Worksheet: Working with Algebraic Expressions
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
____
1. What are the missing terms in
a.
b.
2. Write a simplified algebraic expression for the area of the figure shown below.
a.
b.
____
c.
d.
3. Expand and simplify
a.
.
c.
b.
____
d.
4. Simplify
a.
b.
.
c.
d.
____
5. Simplify
a.
b.
____
6. A rectangle has a length of
a.
b.
____
7. Expand
a.
b.
____
____
?
c.
d.
8. Expand
a.
b.
.
c.
d.
and a width of
c.
d.
.
c.
d.
.
9. What is the missing factor in
a.
–
b. –2
c.
d.
?
c.
d. 2
. What is the perimeter of the rectangle?
____ 10. Simplify
a.
b.
____ 11. Simplify
a.
b.
.
c.
d.
.
c.
d.
____ 12. Simplify
a.
b.
.
c.
d.
____ 13. Determine the area of the shaded portion of the rectangle.
a.
b.
c.
d.
____ 14. Determine the area of the shaded portion of the rectangle.
a.
b.
c.
d.
Short Answer
15. Simplify
.
16. Expand and simplify
.
Problem
17. Evaluate the statement
for t = –4 once before you expand it and once after you expand it.
18. Describe the steps involved in expanding
.
19. Use the figure below to answer the following questions.
a) Determine a simplified expression for the perimeter of the rectangle.
b) Determine the perimeter of the rectangle when x = 6 cm.
c) Determine a simplified expression for the area of the triangle.
d) Determine the area of the triangle when x = 6 cm.
e) Determine a simplified expression for the number of square centimetres it would take to cover the shaded
portion of the triangle.
20. A rental car company has purchased 10 vans and 20 cars to rent out. Based on the values shown in the chart,
Determine an expression that represents the combined value of the vehicles after y years of use. Use this value
to determine the combined value of the vehicles after 5 years of use. Justify your answer by showing your
work.
Number Purchased
Original Value
Yearly Drop in Value
Vans
10
$15 000
$1200
Cars
20
$12 000
$1000
Worksheet: Working with Algebraic Expressions
Answer Section
MULTIPLE CHOICE
1. ANS:
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2. ANS:
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3. ANS:
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4. ANS:
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5. ANS:
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6. ANS:
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9. ANS:
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10. ANS:
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11. ANS:
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12. ANS:
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13. ANS:
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14. ANS:
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C
PTS: 1
REF: Knowledge and Understanding
2.5 - Multiplying a Polynomial by a Monomial
D
PTS: 1
REF: Application
2.5 - Multiplying a Polynomial by a Monomial
C
PTS: 1
REF: Knowledge and Understanding
2.6 - Simplifying Polynomial Expressions
A
PTS: 1
REF: Knowledge and Understanding
2.4 - Adding and Subtracting Polynomials
D
PTS: 1
REF: Knowledge and Understanding
2.4 - Adding and Subtracting Polynomials
D
PTS: 1
REF: Application
2.4 - Adding and Subtracting Polynomials
B
PTS: 1
REF: Knowledge and Understanding
2.5 - Multiplying a Polynomial by a Monomial
D
PTS: 1
REF: Knowledge and Understanding
2.5 - Multiplying a Polynomial by a Monomial
B
PTS: 1
REF: Knowledge and Understanding
2.5 - Multiplying a Polynomial by a Monomial
C
PTS: 1
REF: Knowledge and Understanding
2.6 - Simplifying Polynomial Expressions
B
PTS: 1
REF: Knowledge and Understanding
2.6 - Simplifying Polynomial Expressions
D
PTS: 1
REF: Knowledge and Understanding
2.6 - Simplifying Polynomial Expressions
A
PTS: 1
REF: Application
2.6 - Simplifying Polynomial Expressions
D
PTS: 1
REF: Application
2.6 - Simplifying Polynomial Expressions
SHORT ANSWER
15. ANS:
PTS: 1
REF: Knowledge and Understanding
OBJ: 2.6 - Simplifying Polynomial Expressions
16. ANS:
PTS: 1
REF: Knowledge and Understanding
OBJ: 2.6 - Simplifying Polynomial Expressions
PROBLEM
17. ANS:
Before:
After:
PTS: 1
REF: Thinking
OBJ: 2.5 - Multiplying a Polynomial by a Monomial
18. ANS:
First you would use the distributive property to expand both sets of parentheses. This will give you
. Now combine the like terms to end up with
.
PTS: 1
REF: Communication
OBJ: 2.6 - Simplifying Polynomial Expressions
19. ANS:
a)
b)
c)
d)
e)
PTS: 1
20. ANS:
Vans:
Cars:
REF: Application
OBJ: 2.6 - Simplifying Polynomial Expressions
PTS: 1
REF: Application
OBJ: 2.6 - Simplifying Polynomial Expressions