MPM 1D
Unit 4 (Chapter 3): Polynomials
Name: ________________________
Date: ____________________
Part A: True or False
Identify whether each statement is true or false.
1. For any integer a, (-a) 2 = -a2
_____
2. (3x4)3 = 27x12
_____
3. (-2a2)3 = - 8a6
_____
4. (3 + 4 - 5)2 = 32 + 42 + 52
_____
5. There are five different sets of like terms in the following list of terms.
3x2y, -2, 0.5y, -2x2y, 3x2, 32, y, x/2, 0, 3y, x2y
Part B: Multiple Choice
Choose the correct answer for each question.
6.
7.
_____
8.
10.
9.
11.
12. Which is the simplified form of g x g4 x g3 ?
a) g7
b) g8
c) g12
d) g13
1
13. What is the value of  
2
2
_____
1
4
a)
1
8
b)
c)
1
2
d) 2
14. The expressions in which pair are equal?
a) 5m2 and (5m)2
b) 2(c7)3 and 8c21
c) (yz)4 and y4z4
d) -3a2 and (-3a)2
15. Which expression can NOT be simplified?
a) 2x  9x
c) a 
_____
a
5
_____
_____
b) 5n 2  7 n
d) 3 p 2  14 p 2
16. 2 x 2  3k is a
_____
a) monomial
b) binomial
c) trinomial
d) term
17. What is the degree of 2 x 3 y
_____
a) 1
b) 2
c) 3
d) 4
Part C: Short Answer
Simplify
26. (5n 2  n  8)  (2n 2  7n  2)
27. ( x 2  x  3)  ( x 2  2 x  7)
28. (8 x 5 y 2 )(3x 2 y 6 )
29. (2 x 4 y ) 3
30. 2 y ( y  7)  4 y (2 y  4)
31. 2 x( x  3)  3x( x  4)
6 xy 2
32. a)
2y

  
b) 2 x y  2 x
2
3
2 2
4 x y 9 x y 
c)
2
2
3xy2
2
Part E: Problem Solving/Application
Be sure to show all of your work!
33. Write a simplified expression for the perimeter of this figure.
34. Three authors team up to write a children’s book. The publisher pays them according to the
following contracts.
Author
Fixed Rate($)
Royalty
($ for n books sold)
Michelle
3000
-
Aundrea
1500
2n
Eric
1000
3n
a) Find a simplified expression that represents the total that the publisher must pay the
writing team.
b) Determine the total payout if the book sells 200 copies.
35. Josh, Cody, and Brandon are discussing the number of songs they have downloaded on their
IPods. They find that the following statements are true:
 Josh has 7 less than three times the number of songs as Cody
 Brandon has twice as many songs as Josh.
Using x to represent the number of songs that Cody has, write an expression for the
total number of songs the three friends have. Show your work and simplify your answer,
your answer may only have one variable in it (x).
Category
Knowledge/
Understanding
Level 4
Demonstrates a solid and
thorough understanding of:
-recognizing polynomial
terminology and identifying
key feature of polynomials
Level 3
Demonstrates good
understanding of:
-recognizing polynomial
terminology and identifying
key feature of polynomials
Level 2
Level 1
Below Level 1
Demonstrates moderate
understanding of:
Demonstrates a limited or
inaccurate understanding of :
Need to demonstrate an
understanding of :
-recognizing polynomial
terminology and identifying
key feature of polynomials
-recognizing polynomial
terminology and identifying key
feature of polynomials
-recognizing polynomial
terminology and identifying key
feature of polynomials
-collect like terms
-collect like terms
-collect like terms
-add/subtract polynomials
-add/subtract polynomials
-add/subtract polynomials
-multiply/divide polynomials
-multiply/divide polynomials
-multiply/divide polynomials
-collect like terms
-collect like terms
-add/subtract polynomials
-add/subtract polynomials
-multiply/divide polynomials
-multiply/divide
polynomials
with little error
Thinking
Communication
Application
Demonstrates thorough critical
thinking flow when
simplifying polynomials
Demonstrates good critical
thinking flow when
simplifying polynomials
Demonstrates moderate
critical thinking flow when
simplifying polynomials,
develops a limited and/or
incorrect solution
Demonstrates some critical
thinking flow when simplifying
polynomials but does not arrive
at an answer
Needs to demonstrate a strategy
that could be used to come up
with a solution.
solutions are well formed, with
completeness, accuracy and
full proper mathematical form
solutions are complete but
some proper form is
missing
solutions are somewhat
complete, but disorganized
solutions are incomplete,
scattered and disorganized
Need to communicate your
thinking
Confidently and accurately
applies the knowledge of
polynomials to simplify
problems.
Confidently applies the
knowledge of polynomials
to simplify problems.
Somewhat applies the
knowledge of polynomials to
simplify problems.
Applies little knowledge of
polynomials to simplify
problems.
Need to apply some knowledge
of polynomials to simplify
problems.