A linear relation is a relationship between two variables that produces a straight line when graphed. This unit connects directly to Grade 10 math and analytic geometry.
Operations with fractions, integers, decimals, percents, and exponent laws. Simplifying expressions, solving linear equations, isolating variables, and solving word problems
What does the MPM1D course outline cover?
Here is a quick recap on all the units covered
in Grade 9 Math
UNIT
1
Number Sense & Algebra
Master the algebra basics that make every later unit easier.
1
Collecting Like Terms
✓ Like terms have the same variable and exponent.
✓ Combine them by adding or subtracting coefficients.
3x and 7x → (3 + 7)x = 10x
5x² and −2x² → (5 − 2)x² = 3x²
4xy and −9xy → (4 − 9)xy = −5xy
WORKED EXAMPLE
5x + 3y − 2x + 7y
= (5x − 2x) + (3y + 7y)
= 3x + 10y
2
Expanding & Simplifying
✓ Expanding removes brackets using the distributive property.
a(b + c) = ab + ac
3(x + 4) = 3x + 12
−2(5x − 3) = −10x + 6
x(x + 7) = x² + 7x
WORKED EXAMPLE
3(2x + 5) − 4(x − 1)
= 6x + 15 − 4x + 4
= 2x + 19
Expand first, then collect like terms.
3
Solving Equations
✓ Golden rule: do the same thing to both sides.
2(x + 3) = 14
2x + 6 = 14
2x = 8
x = 4
5x + 3 = 3x + 11
2x = 8
x = 4
Order matters: expand, collect like terms, isolate.
Key
Key Takeaway
Only the coefficient changes when you collect like terms — the variable part stays the same.
UNIT
3
Analytic Geometry
Graphing lines, understanding equations in the form \(y = mx + b\), and identifying parallel and perpendicular lines.
Use coordinates, slope, and trends to describe lines and data.
1
Equation of a Line from Two Points
1 Find slope:
m = (y₂ − y₁) / (x₂ − x₁)
2 Substitute one point
into y = mx + b
3 Solve for b
4 Write the full equation
Example: points (2, 5) and (4, 9)
m = (9 − 5) / (4 − 2) = 2
Substitute (2, 5):
5 = 2(2) + b
5 = 4 + b
b = 1
Equation:
y = 2x + 1
2
Scatter Plots & Line of Best Fit
✓ A scatter plot shows the relationship between two data sets.
✓ A line of best fit goes through the middle of the points.
✓ It should have roughly equal numbers of points above and below.
✓ It helps identify trends and make predictions.
Key Idea
Find the slope first, then use a point to build the equation of the line.
UNIT
4
Measurement and Geometry
Know the right formula, label the shape, and use the theorem carefully.
1
3D Shape Formulas
Shape
Surface Area
Volume
Rectangular prism
2(lw + lh + wh)
lwh
Cylinder
2πr² + 2πrh
πr²h
Cone
πr² + πrl
⅓πr²h
Sphere
4πr²
⁴⁄₃πr³
2
Pythagorean Theorem
a² + b² = c²
★
c is the hypotenuse — the longest side, opposite the right angle.
Remember
Choose the correct shape formula first, then substitute values carefully and keep your units.
Properties of 2D shapes and 3D figures, calculating area, perimeter, and volume, as well as optimizing measurements.
Properties of 2D shapes and 3D figures, calculating area, perimeter, and volume, as well as optimizing measurements.
UNIT
2
Linear Relations
Straight-line relationships connect variables in a predictable way.
1
Key Concepts
Rate of change:
how much y changes for every 1 unit increase in x
Slope:
rise over run, m = (y₂ − y₁) / (x₂ − x₁)
Y-intercept:
where the line crosses the y-axis, when x = 0
X-intercept:
where the line crosses the x-axis, when y = 0
2
Direct vs Partial Variation
Direct Variation
y = mx
Partial Variation
y = mx + b
✓
Passes through (0, 0)?
Yes = direct. No = partial.
3
Slope-Intercept Form
y = mx + b
m
= slope
b
= y-intercept
Example:
y = 2x + 3
m = 2, b = 3
★
This is the most used equation form in Grade 9 math.
