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Course Review Package
Unit 1 – Number Systems
Unit 2 – Polynomials
Unit 3 – Equations & Inequalities
Unit 4 – Linear Relations
Unit 5 – Measurement
Unit 6 – Statistics & Probability
Unit 1 – number systems
Powers
 What is a power and what does it mean?

Power – Expanded Form – Standard Form

A power with an exponent of zero

Exponent Laws:
a0  1
o Product Law
o Quotient Law
o Power of a Power
o Power of a Product
o Power of a Quotient

Order of Operations with Powers (BEDMAS)
Square Roots
 Square roots of Perfect Squares
i.e. 36  6
1, 4, 9, 16, ____, ____, ____, ____, ____, ____, ____, ____, ___, ___, ___

Approximate Square Roots of Non-perfect Squares
i.e.
20
4.5
Rational Numbers
 Comparing and ordering rational numbers (number line)

Problem solving that involve arithmetic operations with rational numbers

Irrational Numbers – non-repeating, non-terminating decimal numbers.
π = 3.14.15965 . . . . . . . . . .
5  2.236067 . . . . . . . . .
Unit 2 – Polynomials

What is a polynomial?
o Create a concrete model or a pictorial representation for a polynomial
 Algebra Tiles: Black is positive, White is negative
ie. Use algebra tiles to model 2 x 2  3 x  5
o Write an expression for a given model of a polynomial
represents
o Classify polynomials as a monomial, binomial or trinomial
o Identify the variable, degree, number of terms, coefficients and constant term
7 y  4
3n
8
3x 2  5 x  6
o Describe a situation for a first degree polynomial expression
o Match equivalent polynomial expressions
5v + v2 – 7

and
-7 + 5v + v2
Addition & Subtraction
o Concretely: using algebra tiles (zero principle)
o Pictorially:
o Symbolically:  4m2  4m  5    2m2  2m  1 
3x  7   2x  2 

Multiplication & Division:
o Concretely: using algebra tiles (area = length x width)
o Pictorially:
o Symbolically:  5x  3 =
24 x 2
=
6
3  2 s 2  7 s  4  =
8n  4
=
2
2w  3w  5 =
40 x 2  16 x
=
8x
Unit 3 – Equations & Inequalities
Linear equations:

Model the solution of a given linear equation, using concrete or pictorial representations.

Verify by substitution whether your answer (x = ) is a solution to a linear equation.
i.e. Indicate whether the following values of x are solutions to 4 x  5  7
x = -2, 0, 3

Solve a linear equation symbolically.
o Various forms:
 5x  15
x
 11

2
 3x  6  18
x
27

4
 6x  14  x
 6  x  8  72
 3x  4  2x  9
 2  3x 1  4  x  5


8
 2
x
Identify and correct an error in a given incorrect solution of a linear equation.

Represent a given problem, using a linear equation.
o Kevin is planning to rent a car for one week. Company A charges $200 per week,
With no charge for the distance driven. For the same car, Company B charges
$25 administration fee plus $0.35 per kilometre.
Linear Inequalities:

Translate a given problem into a linear inequality using the symbols ≥, >, ≤, or <.
o A coffee maker can hold not more than 12 cups of water.
o You must be at least 14 years old to obtain a learner’s permit to drive.

Solve a linear inequality algebraically.
o
o
o
o
2x  8
3x  2  10
7 y  14
4x  3  2x  9

Graph the solution of a linear inequality on a number line.

Solve a given problem involving a linear inequality, and graph the solution.
i.e.
The cost of a prom is $400 to rent a hall, and $30 per person for the meal. The prom
committee has $10 000 to spend. How many students can attend?
Unit 4 – Linear Relations

Write a linear expression representing a given pictorial or written pattern.
ie. Here is a pattern made with toothpicks. The pattern continues.
Write a linear expression that relates the number of
toothpicks (t) and the number of houses (h)

Write a linear equation to represent a situation.
ie. Clint has a window cleaning service. He charges a fixed cost of $12, plus $1.50 per window.
a)
Write an equation that relates the total cost to the number of windows cleaned.
b) Clint

charged $28.50 for a job. How many windows did he clean?
Solve, using a linear equation, a given problem that involves a pictorial or written pattern.
ie. The cost to print brochures is the sum of a fixed cost of $250, plus $1.25 per brochure.
a) Write an equation that relates the total cost, C dollars, to the number of brochures, n.
b) What is the cost of printing 2500 brochures?
c) How many brochures can be printed for $625?

