Review Study Guide for MPM1D Grade 9 Academic

Hello Students,

The topics on this page are what I would consider some of the “Big Ideas” of the MPM1D Grade 9 Academic Math Course to assist you in your course review and preparation for the EQAO Grade 9 Assessment of Mathematics which is worth 20% of your final grade. There are four (4) content strands in the course, so I will organize the topics based on strand and only include what I would consider the most important and/or common difficult concepts that all students should review over these last two weeks.

Note that you can find a full course review by clicking here.

NA – Number Sense and Algebra

NA1 – Operating With Exponents

NA1.01 – I can substitute into and evaluate algebraic expressions involving exponents.

Here’s another video, if you want another perspective.

NA1.03 & NA1.04 – I can … apply the exponent rules for multiplying and dividing monomials, extend the multiplication rule to the power of a power rule … and apply it to simplify expressions involving one and two variables with positive exponents.

Here’s another video for a different perspective.

NA2 – Manipulating Expressions and Solving Equations

NA2.02 – I can solve problems requiring the manipulation of expressions arising from applications of percent, ratio, rate, and proportion.

NA2.04 – I can add and subtract polynomials with up to two variables using a variety of tools.

NA2.05 – I can multiply a polynomial by a monomial involving the same variable using a variety of tools.

NA2.06 – I can expand and simplify polynomial expressions involving one variable using a variety of tools.

NA2.07 – I can solve first-degree equations, including equations with fractional coefficients, using a variety of tools and strategies.

Solving Simple Equations – One and Two Step Equations

Learn how to solve a simple equation involving two-steps:


4m – 6 = 12

Solve Two-Step Equations

Learn how to solve a two-step equation:


7x – 4 = 10

How to Solve Multi-Step Equations Involving Like Terms


3 + 4m + 5m = 21

How to Solve Multi-Step Equations With Variable Terms on Both Sides


4y – 13 = -6y + 7

How to Solve Equations Involving Distributive Property


4(k – 3) = 2 – (2k – 6)

How to Solve Equations with One Fraction


(1/3)(x – 2) = 5


16 = [3(v + 7)]/2

How to Solve Equations with One Fraction and Distribution


[3(z – 5)]/4 = 7

How to Solve Equations with One Fraction and Distribution (Part 2)


3 = [2(n + 7)]/5

Solving Equations with One Fraction Application Questions

A trapezoidal backyard has an area of 100 m^2. The front and back widths are 8 m and 12 m, as shown in the diagram.

What is the length of the yard from front to back?

Create and Solve Equations from Word Problems

The sum of two consecutive even integers is -134. Find the numbers.

Problem Solving Using Equations

The length of Laurie’s rectangular swimming pool is triple its width. The pool covers an area of 192 m^2.

If Laurie swims across the diagonal and back, how far does she travel?

NA2.08 – I can rearrange formulas involving variables in the first degree, with and without substitution.

Rearrange the following equation for ‘h’

V = p(r^2)h

LR – Linear Relations

LR1 – Using Data Management to Investigate Relationships

We see these concepts so much throughout the course, I don’t think much time reviewing is necessary.

LR2 – Understanding Characteristics of Linear Relations

LR2.03 – I can identify, through investigation, some properties of linear relations and apply these properties to determine whether a relation is linear or non-linear (by rate of change/initial value when described in words, by first differences in a table, straight/curved graph, degree of terms in equation).

LR2.04 – I can compare the properties of direct variation and partial variation in applications, and identify the initial value when described in words, represented as a table, a graph, or an equation.

Watch another direct variation practice problem solution video and more in-depth details about Direct Variation here.

LR3 – Connecting Various Representations of Linear Relations

LR3.01 – I can determine values of a linear relation by using a table of values, by using the equation of the relation, and by interpolating or extrapolating from the graph of the relation.

LR3.02 – I can describe a situation that would explain the events illustrated by a given graph of a relationship between two variables.

Recall some of our “Distance from Work” videos:

Practice more distance-time graphs here:

Task 1 [act 1 | act 2 | act 3]
Task 2 [act 2 | act 3]
Task 3 [act 2 | act 3]
Task 4 [act 2 | act 3]
Task 5 [act 2 | act 3]
Task 6 [act 2 | act 3]
Task 7 [act 2 | act 3]
Task 8 [act 2 | act 3]
Task 9 [act 2 | act 3]
Task 10 [act 2 | act 3]

Re-try the gameshow that goes with the tasks here.

LR3.03 – I can represent a linear relation in four ways (description, table, graph, equation) and determine other representations of a linear relation, given one representation.

AG – Analytic Geometry

AG1 – Investigating the Relationship Between the Equation of a Relation and the Shape of Its Graph

AG1.03 – I can express the equation of a line in the form y = mx + b, given the form Ax + By + C = 0.

AG2 – Investigating the Properties of Slope

AG2.01 – I can determine, through investigation, various formulas for the slope of a line segment or a line, and use the formulas to determine the slope of a line segment or a line [from a table or graph using rise over run or m = (y2 – y1)/(x2 – x1)]

AG2.04 – I can identify, through investigation, properties of the slopes of lines and line segments such as direction, positive or negative rate of change (slope), steepness, parallelism, and perpendicularity, using graphing technology to facilitate investigations, where appropriate.


AG3 – Using the Properties of Linear Relations to Solve Problems

AG3.01 – I can graph lines by hand, using a variety of techniques.

AG3.02 – I can determine the equation of a line when given information about the line such as: the slope and y-intercept; the slope and a point; or two points from the line.

Equations of Lines Given Slope and a Point:

Here’s a practice problem video with a solution for you to try.

Equations of Lines Given Two Points:

AG3.05 – I can determine graphically the point of intersection of two linear relations, and interpret the intersection point in the context of an application.

MG – Measurement and Geometry

MG1 – Investigating the Optimal Values of Measurements

MG1.01 – I can determine the maximum area of a rectangle with a given perimeter by constructing a variety of rectangles, using a variety of tools, and by examining various values of the area as the side lengths change and the perimeter remains constant.

MG2 – Solving Problems Involving Perimeter, Area, Surface Area, and Volume

MG2.01 & MG2.02 – I can relate the geometric representation of the Pythagorean theorem and the algebraic representation a^2 + b^2 = c^2 and solve problems using the Pythagorean theorem, as required in applications.

MG2.03 – I can solve problems involving the areas and perimeters of composite two-dimensional shapes.

Here’s another example video.

MG2.06 – I can solve problems involving the surface areas and volumes of prisms, pyramids, cylinders, cones, and spheres, including composite figures.


Surface Area

MG3 – Investigating and Applying Geometric Relationships

MG3.01 – I can determine, through investigation using a variety of tools and describe the properties and relationships of the interior and exterior angles of triangles, quadrilaterals, and other polygons, and apply the results to problems involving the angles of polygons.

MPM1D Digital Textbook

McGraw-Hill Ryerson: Principles of Mathematics, 9

MPM1D Grade 9 Academic Digital Textbook - McGraw-Hill RyersonWhile we don’t use the textbook for much more than a question bank, you can access the McGraw-Hill Ryerson Textbook: Principles of Mathematics, 9 Electronic Textbook in PDF Form. Note that the textbook is password protected for only my students due to copyright law.

Access Textbook