Grade 12 · Math · Calculus

12th grade Slope fields and checking a solution worksheet

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Slope fields and checking a solution

Grade 12 Math Worksheet - Challenge Me

NameDate

Circle the best answer, or write your answer on the line.

1.
Ari differentiates twice to check which function solves y″ + 4y = 0. Which one does?
- y = 3 sin(2x)
- y = 3 sin(4x)
- y = e^(2x)
2.
Esme differentiates twice to check which function solves y″ + 9y = 0. Which one does?
- y = cos(3x)
- y = e^(−3x)
- y = cos(9x)
3.
Jun differentiates twice to check which function solves y″ − 4y = 0. Which one does?
- y = 5 cos(2x)
- y = 5e^(−4x)
- y = 5e^(−2x)
On a solution curve of dy/dx = x² − y, Luz finds d²y/dx² at the point (4, 5). What is it?
On a solution curve of dy/dx = x² − y, Milo finds d²y/dx² at the point (−2, 1). What is it?
On a solution curve of dy/dx = x² − y, Noah finds d²y/dx² at the point (3, −1). What is it?
dy/dx = y² − 6y + 5. Pia finds every constant solution y = c, a flat row in the slope field. List the c-values, separated by commas.
dy/dx = y² − 5y. Ren finds every constant solution y = c, a flat row in the slope field. List the c-values, separated by commas.
dy/dx = y² − 5y − 6. Tala finds every constant solution y = c, a flat row in the slope field. List the c-values, separated by commas.
dy/dx = y² − 2y − 8. Zee finds every constant solution y = c, a flat row in the slope field. List the c-values, separated by commas.

Slope fields and checking a solution. Every version has 10 questions, and the answer key prints on the second page.

I can draw a slope segment at a point and find where segments are flat.
I can match a slope field to its equation and check a solution by substitution.
I can use a solution family, find d²y/dx² on a solution curve and find constant solutions.

Standard: none (beyond CCSS)

slope field: Short segments showing dy/dx at grid points.

solution: A function whose y′ equals the right side for every x.

constant solution: A flat solution y = c, where dy/dx = 0.

Swapped the roles of x and y.

Used only the x-part of the slope formula.

Differentiated e^(kx) as e^(kx), without the factor k.

What is the most common mistake with slope fields and checking a solution?

Swapped the roles of x and y.

Are these 12th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

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