Slope fields and checking a solution

Answer Key - Grade 12 Math Worksheet - Building Confidence

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

1. 1.

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

   5
2. 2.

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

   0
3. 3.

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

   12
4. 4.

   Jun draws the slope field of dy/dx = 3x + 5y on grid paper. What slope does the segment at (4, −1) have?

   7
5. 5.

   Luz checks whether y = x² is a solution of dy/dx = 2y. Which is right?

   • yes: y′ = 2x, which matches 2y
   • yes: any power of x solves an equation like this
   • no: y′ = 2x, but 2y = 2x²
6. 6.

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

   • no: y′ = 5e^(−2x), which is not −2y
   • yes: y′ = −10e^(−2x), which is −2y
   • no: the 5 would have to be 1
7. 7.

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

   • no: y′ = cos x, but −y = −sin x
   • yes: sin and cos are both trig, so it fits
   • yes: y′ = cos x, which matches −y
8. 8.

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

   • flat along the line y = 2
   • flat along the line x = −2
   • flat along the line x = 0
   • flat along the line x = 2
9. 9.

   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
10. 10.

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

    • flat along the line y = 0
    • flat along the line y = 5
    • flat along the line y = −5
    • flat along the line x = 5