Quick Graphing Steps
1
Plot (0, b)
→
2
Use slope
(rise/run)
→
3
Draw the line
Free Resources
Meet Our Tutors
Pricing
FAQ
Rami Alzaytavi
B.ENG. Software Engineer
Yacoob Kathrada
Bsc. Biomedical
Maya Al Khowjeh
B.Tech. Civil Engineering
Taha Arafat
Msc. Pharmacology
Jawad Qourshah
B.ENG. Mechanical Engineering
Manish Bahat
M.ENG. Mechanical Engineering
Oubada Al Tarabishi
M.ENG. Electrical Engineering
Ahmad Dawood
MSc. Computer Science
Rami Alzaytavi
B.ENG. Software Engineer
Yacoob Kathrada
Bsc. Biomedical
Maya Al Khowjeh
B.Tech. Civil Engineering
Taha Arafat
Msc. Pharmacology
Jawad Qourshah
B.ENG. Mechanical Engineering
Manish Bahat
M.ENG. Mechanical Engineering
Oubada Al Tarabishi
M.ENG. Electrical Engineering
Ahmad Dawood
MSc. Computer Science
Rami Alzaytavi
B.ENG. Software Engineer
Yacoob Kathrada
Bsc. Biomedical
Maya Al Khowjeh
B.Tech. Civil Engineering
Taha Arafat
Msc. Pharmacology
Jawad Qourshah
B.ENG. Mechanical Engineering
Manish Bahat
M.ENG. Mechanical Engineering
Oubada Al Tarabishi
M.ENG. Electrical Engineering
Ahmad Dawood
MSc. Computer Science
Rami Alzaytavi
B.ENG. Software Engineer
Yacoob Kathrada
Bsc. Biomedical
Maya Al Khowjeh
B.Tech. Civil Engineering
Taha Arafat
Msc. Pharmacology
Jawad Qourshah
B.ENG. Mechanical Engineering
Manish Bahat
M.ENG. Mechanical Engineering
Oubada Al Tarabishi
M.ENG. Electrical Engineering
Ahmad Dawood
MSc. Computer Science
Is Grade 9 Math Hard?
What is collecting like terms?
What is the difference between direct variation and partial variation?
What comes after MPM1D?
Do you offer MPM1D tutoring online?
Do you provide Grade 9 math homework help?
How Do I Get Started?
100% Money-Back Guarantee on your first session.
Start your high school with a strong math foundation that will set on a great trajactory for your future. Personalized One-on-One tutoring for the Ontario Grade 9 Academic Math (MPM1D) curriculum.
Grade 9 Math; prerequisite for Principles of Mathematics Grade 10 course (MPM2D)
MPM1D Tutoring in Mississauga & Across Canada
Reviews
Contact us
Get in touch with our experts team
What does the MPM1D course outline cover?
MPM1D Tutoring in Mississauga & Across Canada
Grade 9 Math; prerequisite for Principles of Mathematics Grade 10 course (MPM2D)
100% Money-Back Guarantee on your first session.
MPM1D Tutoring in Mississauga & Across Canada
Grade 9 Math; prerequisite for Principles of Mathematics Grade 10 course (MPM2D)
100% Money-Back Guarantee on your first session.
UNIT
1
Number Sense & Algebra
Master the algebra basics that make every later unit easier.
1
Collecting Like Terms
✓ Like terms have the same variable and exponent.
✓ Combine them by adding or subtracting coefficients.
3x and 7x → (3 + 7)x = 10x
5x² and −2x² → (5 − 2)x² = 3x²
4xy and −9xy → (4 − 9)xy = −5xy
WORKED EXAMPLE
5x + 3y − 2x + 7y
= (5x − 2x) + (3y + 7y)
= 3x + 10y
2
Expanding & Simplifying
✓ Expanding removes brackets using the distributive property.
a(b + c) = ab + ac
3(x + 4) = 3x + 12
−2(5x − 3) = −10x + 6
x(x + 7) = x² + 7x
WORKED EXAMPLE
3(2x + 5) − 4(x − 1)
= 6x + 15 − 4x + 4
= 2x + 19
Expand first, then collect like terms.
3
Solving Equations
✓ Golden rule: do the same thing to both sides.
2(x + 3) = 14
2x + 6 = 14
2x = 8
x = 4
5x + 3 = 3x + 11
2x = 8
x = 4
Order matters: expand, collect like terms, isolate.
Key
Key Takeaway
Only the coefficient changes when you collect like terms — the variable part stays the same.
Operations with fractions, integers, decimals, percents, and exponent laws. Simplifying expressions, solving linear equations, isolating variables, and solving word problems
UNIT
3
Use coordinates, slope, and trends to describe lines and data.
1
Equation of a Line from Two Points
1 Find slope:
m = (y₂ − y₁) / (x₂ − x₁)
2 Substitute one point
into y = mx + b
3 Solve for b
4 Write the full equation
Example: points (2, 5) and (4, 9)
m = (9 − 5) / (4 − 2) = 2
Substitute (2, 5):
5 = 2(2) + b
5 = 4 + b
b = 1
Equation:
y = 2x + 1
2
Scatter Plots & Line of Best Fit
✓ A scatter plot shows the relationship between two data sets.
✓ A line of best fit goes through the middle of the points.
✓ It should have roughly equal numbers of points above and below.
