Uploaded March 2025 | Updated September 2026, 2 weeks ago
This question was sent to me by a viewer named Mr. Kong. It is from the 2018 Cambridge STEP 1 exam. "This fully tests your understanding of calc 1 differentiation and integration," Mr. Kong said. The question caught my attention since s(x) and c(x) behave very similarly to sin(x) and cos(x), but with a twist, of course. Thank you, Mr. Kong, for sending me this problem!
Get your Ultimate Calc 2 Integrals sweatshirt: amazon.com/dp/B0C9L798F2
Check out another Cambridge STEP integral problem: youtu.be/05GQzRfW26c?si=wJzfAG1REvPG2A2s
For more info on the Cambridge STEP exam, check out their official site: maths.cam.ac.uk/undergrad/admissions/step
0:00 Email from Mr. Kong
0:28 part i
4:03 part ii
8:21 part iii
12:37 part iv
15:37 part v
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#blackpenredpen #math #calculus #apcalculus
This question was sent to me by a viewer named Mr. Kong. It is from the 2018 Cambridge STEP 1 exam. "This fully tests your understanding of calc 1 differentiation and integration," Mr. Kong said. The question caught my attention since s(x) and c(x) behave very similarly to sin(x) and cos(x), but with a twist, of course. Thank you, Mr. Kong, for sending me this problem!
Get your Ultimate Calc 2 Integrals sweatshirt: amazon.com/dp/B0C9L798F2
Check out another Cambridge STEP integral problem: youtu.be/05GQzRfW26c?si=wJzfAG1REvPG2A2s
For more info on the Cambridge STEP exam, check out their official site: maths.cam.ac.uk/undergrad/admissions/step
0:00 Email from Mr. Kong
0:28 part i
4:03 part ii
8:21 part iii
12:37 part iv
15:37 part v
----------------------------------------
Big thanks to my Patrons for the full-marathon support!
Ben D, Grant S, Mark M, Phillippe S. Michael Z, Jan P. Devun C. Stefan C. Ethan BW Didion S. NN Minkyu Y Brandon F Levon M shortsleeve Jack P Gabriel G Yeeted C David H Mateo F Emma M Eden E Minicat Jose R Nicholas Fey Tyler B Lucas W Ahmet Ö An R Camila L Luupo Farrah Batman 1127 Mathguru Дмитрий П. Michelle L. Alin V. Archer. L Ali. Subotai B. Spencer A. Chris Jason B. Ou S. Nuddi M. Jackson M. Jordan T. Gregorio B. Omkar N. John D.
💪 Support this channel and get my math notes by becoming a patron: patreon.com/blackpenredpen
🛍 Shop my math t-shirt & hoodies: amzn.to/3qBeuw6
----------------------------------------
#blackpenredpen #math #calculus #apcalculus




![Stanford math tournament cubic question
Enhance your math contest skills from Brilliant: 👉https://brilliant.org/blackpenredpen/ (20% off with this link!)
This question is from the Stanford Math Tournament (SMT) the algebra tiebreaker section https://www.stanfordmathtournament.com/archive/2023. We are given a cubic function f(x)=x^3-6x^2+25/2x-7 and we know there exists a closed interval [a,b] such that the sequence x, f(x), f(f(x)), ... is bounded for x on [a, b]. This question is fascinating because not all cubic functions have such properties. I will use the fixed-point approach for this problem, how would you solve this? #brilliant #math #stanford #blackpenredpen
0:00 Stanford Math Tournament algebra tiebreaker
1:00 Check out Brilliant
2:10 My solution to this problem
7:12 Why my solution works for this problem
Note: I avoided calculus derivative here because I wanted to keep it with just algebra. I will do another video on the fixed-point iteration later.
9:56 the official solution
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Thank you all! Stanford math tournament cubic question](https://i.ytimg.com/vi/pHFuLL0VI8E/mqdefault.jpg)





