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12th grade Slope fields and checking a solution worksheet

6 printable versionsBuilding Confidence10 questions · answer keyFree · no account

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Slope fields and checking a solution

Grade 12 Math Worksheet - Building Confidence

NameDate

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

  1. Ari draws the slope field of dy/dx = 2x − 3y on grid paper. What slope does the segment at (4, 1) have?

  2. Bo draws the slope field of dy/dx = 3x + 2y on grid paper. What slope does the segment at (−2, 3) have?

  3. Esme draws the slope field of dy/dx = 5x − 2y on grid paper. What slope does the segment at (2, −1) have?

  4. Kira checks whether y = e^(3x) is a solution of dy/dx = 3y. Which is right?

    • no: e^(3x) has no zeros, so it cannot be a solution
    • no: y′ = e^(3x), which is not 3y
    • yes: y′ = 3e^(3x), which is 3y

  5. Milo checks whether y = 5e^(−2x) is a solution of dy/dx = −2y. Which is right?

    • no: the 5 would have to be 1
    • yes: y′ = −10e^(−2x), which is −2y
    • no: y′ = 5e^(−2x), which is not −2y

  6. Noah checks whether y = sin x is a solution of dy/dx = −y. Which is right?

    • yes: y′ = cos x, which matches −y
    • yes: sin and cos are both trig, so it fits
    • no: y′ = cos x, but −y = −sin x

  7. Pia sketches the slope field of dy/dx = 2x − 4. Where are all the segments horizontal?

    • flat along the line x = 0
    • flat along the line y = 2
    • flat along the line x = −2
    • flat along the line x = 2

  8. Ren sketches the slope field of dy/dx = y + 3. Where are all the segments horizontal?

    • flat along the line y = 0
    • flat along the line y = −3
    • flat along the line x = −3
    • flat along the line y = 3

  9. Tala sketches the slope field of dy/dx = 3x + 6. Where are all the segments horizontal?

    • flat along the line y = −2
    • flat along the line x = 0
    • flat along the line x = −2
    • flat along the line x = 2

  10. Zee sketches the slope field of dy/dx = 2y − 10. Where are all the segments horizontal?

    • flat along the line x = 5
    • flat along the line y = 5
    • flat along the line y = 0
    • flat along the line y = −5
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12th grade Slope fields and checking a solution worksheet – printable
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About this worksheet

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

What your child will learn

  • 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)

Words to know

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.

Common mistakes

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.

Questions parents ask

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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