First time solving an A-Level maths exam! (90 minutes, uncut) 

Correction to Q5: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-pXdEBA6xI1c.html

It's worth noting that you would have access to a fairly extensive equation booklet in the actual exam - not finished the entire video yet so I might have missed you using it. I also wish last year's papers were released by now... would have been interesting to see you do the paper I had to.

Purely out of curiosity, I decided to mark your answers. You scored 53/75, which equates to an A. The boundary for reaching A was 51, and you needed 61 for an A*. I think an A is very reasonable given that you were going slowly to explain your working, and that you didn't use a calculator or a formula sheet. I'd love to see you try 2023's papers, which will be publically available soon, since they were a lot harder, and absolutely slaughtered me in the my mocks. (mild exaggeration). Hoping that 2024's papers treat me better in the real thing!!!! Score breakdown by question: Q1: 6/6 Q2: 4/4 Q3a: 1/3 Q3b: 3/3 Q4a: 3/4 Q4b: 3/3 Q5a: 2/2 Q5b: 1/4 Q6: 7/7 Q7a: 2/2 Q7b: 4/5 Q8a: 5/5 Q8b: 1/1 Q8c: 4/5 (would've been 5/5 if you used a calculator) Q8d: 0/1 (not answered) Q9: 6/6 Q10: 0/14 (not answered) (if you end up trying 2023's papers, use a calculator and a formula booklet!! they make things SO much easier)

oh my gosh! its so weird to see you do my a level further maths paper i thought these questions were familiar!

For 1b, you can just take the sum of the roots, 2+3i+2-3i+Z = -b/a where a is the coefficient of z^3, b is the coefficient of z^2, so 4+Z=0 and therefore Z = -4 to save a lot of time Similarly, you can calculate the coefficient of z by doing the sum of the product pairs = c/a where c is the coefficient of z and a is the coefficient of z^3 For 8a, the typical technique is to let z=e^ix so 2Cos(nx) = e^inx + e-inx letting n=1 and exponentiating both sides to 6, we get 64Cos^6x = (e^ix + e^-ix)^6 = (e^i6x + e^-i6x) + 6(e^4x + e^-4x) + 15(e^2x + e^-2x) + 20 = 2Cos6x + 12Cos4x + 30Cos2x + 20 therefore 32Cos^6x = Cos6x + 6Cos4x + 15Cos2x + 10 This exam is all about finding the quickest solution which is why so many find it difficult. Much love for showing this on your channel ❤

BPRP, I have watched your videos for years, and in 15 minutes I will take my last calculus exam (calc III at university). I am not worried bc your videos have turned me into a calculus weapon and I only need a 53% for an A anyways. I hope to get an ace anyways and make you proud. Thank you BPRP! Just 2 and a half hours and WE ARE DONE!

Amazing video!! Very much enjoyed it!!

Thanks for doing this paper :). I missed out on Further Maths A-Level in my youth due to poor life choices... I've wondered how this may have impacted me since, for this particular exam I have covered most of this in subsequent learning but great to see you go through and struggle with it. It'd be good to see one that many students in the UK said was "A nightmare" or words to this effect.

While the 2022 papers are generally the easiest, whats really impressive is how you do it with no calculator and fodmula booklet. Students in england can use calculators that solve 4 degree polynomials in the exam

In part (b), of Q7, use the previous result a^2 + b^2 = 18 with a^2 - b^2 = 14 to get a and b.

For question 7, when I was doing this past paper, I was so happy when I realised that if you add a^2-b^2 with a^2+b^2 you get 2a^2=32 which saved me ALOT of time since we know now that a=+/-4. Solving for b gives b=root(2). And we know ab has to be positive so the solutions are 4+root(2)i and -4-root(2)i.

For 9C you can write 4sinhx = pcoshx as p = 4tanhx Since the range of 4tanhx is between -4 and 4, the range of values of p is the same -4

I love this vid. I'm not good with math, but i love it. I find it fascinating to solve things and search for limits or lack there of.

At this point, watching you solve problems is like meditation to me. I just sit back and relax as your break down complex sums into simple solutions. You're an unsung hero. Dare I say, slightly better than the organic chemistry tutor.

For qn 6a, to find B and C we can substitute any value for x because the expression is identical on both sides for all values of x. So to find C we let x=0 to get rid of B and then to find B we can let x=1 after knowing the value of C.

