100 Inevitable Algebra Problems for Calculus
100 Inevitable Algebra Problems for Calculus! Designed for AP calculus or college calculus students, this tutorial covers a wide range of topics including factoring trinomials, polynomial long division, synthetic division, logarithmic functions, exponential functions, and more. You'll also learn techniques for simplifying complex expressions and solving partial fraction decompositions. Whether you're looking to improve your math skills or ace your calculus exams, this video has everything you need. #APCalculus #CollegeCalculus #AlgebraProblems #math #blackpenredpen
the file: www.blackpenredpen.com/_files...
with answers: remind me
BIG THANKS TO Alex Zyryanov for the timestamps!
0:00 the extreme algebra workout for calculus!
Q1 to Q10 factor & cancel
0:46 - Q1
2:05 - Q2
4:33 - Q3
6:33 - Q4
9:39 - Q5
11:52 - Q6
15:12 - Q7
23:51 - Q8
25:40 - Q9
27:24 - Q10
Q11 to Q20 expand & cancel
30:21 - 11
39:06 - 12
43:29 - 13
45:40 - 14
49:29 - 15
53:19 - 16
55:48 - 17
58:52 - 18
1:01:12 - 19
1:05:00 - 20
Q21 to Q30 using the conjugate for square root expressions
1:08:15 - 21
1:11:19 - 22
1:13:27 - 23
1:17:00 - 24
1:19:35 - 25
1:22:05 - 26
1:25:22 - 27
1:26:41 - 28
1:30:19 - 29
1:33:31 - 30
Q31 to Q40 complex fractions
1:36:13 - 31
1:39:32 - 32
1:42:30 - 33
1:44:53 - 34
1:47:32 - 35
1:49:56 - 36
1:51:41 - 37
1:54:34 - 38
1:56:36 - 39
1:59:34 - 40
Q41 to Q50 LCD & combine
2:03:16 - 41
2:05:04 - 42
2:07:43 - 43
2:10:27 - 44
2:13:03 - 45
2:17:05 - 46
2:19:52 - 47
2:22:37 - 48
2:25:56 - 49
2:29:47 - 50
Q51 to Q60 exponential & logarithm
2:34:25 - 51
2:38:06 - 52
2:42:15 - 53
2:44:48 - 54
2:46:13 - 55
2:47:53 - 56
2:49:18 - 57
2:50:29 - 58
2:53:30 - 59
2:55:40 - 60
Q61 to Q70 write in terms of x^p
2:57:23 - 61
2:59:04 - 62
2:59:58 - 63
3:01:00 - 64
3:02:58 - 65
3:04:40 - 66
3:06:00 - 67
3:08:00 - 68
3:09:09 - 69
3:12:22 - 70
Q71 to Q80 expressions from the quotient rule of derivative
3:14:09 - 71
3:16:25 - 72
3:19:29 - 73
3:22:19 - 74
3:24:10 - 75
3:26:16 - 76
3:29:50 - 77
3:32:58 - 78
3:36:29 - 79
3:39:15 - 80
Q81 to Q90 expressions from implicit differentiation (solving for dy/dx)
3:43:40 - 81
3:47:55 - 82
3:49:53 - 83
3:52:28 - 84
3:55:13 - 85
3:59:08 - 86
4:02:44 - 87
4:09:32 - 88
4:12:13 - 89
4:15:28 - 90
Q91 to Q100 solving for the unknowns from partial fractions decomposition
4:18:22 - 91
4:26:31 - 92
4:33:42 - 93
4:38:42 - 94
4:43:56 - 95
4:46:58 - 96
4:48:33 - 97
4:53:09 - 98
4:59: 46 - 99
5:04: 20 - 100
5:14:33 for the people who just want to see the end : )
**Thanks to ALL my lovely patrons for supporting my channel and believing in what I do**
AP-IP Ben Delo Marcelo Silva Ehud Ezra 3blue1brown Joseph DeStefano
Mark Mann Philippe Zivan Sussholz AlkanKondo89 Adam Quentin Colley
Gary Tugan Stephen Stofka Alex Dodge Gary Huntress Alison Hansel
Delton Ding Klemens Christopher Ursich buda Vincent Poirier Toma Kolev
Tibees Bob Maxell A.B.C Cristian Navarro Jan Bormans Galios Theorist
Robert Sundling Stuart Wurtman Nick S William O'Corrigan Ron Jensen
Patapom Daniel Kahn Lea Denise James Steven Ridgway Jason Bucata
Mirko Schultz xeioex Jean-Manuel Izaret Jason Clement robert huff
Julian Moik Hiu Fung Lam Ronald Bryant Jan Řehák Robert Toltowicz
