Would you do more topics in this style, it's not that I dislike the style of the lesson slides, I just adore the aesthetic of how the information is arranged here; I'm sure we would all appreciate it! Thanks alot :D
@@BicenMaths yes please : ) that would be very helpful thanks also thanks for all your videos on further maths, there is hardly any resources on yt for them apart from tlmaths and fmvideos, and it's just nice hearing another POV.
This video was so helpful picked apart all the gaps in my knowledge and filled them with very useful information, kicking myself as to how I didn't know these things with a matter of weeks before my A levels, thank you so much.
Wow! Needed a recap of this for STEP revision and this was by far the most efficient method to jog my memory. I really love how each question has been expertly crafted to use most of the content. Thank you so much for going above and beyond in every video!
Thank you! I work hard to condense the information as much as possible so there aren’t endless examples, thank you for noticing that. As for the graphs of cosec, sec, and cot, these are rarely examined as lots of students now have graphics calculators… especially all my students. But a good point!
@@BicenMaths Ah right that makes a lot more sense, and the same is probably true for the inverse trig graphs. I still can't get over how each question is so perfect in testing all of the content we just revised. It's so satisfying, thank you so much!
Hi Mr. Bicen! Thank you so much for your plethora of videos!! It really helps me to self study! I was wondering if you would be able to do an "all about graphing" video for a level maths yr1 and 2? Thank you so much!!
That’s a great idea! I’m currently working on one for differentiation, and have got vectors on my list. This is an excellent suggestion that I will also work on soon! Good luck with your studies 👍🏼
Really great video, it was definitely worthwhile watching through the entire thing. The iPad is an amazing resource for teaching. Thank you Mr Bicen :)
This is the harmonic identity. If you square the expressions and add them, you can factor out R, leaving behind sin^2 + cos^2, which we know equals 1! Hence we are just left with R=
Hi Mr Bicen! I'm really unsure on how to start ny revision using the text book. I always hear "practice practice practice" but i cannot do all of the questions there because it's too much and i don't have time- i still need to do past paper questions too. I also don't want to skip any questions, just in case it might be a really "good" one. There are also different types of questions in the textbook too. Where should i start?
If you’re finding you don’t have enough time to do them all, maybe you should do every other question in an exercise, or once you feel confident with the skills, just try some of the later questions as they tend to be harder. It might seem like you are “wasting” time doing lots of questions, but in the long run this will develop your understanding and also speed up your ability to answer quickly, which is crucial for the exams!
@@BicenMaths Thankyou for your reply! Would you say that watching a video of a person going through the textbook questions is a good form of getting to understand the content better?
No I wouldn’t - I think this doesn’t put enough emphasis on YOU doing the maths actively and is too passive. Tutorial videos are good (like the ones on my page organised by chapter) but in those videos I usually suggest which questions you should practice. Doing maths is better than watching maths! Good luck
Hi Mr Bicen, hope you are doing great. I found a cheeky question on the Year 2 Pearson book... Would appreciate if you looked at it... Page 355 review exercise, Question 29... I always knew and kind of regretted the product to sum/sum to product trig identities were not in A Level spec. I found this question and when finding the area between A and B, top halve, I had to resort to product to sum identities to integrate. I thought surely this cant be the case so I checked the solution bank, and sure enough they were using it there. Interestingly no marks are specified like other (E/P) questions and no where in the spec did they teach these... am I missing something here? Have a great weekend! PS. the sum to product happens to be in the formula book but not product to sum.
So these formulae are very overlooked, and to be honest with you, I have never taught them - I’m never seen anything examined on them, especially in the new spec, and my belief is that in the rare case it were examined, it would guide you through the thinking with parts (a) and (b) etc. so you end up seeing what needs to be done. Perhaps it’s something I should add in to my videos, but it’s quite complex for something that I don’t feel is at all likely to appear. Interesting to have explored it though, well done!
@@BicenMaths Thanks so much, really appreciate it. I was doing a few practice integration problem from a different book and I found that thosee rules often crop up (needing to seperate products of sines and cosines) but they were not discussed in A level... doesnt seem ti be in further maths either. Thanks again.
