# AQA Further maths Examiners - Would they give the marks?

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#1

I was doing a further maths past paper (AQA) and I got the right answer but used a different method not mentioned in the mark scheme.

The question gave a cubic line and asked to find any stationary points and determine their nature. I worked out the first derivative and then found the x value of the stationary point. Then I worked out the second derivative and saw that it equalled 0 at that x value and said that it was a point of inflection. I got the right answer.
However, the mark scheme wanted me to find the x value where the stationary point was and find the gradients either side of the stationary point and then say that it was a point of inflection because it was the same gradient (both positive) either side of the stationary point.

My question is whether I would get full marks for using a different method that is not mentioned in the mark scheme, though still getting the correct answer.

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2 years ago
#2
(Original post by bvipulananthan)

I was doing a further maths past paper (AQA) and I got the right answer but used a different method not mentioned in the mark scheme.

The question gave a cubic line and asked to find any stationary points and determine their nature. I worked out the first derivative and then found the x value of the stationary point. Then I worked out the second derivative and saw that it equalled 0 at that x value and said that it was a point of inflection. I got the right answer.
However, the mark scheme wanted me to find the x value where the stationary point was and find the gradients either side of the stationary point and then say that it was a point of inflection because it was the same gradient (both positive) either side of the stationary point.

My question is whether I would get full marks for using a different method that is not mentioned in the mark scheme, though still getting the correct answer.

I don't know the mark scheme, but I did this exam last year and you would probably get 2-3 method marks for finding x-value of stationary point and finding the 1st and 2nd derivative. My school sent for my papers back to see where I got my marks (idk why), and they seemed quite lenient with method marks compared to how tough and rigid the mark scheme looks. At the end of a question like that, I would write a brief closing statement, about 1 or 2 sentences long, to explain your reasoning and help the marker identify where they can award marks in your working

Update: I've just looked through the paper I got given back last year and I used the 2nd derivative for a similar question and got given the full marks for it, so you would likely get the full marks too.
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2 years ago
#3
(Original post by bvipulananthan)

I was doing a further maths past paper (AQA) and I got the right answer but used a different method not mentioned in the mark scheme.

The question gave a cubic line and asked to find any stationary points and determine their nature. I worked out the first derivative and then found the x value of the stationary point. Then I worked out the second derivative and saw that it equalled 0 at that x value and said that it was a point of inflection. I got the right answer.
However, the mark scheme wanted me to find the x value where the stationary point was and find the gradients either side of the stationary point and then say that it was a point of inflection because it was the same gradient (both positive) either side of the stationary point.

My question is whether I would get full marks for using a different method that is not mentioned in the mark scheme, though still getting the correct answer.

I believe it is quite possible that you will loose marks. Use the method that you learnt in GCSE further maths.

Whilst I appreciate that you are a method that is learnt in A level maths, it isn't perfect.

The reason is, as you will learn, when f"(x)=0, most of the time it will be a point of inflection but it can also be a local maximum or a local minimum. As a result, it is best to check that it is a inflection point by checking the gradient just before and after the point.

A notable example of this is y=x^4
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2 years ago
#4
(Original post by stoyfan)
I believe it is quite possible that you will loose marks. Use the method that you learnt in GCSE further maths.

Whilst I appreciate that you are a method that is learnt in A level maths, it isn't perfect.

The reason is, as you will learn, when f"(x)=0, most of the time it will be a point of inflection but it can also be a local maximum or a local minimum. As a result, it is best to check that it is a inflection point by checking the gradient just before and after the point.
The 2nd derivative is part of GCSE FM and appears on some of the mark schemes. Although saying that, I haven't seen the mark scheme saying to use 2nd derivative to find inflection points, only using 2nd derivative to find maximum/minimum points.
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2 years ago
#5
(Original post by Loci Pi)
The 2nd derivative is part of GCSE FM and appears on some of the mark schemes. Although saying that, I haven't seen the mark scheme saying to use 2nd derivative to find inflection points, only using 2nd derivative to find maximum/minimum points.
I did AQA GCSE further maths, and I never learnt about second dervivatives.

Also, I checked the specification again and it doesn't mention the word 'second derivative' anywhere.

The only closest description I've found is this:

4.5 Use of differentiation to find stationary points onUnderstand the terms ‘increasing function’ and a curve: maxima, minima and points of inflection‘decreasing function’ and applying them to determinethe nature of stationary points.

However this reffers to the use of differentiation that was explained in your mark scheme.

I guess you could either use the second derivative method for only maximum and minimum points or not use it at all.
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2 years ago
#6
(Original post by stoyfan)
I did AQA GCSE further maths, and I never learnt about second dervivatives.

Also, I checked the specification again and it doesn't mention the word 'second derivative' anywhere.

The only closest description I've found is this:

4.5 Use of differentiation to find stationary points onUnderstand the terms ‘increasing function’ and a curve: maxima, minima and points of inflection‘decreasing function’ and applying them to determinethe nature of stationary points.

However this reffers to the use of differentiation that was explained in your mark scheme.
2nd derivatives are in the CGP revision guide for AQA L2 FM. I used it in my paper last year and got maximum marks on that question. I though it was an accepted method in FM, although you could still use the gradient each side of the point method if you wanted, sorry if I'm wrong.
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#7
(Original post by Loci Pi)
I don't know the mark scheme, but I did this exam last year and you would probably get 2-3 method marks for finding x-value of stationary point and finding the 1st and 2nd derivative. My school sent for my papers back to see where I got my marks (idk why), and they seemed quite lenient with method marks compared to how tough and rigid the mark scheme looks. At the end of a question like that, I would write a brief closing statement, about 1 or 2 sentences long, to explain your reasoning and help the marker identify where they can award marks in your working

Update: I've just looked through the paper I got given back last year and I used the 2nd derivative for a similar question and got given the full marks for it, so you would likely get the full marks too.
Thank for the reply, I think I'll also ask my teacher because (I think) he marks papers for the exam board
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2 years ago
#8
(Original post by bvipulananthan)
Thank for the reply, I think I'll also ask my teacher because (I think) he marks papers for the exam board
That's probably the best idea lol
Good luck on your FM exam.
0
2 years ago
#9
(Original post by bvipulananthan)

I was doing a further maths past paper (AQA) and I got the right answer but used a different method not mentioned in the mark scheme.

The question gave a cubic line and asked to find any stationary points and determine their nature. I worked out the first derivative and then found the x value of the stationary point. Then I worked out the second derivative and saw that it equalled 0 at that x value and said that it was a point of inflection. I got the right answer.
However, the mark scheme wanted me to find the x value where the stationary point was and find the gradients either side of the stationary point and then say that it was a point of inflection because it was the same gradient (both positive) either side of the stationary point.

My question is whether I would get full marks for using a different method that is not mentioned in the mark scheme, though still getting the correct answer.

Using different methods is fine as long as they are valid. This is an invalid method for determining points of inflection.

f''(x) = 0 is not proof that a stationary point is a point of inflection.

If instead you found that f''(x)>0 and used to this to prove that a point is a minimum then that would be fine.

It's best to stick to GCSE FM methods unless you are very confident with the higher level methods. Questions are often designed so that the GCSE FM method is the fastest / most efficient.
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