16:50 You did a mistake there is e^2x not e^x.

On the second part of question 5,you could find the characteristic polyonym of the matrix.There is a theorem stating that a matrix is a root of its characteristic polyonym so you plug the matrix into the polyonym and set it equal to 0. You move the polyonym matrix/constant to the other side, multiply both sides with M^(-1)(you already prooved that there is an inverse) and you get the matrix M^(-1) in terms of M,which should be a valid answer since M is in terms of a

was so so awesome to see you doing my a level paper, now 2 years into uni :D

A nice way to do Q1 is to say that for roots alpha, beta and gamma: c/a (3rd term and 1st term of polynomial) = alpha beta + beta gamma + alpha gamma. This gives you the other root in terms of z, which you can then find by solving b/a = alpha + beta + gamma (2+3i + 2-3i + z = 0, z = -4).

there are also option modules for further maths, and the "highest" level pure work for a levels is on the further pure 2 paper. Please try that

I sat the further maths exam last year, it's really exciting to see this video from you lol

Crazy to watch you do the paper that I sat almost two years ago now. This was the easiest fm paper in a while, because most questions were fairly standard i.e. they relatively closely matched the sort of questions you would find in textbooks. For example, the trig identity you struggled with is something that a student would be expected to basically know by heart, as it is a question directly pulled from an example in the textbook. Iirc paper 2 was a bit harder. Other years papers, such as 2021, were much harder as they required a lot more 'creative' thinking and had a lot more 'funky' questions that weren't just direct application of the material. However, the grade boundaries are adjusted based on the cohorts performance, so 2022 had what are likely to be the highest grade boundaries (the marks you need to get each grade) that fm will ever see. So a much harder paper does not necassarily disadvantage you as the marks you need to get the grade you want are likely to be much lower. I got an A* in these exams, but I am glad I never have to do A levels again because they're so robotic and all about training yourself to do routine questions quickly aso that you have time to think about the more challenging questions. Whereas, at least on my uni course, the exams are much more based around understanding to the point where extensive question practice beyond the point where you understand the concepts is redundant, as all exam questions expect you to apply your understanding to 'unseen' problems and contexts. While this is obviously much more difficult, it allows you to actually spend time attempting to understand the material rather that training yourself to solve a question as quickly as possible

Hi BPRP! If you'd like to do another video similar to this, it would be cool if you tried to do one of the Australian VCE Specialist maths exams from last year without knowing the answer guide (exam 1 is technology-free). Thanks for the video :)

OMG, seeing these questions bring me back memories of me sitting in front of the desk in my room, doing past papers after past papers. Just missed mine by 6 years (Jun 2016)

you should also try the AQA further maths mechanics paper 3

Would love to see you do some of the nzqa scholarship calculus papers. They have some pretty interesting questions spanning a wide range of topics.

Consider doing the IB Maths Analysis and Approaches HL Exam. I suggest a paper 1 (the non-calculator paper) or a paper 3 (a fun, challenging, unseen investigation). I would love seeing you do it :)

I really like his passion for mathematics.

On #7, the second answer should be -4 - (root 2)i

Hey BPRP, it would be amazing if you could take a look at the IB Maths AA HL papers- they are notoriously one of the hardest, and there are 3 different exams to choose from compared to A-levels

Finally, someone who takes on the A2 Further Mathematics paper. Many of the other videos on YT chicken-out and only go as far as the AS paper.

I love that solving some test on RU-vid can be done "for entertaining purposes" 😁

For problem 3 you can save a little time. The original form y'(cos x) + y(sin x) = F(x) already looks like the product rule, so you can hope to rewrite it as a derivative of a product and avoid having to calculate the integrating factor. However, it is not quite the product rule, because the sign of the second term is wrong. But the insight is that if something "looks like the product rule with the sign of the second term wrong" that means it is almost the quotient rule. You can therefore rewrite the original equation as (y/(cos x))' * cos(x)^2 = F(x) and from there the algebra is very simple.

