Chapter 5 Final Exam Review
Multiple Choice
Identify the choice that best completes the statement or answers the question.
1. A large white square represents an x2-tile, a black rectangle represents a x-tile, and
a small white square represents a 1-tile.
Write the polynomial represented by this set of algebra tiles.
a.
b.
c.
2. Which of the following expressions is a binomial
with degree 2?
i)
ii)
iii)
Write the simplified polynomial.
iv)
a.
b.
c.
d.
d.
5. 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.
i
ii
iv
iii
3. Name the coefficients of the variable in the
polynomial
.
a. 4
b. 4, 10
c. 4, 12
d. 4, 10
4. Identify the polynomial that is equivalent to
.
i)
ii)
iii)
iv)
a. iv
b. ii
c. i
d. iii
a.
b.
c.
d.
6. Combine like terms. Sketch algebra tiles if it helps.
a.
b.
c.
d.
7. Simplify:
a.
b.
c.
d.
8. Add:
a.
b.
c.
d.
c.
d.
9. Write the perimeter of this rectangle as a polynomial
in simplest form.
4t
8t + 7
a.
b.
c.
d.
14. Multiply:
a.
b.
c.
d.
15. Divide:
a.
b.
c.
d.
10. Add:
a.
b.
c.
d.
16. Determine the area of this rectangle.
–3x 2 –4x + 2
8
11. Subtract:
a.
b. 0
c.
d.
a.
b.
c.
d.
12. Subtract:
a.
b.
c.
d.
17. A large white square represents an x2-tile, a white
rectangle represents an x-tile, and a small white
square represents a 1-tile.
13. The perimeter of this isosceles triangle is
represented by the polynomial
.
Write a simplified polynomial for the length of the
unknown side.
Which of these multiplication sentences is modelled
by the algebra tiles below?
i)
ii)
iii)
5p + 3
?
a.
b.
iv)
a.
b.
c.
d.
iii
ii
i
iv
d.
19. Divide:
18. Multiply:
a.
a.
b.
b.
c.
c.
d.
Short Answer
20. Name the coefficients, variable, degree, and
constant term in the polynomial
.
21. Write a polynomial that matches this description:
variable: p; degree: 2; binomial; constant: 7
23. Simplify:
24. Write a polynomial to represent the perimeter of the
rectangle.
x
22. 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.
x
1
1
x
x
x
x
Write the simplified polynomial.
x
x
1
1
25. 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.
Write the polynomial sum modelled by this set of tiles.
+
|
|
26. Write the perimeter of this equilateral triangle as a
polynomial in simplest form.
|
9x + 5
27. Write the perimeter of this rectangle as a polynomial
in simplest form.
2x + 5
Identify the errors in the solution.
6x +10
33. A large white square represents an x2-tile, a white
rectangle represents an x-tile, and a small white
square represents a 1-tile.
28. Add:
Write a division sentence that is modelled by these
algebra tiles.
29. Subtract:
30. The polynomial
represents the cost, in
dollars, of shipping a parcel with mass w kg by
ground. The polynomial
represents the cost
of shipping a parcel with mass w kg by air.
a) Write a polynomial for the difference in the
costs of the two methods of shipping.
b) How much more does it cost to ship a 15-kg
parcel by air?
31. Write the multiplication sentence modelled by this
rectangle.
4x
8
34. Divide:
35. Here is a student’s solution for this question:
Multiply:
5
32. Here is a student’s solution for this question:
Problem
36. Write a polynomial with the given variable, degree,
coefficient, and number of terms.
a) Variable: p; degree: 2; coefficients: 2, 4;
number of terms: 2
b) Variable: c; degree: 1; coefficient: 6; number of
terms: 1
c) Variable: t; degree 2, coefficients: , 7; number
of terms: 3; constant: 5
37. 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.
Identify any errors in the solution.
c) If
, which shape has the greater perimeter?
2p + 2
4p + 3
5 p+ 4
4p
7 p+2
38. a) Write the multiplication sentence modelled by
this rectangle.
b) Determine the area of the rectangle when x = 12.