It would be very hard for me to do as I haven’t taught this module before - but I have been studying it, so I may be able to make one soon… will have to wait and see!
@@BicenMaths So i could watch every single video and learn everything, nothing missed. Does this include only pure year 1 and year 2 or also your applied year 1 and year 2 playlists.
Hi Sir, Hope you are well. I have just finished year 12 and beginning to learn year 13 content. I feel like it is a large jump in difficulty, and im not sure how to effectively learn and revise harder topics. Any tips?
Sorry for the delay in replying to you - I would say to try and get ahead on some of the challenging content, even if it is just starting to understand some of the concepts. For example, have a look at some of the trig and differentiation playlists from Year 2. This means when you come across them in class, you’ll already have an idea of what’s going on, and can focus on practice, rather than needing to think really deeply. This will help you feel more at ease and confident. There is a jump up, but I think a lot of the jump up is on the surface - the questions look a lot harder, but once you *understand* what is going on, you’ll find yourself coping, I hope.
I think the most useful video in this style for my Further Maths students would be AS Core Pure Vectors. It feels like a huge and overwhelming topic for them, so many different forms of lines and planes and so many different methods to do with those forms. I tell them to make a one page summary - and they never do, so if I could point them at your video and tell them to make a one page summary based on that, they might?
Yep! I have videos for literally every aspect of stats and mechanics for Edexcel. If you go to my homepage, scroll down to the applied section, and you’ll find everything you need there!
@@BicenMaths ahh thats awesome, I have a question though, I am taking the Edexcel A-Level Maths Pure, Stats, and Mech, however this shows applied, are they the same?
sir im teaching my self further maths and it just come to me that if i do the taylor expansion of sin, cos , and tan of x, i get a result and the first few terms of the result actually do match with the small angle approximation of sin,cos and tan. is that coincidance or is it the actually definition or the way we get them from?
Great question! And apologies for the delay in my reply - the small angle approximations are indeed just the first few terms of the Maclaurin/Taylor expansion from Further Maths. There are other ways to explain them, but I think seeing the connection to these expansions is great. Well done!
Not really, no - these can just be thought of as graph transformations, like from f(x) to f(qx), which is a stretch in the x direction of 1/q, meaning the period is 360/q as you state. Period is discussed more in further maths when you look at harmonic motion, but not so much in regular maths.
Hi for the maximum and minimum questions, you used zero as your value but in school we learnt that we can only use 1 or -1 as these are the values that the sin graph is a maximum or minimum, so now i’m a bit confused
It is usually using 1 or -1, but that’s not always true, as demonstrated in my example. If you’re looking for a maximum or minimum value, you need to look at the overall function and decide what will make it smallest or biggest. The squaring function meant that 0 created the max/min in this case! Your teachers are trying to simplify it for you, but there are other cases with things other than 1 or -1 you should be aware of. Hope that helps!
@@BicenMaths ow yes going through exam questions topic by topic will be so amazing.There are some who does further maths Exam questions but the good thing about this chanel you explain it.where as some just answer it and you don't even know how they get there.
Really surprised the unit circle doesn't appear in this syllabus/summary. (I work in Australia - different syllabus). IMHO it's the central unifying idea for the topic ...
I appreciate that point - I do teach the unit circle to get understanding in my longer videos - but on reflection didn’t include here as I don’t personally think about the unit circle much when working with trig. But I’m sure others do think about it! Thanks 😊
@@BicenMaths Interesting! Pretty much every trig equation (esp general solution) I'm having my students draw little unit circle diagrams to help see all the solutions in the various quadrants. Helps with boundary angle values too. Horses for courses 🙂. Thanks for all your great videos BTW, great tutorials for my students and nice for me to see various UK courses. And always gives me ideas for exam questions.
