Slope fields and checking a solution

Answer Key - Grade 12 Math Worksheet

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

1. 1.

   Ari draws the slope field of dy/dx = 2xy. What slope does the segment at (3, −1) have?

   -6
2. 2.

   Esme draws the slope field of dy/dx = 4xy. What slope does the segment at (2, 3) have?

   24
3. 3.

   Jun draws the slope field of dy/dx = 5xy. What slope does the segment at (−1, −2) have?

   10
4. 4.

   Slopes depend only on x. Kira reads the slope field described in the figure. Which differential equation made it?

   • dy/dx = x + 1
   • dy/dx = 1 − x
   • dy/dx = x − 1
   • dy/dx = y − 1
5. 5.

   Luz reads the slope field described in the figure. Which differential equation made it?

   • dy/dx = y + 2
   • dy/dx = 2 − y
   • dy/dx = x − 2
   • dy/dx = y − 2

6. 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. 6.

   Milo reads the slope field described in the figure. Which differential equation made it?

   • dy/dx = −(y + 3)
   • dy/dx = −(x − 3)
   • dy/dx = −(x + 3)
   • dy/dx = x + 3
8. 7.

   Noah reads the slope field described in the figure. Which differential equation made it?

   • dy/dx = −(x + 1)
   • dy/dx = −(y − 1)
   • dy/dx = −(y + 1)
   • dy/dx = y + 1
9. 8.

   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?

   8.87
10. 9.

    Every solution of dy/dx = y + x has the form y = Ceˣ − x − 1. Ren picks the one with y(0) = 5. What is y(1), to the nearest hundredth?

    14.31
11. 10.

    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?

    19.17