media which will have only been heard by their peers and people they actually talk to previously. Of course the grade boundaries will be adjusted according to how the nation does on the paper. Afterall the exam board needs the business for next year.

8. Philip Watson says:

If she has 6 orange sweets out of n, the probability of picking an orange first time is 6/n.
The questions doesn’t say explicitly that she doesn’t put the orange sweet back after picking it (to my mind, that’s the only issue with the question), but that’s implied for the rest to work.
So she picks her second sweet: she now has 5 orange sweets available, out of a total of (n-1) sweets, so the probability of picking a second orange sweet is 5/(n-1).
To find the combined probability of two successive but independent events, we multiply their individual probabilities, so get (6/n) x (5/(n-1)), which we are told is equal to 1/3.
Multiply through the LHS to get 30/(n²-n) = 1/3
Rearrange, and you get the quadratic n² – n – 90 = 0
QED

9. Jon says:

I think that the uproar shows a deep misunderstanding in the examinations process.

The question was do able. and actually relatively easily, however, the fact that it involved a scary looking equation that you had to prove put a lot of people off.

A lot of people will sit an edexcel higher tier paper in order to get a C grade, A C grade requires approximately 30 marks on the edexcel higher tier papers, the call to lower exam boundaries, is surely ridiculous!

Mathematically edexcel is often challenging however, the problem solving aspect is far less so than when compared to the worded questions that are present in WJEC.

Lastly the question that caused uproar I believe was 2 marks, so 2% of the paper.

I think more questions like this should be included, ones that can’t simply be predicted.

10. Ultimate Maths Tutors says:

This is a reasonable question for any learner working at A/A* level. It requires the application of principles of probability, made simple by using algebra. I see this as assessing the learner’s ability to problem solve and being confident to use algebra in the process. Approach the solution by simply writing the probability of choosing “an orange sweet AND another orange sweet”, equating this to 1/3… Thus (6/n)(5/n-1)=1/3. Generally a pupil working at or towards A/A* would be able to rearrange to obtain the required quadratic equation.

11. Jon says:

Factorisation is do able but unnecessary.

It is conditional probability, 6 orange sweets to start with out of n. One is eaten and out of 5 out of n-1 sweets. And the probability is 1/3.
So.

6/n x 5/(n-1) = 1/3

30/(n^2 – n) = 1/3

90 = n^2 – n

However the factorisation comment shows different possible methods.

12. Mark says:

All that was needed was to draw a tree diagram and use some common sense. It was a hard question but surely an A* should be difficult to get.

13. John says:

I have no problem with the question, are we as teachers not trying to get students to apply their learning, rather than just regurgitating everything they’re taught. There has been similar questions on the IGCSE maths papers in the past couple of years and the same fuss wasn’t made them.

14. Jo V says:

5/n x 6/(n-1) = 1/3.

30/(n^2 – n) = 1/3

90/(n^2 – n) = 1

n^2 – n – 90 = 0.

15. Jo V says:

Sorry, should be
6/n x 5/(n-1) = 1/3.

16. Paulinq says:

Far too many pupils are getting A and A* these days, making a mockery of the grades. The reason is that pupils are taught the answers, rather than the strategies for finding the answers. This question easily solvable using strategies. I managed and I only got a C for my GCSE Maths, having said that, Algebra was my strongest subject.

17. Pat Dehm says:

The daft thing us that you can ignore the stem of the question to do with probability and use trial and error. I just guessed 8, calculated that to be wrong, recognised that I needed to use a larger number, rejected 9 for an answer and arrived at 10.

18. Andy says:

When I was at school doing my O’Level maths this was a standard question which was easy enough to do and I was NOT an A* student!!! Problem is not the question the problem is that today’s kids want everything done for them and made easy. If A* students struggle with questions like this then God help us all!!!!!!!!!!!

19. Paul says:

If they were taught permutations, combinations, and probabilities it was not that difficult a question.

Using combinations and prob formulas ( 6 choose/”n” choose 2) = 1/3 and then just simplify and you have the answer.

Surely they will find it difficult because these days students lack basic algebraic skills in general thanks to the ministry guidelines.

20. Paul says:

Correction: it should have been (6 choose 2/”n” choose 2) = 1/3

21. Philip West says:

I am staggered at the fuss this question has caused.
We have dumbed down to such an extent that any question requiring a minimal amount of thought is considered “unfair”.
I would rate this a 6/10 difficulty-wise, but surely forming 6/n * 5/(n-1) = 1/3 and cross multiplying shouldn’t be beyond the majority?

22. j says:

I think it’s more the position of the question within the paper that caused the issue. It was in the middle of the paper wwhich should be aimed at grade B.
Also, the most difficult element was the deification of the quadratic, not the solving of it.

23. Gillian says:

Surely the point of any exam paper is to sort out the ability levels of the students. If all the questions were easy then everyone would get an A* which would then mean nothing. If you want to get a good grade you should expect to be challenged. I did Maths O level 30 years ago and haven’t used maths other than in everyday situations since then and I managed to work it out!

24. John says:

I am a retired math teacher. I am do not consider this problem difficult at all. They are many things wrong with education these day. It is made so easy that problems that i considered easy when i was in high school are now considered impossible. If that is the question to separate the A* students, then i would have gotten A*****. This really means that when you make it easy (ie. dumb down the system so that everyone must pass), you are really making the students loose the ability to learn how to think critically.

25. Wmffre says:

My last Maths exam was in 1966 but this took me about two minutes to solve. Not only is the probability easy to calculate but the answer is effectively given in the question. I’m surprised that students found this hard and astonished that their reaction is to complain that standards should be reset to the level of their ignorance.

26. Jeffrey Day says:

I think I could have tackled this in “year 8″ or Form 2 as it was back then. Like others here it took me about 2 minutes to solve, and I am 68, having taken my “O-levels” in 1964. I passed “Ad. Maths,” (which this is not), by 1 mark, and got grade 4 in El. Maths., so no A* for me. Stop complaining young people, play less on your i-Pads and think more!

27. Kacey says:

I thought the question was, in all honesty, not at all difficult.

Not wanting to tread on teachers’ toes or deride pupils, but I seriously question what happened in that school. Is it :-

1) the pupil(s) cannot logically relate/’see’ the mechanics of the question?,

2) the teaching standard given to the pupil(s)?, or

3) a combination of 1) and 2) above

I’ve no children, but I’d be alarmed at this.

28. sean says:

it was ok really , but I would solve this question in a different way to what I have seen here
P(Event happening) = number of successful outcomes / number of possible outcomes
So number of successful outcomes = 6C2 , = 6×5 /2×1 = 15
So to get number of possible outcomes just put 1/3 = 15 / x( no. of possible outcomes)
so this gives X = 45
So for n, the combinations of possible outcomes is
nc2 = 45
This is solved as follows .. n(n-1) / 2 = 45 … this will give the quadratic required
n2 – n = 90 or n2 – n – 90 = 0
have a nice day

29. Rosanna Gillison says:

Compare the Level 6 Key Stage 2 Mathematics papers (i.e. a 30 minute paper taken by able 11 year olds) with the Lower Tier GCSE Maths (taken by some after 5 further years of Maths teaching). Not sufficient difference in challenge. If I were the parent of one of the former, I would want to know that their maths skills had continued to be developed in a 5 year period – as evidenced by being able to answer the question under discussion.