GCSE Maths AQA November 2017 Paper 3 Higher Tier Walkthrough (*)

[@MrTompkins]

Get all your AQA past papers, mark schemes and video walkthroughs in one handy place! - mr.tompkins.online/aqa Question timestamps for mobile users: 0:00:00 - Intro 0:01:45 - Q 1 - Inequalities 0:02:54 - Q 2 - Ratios with percentages 0:03:28 - Q 3 - finding the nth term of a linear sequence 0:04:26 - Q 4 - Equations of straight lines parallel to an axis 0:06:05 - Q 5 - Expanding double brackets 0:07:26 - Q 6 - Indices 0:10:12 - Q 7 - Median class interval 0:11:54 - Q 8 - Angles in triangles and parallel lines 0:15:23 - Q 9 - Changing the subject of a formula, compound units 0:18:52 - Q10 - Loci and construction 0:20:10 - Q11 - Frequency trees, Reverse percentages 0:26:18 - Q12 - Distance speed time 0:29:56 - Q13 - Box plots 0:32:14 - Q14 - Venn Diagrams with conditional probability 0:37:22 - Q15 - Factorising terms 0:38:12 - Q16 - Function notation - substitution 0:39:06 - Q17 - Ratio problem 0:42:10 - Q18 - Expanding and simplifying brackets 0:44:50 - Q19 - Circle Theorems - alternate segment theorem 0:46:11 - Q20 - Inequalities with percentages 0:47:55 - Q21 - Product of prime factors with laws of indices 0:50:12 - Q22 - Trigonometry in non-right-angled triangles (cosine rule) 0:55:59 - Q23 - Inequalities regions 1:01:38 - Q24 - Ratio problem 1:04:29 - Q25 - Finding rate of change by drawing a tangent to a curve 1:08:39 - Q26 - Proofs 1:12:24 - Q27 - Volume of a pyramid with pythagoras and trigonometry in 3D 1:21:41 - Q28 - Solving simultaneous equations 1:26:00 - Q29 - Quadratic graphs 1:29:12 - Q30 - Function notation 1:31:36 - Outro

[@atiarimi5994]

Why is it that "the smallest a can be is two" (at 1:10:56)

[@noobyoutubers9417]

These videos are great- I’ve spent so long not understanding mark schemes and wondering how they got the answer, but now I can see how you run through it and it’s way easier to understand. I just wish i found your channel sooner!

[@MrTompkins]

Yes, mark schemes are written for maths teachers, not for students. They can be very difficult to follow and often confuse students and make them doubt themselves and lose confidence. Video walkthroughs are much better. I’m really glad you found me!

[@joethepro7018]

Cheers mate, really helpful for revision. Improved by 20 marks on each paper almost from watching these vids and doing past papers

[@MrTompkins]

Ah, that's great to hear Joey!!123! Really pleased that your efforts are paying off.

[@caitlinklein9608]

thank you so much, your videos are so helpful! i would really appreciate if you could make more for GCSE and A Level, thanks again ;)

[@MrTompkins]

Hey Princess Consuela Banana Hammock - loving the name! Thank you for the positive feedback - I'll try to keep the videos coming 😀👍

[@benhallo1553]

You are amazing sir thanks so much for all this! You have changed lives!

[@MrTompkins]

Glad you are finding them useful Ben! There are a plenty more on the channel, and a few more in the members-only area =)

[@benhallo1553]

@@MrTompkins I plan on watching them my friend don’t you worry! Have you got any Edexcel paper walkthroughs ?

[@MrTompkins]

Nope sorry! Just AQA and OCR at the moment...

[@benhallo1553]

@@MrTompkins That's more than enough thanks ever so much. Do you do tutoring by any chance?

[@MrTompkins]

@@benhallo1553 I'm personally at full stretch, right now, but I do have a tutor referral programme here: mr.tompkins.online/tutors - all my tutors I know personally, have worked with for years, and thoroughly recommend!

[@nasarali8202]

At 50:10 wouldn't the 3 outside the bracket need to be multiplied by each individual term inside the bracket not just 3 to the power of 8

[@MrTompkins]

Hey Nasar - the property you are refering to is called the "distributive law". Multiplication is distributive over addition, so a(b+c+d)=ab+ac+ad, so here the "a" gets distributed to each term inside the bracket. However, multiplication is not distributive over multiplication as a(b x c x d)=a x b x c x d, and not ab x ac x ad.

[@annmathew0794]

@ 1:02:41 shouldn't it be 10:7 and not the other way round?

[@MrTompkins]

Hey Ann Mathew0! Please see my reply to Nasar Ali below, who asked the same thing!

