Uploaded December 2022 | Updated September 2026, 2 weeks ago
University of Oxford Mathematician Dr Tom Crawford works through his solution to a killer question from the 2022 Korean Suneung CSAT exam with some help from @drpkmath12345.
Use my link gauthmath.onelink.me/SUq5/d58dv886 to download Gauthmath and don't forget to use code 4SBW8X to get a 1 month discount now!
Check out PK's channel here: youtube.com/c/DrPKMath
The question is taken from the Korean SAT exam taken in November 2022. This was apparently a 'killer' question which hardly any students were able to solve within the time limit. The exam is taken at the end of high school as part of the college admissions process in the Republic of Korea (South Korea).
PK begins by explaining a little about the exam before sharing the question. We are asked to work out the value of a cubic function at the point x=2, but in order to determine the coefficients of the cubic we must solve a series of equations involving exponential functions, trigonometric functions, derivatives and composite functions.
The full question is as follows:
A cubic function f(x) with positive leading coefficient, the function g(x) = exp(sin(pi*x)) - 1, and the composite function h(x) = g(f(x)) on the domain of all real numbers, satisfy the following conditions:
1) Function h(x) has the maximum value of 0 when x is 0.
2) In the open interval (0, 3), there are 7 distinct real solutions to h(x) = 1.
3). f(3)= 1/2, f’(3)=0, and f(2)= p/q.
What is p+q? (where p and q are coprime integers).
This video is sponsored by Gauthmath.
Produced by Dr Tom Crawford at the University of Oxford. Tom is an Early-Career Teaching and Outreach Fellow at St Edmund Hall: seh.ox.ac.uk/people/tom-crawford
For more maths content check out Tom's website tomrocksmaths.com
You can also follow Tom on Facebook, Twitter and Instagram @tomrocksmaths.
facebook.com/tomrocksmaths
twitter.com/tomrocksmaths
instagram.com/tomrocksmaths
Get your Tom Rocks Maths merchandise here: beautifulequations.net/collections/tom-rocks-maths
University of Oxford Mathematician Dr Tom Crawford works through his solution to a killer question from the 2022 Korean Suneung CSAT exam with some help from @drpkmath12345.
Use my link gauthmath.onelink.me/SUq5/d58dv886 to download Gauthmath and don't forget to use code 4SBW8X to get a 1 month discount now!
Check out PK's channel here: youtube.com/c/DrPKMath
The question is taken from the Korean SAT exam taken in November 2022. This was apparently a 'killer' question which hardly any students were able to solve within the time limit. The exam is taken at the end of high school as part of the college admissions process in the Republic of Korea (South Korea).
PK begins by explaining a little about the exam before sharing the question. We are asked to work out the value of a cubic function at the point x=2, but in order to determine the coefficients of the cubic we must solve a series of equations involving exponential functions, trigonometric functions, derivatives and composite functions.
The full question is as follows:
A cubic function f(x) with positive leading coefficient, the function g(x) = exp(sin(pi*x)) - 1, and the composite function h(x) = g(f(x)) on the domain of all real numbers, satisfy the following conditions:
1) Function h(x) has the maximum value of 0 when x is 0.
2) In the open interval (0, 3), there are 7 distinct real solutions to h(x) = 1.
3). f(3)= 1/2, f’(3)=0, and f(2)= p/q.
What is p+q? (where p and q are coprime integers).
This video is sponsored by Gauthmath.
Produced by Dr Tom Crawford at the University of Oxford. Tom is an Early-Career Teaching and Outreach Fellow at St Edmund Hall: seh.ox.ac.uk/people/tom-crawford
For more maths content check out Tom's website tomrocksmaths.com
You can also follow Tom on Facebook, Twitter and Instagram @tomrocksmaths.
facebook.com/tomrocksmaths
twitter.com/tomrocksmaths
instagram.com/tomrocksmaths
Get your Tom Rocks Maths merchandise here: beautifulequations.net/collections/tom-rocks-maths