If you can find one, I'd be interested how you get on with a Further Maths Special paper. All A-levels before 1989 (I think this is the year they were abolished) had optional Special papers to allow extra grades to be available for mainly Oxford and Cambridge to use. The entry requirement for Cambridge to do Maths was commonly three grade A's, including Maths, Further Maths and a science, and Distinctions in the Special papers in Maths and Further Maths (70%+). I managed A with Distinction in the Special paper in Maths a year early, A in Further Maths, B in Physics and B in Chemistry, so missed out on Cambridge. These were all three-hour exam papers. Nowadays there are three shorter exams for the Maths A-level so the dears aren't put under too much pressure.

you should have a formuale sheet it would have helped also you could have used Vieta's formulas for the first questions and u can use the formuale cosh(x) = ln(x+sqrt(x^2-1)) then in the end attach plus minus since cosh x will have two solutions for this problem, also ur allowed to ue a graphical calculatorrr as long as it doesnt have alegraic manipulation

Try a Further Pure 2 paper! They include topics like number theory, group theory etc

This brings back memories of just about passing further maths in 1977. Can't remember much about that paper!

At 59:03 the next value of z will be -4-sqrt(2). because product of a and b must be positive. as ab=4 sqrt(2).

Going in raw no calculator, no formulae is honestly the kind of thing I have nightmares about so this is pretty crazy.

Great stuff

At 56:09 when trying to solve for a and b, instead of substituting you could do the following: a² - b² = 14 (add 2b² to both sides) a² + b² = 14 + 2b² 18 = 14 + 2b² 4 = 2b² 2 = b² √2 = |b| ab =4√2 |a|=4

Love your work! For Q3 I can't help but notice in the second line you accidently wrote e^x instead of e^2x? I got y=1/2*cosx(e^2x+5) for my answer

I teach A-Level FM and the 2023 papers were comparatively harder than anything seen since the 2018 format. Looking forward to what the 2024 and 2025 papers come up with for my current cohort...

this was insane to watch you do without a calculator, you should try a further pure 2 paper. when taking further maths you have to choose 2 option modules, it would be interesting to see you do further pure 1 or further pure 2, which are the highest level of pure

with the first question, you can get the coefficients in terms of the roots, in this case, the polynomial has roots α, β, & γ, from this you know α&β, and you know αβγ= 52, so you can find γ, and with that you know that a = αβ + βγ + γα, this is the quick way of doing it that is taught on further maths

would you consider doing a singaporean a-level further maths paper?

Sat this paper last year, now im doing maths at uni :))

I highly recommend an A-level futher mechanics exam, which tends to have some tricky questions and a tight timer. In fact, I think to get an A* in most of those exams, you only need half of the maximum score

You don’t need to take 1/2 the volume in equation number 8, just integrate from 0 to 4.

We need more videos about a level maths pls

It would be interesting to hear your opinion on UK maths exams papers in general. GCSE is for 15-16 year olds while A-levels are for 17-18 year olds.

Can we take e^x = sqrt(2)? 12:07 The method you used to find the inverse Matrix is the only method I know of.

@blackpenredpen can you also try the math paper of IBDP (Maths AA HL ) Paper 1 and paper 3 they are really tough.

Please do these from the CAIE international exam. You wont regret it. I hope.

A lot of people were glad after this paper, it was easier than many other year's exams. 2023 paper was apparently horrific and who knows what they'll do this year.

I jumped straight to the 1/8 equals cosh^2 idk you kinda crossed it out earlier then it re appeared and you started solving it

how things have changed . I sat further maths in 1979 , and the Northern Universities Joint Matriculation paper was a mix of pure and applied . There was a selection of questions , and you needed to answer 7 of them (I think it was 7) Our applied maths teacher had saved all the papers for years , and as we approached our exams , we sat a paper every week until we could almost do them in our sleep

Nice job - even though you weren't able to solve everything!

59:11 should be *-*4-2i for the 2nd solution

For Q8, having done HKPM '09 I Q13, I immediately recognize the de'Moivre's theorem here. I would handle the L.H.S. as (2costheta)^6, then its binomial and with the even property of cosine, you get the 2x on R.H.S. which ultimate cancel with the 64 on L.H.S. and get back 32

Please do an IB Mathematics AA HL paper 1 next!

Try out the Cambridge syllabus

omg this is awesome! I agree with the other comments saying you should try the 2023 further core pure paper, but I personally want you to try the year 2 *further pure maths* paper. (the difference is that FPM is an optional module for further maths students where they teach even MORE advanced mathematics like group theory etc), I think it would be good fun

You might also want to check IB Math AA HL

Thanks You Professor Sir! I am a 65 Years Old ,I am from ROMANIA and I like Calculus invented by the genius polymath LEIBNIZ!

