AP Calculus AB Differential Equations and Slope Fields Quiz: 10 Questions with Explanations

AP Calculus AB math quiz: Differential Equations and Slope Fields – Maths PDF

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This differential equations quiz for AP Calculus AB covers differential equations and slope fields (Common Core AP CALC AB 7.1, AP CALC AB 7.2, AP CALC AB 7.3, AP CALC AB 7.4, AP CALC AB 7.5, AP CALC AB 7.6, AP CALC AB 7.7), with a free PDF to print.

Test yourself on differential equations, slope fields, Euler’s method, separation of variables and exponential growth and decay with 10 multiple-choice questions. Pick one answer for each question, then read the explanation to see why it is right and which common mistake the other choices represent.

AP Calculus AB · Common Core State Standards: AP CALC AB 7.1, AP CALC AB 7.2, AP CALC AB 7.3, AP CALC AB 7.4, AP CALC AB 7.5, AP CALC AB 7.6, AP CALC AB 7.7

Differential equations quiz: 10 questions

Question 1

Which differential equation is satisfied by \(y=4e^{3x}\)?

Question 2

A slope field.

Which equation produces this slope field?

Question 3

In Euler’s method, which formula finds the next y-value?

Question 4

Using Euler’s method with \(h=1\) for \(\frac{dy}{dx}=y\), \(y(0)=2\), what is \(y(1)\)?

Question 5

After separating variables in \(\frac{dy}{dx}=xy\), what do you integrate?

Question 6

Exponential decay.

Which equation and initial condition match the graph of the decay?

Question 7

If \(\frac{dP}{dt}=0.04P\) and \(P(0)=100\), then \(P(t)\) equals

Question 8

Euler values.

Using the table, what is the Euler estimate of \(y(0.2)\)?

Question 9

A solution of \(\frac{dy}{dx}=y^{2}\) with \(y(0)=1\) is

Question 10

For \(\frac{dy}{dx}=x-y\), where is the slope zero?

Remember

Verify a solution by substituting y and y′ into the equation.
A slope field shows dy/dx at grid points; solution curves follow the segments.
Euler: y_new = y_old + h · (dy/dx at the old point), x_new = x_old + h.
dy/dt = ky has the general solution y = Ce^(kt); growth if k is positive, decay if k is negative.

How to use this differential equations quiz

Answer each question, read the explanation that appears, and keep track of your score. A score of 8 out of 10 or more means you are ready for the test.

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