Math Software Online: MathScore.com
 
MathScore EduFighter is one of the best math games on the Internet today. You can start playing for free!

Nonlinear Functions - Sample Math Practice Problems

The math problems below can be generated by MathScore.com, a math practice program for schools and individual families. References to complexity and mode refer to the overall difficulty of the problems as they appear in the main program. In the main program, all problems are automatically graded and the difficulty adapts dynamically based on performance. Answers to these sample questions appear at the bottom of the page. This page does not grade your responses.

Want unlimited math worksheets? Learn more about our online math practice software.
See some of our other supported math practice problems.


Complexity=5, Mode=quadratic

Give the equation of this quadratic function. It should be in the form of 'y = nx2' where n is an integer. Type x2 as x^2, etc.

1.  
2.  

Complexity=3, Mode=cubic

Give the equation of this cubic function. It should be in the form of 'y = nx3' where n is an integer. Type x2 as x^2, etc.

1.  
2.  

Complexity=5, Mode=mixed

Give the equation of the following functions. They may be quadratic or cubic functions. They should be of the form 'y = nx2 + b' or 'y = nx3 + b' where n and b are integers. Type x2 as x^2, etc.

1.  
2.  

Answers


Complexity=5, Mode=quadratic

Give the equation of this quadratic function. It should be in the form of 'y = nx2' where n is an integer. Type x2 as x^2, etc.

#ProblemCorrect AnswerYour Answer
1
Solution
The parabola opens upward so we know that, in y = nx2, n > 0.
We also know (2, 8) is on the parabola. So
8 = n * 22
8 = 4n
n = 2
So y = 2x2
#ProblemCorrect AnswerYour Answer
2
Solution
The parabola opens downward so we know that, in y = nx2, n < 0.
We also know (2, -8) is on the parabola. So
-8 = n * 22
-8 = 4n
n = -2
So y = -2x2

Complexity=3, Mode=cubic

Give the equation of this cubic function. It should be in the form of 'y = nx3' where n is an integer. Type x2 as x^2, etc.

#ProblemCorrect AnswerYour Answer
1
Solution
The cubic function increases as x increases so we know n > 0.
(2, 8) is in the cubic function.
y = nx3
8 = n * 23
8 = 8n
n = 1
y = x3
#ProblemCorrect AnswerYour Answer
2
Solution
The cubic function decreases as x increases so we know n < 0.
(2, -16) is in the cubic function.
y = nx3
-16 = n * 23
-16 = 8n
n = -2
y = -2x3

Complexity=5, Mode=mixed

Give the equation of the following functions. They may be quadratic or cubic functions. They should be of the form 'y = nx2 + b' or 'y = nx3 + b' where n and b are integers. Type x2 as x^2, etc.

#ProblemCorrect AnswerYour Answer
1
Solution
The function decreases as x increases and doesn't open in a direction like a parabola, so it is a cubic function of the form y = nx3 + b with n < 0.
The equation intersects the y-axis at(0, -1), so
y = nx3 + b
-1 = n * 03 + b
-1 = b
y = nx3 -1
We also know (1, -3) is in the parabola.
-3 = n * 13 -1
-3 = n -1
n = -2
y = -2x3 -1
#ProblemCorrect AnswerYour Answer
2
Solution
The function decreases as x increases and doesn't open in a direction like a parabola, so it is a cubic function of the form y = nx3 + b with n < 0.
The equation intersects the y-axis at(0, 3), so
y = nx3 + b
3 = n * 03 + b
3 = b
y = nx3 + 3
We also know (1, 2) is in the parabola.
2 = n * 13 + 3
2 = n + 3
n = -1
y = -x3 + 3
Learn more about our online math practice software.

"MathScore works."
- John Cradler, Educational Technology Expert
© Copyright 2010 Accurate Learning Systems Corp. All rights reserved.