Write a linear equation representing the pattern in a given table of values.

Verify the equation by substituting values from the table.

Describe a pattern found in a given graph.

Graph a linear relation, including vertical lines (x = ) and horizontal lines (y = ).

Match a given equation of a linear relation to its graph.

Interpolate the approximate value of one variable on a graph, given the value of the other
variable.

Extrapolate the approximate value of one variable on a graph, given the value of the other
variable.
Unit 5 – Measurement
Surface Area
 Determine the surface area of a 3D object
o cylinders, rectangular prisms, triangular prisms
 Determine the surface area of a composite 3D object
o area of overlap (overlap shape x 2)
o cylinders, rectangular prisms, triangular prisms
 Solve problems with composite 3D objects
Similarity
 Determine if the polygons in a given set are similar and explain why.
 Draw a polygon similar to a given polygon given the scale factor
 Solve a problem, using the properties of similar polygons
i.e
A rectangular door has height 200 cm and
width 75 cm. It is similar to a door in a
doll’s house. The height of the doll’s house
door is 25 cm.
a) Sketch and label both doors.
b) Calculate the width of the doll’s house door.

Determine the scale factor for a given diagram drawn to scale s.f. 


enlargement (s.f. > 1) or a reduction (s.f. < 1)
Solve a problem that involves the properties of similar triangles
i.e.
Jaquie is 1.6 m tall.When her shadow is
2.0 m long, the shadow of the school’s
flagpole is 16 m long. How tall is the
flagpole, to the nearest tenth of a metre?
length on scale diagram
length on original
Symmetry
 Line symmetry – a reflection about a horizontal, vertical or oblique line.
 Rotation symmetry
o Order of rotation symmetry – number of times a rotation coincides with itself
360
o Angle of rotation symmetry =
order of rotation


Rotate a given 2-D shape about a vertex, and draw the resulting image – tracing paper.
Identify the type of symmetry from a given transformation on a grid

Identify and describe the types of symmetry created in a given piece of artwork

Determine whether or not two given 2-D shapes on a grid are related by either rotation or line
symmetry.

Translation an object on a grid – right 2, and up 3
Circle Properties
 Perpendicular from the centre of a circle to a chord bisects the chord

Central angle is equal to twice the measure of the inscribed angle subtended by the same arc

Inscribed angles subtended by the same arc are equal

The inscribed angle on a semi-circle is a right angle.

A tangent to a circle is perpendicular to the radius at the point

Solve problems involving the application of one or more of the circle properties
Unit 6 – Statistics & Probability

Experimental Probability, Theoretical Probability, Subjective Judgement

Describe the effect of:
o Bias
o use of language
o ethics
o cost
o time and timing
o privacy
o cultural sensitivity
on the collection of data.

Select and defend the choice of using either a population or a sample of a population to
answer a question.
o Identify whether a given situation represents the use of a sample or a population.
i.e. To determine the favourite TV show of grade 9 students in a school, all grade 9
students in the school are surveyed.
o Describe some of the limitations of using a population – (too costly, not enough time,
limited resources)
o Describe when a generalization from a sample of a population may nor may not be
valid for the population.
i.e. Courtney surveys her friends and finds that 68% of them have an MP3 player.
She reports that 68% of the grade 9 students have an MP3 player. James
surveys the entire grade 9 population and discovers that 51% have an MP3
player.
a) Whose conclusion is more likely to be valid? Explain.
b) Why might the other student’s conclusion not be valid?
Practice
o Significance of a sample size in interpreting data.

Common Sampling Methods:
o
o
o
o
o
o
Simple Random Sample
Systematic or Interval Sampling
Cluster Sampling
Self-Selected Sampling
Convenience Sampling
Stratified Random Sampling