Slope Fields and Differential Equations

Student Study Session

Slope Fields and Differential Equations

Students should be able to:

Draw a slope field at a specified number of points by hand.
Sketch a solution that passes through a given point on a slope field.
Match a slope field to its differential equation.
Match a slope field to its solution.
Determine features of the solution to a differential equation based on its slope field and/or its solution.
Solve separable differential equations.
Determine a particular solution using an initial condition.
Model a real world situation using a differential equation.

Slope Fields and Differential Equations

Student Study Session

Multiple Choice

1.(calculator not allowed) (1993 BC13 appropriate for AB)

If , then could be

(A)

(B)

(C)

(D)

(E)

2.(calculator not allowed) (Course Description Sample Questions for Calculus AB #7)

Which of the following is the solutiom to the differential equation ,

where

(A) for

(B) for

(D) for

(E) for

3.(calculator not allowed) (Course Description Sample Questions for Calculus AB #14)

Which of the following is a slope field for the differential equation

4.(calculator not allowed) (2003 B14 appropriate for AB)

Shown above is a slope field for which of the following differential equations?

(A)

(B)

(C)

(D)

(E)

5.(calculator not allowed) (1988 BC43 appropriate for AB)

Bacteria in a certain culture increase at a rate proportional to the number present. If the number of bacteria doubles in three hours, in how many hours will the number of bacteria triple?

(A)

(B)

(C)

‘(D)

(E)

6.(calculator not allowed) (1985 BC33 appropriate for AB)

If and if when , what is the value of t for which ?

(A)

(B)

(C)

(D)

(E)

7.(calculator not allowed) (1993 AB 33)

(A)

(B)

(D)

(E)

8.(calculator not allowed) (1985 BC44 appropriate for AB)

At each point on a certain curve, the slope of the curve is . If the curve contains thepoint , then its equation is

(A)

(B)

(C)

(D)

(E)

9.(calculator not allowed) (1969 BC 23 appropriate for AB)

If the graph of contains the point , and

for all then

(A)

(B)

(C)

(D)

(E)

10.(calculator not allowed) (1969 AB 27/BC27)

If , then

(A)

(B)

(C)

(D)

(E)

Free Response

11. (calculator not allowed) 2005 AB6

Consider the differential equation .

(a)On the axes provided, sketch a slope field for the given differential equation at the twelve points indicated.

(b)Let be the particular solution to the differential equation with the initial condition . Write an equation for the line tangent to the graph of at and use it to approximate .

(c)Find the particular solution to the given differential equation with the initial condition .

12.(calculator not allowed) 2006 Form B AB5

Consider the differential equation .

(a)On the axes provided, sketch a slope field for the given differential equation at the nine points indicated.

(b)There is a horizontal line with equation that satisfies this differential equation. Find the value of c.

(c)Find the particular solution to the differential equation with the initial condition .

13.(calculator not allowed) 2011 AB 5/BC5

At the beginning of 2010, a landfill contained 1400 tons of solid waste. The increasing function models the total amount of solid waste stored at the landfill. Planners estimate that will satisfy the differential equation for the next 20 years. is measured in tons, and is measured in years from the start of 2010.

(c)Find the particular solution to the differential equationwith initial condition.