Mathematical Modeling

Derivatives

200

f(x) = 2x

2

400

f(x) = ln(x)

1/x

600

f(x) = sinxcosx

cos²x - sin²x

800

f(x) = ln(x)/cos(x)

[cos(x)(1/x)-ln(x)(-sin(x))]/cos^2(x)

1000

f(x) = [cos(x)/sin(x)] + ln(x)/x

[sin(x)(-sin(x))-cos(x)(cos(x))]/sin^2(x) + [(x/x)-lnx]/x^2

Integrals

200

Integral of x dx

x²/2 + C

400

integral of 2dx from 0 to 2

4

600

integral of cos(x)

sin(x)+C

800

integral of 1/(x-5)

ln|x-5|+C

1000

integral of sin(x) from 0 to pi/2

1

Create a Model!

200

If an individual made a base rate of $80 per day and an additional $15 for every pairs of shoe that they sold. What equation would model their daily income. 

y = 15x + 80

400

how would you model an initial investment of of $5000 with 4.02% interest rate compounded monthly for 10 years. 

7469.037

600

How would you model an investment of 8000 which was compounded continuously over 15 years at an interest rate of 5.04% 

I = 8000e^.0504*15

800

If you knew that acceleration was the derivative of velocity which is time dependent. How can you express the acceleration as a differential equation? 

a = dv/dt

1000

How would you model a population y which grows or decays in proportion to its size with a diff eq. 

y'=ky

Yellow

200

This children's TV show featured the title monkey character and the Man with the Yellow Hat.

What is Curious George?

400

Cardi B's first hit was this 2017 song where she proudly proclaims that she now make "money moves."

What is "Bodak Yellow"?

600

This Beatles song begins "In the town where I was born, lived a man who sailed to sea"

What is "Yellow Submarine"?

800

This sometimes bright yellow gastropod that can grow up to 9 inches long gets its name from a fruit.

What is a banana slug?

1000

In this short story by Charlotte Perkins-Gilman, a woman deemed "hysterical" by her husband begins to see things when she is confined to a room as part of a "rest cure." 

What is "The Yellow Wallpaper"?

Pop Culture

200

Last year, these two rappers sparred in a rap battle for the ages, but I think we can all agree the one who got to play the 2025 Super Bowl won.

Who are Kendrick Lamar and Drake?

400

This rapper released the music video for "Denial is a River" in January 2025, inspired by '90s sitcoms.

Who is Doechii?

600

In The Summer I Turned Pretty, the main character, Isabel, goes by this nickname.

What is Belly?

800

It has been joked that this Internet star's babies are reincarnations of world rulers after she gave birth to her first child only six days after Queen Elizabeth II's death.

Who is Trisha Paytas?

1000

This film took home the Oscar for Best Adapted Screenplay in 2025, a little over a month before the title event took place after Pope Francis' death.

What is Conclave?