Saskatchewan Common Mathematics Assessments
Post Assessment
Outcome: P9. Demonstrate understanding of polynomials (limited to polynomials of
degree less than or equal to 2) including:





Modeling
generalizing strategies for addition, subtraction, multiplication, and division
analyzing
relating to context
comparing for equivalency
1. Name the coefficients, variables, degree and constant term in the polynomial -6x² - 32x + 5
Coefficient
_____
Variable
_____
Degree
_____
Constant term
_____
2. In each expression identify which of the following is a monomial, binomial, or trinomial.
a.
b.
c.
d.
14x - 36
18xy
44 – 22x² – 21y
7x³y – 13y
__________
__________
__________
___________
3. Simply the following by addition or subtraction.
a. ( 4p - 6 ) + ( 2p + 7 )
b. ( 3x² - 11 ) - ( 7x² - 7x – 11 )
Level
1
Multiply the following.
a. 3 ( 7xy - 11 )
b. -4 ( -11b + 6x – 11x² )
4. Divide the following.
a.
33x  12 y  18
3
b.
35 x 2  60 x  70 y
5
5. a) What polynomial does this collection of algebra tiles represent?
Level
2
b) Explain your answer.1mk
c) Explain the difference between x and x². 1mk
6.
Determine the area of this rectangle.
3x² + 4x + 2
8
7. Which equations are equivalent? Explain how you know.
i.
35 x  14 x 2  21
7
ii.
15  9 x  6 x 2
3
iii.
24 x  40  16 x 2
8
iv.
10  4 x 2  6 x
2
8. A student subtracted like this:
( 8x² - 3x + 7) – ( 5x² + 5x – 5)
= 8x² - 3x +7 ) – 5x² + 5x – 5
= 8x² - 5x² -3x + 5x + 7 – 5
= 3x² + 2x + 2
a. Is the solution correct or not?
b. Explain? (Your explanation should give the correct answer if it was wrong!)
Level
3
9. a) Determine a polynomial for the perimeter of the shape below.
b) Determine a polynomial for the area of the shape below.
c) Determine the perimeter and area when x = 5cm
4x
4x
5x + 5
4x
10. Sketch algebra tiles to model the polynomial 6 – 4v³ + v.
Level
4
11. Simplify the following expression.
𝟒
(𝒃𝟓 ) − (𝒃𝟗 )𝟐
− (3b)(−2b) − (b − 1)2
(𝒃𝟔 )𝟑
12. The product 2𝜋𝑟(𝑟 + ℎ) represents the surface area of a cylinder.
a. Determine the product.
b. To check your work, determine the surface area of a cylinder with radius 5 cm and height
3 cm two ways:
 Using the product
 Using your answer to part a
Teacher Section
Teacher Notes:
Indicator
1a
1b
1c
1d
2a
2b
2c
2d
3a
3b
4a
4b
5a
5b
6a
6b
6c
7
8i
8ii
8iii
8iv
9a
9b
10a
10b
10c
11
12
13a
13b
d
d
d
d
f
f
f
f
j
J
m
m
n
n
a/c
a/c
a/c
m
h
h
h
h
j
j
o
o
o
Answer
Level
Question
Answer Key
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
3
3
3
3
3
4
4
4
4
-6, -32
x
2
5
binomial
monomial
trinomial
binomial
6p+1
4𝑥 2 -7x
21xy-33
44𝑏 − 24𝑥 + 44𝑥 2
11x+4y+6
7𝑥 2 − 12𝑥 − 14𝑦
𝑥 2 + 3𝑥 + 2
Answers will vary. May discuss cancelling using alge tiles etc
Answers will vary. May use alge tiles to show the difference.
24𝑥 2 + 32𝑥 + 16
5𝑥 + 2𝑥 2 − 3
−5 + 3𝑥 + 2𝑥 2
3𝑥 − 5 + 2𝑥 2
5 + 2𝑥 2 + 3𝑥
Did not distribute the negative
No, the correct answer is 3𝑥 2 − 8𝑥 + 12
34x+10
52𝑥 2 + 20𝑥
P=180cm, A=1400𝑐𝑚2
𝑏 20 + 5𝑏 2 − 2𝑏
2𝜋𝑟 2 + 2𝜋𝑟ℎ
251𝑐𝑚2
Outcome: Demonstrate understanding of polynomials (limited to polynomials of degree less than or equal to 2) including:
 Modeling
 generalizing strategies for addition, subtraction, multiplication, and division
 analyzing
 relating to context
 comparing for equivalency
up to Level 1
up to Level 2
up to Level 3
up to Level 4
There is a partial
No major errors or
No major errors or omissions
In addition to level
omissions regarding the
regarding any of the
3 performance, inDescription understanding of
some of the
simpler details or
information and/or processes
depth inferences
of Levels:
simpler details and processes, but major
that were explicitly taught.
and applications
(based on
processes.
errors or omissions
go beyond what
Marzano,
This is the target level for
Prior knowledge is regarding the complex
was explicitly
2007)
proficiency.
understood.
processes may be present.
taught.
Demonstrate an
b. Represent polynomials a.Model (concretely or
In addition to level
understanding of
concretely or pictorially
pictorially) and describe the
3 performance, inequations and
and describe how the
relationship between x and x2. depth inferences
expressions by:
concrete or pictorial
c.Write a polynomial for a
and applications
model reflects the
given concrete or pictorial
go beyond what
 Distinguishing
symbolic form.
representation.
was explicitly
between
d. Identify the variables,
h.Write equivalent forms of a
taught.
equations and
degree, number of terms
polynomial expression by
expressions
and coefficients,
interchanging terms or by
 Evaluating
including the constant
decomposing terms, and
Indicators
expressions
term,
of
a
given
justify the equivalence.
and
 Verifying
simplified
polynomial
k.Verify whether or not the
Learning
solutions to
expression
and
explain
simplification of the addition
Targets for
equations
the role or significance of or subtraction of two
each Level:
each.
polynomials is correct and
f.Sort a set of
explain.
polynomials into
o.Verify whether or not the
monomials, binomials,
simplification of the
and trinomials.
multiplication or division of a
i.Explain why terms with polynomial by a monomial is
different variable
correct.
exponents cannot be
added or subtracted.
(b).I can use models/tiles (a) I can show with
I can create, solve
to represent symbolic
models/diagrams the
and share a
polynomial expressions
relationship of squared values. problem with one
(d).I can identify parts of (c)I can write a polynomial
or more operations
a polynomial expression expression from
involving
and explain their purpose models/algebra tiles
polynomials.
(f)I can sort polynomials (h)I can simplify/manipulate
Studentfriendly
into monomials,
polynomials and show their
binomials, and trinomials. equivalence.
descriptions
(i) I can explain why
(k) I can check/explain if the
of learning
targets.
terms with different
simplification of the addition
variable exponents cannot or subtraction of two
be added or subtracted.
polynomials is correct
(o) I can check whether or not
the multiplication or division
of a polynomial by a
monomial is correct.