Show your work.
5
4( x +3)
39. 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 and rectangle B.
5x
3
A
B
4x + 6
40. The area of a rectangular deck, in square metres, is
given by the polynomial
.
The deck is 8p metres wide.
a) Write a polynomial to represent the length of the
deck.
b) Determine the length, width, and area of the
deck when p = 4 m.
Chapter 5 Final Exam Review
Answer Section
MULTIPLE CHOICE
1. ANS:
LOC:
KEY:
2. ANS:
LOC:
KEY:
3. ANS:
LOC:
KEY:
4. ANS:
LOC:
KEY:
5. ANS:
LOC:
KEY:
6. ANS:
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KEY:
7. ANS:
LOC:
KEY:
8. ANS:
LOC:
KEY:
9. ANS:
LOC:
KEY:
10. ANS:
LOC:
KEY:
11. ANS:
LOC:
KEY:
12. ANS:
LOC:
KEY:
13. ANS:
LOC:
KEY:
14. ANS:
REF:
LOC:
KEY:
C
PTS: 1
DIF: Easy
REF: 5.1 Modelling Polynomials
9.PR5
TOP: Patterns and Relations (Variables and Equations)
Conceptual Understanding
D
PTS: 1
DIF: Easy
REF: 5.1 Modelling Polynomials
9.PR5
TOP: Patterns and Relations (Variables and Equations)
Conceptual Understanding
B
PTS: 1
DIF: Easy
REF: 5.1 Modelling Polynomials
9.PR5
TOP: Patterns and Relations (Variables and Equations)
Conceptual Understanding
D
PTS: 1
DIF: Moderate
REF: 5.1 Modelling Polynomials
9.PR5
TOP: Patterns and Relations (Variables and Equations)
Procedural Knowledge
C
PTS: 1
DIF: Moderate
REF: 5.2 Like Terms and Unlike Terms
9.PR5
TOP: Patterns and Relations (Variables and Equations)
Procedural Knowledge
B
PTS: 1
DIF: Moderate
REF: 5.2 Like Terms and Unlike Terms
9.PR5
TOP: Patterns and Relations (Variables and Equations)
Procedural Knowledge
B
PTS: 1
DIF: Moderate
REF: 5.2 Like Terms and Unlike Terms
9.PR5
TOP: Patterns and Relations (Variables and Equations)
Procedural Knowledge
B
PTS: 1
DIF: Moderate
REF: 5.3 Adding Polynomials
9.PR6
TOP: Patterns and Relations (Variables and Equations)
Procedural Knowledge
B
PTS: 1
DIF: Moderate
REF: 5.3 Adding Polynomials
9.PR6
TOP: Patterns and Relations (Variables and Equations)
Procedural Knowledge
D
PTS: 1
DIF: Moderate
REF: 5.3 Adding Polynomials
9.PR6
TOP: Patterns and Relations (Variables and Equations)
Procedural Knowledge
C
PTS: 1
DIF: Easy
REF: 5.4 Subtracting Polynomials
9.PR6
TOP: Patterns and Relations (Variables and Equations)
Procedural Knowledge
C
PTS: 1
DIF: Moderate
REF: 5.4 Subtracting Polynomials
9.PR6
TOP: Patterns and Relations (Variables and Equations)
Procedural Knowledge
B
PTS: 1
DIF: Difficult
REF: 5.4 Subtracting Polynomials
9.PR6
TOP: Patterns and Relations (Variables and Equations)
Procedural Knowledge
B
PTS: 1
DIF: Moderate
5.5 Multiplying and Dividing a Polynomial by a Constant
9.PR7
TOP: Patterns and Relations (Variables and Equations)
Procedural Knowledge
15. ANS:
REF:
LOC:
KEY:
16. ANS:
REF:
LOC:
KEY:
17. ANS:
REF:
LOC:
KEY:
18. ANS:
REF:
LOC:
KEY:
19. ANS:
REF:
LOC:
KEY:
C
PTS: 1
DIF: Moderate
5.5 Multiplying and Dividing a Polynomial by a Constant
9.PR7
TOP: Patterns and Relations (Variables and Equations)
Procedural Knowledge
D
PTS: 1
DIF: Moderate
5.5 Multiplying and Dividing a Polynomial by a Constant
9.PR7
TOP: Patterns and Relations (Variables and Equations)
Procedural Knowledge
C
PTS: 1
DIF: Easy