[@annmathew0794]

@@MrTompkins Thank you so much, I understand it now

[@mamilla2]

Thank you this was very helpful!

[@MrTompkins]

Glad it was helpful! Good luck for tomorrow =)

[@orangepotato2112]

thank you very much for these, I'm finding it quite hard but you ave made it very simple and easy to understand :D

[@MrTompkins]

You're very welcome! Really glad this is helping you break it down. Wishing you success with your exams! :-)

[@sushikii]

I got 45:14 for question 24 because B is 10, not 7?

[@sushikii]

Oh, nevermind, I just looked at the comments and found your reply to another person with the same concern. Thank you :)

[@MrTompkins]

​@@sushikii these sort of equation to ratio conversion question have become quite common, so hopefully it now makes sense to you!

[@sushikii]

@Mr Tompkins EdTech I just sat AQA Maths Paper 3, and 2 of these ratio questions came up! Thank you, Mr Tompkins! I wish I found you earlier.

[@MrTompkins]

@@sushikii phew! Good timing then! Hope the rest of the paper was also good. All the best!

[@rehya8810]

1:29:09 would there be a question to find f(-x)

[@MrTompkins]

There could be. It says function substitution in the advance information, which makes me think it's more likely to be a number, like f(3) or f(-2)

[@kai_johnsonn]

I find it hard to understand AB=BP. Which angles are they referring to? Is P the same as A or B? 11:54 And how do you know what to remember?

[@MrTompkins]

When they use two letters like this AB or BP, they are referring to lengths, not angles. So AB=BP means that the lines between A to B, and B to P are the same length. You can see this has been indicated on the diagram already by the little marks. If they are referring to angles, they will either use a single letter (like angle B) if this is not confusing, or use 3 letters (like angle BAP).

[@kai_johnsonn]

@@MrTompkins Ah I see, thankyou. As for the Isosceles triangle, if the two lines are on the side of the triangle, does that mean the two base angles are the same?

[@MrTompkins]

Yes that’s right!

[@kiritysiva7463]

For q11 could i not just do 1.15x27.20 but it gives me 31.28 instead of 32

[@MrTompkins]

Nope - that would just be a straightforward 15% increase. If you decrease something by 15% and then increase what you get by 15%, you wont get bact to where you started from. Another example - decrease 100 by 10% takes you to 90. Increase 90 by 10% only takes you to 99, not back to 100! This question is a reverse percentage question, so you need to use a reverse percentage method. I like the method I show here, but there are other methods too.

[@violet486]

Q29 f(x)bigger or equal to 0 therefore shouldn't be all just positive values?

[@MrTompkins]

F(x) is the output value of the function and is plotted on the y axis. So to find f(x)>0, you need to look where the graph has a positive value in the y direction. In other words, where the graph is above the x-axis. It is very possible (as is the case here) that negative values of x give positive values for f(x).

[@yillokimo3353]

Hey, 50:12 dont you expand 3(2^2 x 3^8 x y^6) ?

[@MrTompkins]

Hey Yillo Kimo - the question asks you to give the answer as a "product of prime factors in index form", so I think you would end up losing marks if you multiplied it all out.

[@BigSmoke-xh5hi]

How do u reccomend revising ? thank you sir

[@MrTompkins]

Do a practice paper, watch the video walkthroughs and mark/uplevel your work. Do focused revision on 1 or 2 topics identified, rinse and repeat! Aim to complete all the past papers before the exams…Do this and you will do great.👍

[@Hairy_Monster25]

Q.10 why did u draw a perpendicular bisector isn't a locus like an oval type thing around both points

[@MrTompkins]

you can create an oval from two points. If you imagine 2 nails hammered into a wall which you tied either end of a longer piece of string to the nails, then if you pull the string taut the locus of all possible points would be an oval. The sum of the two distances will be the same for every point on the oval. This is not what's happening here though. The question asks for the locus of points that lie equidistant from those two given points, which is going to be the perpendicular bisector. If you pick any point on this bisector and measure the distance from that point to each of your two given points, you will find that it's exactly the same.

[@Hairy_Monster25]

@@MrTompkins thaks a lot makes sense now

[@uteagyeman8283]

I want to boost my maths grade coming May from a 4 to 6,7 or 8. Should I do What topics should focus much please. I am taking the AQA Higher Tier paper. Thank you.

[@MrTompkins]

My advice is to use the past papers as a diagnostic tool. So complete a paper and make a note of topics you didn't score well on, spend some time doing some revision on those topics, then do another diagnostic test. Rinse and repeat. Hopefully by the time the exam comes around you will have completed all the practice papers and past papers, and will be ready for the real thing!

