
Slope Fields
Quiz
•
Mathematics
•
9th - 12th Grade
•
Practice Problem
•
Medium
Standards-aligned
Kenneth Raftery
Used 14+ times
FREE Resource
Enhance your content in a minute
8 questions
Show all answers
1.
MULTIPLE CHOICE QUESTION
5 mins • 1 pt
Which of the following could be a specific solution for the differential equation whose slope field is shown?
y=lnx
y=sinx
y=ex
y=x2
y=cosx
Answer explanation
Remember that the derivative of e^x is e^x. The slope of the tangent to the graph of e^x increases without bound as x increases. Notice how the slope gets very sleep as x gets larger.
Tags
CCSS.HSA-REI.B.4B
2.
MULTIPLE CHOICE QUESTION
5 mins • 1 pt
Shown is the slope field for which of the following differential equations?
dy/dx=x2
dy/dx=y^3
dy/dx=x
dy/dx=2x+y
dy/dx=xy
Answer explanation
Notice how all slopes at non-zero coordinates are positive. You should also notice how the slopes are zero when x=0. You might also notice how the slope field segments seem to match the shape of a cubic function. Also note how slopes in columns are the same so you know the d.e. would only contain the variable x.
3.
MULTIPLE CHOICE QUESTION
5 mins • 1 pt
Which differential equation corresponds to the slope field shown?
dy/dx=x^2-y^2
dy/dx=y^2-x^2
dy/dx=x/y
dy/dx=y/x
dy/dx= -x/y
Answer explanation
Slopes are 0 along the y-axis (this is when x=0) and are infinite along the x-axis (this is when y=0). You can also notice the signs in the different quadrants. The slopes are positive in quadrants I and III, and in these quadrants x and y have the same sign.
4.
MULTIPLE CHOICE QUESTION
5 mins • 1 pt
The figure shows the slope field for which differential equation?
dy/dx=2x
dy/dx=-2x
dy/dx=y
dy/dx=-y
dy/dx=x+y
Answer explanation
Notice how the slopes are the same within the same row. This means that the numerical value of dy/dx depends solely on the y-coordinate. You should also note how the tangents have negative slope when y>0 and positive slope when y<0.
5.
MULTIPLE CHOICE QUESTION
5 mins • 1 pt
Which of the following differential equations has the slope field shown?
dy/dx=x-y
dy/dx=√y-√x
dy/dx=-xy
dy/dx=2x/y
Answer explanation
Note how dy/dx=0 when the x-coordinate or the y-coordinate of the point is 0.
6.
MULTIPLE CHOICE QUESTION
5 mins • 1 pt
Shown is a slope field for which of the following differential equations?
dy/dx=xy-x
dy/dx=xy+x
dy/dx=y-x2
dy/dx=(y-1)x2
dy/dx=(y-1)^3
Answer explanation
Note that the slopes are zero when y=1 and x=0.
If you factor the choice that says
dy/dx=xy-x, you will have
dy/dx=x(y-1). Note that this expression would be zero if you plugged in either y=1 or x=0. You also could analyze the signs of slopes to further confirm that the correct choice is valid.
7.
MULTIPLE CHOICE QUESTION
5 mins • 1 pt
Shown is a slope field for which of the following differential equations?
dy/dx=xy
dy/dx=xy-y
dy/dx=xy+y
dy/dx=xy+x
dy/dx=(x+1)^3
Answer explanation
Notice how the slopes are zero when y=0 and when x=-1. If you factor the choice that says dy/dx=xy+y, you will have dy/dx=y(x+1). Notice how this differential equation would equal zero if you plugged in y=0 or x=-1.
Tags
CCSS.8.EE.C.8B
Access all questions and much more by creating a free account
Create resources
Host any resource
Get auto-graded reports

Continue with Google

Continue with Email

Continue with Classlink

Continue with Clever
or continue with

Microsoft
%20(1).png)
Apple
Others
Already have an account?
Similar Resources on Wayground
12 questions
Vlastnosti funkcií
Quiz
•
9th Grade
12 questions
Variaciones Compuestas y Polinomios.
Quiz
•
12th Grade
12 questions
Hukum Indeks : Pendaraban/Pembahagian
Quiz
•
9th - 11th Grade
10 questions
Cek Pemahaman SPtLDV
Quiz
•
10th Grade
12 questions
Fórmula general ecuaciones cuadráticas
Quiz
•
9th Grade
10 questions
Limit Tak hingga 1
Quiz
•
12th Grade - University
11 questions
Medidas de almacenamiento
Quiz
•
11th Grade
10 questions
Congruencia de Triangulos
Quiz
•
7th - 9th Grade
Popular Resources on Wayground
15 questions
Fractions on a Number Line
Quiz
•
3rd Grade
20 questions
Equivalent Fractions
Quiz
•
3rd Grade
25 questions
Multiplication Facts
Quiz
•
5th Grade
54 questions
Analyzing Line Graphs & Tables
Quiz
•
4th Grade
22 questions
fractions
Quiz
•
3rd Grade
20 questions
Main Idea and Details
Quiz
•
5th Grade
20 questions
Context Clues
Quiz
•
6th Grade
15 questions
Equivalent Fractions
Quiz
•
4th Grade
Discover more resources for Mathematics
20 questions
Graphing Inequalities on a Number Line
Quiz
•
6th - 9th Grade
18 questions
SAT Prep: Ratios, Proportions, & Percents
Quiz
•
9th - 10th Grade
12 questions
Exponential Growth and Decay
Quiz
•
9th Grade
12 questions
Parallel Lines Cut by a Transversal
Quiz
•
10th Grade
12 questions
Add and Subtract Polynomials
Quiz
•
9th - 12th Grade
15 questions
Combine Like Terms and Distributive Property
Quiz
•
8th - 9th Grade
20 questions
Function or Not a Function
Quiz
•
8th - 9th Grade
10 questions
Elijah McCoy: Innovations and Impact in Black History
Interactive video
•
6th - 10th Grade