5.6 Multiplying and Dividing a Polynomial by a Monomial
9.PR7
TOP: Patterns and Relations (Variables and Equations)
Procedural Knowledge
A
PTS: 1
DIF: Moderate
5.6 Multiplying and Dividing a Polynomial by a Monomial
9.PR7
TOP: Patterns and Relations (Variables and Equations)
Procedural Knowledge
B
PTS: 1
DIF: Moderate
5.6 Multiplying and Dividing a Polynomial by a Monomial
9.PR7
TOP: Patterns and Relations (Variables and Equations)
Procedural Knowledge
SHORT ANSWER
20. ANS:
Coefficients: 4, 6
Variable: x
Degree: 2
Constant term: 8
PTS: 1
DIF: Moderate
REF: 5.1 Modelling Polynomials
LOC: 9.PR5
TOP: Patterns and Relations (Variables and Equations)
KEY: Conceptual Understanding
21. ANS:
Sample answer:
PTS: 1
DIF: Moderate
REF: 5.1 Modelling Polynomials
LOC: 9.PR5
TOP: Patterns and Relations (Variables and Equations)
KEY: Procedural Knowledge
22. ANS:
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
23. 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
24. 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
25. ANS:
PTS: 1
DIF: Moderate
REF: 5.3 Adding Polynomials
LOC: 9.PR6
TOP: Patterns and Relations (Variables and Equations)
KEY: Procedural Knowledge
26. ANS:
PTS: 1
DIF: Moderate
REF: 5.3 Adding Polynomials
LOC: 9.PR6
TOP: Patterns and Relations (Variables and Equations)
KEY: Procedural Knowledge
27. ANS:
PTS: 1
DIF: Moderate
REF: 5.3 Adding Polynomials
LOC: 9.PR6
TOP: Patterns and Relations (Variables and Equations)
KEY: Procedural Knowledge
28. ANS:
PTS: 1
DIF: Moderate
REF: 5.3 Adding Polynomials
LOC: 9.PR6
TOP: Patterns and Relations (Variables and Equations)
KEY: Procedural Knowledge
29. ANS:
PTS: 1
DIF: Difficult
REF: 5.4 Subtracting Polynomials
LOC: 9.PR6
TOP: Patterns and Relations (Variables and Equations)
KEY: Procedural Knowledge
30. ANS:
a)
b) $63
PTS: 1
DIF: Difficult
REF: 5.4 Subtracting Polynomials
LOC: 9.PR6
TOP: Patterns and Relations (Variables and Equations)
KEY: Problem-Solving Skills
31. 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
32. ANS:
Errors:
, not –5x
, not 0
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: Conceptual Understanding | Communication
33. ANS:
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
34. ANS:
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
35. ANS:
Error:
5 should be multiplied by 4x to give 20x.
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 | Communication
PROBLEM
36. ANS:
a)
b) 6
c)
PTS: 1
DIF: Difficult
REF: 5.1 Modelling Polynomials
LOC: 9.PR5
TOP: Patterns and Relations (Variables and Equations)
KEY: Problem-Solving Skills
37. 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
38. ANS:
a)
b) Substitute x = 12 into
.
The area of the rectangle when x = 12 is 300 square units.
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: Problem-Solving Skills | Communication
39. 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
40. ANS:
a) Length of deck
b) Length:
Substitute p = 4 into
.
The length of the deck is 23 m.
Width:
Substitute p = 4 into 8p.
The width of the deck is 32 m.
Area:
A = l w
= 23 32
= 736
The area of the deck is 736 m2.
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 | Communication