[@uteagyeman8283]

Thanks a lot for your time and explanation. I will do this and stick to it. Thanks once again I appreciate.

[@Zainab-rd4ys]

thewebsite onmaths identifyes the topics you didnt score well in it is a good tool to use for revision

[@MrTompkins]

@@Zainab-rd4ys thanks for the suggestion.

[@Seeking422]

just confused on question 24, as i thought 10b=7c would mean the ratio is 10:7, and then I used the same method as you but because of this difference i got an answer of 45: 14 which is wrong, can you please clean up this confusion ?

[@MrTompkins]

equations expressed as ratios often confuse students because the numbers appear on the opposite sides, so 10b=7c expressed as a ratio of b:c would be 7:10, and not 10:7. Think of it this way, - if y=2x, and you let x=1, then y=2(1)=2, so y=2 when x=1, and the ratio of y:x is 2:1. So y=2x gives the ratio 2:1.

[@Seeking422]

@@MrTompkins ah I understand now, since x is being split into more parts its going to have a smaller value in the ratio compared to y, and the same applies for other ratios, thanks for clearing up the confusion 👍

[@jakobnaylor6566]

How do you work this out please a = b - x / x making x the subject

[@MrTompkins]

hey Jakob - (1) multiply through by x, giving ax=b-x, (2) add x to both sides, giving ax +x=b, (3) factorise, giving x(a+1)=b, (4) divide through by (a+1), giving x=b/(a+1). Job done!

[@scousemali]

sometimes no need to brag about how easy the question are no EVERYONE GETS IT

[@MrTompkins]

Oh! it was not meant to be condescending. If it came over that way then I’m really sorry about that. I do think that the more practice papers you do, the easier the questions get though. So keep practicing and hopefully they get a little easier for you too.

[@scousemali]

I am hugely Sorry it was my fault I get angry when I. Don’t know something but in reality you helped me being stupid I forgot to watch how you answered it I am really sorry

[@MrTompkins]

Hey no problem. I know learning can be a frustrating journey sometimes. What is great to see is that you are being really proactive and seeking help, and not just giving up. 😀 👍

[@scousemali]

Mr Tompkins EdTech thanks

[@nasarali8202]

At 1:02:32, why is the ratio of b:c not 10:7

[@MrTompkins]

We are given the formula 10b=7b. I can see why you might think the ratio must be 10:7, but if you think it through you will see that it's actually the other way around. Lets start with an easier example. If y=2x, and we let x=1, then y=2, thus y:x would be 2:1 and not 1:2.

[@ImranKhan-kz9qo]

for question 23 why is X

[@MrTompkins]

Imran Khan it’s just a convention - it’s meant to show that points on the line are not included in the region.

[@ImranKhan-kz9qo]

thank you

[@HH-zr1iu]

Where do you get your calculator from and are you using a pc or ipad?

[@MrTompkins]

Hey Daniel - I got this emulator direct from Casio: education.casio.co.uk/download-emulator-cw. I use a PC to make nearly all my videos. .

[@HH-zr1iu]

@@MrTompkins Thx - (was not expecting a response at this time) do you write the working out using a mouse and if so what is the software cuz im trying to find something like this.

[@MrTompkins]

@@HH-zr1iu my PC has a touchscreen/stylus, so I'm using that with OneNote. If you dont have a stylus for your laptop, you could try a graphics tablet instead. Its a bit more fiddly at first, but it gets easier with practice!

[@HH-zr1iu]

@@MrTompkins thank you

[@emilymorris3687]

really helped, thank you

[@MrTompkins]

Thanks for the feedback Emily, and good luck with you exams! I've just started a new series of topic tests which you might also like: kzbin.info/aero/PLxp90x5c0ttZJlDrO4TLdtyp-uwzp7xHw

[@naomi5710]

Hello, first of all thank you very much for this amazing content! I was wondering when finding the median when you need to add 1 before dividing by 2 and when not to (so just dividing by 2). I would really appreciate a reply and once again thank you!

[@MrTompkins]

Hey Naomi - if you have n elements, then the middle one is the (n+1)/2 th element. So if you have 3 elements, thats (3+1)/2 or the 2nd element. Now this is always the case, no matter how big n gets. But as n gets larger and larger, the difference between (n+1)/2 and n/2 becomes smaller and smaller, and there comes a point when the difference is so small it makes no real difference. So in an exam, if you are finding the median of a list of given numbers, use (n+1)/2. But if you are looking up a median on a cumulative frequency graph of 100 items, then just use n/2 as you are not going to be able to find (n+1)/2 any more accurately on your scale. Does that make sense?