We don’t teach the general solution in the UK - but I can see how unit circle would really benefit for this though! I have tried teaching solving trig equations i) drawing graphs ii) with unit circle/CAST diagram and iii) with the rules I outline in this video, and I have eventually settled on the rules here - I’ve just found there’s less room for error. And now it’s my go-to method how I solve them myself, despite being taught the unit circle method at school! Really interesting hearing different views on this though, thank you for sharing. I’m pleased you’re enjoying/benefiting from the videos - thanks for supporting my channel! 😃
![How to integrate ANYTHING • Part 1: Techniques ✍️ [A-Level Maths]](http://i.ytimg.com/vi/L6UkjiDVmWk/mqdefault.jpg)
![How to integrate ANYTHING • Part 1: Techniques ✍️ [A-Level Maths]](/img/tr.png)
Would you do more topics in this style, it's not that I dislike the style of the lesson slides, I just adore the aesthetic of how the information is arranged here; I'm sure we would all appreciate it! Thanks alot :D
Of course! I’m pleased you like this style of video. Any suggestions for next topic? I’m thinking of doing a full overview of differentiation?
@@BicenMaths yes please : ) that would be very helpful thanks
also thanks for all your videos on further maths, there is hardly any resources on yt for them apart from tlmaths and fmvideos, and it's just nice hearing another POV.
Thank you!
You’re the personification of a lifesaver
🤩
This video was so helpful picked apart all the gaps in my knowledge and filled them with very useful information, kicking myself as to how I didn't know these things with a matter of weeks before my A levels, thank you so much.
You are very welcome! Pleased it helped!
Wow! Needed a recap of this for STEP revision and this was by far the most efficient method to jog my memory. I really love how each question has been expertly crafted to use most of the content. Thank you so much for going above and beyond in every video!
Only bit you perhaps forgot to mention was the graphs of cosec, sec and cot and the inverse trignometric functions/graphs
Thank you! I work hard to condense the information as much as possible so there aren’t endless examples, thank you for noticing that. As for the graphs of cosec, sec, and cot, these are rarely examined as lots of students now have graphics calculators… especially all my students. But a good point!
@@BicenMaths Ah right that makes a lot more sense, and the same is probably true for the inverse trig graphs. I still can't get over how each question is so perfect in testing all of the content we just revised. It's so satisfying, thank you so much!
Hi Mr. Bicen! Thank you so much for your plethora of videos!! It really helps me to self study! I was wondering if you would be able to do an "all about graphing" video for a level maths yr1 and 2?
Thank you so much!!
That’s a great idea! I’m currently working on one for differentiation, and have got vectors on my list. This is an excellent suggestion that I will also work on soon! Good luck with your studies 👍🏼
Thanks for this! I have jan mocks coming up and will definitely use this in my revision :)
Yo I’ve never seen these co function equations before - thanks !
They’re useful! Pleased I was able to show you these 👍🏼
Great video sir. Keep it up!
First year of Uni and im still coming back for help.
I hope things are going well! Come back and visit in the new year! 😃
Couldn’t do trig that well, this helped a lot
Differentiation
Good suggestion!
Really great video, it was definitely worthwhile watching through the entire thing. The iPad is an amazing resource for teaching. Thank you Mr Bicen :)
Hi, why did you use Pythagoras to get the value of R in question 1a? Thanks for this video!!
This is the harmonic identity. If you square the expressions and add them, you can factor out R, leaving behind sin^2 + cos^2, which we know equals 1! Hence we are just left with R=
Inverse trig functions?
i’m only a few minutes in but this video has already been so helpful!! thank you so much for this 😭
fricking legend
Hi Mr Bicen! I'm really unsure on how to start ny revision using the text book. I always hear "practice practice practice" but i cannot do all of the questions there because it's too much and i don't have time- i still need to do past paper questions too. I also don't want to skip any questions, just in case it might be a really "good" one. There are also different types of questions in the textbook too. Where should i start?
If you’re finding you don’t have enough time to do them all, maybe you should do every other question in an exercise, or once you feel confident with the skills, just try some of the later questions as they tend to be harder. It might seem like you are “wasting” time doing lots of questions, but in the long run this will develop your understanding and also speed up your ability to answer quickly, which is crucial for the exams!
@@BicenMaths Thankyou for your reply! Would you say that watching a video of a person going through the textbook questions is a good form of getting to understand the content better?
