MPM1D
Name:_____________________
Exam Review Guide: MPM1D
This review guide has been designed to help direct studying towards important topics covered this
semester during the MPM1D course. This package should be used as a guide only. You are responsible for all
material covered in this package as well as all material covered during class this semester.
Part A: The Line
I. Equations
• Slope/ y-intercept form
• Standard form
______________________________________
______________________________________
II. Direct vs. Partial Variation:
Definition
Equation
III. Finding the equation of a line:
Case
1. Given m and b
2. Given m and a point
3. Given two points
4. Given x and y intercepts
Example of graphical
representation
Example
Given
m= 3
b=-5
m= 5
(-2, -14)
(-3,2)
(4, -2)
x-intercept is -3
y-intercept is 5
Equation
(hint: find b)
(hint: find slope first, then use slope value and one point to
find b)
MPM1D
Name:_____________________
5. Special cases:
a. Zero slope and a
point
Given
m=0
(3, -5)
b. Slope undefined and
a point
m= undefined
(3, -5)
c. Parallel slope to a
given line and a point
m=2
(2, -1)
d. Perpendicular slope to
a given line and a
point
Perpendicular to
1
y =− x+2
3
(2, 1)
IV. Graphing:
a. From a table of values:
y= 3x-2
Equation
MPM1D
Name:_____________________
b. From the equation (no calculations!)
y= 2x + 3
Steps
1. Write the equation of the line in
slope y-intercept form
2. Plot the y-intercept
3. Write the slope as a fraction
4. From the y-intercept:
a. if slope is a positive number:
b. if slope is a negative number:
V. Finding First Differences: (fill-in-the-blanks)
First Difference (definition):
•
for a _____________relation: the first difference is a constant, which
•
for a _______________________ relation: the first difference is not constant
represents a constant rate of change
x
-2
-1
0
1
2
1st Difference
-
y
6
3
0
-3
-6
Part B: Applying Linear Systems
I. Scatter Plots- definition:
Data:
Student
mark
Hours of TV
y
x
1
82
2
2
64
4
3
84
0
4
70
3
5
74
2
6
76
2
7
85
1
8
73
3
9
94
1
10
90
2
MPM1D
Name:_____________________
Plot the data from the previous page on the grid below:
II. Draw a line of best fit:
Definition-
Draw Line of best fit on the graph above
III. Types of correlation: Complete the graph or fill-in-the-blank
Type of correlation:_____________________
Type of correlation:_______________________
Type of correlation:_______________________
Strong, positive correlation
MPM1D
Name:_____________________
Weak, negative correlation
Part C: 2-D and 3-D measurement and geometry
I. Formulae
• Please refer to attached formula sheet: know how to use these formulae!
• Please review any additional formulas discussed in class (i.e. general formula for SA of a regular
polygon).
II. Properties of Polygons:
• All regular polygons have equal ___________________ and equal ______________________ .
• In a polygon with “n” sides, the sum of the interior angles is equal to:______________________.
• In a polygon with “n” sides, the sum of the exterior angles is equal to:______________________.
• Define “bisect”: _____________________________________________________________.
• The segment that joins the midpoints of two adjacent sides is a _______________________ of
the polygon.
• The line that joins one vertex to the midpoint of the opposite side of a triangle is called the
_____________________.
The midsegments of a
quadrilateral form a
_________________________.
A midsegment of a triangle is
parallel to the
_______________________.
This midsegment is half the
length of the parallel side.
The diagonals of a square are
equal in __________ and bisect
each other at __________
_________.
The diagonals of a rhombus bisect
each other at _____________
_______________ and bisect
the angles at the ____________.
The diagonals of a rectangle are
___________ and _________
each other.
The diagonals of a
_________________ bisect
each other.
MPM1D
Name:_____________________
III. Optimal values
Rectangular Prism
Cylinder
Required
Maximum volume
Optimal Shape
cube
Minimum surface area
cube
Maximum volume
cylinder
Minimum surface area
cylinder
Condition
Formula
Part D: Exponents Review
I.
Rules
Rule
Example
X4 X5 =
Multiplication
Division
x6
x3
(x4)5=
Power of a Power
II.
Simplifying Equations
Example
a. Distributive Property
a(b + c)=
b. Collect ________ terms
III.
-3x( 2x-5)=
2x + 3y2 – 4x + 5y2=
Solving equations
Example
Adding rule
x + 3= 4
Subtracting
rule
x – 5= 3
Multiplying
rule
-3x = 9
Dividing
rule
x
=4
6
Special
attention
6
=2
x
MPM1D
IV.
Name:_____________________
Pythagorean Theorem
“c” is called the _____________________
The theorem is:_________________________
c
a
Example: Find the value of “b” for the triangle on the
left when a= 4 and c= 5.
b
Part E: Slope
I.
From a graph
Type of slope (+, -, …)
Slope value (reading from graph)
m=
(2,4)
(-3,-1)
m=
(-1, 3)
(3,-2)
m=
MPM1D
Name:_____________________
m=
II.
Special cases
Parallel slopes are:_______________________
Perpendicular slopes are:___________________
__________________
III.
m=
rise
____
Example
m=2 is parallel to a line with a slope of _____
m= 3 is perpendicular to a line with a slope of ____
Calculating slope
m=
∆ ___
∆x
Ex. Find the slope of the line (show your work):
m=
y 2 − y1
_____