Unit 4 Polynomials Practice Test
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 1. Which of the following expressions are monomials with degree 2?
i)
ii)
iii)
iv)
a. ii and iii b. ii and iv c. iii and iv d. i and ii
____ 2. Identify the polynomial that is equivalent to .
i)
ii)
iii)
iv)
a. iv b. ii c. i d. iii
____ 3. From the list, which terms are like 5x?
5x2, 4x, 3, 8x, 5x, 9x2, 5
a. 5x c. 4x, 8x, 5x
b. 5x2, 5 d. 5x2, 5x, 5x2
____ 4. Combine like terms. Sketch algebra tiles if it helps.
a. c.
b. d.
____ 5. Add:
a. b. c. d.
____ 6. Subtract:
a. b. c. d.
____ 7. Subtract:
a. b. 0 c. d.
____ 8. Subtract:
a. c.
b. d.
____ 9. Subtract:
a. c.
b. d.
____ 10. Multiply:
a. b. c. d.
____ 11. Divide:
a. b. c. d.
____ 12. Which of these multiplication sentences is modelled by the rectangle below?
i)
ii)
iii)
iv)
4x
6x 3
a. iii b. ii c. i d. iv
____ 13. Divide:
a. b. c. d.
____ 14. Multiply:
a. b. c. d.
____ 15. Multiply:
a. b. c. d.
Short Answer
16. A large white square represents an x2-tile, a large black square represents a x2-tile, a white rectangle
represents an x-tile, a black rectangle represents a x-tile, a small white square represents a 1-tile, and a small
black square represents a 1-tile.
Match each polynomial with its corresponding algebra tile model.
i)
ii)
iii)
iv)
v)
vi)
Model A
Model B
Model C
Model D
Model E
Model F
17. Write a polynomial to represent the perimeter of the rectangle.
x x 1 1
x x
x x
x x 1 1
18. Multiply:
19. Divide:
Problem
20. What polynomial must be added to to obtain a sum of 0?
21. a) Write a simplified polynomial for the perimeter of each shape below.
b) Subtract the perimeter of the rectangle from the perimeter of the triangle.
c) If , which shape has the greater perimeter?
2p + 2
4p + 3
5 p+ 4
4p
7 p+ 2
22. Which expressions are equivalent? Explain how you know.
i)
ii)
iii)
iv)
23. a) Write a polynomial to represent the area of rectangle A.
b) Write a polynomial to represent the area of rectangle B.
c) Write a polynomial to represent the total area of rectangle A added to rectangle B.
A
5x
3 B
4x + 6
24. Simplify: .
Unit 4 Polynomials Practice Test
Answer Section
MULTIPLE CHOICE
1. ANS: A PTS: 1 DIF: Easy REF: 5.1 Modelling Polynomials
LOC: 9.PR5 TOP: Patterns and Relations (Variables and Equations)
KEY: Conceptual Understanding
2. ANS: D PTS: 1 DIF: Moderate REF: 5.1 Modelling Polynomials
LOC: 9.PR5 TOP: Patterns and Relations (Variables and Equations)
KEY: Procedural Knowledge
3. ANS: C PTS: 1 DIF: Easy REF: 5.2 Like Terms and Unlike Terms
LOC: 9.PR5 TOP: Patterns and Relations (Variables and Equations)
KEY: Conceptual Understanding
4. ANS: B PTS: 1 DIF: Moderate REF: 5.2 Like Terms and Unlike Terms
LOC: 9.PR5 TOP: Patterns and Relations (Variables and Equations)
KEY: Procedural Knowledge
5. ANS: A PTS: 1 DIF: Moderate REF: 5.3 Adding Polynomials
LOC: 9.PR6 TOP: Patterns and Relations (Variables and Equations)
KEY: Procedural Knowledge
6. ANS: B PTS: 1 DIF: Easy REF: 5.4 Subtracting Polynomials
LOC: 9.PR6 TOP: Patterns and Relations (Variables and Equations)
KEY: Procedural Knowledge
7. ANS: C PTS: 1 DIF: Easy REF: 5.4 Subtracting Polynomials
LOC: 9.PR6 TOP: Patterns and Relations (Variables and Equations)
KEY: Procedural Knowledge
8. ANS: B PTS: 1 DIF: Moderate REF: 5.4 Subtracting Polynomials
LOC: 9.PR6 TOP: Patterns and Relations (Variables and Equations)
KEY: Procedural Knowledge
9. ANS: C PTS: 1 DIF: Moderate REF: 5.4 Subtracting Polynomials