No I wouldn’t - I think this doesn’t put enough emphasis on YOU doing the maths actively and is too passive. Tutorial videos are good (like the ones on my page organised by chapter) but in those videos I usually suggest which questions you should practice. Doing maths is better than watching maths! Good luck
Hi Mr Bicen, hope you are doing great. I found a cheeky question on the Year 2 Pearson book... Would appreciate if you looked at it... Page 355 review exercise, Question 29... I always knew and kind of regretted the product to sum/sum to product trig identities were not in A Level spec. I found this question and when finding the area between A and B, top halve, I had to resort to product to sum identities to integrate. I thought surely this cant be the case so I checked the solution bank, and sure enough they were using it there.
Interestingly no marks are specified like other (E/P) questions and no where in the spec did they teach these... am I missing something here?
Have a great weekend!
PS. the sum to product happens to be in the formula book but not product to sum.
So these formulae are very overlooked, and to be honest with you, I have never taught them - I’m never seen anything examined on them, especially in the new spec, and my belief is that in the rare case it were examined, it would guide you through the thinking with parts (a) and (b) etc. so you end up seeing what needs to be done. Perhaps it’s something I should add in to my videos, but it’s quite complex for something that I don’t feel is at all likely to appear. Interesting to have explored it though, well done!
@@BicenMaths Thanks so much, really appreciate it. I was doing a few practice integration problem from a different book and I found that thosee rules often crop up (needing to seperate products of sines and cosines) but they were not discussed in A level... doesnt seem ti be in further maths either. Thanks again.
Will you make an Everything you need to remember for further maths edexcel fs1 statistics 1
Please do, that would really help
It would be very hard for me to do as I haven’t taught this module before - but I have been studying it, so I may be able to make one soon… will have to wait and see!
Ill look forward to it
Hello sir, wonderful video as always.
At 17:30 why do we subtract 20 and not add it?
Because we are trying to mimic the part inside the tan function, which is 2x-20 not 2x+20! Hope that makes sense!
Hey sir, do your playlists on content cover everything or are there some areas missing?
Covers it all!
@@BicenMaths So i could watch every single video and learn everything, nothing missed. Does this include only pure year 1 and year 2 or also your applied year 1 and year 2 playlists.
Also, does it include of areas of further maths as well?
Please can you make an everything you need to know for further stats 1 edexcel, it will save my life.
I’ve not taught this so it would be very tricky for me - however I am studying it at the moment, so it might happen eventually!
I would do it for you, might be a Christmas project though as lots to do for UA-cam.
You are the best teacher I have ever seen in my whole life .
This is definitely an overstatement - but thank you!
Great video. Nicely explained!
Hi Sir, Hope you are well. I have just finished year 12 and beginning to learn year 13 content. I feel like it is a large jump in difficulty, and im not sure how to effectively learn and revise harder topics. Any tips?
Sorry for the delay in replying to you - I would say to try and get ahead on some of the challenging content, even if it is just starting to understand some of the concepts. For example, have a look at some of the trig and differentiation playlists from Year 2. This means when you come across them in class, you’ll already have an idea of what’s going on, and can focus on practice, rather than needing to think really deeply. This will help you feel more at ease and confident. There is a jump up, but I think a lot of the jump up is on the surface - the questions look a lot harder, but once you *understand* what is going on, you’ll find yourself coping, I hope.
@@BicenMaths Hi Sir, thank you for the help. I appreciate it.
Hi mr Bicen if I watch ur vids is it enough for AQA a lvl maths ?
It should be, yes! The content has largely been made the same for all exam boards, just different style of asking questions and paper structure
beautiful man!
I think the most useful video in this style for my Further Maths students would be AS Core Pure Vectors. It feels like a huge and overwhelming topic for them, so many different forms of lines and planes and so many different methods to do with those forms. I tell them to make a one page summary - and they never do, so if I could point them at your video and tell them to make a one page summary based on that, they might?
I love this idea! Not too much work either. I have a list of things I’d like to do, so adding this on!
Hey Mr. Bicen, hope ya well! Do you have any videos on Statistics and Mechanics for Edexcel A-Level? Thanks.