Angel Marchev, Jr. Antonio Luiz Brandao SquadriWilliam Laderer Natasha Caron Yevonnael Andrew Angel Marchev Sam Padilla ScienceBro Ryan Bingham
Papa Fassi Hoang Nguyen Arun Iyengar Michael Miller Sandun Panthangi
Skorj Olafsen Riley Faison Rolf Waefler Andrew Jack Ingham P Dwag Jason Kevin Davis Franco Tejero Klasseh Khornate Richard Payne Witek Mozga Brandon Smith Jan Lukas Kiermeyer Ralph Sato Kischel Nair Carsten Milkau Keith Kevelson Christoph Hipp Witness Forest Roberts Abd-alijaleel Laraki Anthony Bruent-Bessette Samuel Gronwold Tyler Bennett christopher careta Troy R Katy Lap C Niltiac, Stealer of Souls Jon Daivd R meh Tom Noa Overloop Jude Khine R3factor. Jasmine Soni L wan na Marcelo Silva Evangeline McDonald Joe Taxpayer
----------------------------------------
💪 If you would also like to support this channel and have your name in the video description, then you could become my patron here / blackpenredpen
Пікірлер: 289
Hope i have no mistakes 0:46 - 1 question 2:05 - 2 question 4:33 - 3 question 6:33 - 4 question 9:39 - 5 question 11:52 - 6 question 15:12 - 7 question 23:51 - 8 question 25:40 - 9 question 27:24 - 10 question 30:21 - 11 question 39:06 - 12 question 43:29 - 13 question 45:40 - 14 question 49:29 - 15 question 53:19 - 16 question 55:48 - 17 question 58:52 - 18 question 1:01:12 - 19 question 1:05:00 - 20 question 1:08:15 - 21 question 1:11:19 - 22 question 1:13:27 - 23 question 1:17:00 - 24 question 1:19:35 - 25 question 1:22:05 - 26 question 1:25:22 - 27 question 1:26:41 - 28 question 1:30:19 - 29 question 1:33:31 - 30 question 1:36:13 - 31 question 1:39:32 - 32 question 1:42:30 - 33 question 1:44:53 - 34 question 1:47:32 - 35 question 1:49:56 - 36 question 1:51:41 - 37 question 1:54:34 - 38 question 1:56:36 - 39 question 1:59:34 - 40 question 2:03:16 - 41 question 2:05:04 - 42 question 2:07:43 - 43 question 2:10:27 - 44 question 2:13:03 - 45 question 2:17:05 - 46 question 2:19:52 - 47 question 2:22:37 - 48 question 2:25:56 - 49 question 2:29:47 - 50 question 2:34:25 - 51 question 2:38:06 - 52 question 2:42:15 - 53 question 2:44:48 - 54 question 2:46:13 - 55 question 2:47:53 - 56 question 2:49:18 - 57 question 2:50:29 - 58 question 2:53:30 - 59 question 2:55:40 - 60 question 2:57:23 - 61 question 2:59:04 - 62 question 2:59:58 - 63 question 3:01:00 - 64 question 3:02:58 - 65 question 3:04:40 - 66 question 3:06:00 - 67 question 3:08:00 - 68 question 3:09:09 - 69 question 3:12:22 - 70 question 3:14:09 - 71 question 3:16:25 - 72 question 3:19:29 - 73 question 3:22:19 - 74 question 3:24:10 - 75 question 3:26:16 - 76 question 3:29:50 - 77 question 3:32:58 - 78 question 3:36:29 - 79 question 3:39:15 - 80 question 3:43:40 - 81 question 3:47:55 - 82 question 3:49:53 - 83 question 3:52:28 - 84 question 3:55:13 - 85 question 3:59:08 - 86 question 4:02:44 - 87 question 4:09:32 - 88 question 4:12:13 - 89 question 4:15:28 - 90 question 4:18:22 - 91 question 4:26:31 - 92 question 4:33:42 - 93 question 4:38:42 - 94 question 4:43:56 - 95 question 4:46:58 - 96 question 4:48:33 - 97 question 4:53:09 - 98 question 4:59:46 - 99 question 5:04:20 - 100 question
@blackpenredpen
Жыл бұрын
Thank you very much, Alex : )
@alexzyryanov1947
Жыл бұрын
@@blackpenredpen Thanks for the videos. You're doing a great job. Keep it up!