✓ It helps identify trends and make predictions.
Key Idea
Find the slope first, then use a point to build the equation of the line.
Graphing lines, understanding equations in the form \(y = mx + b\), and identifying parallel and perpendicular lines.
Analytic Geometry
UNIT
4
Know the right formula, label the shape, and use the theorem carefully.
1
3D Shape Formulas
Shape
Surface Area
Volume
Rectangular prism
2(lw + lh + wh)
lwh
Cylinder
2πr² + 2πrh
πr²h
Cone
πr² + πrl
⅓πr²h
Sphere
4πr²
⁴⁄₃πr³
2
Pythagorean Theorem
a² + b² = c²
★
c is the hypotenuse — the longest side, opposite the right angle.
Remember
Choose the correct shape formula first, then substitute values carefully and keep your units.
Measurement and Geometry
Properties of 2D shapes and 3D figures, calculating area, perimeter, and volume, as well as optimizing measurements.
UNIT
2
A linear relation is a relationship between two variables that produces a straight line when graphed. This unit connects directly to Grade 10 math and analytic geometry.
Straight-line relationships connect variables in a predictable way.
1
Key Concepts
Rate of change:
how much y changes for every 1 unit increase in x
Slope:
rise over run, m = (y₂ − y₁) / (x₂ − x₁)
Y-intercept:
where the line crosses the y-axis, when x = 0
X-intercept:
where the line crosses the x-axis, when y = 0
2
Direct vs Partial Variation
Direct Variation
y = mx
Partial Variation
y = mx + b
✓
Passes through (0, 0)?
Yes = direct. No = partial.
3
Slope-Intercept Form
y = mx + b
m
= slope
b
= y-intercept
Example:
y = 2x + 3
m = 2, b = 3
★
This is the most used equation form in Grade 9 math.
Quick Graphing Steps
1
Plot (0, b)
→
2
Use slope
(rise/run)
→
3
Draw the line
Linear Relations
Rami Alzaytavi
B.ENG. Software Engineer
Yacoob Kathrada
Bsc. Biomedical
Maya Al Khowjeh
B.Tech. Civil Engineering
Taha Arafat
Msc. Pharmacology
Jawad Qourshah
B.ENG. Mechanical Engineering
Manish Bahat
M.ENG. Mechanical Engineering
Oubada Al Tarabishi
M.ENG. Electrical Engineering
Ahmad Dawood
MSc. Computer Science
Rami Alzaytavi
B.ENG. Software Engineer
Yacoob Kathrada
Bsc. Biomedical
Maya Al Khowjeh
B.Tech. Civil Engineering
Taha Arafat
Msc. Pharmacology
Jawad Qourshah
B.ENG. Mechanical Engineering
Manish Bahat
M.ENG. Mechanical Engineering
Oubada Al Tarabishi
M.ENG. Electrical Engineering
Ahmad Dawood
MSc. Computer Science
Rami Alzaytavi
B.ENG. Software Engineer
Yacoob Kathrada
Bsc. Biomedical
Maya Al Khowjeh
B.Tech. Civil Engineering
Taha Arafat
Msc. Pharmacology
Jawad Qourshah
B.ENG. Mechanical Engineering
Manish Bahat
M.ENG. Mechanical Engineering
Oubada Al Tarabishi
M.ENG. Electrical Engineering
Ahmad Dawood
MSc. Computer Science
Rami Alzaytavi
B.ENG. Software Engineer
Yacoob Kathrada
Bsc. Biomedical
Maya Al Khowjeh
B.Tech. Civil Engineering
Taha Arafat
Msc. Pharmacology
Jawad Qourshah
B.ENG. Mechanical Engineering
Manish Bahat
M.ENG. Mechanical Engineering
Oubada Al Tarabishi
M.ENG. Electrical Engineering
Ahmad Dawood
MSc. Computer Science
Pricing
FAQ
Reviews
Is Grade 9 Math Hard?
Is Grade 9 Math Hard?
What is collecting like terms?
What is collecting like terms?
What is the difference between direct variation and partial variation?
What is the difference between direct variation and partial variation?
What comes after MPM1D?
What comes after MPM1D?
Do you offer MPM1D tutoring online?
Do you offer MPM1D tutoring online?
Do you provide Grade 9 math homework help?
Do you provide Grade 9 math homework help?
How Do I Get Started?
How Do I Get Started?
Meet Our Tutors
Free Resources
Contact us
Get in touch with our experts team
Start your high school with a strong math foundation that will set on a great trajactory for your future. Personalized One-on-One tutoring for the Ontario Grade 9 Academic Math (MPM1D) curriculum.
Here is a quick recap on all the units covered
in Grade 9 Math
Contact us
Get in touch with our experts team