LOC: 9.PR6 TOP: Patterns and Relations (Variables and Equations)
KEY: Procedural Knowledge
10. ANS: C PTS: 1 DIF: Easy
REF: 5.5 Multiplying and Dividing a Polynomial by a Constant
LOC: 9.PR7 TOP: Patterns and Relations (Variables and Equations)
KEY: Procedural Knowledge
11. ANS: C PTS: 1 DIF: Easy
REF: 5.5 Multiplying and Dividing a Polynomial by a Constant
LOC: 9.PR7 TOP: Patterns and Relations (Variables and Equations)
KEY: Procedural Knowledge
12. ANS: D PTS: 1 DIF: Easy
REF: 5.6 Multiplying and Dividing a Polynomial by a Monomial
LOC: 9.PR7 TOP: Patterns and Relations (Variables and Equations)
KEY: Procedural Knowledge
13. ANS: A PTS: 1 DIF: Easy
REF: 5.6 Multiplying and Dividing a Polynomial by a Monomial
LOC: 9.PR7 TOP: Patterns and Relations (Variables and Equations)
KEY: Procedural Knowledge
14. ANS: A PTS: 1 DIF: Moderate
REF: 5.6 Multiplying and Dividing a Polynomial by a Monomial
LOC: 9.PR7 TOP: Patterns and Relations (Variables and Equations)
KEY: Procedural Knowledge
15. ANS: D PTS: 1 DIF: Moderate
REF: 5.6 Multiplying and Dividing a Polynomial by a Monomial
LOC: 9.PR7 TOP: Patterns and Relations (Variables and Equations)
KEY: Procedural Knowledge
SHORT ANSWER
16. ANS:
Model A: v
Model B: vi
Model C: iv
Model D: i
Model E: ii
Model F: iii
PTS: 1 DIF: Moderate REF: 5.1 Modelling Polynomials
LOC: 9.PR5 TOP: Patterns and Relations (Variables and Equations)
KEY: Procedural Knowledge
17. ANS:
PTS: 1 DIF: Difficult REF: 5.2 Like Terms and Unlike Terms
LOC: 9.PR5 TOP: Patterns and Relations (Variables and Equations)
KEY: Procedural Knowledge
18. ANS:
PTS: 1 DIF: Moderate REF: 5.5 Multiplying and Dividing a Polynomial by a Constant
LOC: 9.PR7 TOP: Patterns and Relations (Variables and Equations)
KEY: Procedural Knowledge
19. ANS:
PTS: 1 DIF: Moderate REF: 5.5 Multiplying and Dividing a Polynomial by a Constant
LOC: 9.PR7 TOP: Patterns and Relations (Variables and Equations)
KEY: Procedural Knowledge
PROBLEM
20. ANS:
To get 0, make the coefficients of like terms opposites. So, add .
( )+( )
PTS: 1 DIF: Difficult REF: 5.3 Adding Polynomials
LOC: 9.PR6 TOP: Patterns and Relations (Variables and Equations)
KEY: Problem-Solving Skills | Communication
21. ANS:
a) Perimeter of rectangle:
Perimeter of triangle:
b) Perimeter of triangle perimeter of rectangle =
c) Substitute into the polynomial for the perimeter of the rectangle.
Substitute into the polynomial for the perimeter of the triangle.
So, the triangle has the greater perimeter.
PTS: 1 DIF: Difficult REF: 5.4 Subtracting Polynomials
LOC: 9.PR6 TOP: Patterns and Relations (Variables and Equations)
KEY: Problem-Solving Skills | Communication
22. ANS:
i) ii)
iii) iv)
Expressions ii and iii are equivalent because the quotients are the same.
PTS: 1 DIF: Difficult REF: 5.5 Multiplying and Dividing a Polynomial by a Constant
LOC: 9.PR7 TOP: Patterns and Relations (Variables and Equations)
KEY: Problem-Solving Skills | Communication
23. ANS:
Area of rectangle A
Area of rectangle B
Total area of rectangle A and rectangle B
PTS: 1 DIF: Difficult
REF: 5.6 Multiplying and Dividing a Polynomial by a Monomial
LOC: 9.PR7 TOP: Patterns and Relations (Variables and Equations)
KEY: Problem-Solving Skills
24. ANS:
PTS: 1 DIF: Difficult
REF: 5.6 Multiplying and Dividing a Polynomial by a Monomial
LOC: 9.PR7 TOP: Patterns and Relations (Variables and Equations)
KEY: Problem-Solving Skills