@adivhahomathivha1881
Жыл бұрын
Not all heros wear capes!
@bhavydugar6665
Жыл бұрын
@The New 3D World Fan have you heard about the law of cosines
@Jaylenrai
7 ай бұрын
Thank you bro
100 integrals part 2 please!!!!
@mathisnotforthefaintofheart
Жыл бұрын
Why, you already finished?🤣🤣
@lekiwi_4145
Жыл бұрын
EVERYONE GO !!
@countryhumansgermany1267
Жыл бұрын
Better : 100 non-elementary integrals
@blackwhengames_2550
Жыл бұрын
Bro you guys gonna kill him if he gotta do this much 💀💀
@SuperYoonHo
Жыл бұрын
@@blackwhengames_2550 yeah, lol, steve needs some rest, lol
You can see the dedication of this man , not by watching the whole video but by just lookin at the no. of marker boxes he has .......
I only have time (and energy) to do the timestamps for each category. Could anyone please help with the timestamps for each question? I will credit you in the description. Thank you very much. 0:46 Q1 to Q10 factor & cancel 30:21 Q11 to Q20 expand & cancel 1:08:15 Q21 to Q30 using the conjugate for square root expressions 1:36:13 Q31 to Q40 complex fractions 2:02:41 Q41 to Q50 LCD & combine 2:33:57 Q51 to Q60 exponential & logarithm 2:57:23 Q61 to Q70 write in terms of x^p 3:14:09 Q71 to Q80 expressions from the quotient rule of derivative 3:43:40 Q81 to Q90 expressions from implicit differentiation (solving for dy/dx) 4:18:22 Q91 to Q100 solving for the unknowns from partial fractions decomposition 5:14:33 for the people who just want to see the end : ) Thanks for all the love and support. Thank you. bprp
@watchoutforcopyright9339
Жыл бұрын
you are one of the youtubers that helped me ❤
@MathCuriousity
Жыл бұрын
this is actually better than listing out all of the time stamps. I love how you categorized it!
me when the only questions i get wrong are the dumb algebra errors
@pseudolullus
Жыл бұрын
They're not so dumb, they're the main stumbling block in calculus for a lot of people ngl
@alexalt1215
Жыл бұрын
@@pseudolullus i think me means they can do the hard algebra, but makes stupid mistakes, like maybe factoring the sum of squares like difference of squares
@Liwidyanto789
Жыл бұрын
Weeb
you're a genius! literally , Thank you for spending your time making maths fun for people all over the world. Thank you for your energy sir ! thank you for your pens :) You're an artist
@blackpenredpen
Жыл бұрын
I appreciate your complement. Thank you!
i cannot believe how fun this is. I hated math for most of my life due to teachers yelling and being generally inattentive but doing this is genuinely nice thank you!
For the nineth question: x^3-5x+2 = x^3-5x+2+10-10, and we can rearrange that to x^3-8-5x+10. The first part is just a cubic difference (x3-2^3) and from the second part we can factor out -5 to obtain -5(x-2). The factorization of the cubic difference is (x-2)(x^2+2x+4), so by plugging that into the the first equation we got: (x-2)(x^2+2x+4) -5(x-2). From that, we can factor out the term (x-2) to obtain (x-2)(x^2+2x+4-5) that is the same as saying (x-2)(x^2+2x-1). That (x-2) term cancels out with the other (x-2) on the denominator, simplifying our first polynomial to x^2+2x-1
This is awesome. I gave my Calc students 100 limit problems (on paper) and they thought the sky is falling. I looked at them and I said "sell the TV"
@blackpenredpen
Жыл бұрын
lol
I like these longer videos quite a bit. I'm a software developer, and I just play these in the background while I'm working. I take breaks from coding to do a few problems w bprp. Quite enjoyable!
@ryandalm
Жыл бұрын
You probably also found 1:33:22 a funny reference then!
@adameleuch363
11 ай бұрын
@@ryandalm explain pls
@ryandalm
11 ай бұрын
@@adameleuch363 Because in software development you also have nested elements, just like in this example (nested square root) Edit: iykyk
@adameleuch363
11 ай бұрын
@@ryandalm ohh alright thanks
he's a man of focus, commitment, and sheer f*cking will. bravo dude!