I have no relation whatsover to Maths since I chose Biology but its nice to see a teacher like you taking your time with quesgtions and explaining gthem. Wish you all the best

I want a video on rank of apparition (related to fibonacc sequence

In Question 5 at 33:33 you misremembered the trick for the inverse of a 3x3 matrix and got the last corner part wrong, it should have been a copy of the top left corner of the original not the bottom right corner. Given matrix (ABC,DEF,GHI) the 4x4 should be (EFDE,HIGH,BCAB,EFDE).

wish me luck on this in 3 weeks 🙏🙏 i need a*.

you should attempt Irish leaving certificate papers (make sure you have a the formulae booklet and calc)

CAIE requires at least a few cancellations, very good stuff however for a random try, these papers are very tricky👍🏿

Cant you use basic multiple angle formulas in question 9? Like break all of rhs to 2theta?

Thanks for this. In question 3, why did e^(2x) become e^x?

for 9c to solve it quicker u could've done 4 sinh x / cosh x = p so p = 4 tanh x and because we know the range of tanhx is -1 to 1. The range of p is -4 to 4

sir please find inverse of function x times c to the power x where x is variable and c is constant

this guy is going to solve all the math paper around the world

For Question 1b, I found a first then found the other root. Is that acceptable or you must do it in order?

Can you do scottish higher and advanced higher math paper?

End of number 7 is 4+rt2i or -4-rt2i

I aced A level further maths but got a C in calculus 3. Granted didn't sit for first half of a level exams due to covid

Can you do the intermediate maths challenge 🙏

A^2 + B^2 = 18 A^2 - B^2 = 14 This is how us dummies do it (system addition and subtraction) 2A^2 = 32,: A^2 = 16: A = +/- 4 2B^2 = 4 : B^2 = 2: B = +/- SQRT(2)

In Q3, we divide all by cosx. Then, cosx cannot be 0, right? But in part (b), we equated cosx=0 and found x=pi/2. Isn't that a contradiction?

I just did my Further Maths Pure exam today… pretty tough but I liked the challenge and managed to answer most questions. It’s slightly different to your one in that mine tests all the content at once in a 2 h 40min sitting… I’m sure you would have loved to do some of the questions though :3

Our calculus teacher asked us to find out what is inverse of function x c^x where is is constant. But for around two days the problem is unsolvable and sir told that find it without W function. If not possible find it with Lambert W function)

1:24:05 What is a infinite interval? Because, if it's a interval with a infinite amount of numbers, then any non-degenerate inverval is a infinite interval :| (degenerate inteval being like: [a , a])

You could have used the adjugate formula for m inverse

At 34:09, shouldn’t you copy down the upper-left corner again? The way you copied it, the top-left and bottom-right determinants are always the same. And I think cofactor says to do the upper-left determinant

As a US high school student, I did this myself for fun and got a 63/75. someone let me know if that is a good score and if I graded myself well. Q1: -0 Q2: -0 Q3: -0 Q4: -1 (forgot the 35 in front) Q5: -1 (made some sign mistakes during the inverse but had more than 5 correct entries) Q6: -0 Q7: -5 (did part b completely wrong) Q8: -3 (copied x instead of x/4 during substitution from part a, idk how many points that is so I took 3) Q9: -2 (part b2 was completely wrong) Q10: -0 (this was super similar to questions we had in diff eq class, glad I remembered all of that)

Did the past paper im leaving until closer to my exam, guess i have to wait before i watch this 😂

Hello! Could you try the sequence and series question from JEE Advanced 2023! (The question ends with Find m+n) ❤

Do a further pure 2 paper ?

Fascinating. I passed A level Further maths in 1964....with a B grade. Did Maths and Statistics at Uni.

“What does this have to do with z?!”😂😂😂 that was very funny

could u do a Cambridge step 3 paper😢

UK maths student gang is very happy :)

I did maths gcse and did not continue with maths A level , this is my last A level year

try an IB maths AA HL paper

8. (d) The equation of the curve may not be suitable. Or, the measurements may not be accurate. Or, the paperweight may not be smooth.

The amount of times he sighed in this video. I feel his pain.