Yep! I have videos for literally every aspect of stats and mechanics for Edexcel. If you go to my homepage, scroll down to the applied section, and you’ll find everything you need there!
@@BicenMaths ahh thats awesome, I have a question though, I am taking the Edexcel A-Level Maths Pure, Stats, and Mech, however this shows applied, are they the same?
Yep, Applied is just the name for stats and mechanics together!
Woah new vid!
good video i think
Ratio jawad
Cos(x)/Sin(x)=Tan(x) u forgot this one for YEAR 1
Wow, sir 👏!
sir im teaching my self further maths and it just come to me that if i do the taylor expansion of sin, cos , and tan of x, i get a result and the first few terms of the result actually do match with the small angle approximation of sin,cos and tan. is that coincidance or is it the actually definition or the way we get them from?
Great question! And apologies for the delay in my reply - the small angle approximations are indeed just the first few terms of the Maclaurin/Taylor expansion from Further Maths. There are other ways to explain them, but I think seeing the connection to these expansions is great. Well done!
Do we need to know about periods , t= 360/q when in the form eg. Cos(qx + r)
Not really, no - these can just be thought of as graph transformations, like from f(x) to f(qx), which is a stretch in the x direction of 1/q, meaning the period is 360/q as you state. Period is discussed more in further maths when you look at harmonic motion, but not so much in regular maths.
this man is an absolute legend
Thank you 🙌🏼
Hi for the maximum and minimum questions, you used zero as your value but in school we learnt that we can only use 1 or -1 as these are the values that the sin graph is a maximum or minimum, so now i’m a bit confused
It is usually using 1 or -1, but that’s not always true, as demonstrated in my example. If you’re looking for a maximum or minimum value, you need to look at the overall function and decide what will make it smallest or biggest. The squaring function meant that 0 created the max/min in this case! Your teachers are trying to simplify it for you, but there are other cases with things other than 1 or -1 you should be aware of. Hope that helps!
Hope you will do exam questions topic by topic for further maths or maths!But still everything is enough
As in me going through each question? That’s a good idea!
@@BicenMaths ow yes going through exam questions topic by topic will be so amazing.There are some who does further maths Exam questions but the good thing about this chanel you explain it.where as some just answer it and you don't even know how they get there.
Really surprised the unit circle doesn't appear in this syllabus/summary. (I work in Australia - different syllabus). IMHO it's the central unifying idea for the topic ...
I appreciate that point - I do teach the unit circle to get understanding in my longer videos - but on reflection didn’t include here as I don’t personally think about the unit circle much when working with trig. But I’m sure others do think about it! Thanks 😊
@@BicenMaths Interesting! Pretty much every trig equation (esp general solution) I'm having my students draw little unit circle diagrams to help see all the solutions in the various quadrants. Helps with boundary angle values too. Horses for courses 🙂. Thanks for all your great videos BTW, great tutorials for my students and nice for me to see various UK courses. And always gives me ideas for exam questions.
We don’t teach the general solution in the UK - but I can see how unit circle would really benefit for this though! I have tried teaching solving trig equations i) drawing graphs ii) with unit circle/CAST diagram and iii) with the rules I outline in this video, and I have eventually settled on the rules here - I’ve just found there’s less room for error. And now it’s my go-to method how I solve them myself, despite being taught the unit circle method at school! Really interesting hearing different views on this though, thank you for sharing.
I’m pleased you’re enjoying/benefiting from the videos - thanks for supporting my channel! 😃
Hi sir, by any chance do you offer tuition for as level
I don’t have any space at the moment but if I do I would advertise it here on my UA-cam page and socials!
Very clear flow and presentation, thanks
You are welcome!
THANKYOU
Please do vectors year1 and year2 in one video.
Great! I’ll work on this one soon, good idea!
legend
Legend
Man saved my life
hello! 17:36 is there a reason why even though -20 is inside the brackets we do not add 20 instead?
hope the question makes sense
Hi bicen, isn't the answer at 12:12 105 degrees? great video!
I don’t think so - why would it be 105?