What a devoted mathematician, you must have great students!
YES!!!👏👏 I was anticipating this video, and he pulled through! I know this is going to be so useful for me as I'm in calc 1 now😁
I respect your hardwork sir
@blackpenredpen
Жыл бұрын
This means a lot, especial it’s coming from you, Mr Einstein!
This is very important what he said about Calculus. The hardest part about Calculus (ignoring definition of limit) is the Algebra. It is easy if you know Algebra. If you can understand that 1/x goes to 0 as x increases without bound and you know Algebra, you should be able to learn Calculus.
Definitely you are the best math teacher, who actually loves to teach!
Thanks man.really appreciate this.
it's definitely a unique tutorial, love you brother!
Amazing ! Thank you !
yay, ive been waiting for this one!!!
This is great. I might offer this as a summer review practice set for students going from precalc to AP Calc. But I would rewrite #81-90 with something like "A" instead of "dy/dx" since they wouldn't know what the derivative notation means and I would probably get a lot of questions along the lines of distributing the "d" and the "y" and then just solving for y. Need one for trig and one for features of graphs (end behavior, intercepts, especially for parent functions)!
@blackpenredpen
Жыл бұрын
Thank you. I thought about using D for dy/dx for those questions but I still ended up using dy/dx... why? because honestly, I forgot to change them before I record lol!
@stephenbeck7222
Жыл бұрын
@@blackpenredpen hah, well it is good for current calc students when they get to these topics.
just got into calculus and i’ve been struggling with this. THANK YOU BRO U SAVED MY LIFE
@cesarrivas2295
Жыл бұрын
Did you pass?
I really needed this ty ty :)
Thanks to you, I have learned how to factor cubic equations. I always have a hard time in those.👊👊👊
Sir I was watching your old videos and you haven't changed at all you looks same as in your old videos which is very interesting thank you sir for your hard work 👍
The King of maths teacher !🎉
This is exactly what i need thank you
So nice! You should make a video of an equation using tetration (hyper-4)!
I do love algebra. Doing algebra is soothing to my brain.
Please teach us how to sketch graph of most of the functions and curves The graphical approach in differential calculus seems much helpful and time saving
@daddy_myers
Жыл бұрын
You can learn to sketch stuff pretty easily using Calculus, even graphs which you've never seen before; you should definitely give that a look if you're comfortable with Calculus 1.
This is so useful!
Excellent, perfect to repast _Saludos_ 🤝 from Colombia 🇨🇴
This is AMAZING!!!!
Thank you so much.this is great.❤❤
Nice! Did all of these over the span of 6 hours. Now I feel a little more comfortable with algebra but not even close to becoming an algebra master.
Thank you!!!
Great video!
the best one!, bless you brother,
I love this so much. This dude is so sweet!
The longest video I've ever watched. It's really fun and useful. The good thing is that everything is easy
@blackpenredpen
8 ай бұрын
Glad you liked it!
Thank you.
Thanks Steve!!! But the equation, never will gonna have an answer, but it is your channel, I can’t do anything
Yesss, here we go!!!
Thanks alot you're my best of best youtuber
Thanks this will help for my college entrance exams 👍
do you think you could ever do 100 calculus 3 questions, it would really help me and others out, love ur vids anyways
This man is the reason why I am passing math
Wow. thank you!!!
This guy is just awesome
Thank you 💕
Hi I am a big fan and I just got the integrals for you t-shirt with + constant or just +c on the front and I would just like to say hello from Canada I am 13 and love your videos and I will continue to support them I’ve been watching them for a while now since last year and I am very impressed by your skills in mathematics
Try checking chapter p.6 old exams by KFUPM (a uni). They have some pretty good and tough factoring problems.
My favorite Video ever 💖😃
15:48 A trick I learned for the signs in expanding the sum of 2 cubes is SOAP. Same, Opposite, Always Positive.
WOW blackpenredpen, you are so close to 1,000,000 subscribers! Keep going with the hard work. :)
@blackpenredpen
Жыл бұрын
Thank you!
@PrudentialViews
Жыл бұрын
@@blackpenredpen No problem!
I'm not taking any classes. I'm just interested in maths.
