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

NameDate

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

Ari draws the slope field of dy/dx = 2xy. What slope does the segment at (3, −1) have?
Bo draws the slope field of dy/dx = 3xy. What slope does the segment at (−2, 4) have?
Esme draws the slope field of dy/dx = 4xy. What slope does the segment at (2, 3) have?
Jun draws the slope field of dy/dx = 5xy. What slope does the segment at (−1, −2) have?
5.
Slopes depend only on x. Kira reads the slope field described in the figure. Which differential equation made it?
- dy/dx = 1 − x
- dy/dx = x + 1
- dy/dx = y − 1
- dy/dx = x − 1
6.
Luz reads the slope field described in the figure. Which differential equation made it?
- dy/dx = x − 2
- dy/dx = y + 2
- dy/dx = 2 − y
- dy/dx = y − 2
Read this first
Use this
Slopes depend only on x. They are 0 along x = -3, negative to the right of it, positive to the left.
7.
Milo reads the slope field described in the figure. Which differential equation made it?
- dy/dx = x + 3
- dy/dx = −(x − 3)
- dy/dx = −(y + 3)
- dy/dx = −(x + 3)
Every solution of dy/dx = y + x has the form y = Ceˣ − x − 1. Pia picks the one with y(0) = 3. What is y(1), to the nearest hundredth?
Every solution of dy/dx = y + x has the form y = Ceˣ − x − 1. Tala picks the one with y(0) = 2. What is y(2), to the nearest hundredth?
Every solution of dy/dx = y + x has the form y = Ceˣ − x − 1. Zee picks the one with y(0) = 4. What is y(0.5), to the nearest hundredth?

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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