[@naomi5710]

Mr Tompkins EdTech so strictly speaking it should always be n+1/2? Thank you for the quick reply!

[@MrTompkins]

Naomi Brand strictly speaking it should always be (n+1)/2. [😜 BRACKETS! 😂] But in practice, it's acceptable to use n/2 for large data sets. Good luck with your exam prep!

[@naomi5710]

Mr Tompkins EdTech haha😂true. It is nice to see someone so passionate about maths

[@nehamohan5594]

Mr Tomkins did you put the wrong value for C for question 24 as the answer I found that question confusing, also for question 25 when do we use positive and negative and for those types of questions are there a range of answers for that specific question?

[@MrTompkins]

Hi Neha! I have double-checked my method for Q24, but it looks fine to me. You might be confused by the fact 10b = 7c gives rise to the ratio for b:c of 7:10. It might look at first glance like I have written these the wrong way around, but if you think it through you'll see the logic of it. Consider the simpler equation y = 2x. If x=1, then y=2, so y = 2x gives a ratio for y:x of 2:1. If its not this step that was confusing you, let me know which bit did and i'll try to explain it another way.

[@MrTompkins]

In Question 25, when I start calculating this in the video, i use the gradient of the tangent to find "rate of change". This change is clearly a negative value as the depth is falling over time. You can also clearly see that the tangent is heading downwards from left to right, which we would consider to be a negative gradient. However, as the question specifically asks for the "rate of decrease" and not the "rate of change", I decided to switch the sign of my answer to better match this request.The depth is "changing" at the rate of -21/33 cm/s, but it is "decreasing" by the rate of 21/33 cm/s.

[@MrTompkins]

Also in Q25, because the numbers you use rely on you pushing your ruler up against the curve and wiggling it about until it "looks right", there is clearly going to be some variation here and there is a range of acceptable answers to this question, so don't worry if yours is not exactly the same as mine. The markscheme gives a tolerance of +/- half a square on drawing the tangent, and accepts answers anywhere between 0.6 and 0.8. It also condones students giving the final answer as a negative value, as long as they have constructed the tangent properly.

[@nehamohan5594]

thanks a lot!

[@violet486]

On Q 20 why y=99% when it says y 10% less from x means 110%-10%= 100% which means w=y

[@MrTompkins]

Naomi Bartley it’s because 10% of 110 is 11 (not 10), and 110 - 11 = 99. Does that make sense?

[@batoolbx]

thank you so much

[@MrTompkins]

You’re welcome Batool B! I have a few more papers in the members only area if you are interested?

[@nahidgani]

Thankyou. Very clear.

[@MrTompkins]

That's right! This is a three step problem 1) First use pythagoras theorem in ABC to find the length AC, and halve it to find AM, 2) use trigonometry in AMV to find the height of the pyramid MV, 3) finally use the area of the base and the height to work out the volume of the pyramid.

[@nahidgani]

@@MrTompkins Have you seen paper 1 AQA Higher Nov 2018?

[@nahidgani]

Thankyou for a clear explanation. What are the chances of topics being repeated in paper 2 and 3?

[@MrTompkins]

@@nahidgani - topics often appear multiple times across the 3 papers, so I wouldnt rule anything out based on the content of paper 1. After we've seen paper 2, it's usually possible to identify topics that have not yet featured and therefore very likely to make an appearance in paper 3.

[@MrTompkins]

@@nahidgani not yet! How did it go for you? Any suprises?

[@uteagyeman8283]

Thank you sir.

[@MrTompkins]

You're most welcome! 😀

[@seanhn5415]

Why is this paper really easy compared to the others

[@MrTompkins]

Maybe you've got better? 😀

[@seanhn5415]

@@MrTompkins I don't know about that but I did my mock exams this week for maths and they were much harder

[@MrTompkins]

@@seanhn5415 , the required skills do not change from paper to paper. Questions are "hard" when you don't easily recognise what the question is asking you to do and therefore what skill you need to apply. The more practice papers you complete, the more you will recognise the question types and the fewer surprises you will get in the exams. Make sure you have worked your way through all of these before the real exam comes around and you will do fine! kzbin.info/aero/PLxp90x5c0ttb-W-mdpSIoN3hUzephpjqk

[@maxwheatley-footballmore8668]

Cheers

[@MrTompkins]

You’re very welcome Max!

[@Oscar-pe5ve]

Thanks so much

[@MrTompkins]

Your welcome Oscar!