I would really like to see some problems utilizing Intermediate Value Theorem and Mean Value Theorem
very well teched
That was amazing . One question in the last Question, it was a mistake the CX should be -Cx samething on D sould be -D , it sould be (Cx+D)(X^2-1): Cx^3-Cx+Dx^2-D
"every morning: 10 sit ups 10 push ups 10 algebra problems 10 pancakes" -Chris Butler, my Calc 2 prof
Awesome! 🎉😊
just a while ago I completed practising those questions, which I solved using different methods than those you have shown, the adventure was long but I learnt a lot of new ideas on how to solve these equations, and you kinda proved my idea that every question has infinite way to solve it, which I liked, also thanks for your time
waiting it for 5 hours😂😂tnx
I’ve worked out all this with you twice now! Whew! 😂
thx help me a lot
This workout was extreme for you (in fysical terms :)) But nevertheless many thanks ! for your hard work.
Sleepy pen hungry pen, you are purely genius. I learn something new each time you have new videos
I am glad to learn what Pascal's Triangle is used for .
@blackpenredpen
Ай бұрын
Nice!
you are the best
Great video! This has been an awesome review for algebra. I think there is an issue with the final answer of question 70, the exponent of -3/4 for -24x should be -3/2. 1/2 - 2 = 1/2 - 4/2 = -3/2
100 differential equations!!
3:13:18 #70: middle term should be -24^-3/2 not -24^-3/4 right?? Or am I wrong? 🧐
what is the formula on your shirt?
I have a question, what are the possible solutions for y if sin^-1(cosh(x^x))=y?
#3 is better with (x + 7)/(2 - x), looks more perfect. :D
100 algebra part 2 plssss
1.00am? I hope you had plenty of caffeine, Steve! 👍
mistake @3:13:02 (1/2) - 2 = -3/2 not -3/4. thank you for the problems, they were very fun!
I should procrastinate my studying by watching you do these problems 😂
I am watching this complete tutorial. Please can you also make a full calculus playlist. Calculus 1, Calculus 2 and Calculus 3. It gets confusing and scary when I see the channel videos and I don't even know where to start.
using integration find the area of triangular region whose sides have the y=2x+1 ,y=3x +1 and x=4.
I love the way you say "cancelleded" 😁
Wait I have a question 🙋♂️ Why would you work out the equation in question 28 (1:26:41) for example, since the final answer seems longer… or am I missing something? I can’t express how much gratitude I have for you by the way. I think we all owe you something. 😅
@blackpenredpen
Жыл бұрын
These "algebraic moves" are mainly for calculus purposes. We do it like that for that problem at 1:26:41 is because if we are working with the limit as x goes to 6 for that expression, then we can't simply plug in x=6 (bc it will cause 0/0). But once we simply it like in the video, then we can plug in x=6 and figure out the limit.
@blackpenredpen
Жыл бұрын
Here's an example kzread.info/dash/bejne/hpugppaSZs_Tgc4.html
@ryandalm
Жыл бұрын
@@blackpenredpen this helps so much, everything makes sense now. Thank you for your time! You’re a genius Steve. Edit: I kept watching and noticed that you actually explained it here briefly too: 2:18:49 👌
could you please put a link for the file because that at the description is not working , thanks for your work
31:51 I know it’s not the method we should be using, but we can use the difference of squares and difference of cubes formulae and get the result without actually doing any expanding. Rather, the opposite - we factorise and cancel!
I was hoping to get a file with a list of the problems. Does this exist somewhere? Clicking on the "black pen" link above did not work. Thank you for your help.
Simplifying trigonometry pls!!!😊
do 100 Trigonometric questions please!!!!
Thks .good jod
Perfect
100 complex calculus series please
can you make a video solving 100 geometry problems ?
can you do number theory basic demonstrations plz🙃
like the title says, a real workout but fun
For the first few (factor and cancel) i think it would be better if you give a domain for x
@artsmith1347
Жыл бұрын
This has been important in other videos. The first equation, as given, is not defined at x = 7, but there is no restriction on the simplified version after canceling. I guess it is okay in this case because the limit of the given equation as x approaches 7 is 4 and the simplification gives the same answer.
3:22:00 this just the d/dx of sqrtx / (1+x²)
Make a video of 100 question on difnite integration and take tough question
Absolutely brilliant- now, lie down.
76 should be (1+x^2)^(-5/2); love the video
@michaelroberts694
Жыл бұрын
Also for 100, D=-1 (not 1)
Unfortunately, I can't acces the document anymore. By chance is there an alternate upload somewhere?