Download MPM1D Exam Outline 2009

2008 – 2009
MPM1D
Exam Outline
McGraw-Hill Ryerson: Principles of Mathematics 9
First Term
Equivalent Proportions


Conduct surveys, analyze and report results as data
Use equivalent fractions and cross multiplication to make predictions about a population based
on a sample, e.g., if 8 of the 30 students in the class preferred Brand A then in a school with x
students, # will likely also prefer Brand A
Collecting and analyzing linear data

2.1
o
o

2.2
o
o
o

2.3
o
o
o

2.4
o
o
o
o
o

2.5
o
1
Hypotheses and sources of Data
identify sources of data
state a hypothesis and propose a way to test it
Process of Designing of Experiment
decide what data is needed
decide on a sampling method to collect the data
identify bias
Drawing and Interpreting Scatter Plots
identify independent and dependent variables from a description, e.g., cause-effect
relationship
collect data and organize into tables or ordered pairs (coordinates)
present points on graph with labelled axes
Line of Best Fit
analyze data and graph to identify trends
draw a line of best fit for a scatter plot
use the line of best fit to make predictions by interpolation and/or extrapolation
discuss the correlation of a line of best fit as strong/weak, positive/negative
identify scatter plots that suggest that no correlation exists
Linear vs Non-Linear
decide if a graph is linear or non-linear
Working with rational numbers and exponents


Review
o Rational Number Operations
 perform operations involving multiplication, division, addition and subtraction
with rational numbers (positive and negative) in decimal and fraction form
(improper and proper)
3.1-3 Exponents
o Powers with Rational Bases
 manipulate numerical expressions containing powers with rational bases
(fractions) with exponents
m

o
am
a

, when m is positive
 
bm
b
3.11 Exponent Laws
 Simplify numerical and algebraic expressions containing exponents by using:

a m a n  a mn

am
 a m n
an

a 
m n
 a mn
Working with Expressions

3.4
o
o
o

3.5
o

3.6
o

3.7
o
o
 Page 2
Communicating with Algebra
identify variables, coefficients, constants
describe the degree of a term and of an expression
identify polynomials as monomials, binomials and trinomials
Collecting Like Terms
identify like and unlike terms in an expression
Adding and Subtracting Polynomials
simplify expressions containing like terms
The Distributive Property
expanding an expression by multiplying or distributing a constant or common factor
expand and simplifying polynomial expressions
Working with Equations

4.1
o

4.2
o
o

4.3
o

4.4
o

4.5
o
o
o
o
o
 Page 3
Solving Simple Equations
solve for the value of a variable in an equation involving one step done to both sides
Solving Multi-Step Equations
solving polynomial equations by simplifying/expanding/multiplying (distributive
property) first
solving equations by using ‘reverse’ order operations
Solving Equations involving Fractions
solving equations involving fractions by multiplying each term by lowest common
denominator
Solving Formulas
isolating a variable within a formula
Modelling with Algebra
making an algebraic statement to model a situation
finding the value of a variable in a linear equation,
e.g, substitute x=# into an equation and solve for y
solve for the value of a variable in a linear equation based on a description
rearrange an equation to isolate a specified variable, e.g., write in terms of y
SECOND TERM
Graphing Linear Relationships




Review
o Graphing in Four Quadrants
 plot points represented as ordered pairs (coordinates) on a coordinate plane
5.1-2 Direct vs Partial
o identify linear relationships with direct variation, i.e., line going through the origin
o identify linear relationships with partial variation, i.e., line with a y-intercept other than
the origin
5.3-4 Roles of Slope
o recognize slope as a measure of steepness
o relate slope as the rate of change of a linear relation representing y-units/x-units, e.g,
$/hr, km/hr, etc.
5.5
First Differences
o determine first differences in tables of values where appropriate, i.e, the increment of
the independent variable x in the table is constant
o determine whether a relationship is linear (or non-linear) by looking for first differences
that are also constant
Working with Linear Equations

5.6
Finding Slope
o
o
o

6.1
o
o
o
o
o
o

6.2
y 2  y1
to determine slope
x2  x1
as a comparison of rise and run
as a ratio representing a rate of change
Graphing a linear equation from y=mx+b form
connecting equations and graphs
write an equation based on a description
construct a table of values and graph relationship from a description, e.g., earns
charges $15/hr with a consultation fee of $25
by using y-intercept and slope (as rise over run)
identify the y-intercept as an “initial” value in many “real-life” situations, such as a flatfee, or service charge
identify the slope and y-intercept as m and b respectively in y  mx  b
Standard form Ax + By + C = 0
translate between the standard and slope-y-intercept forms of linear equations;
Ax+By+C=- and y=mx+b
o re-writing equations into standard form by by ‘emptying’ one side =0, multiplying by
denominator or lowest common denominator to cancel any fractions, and multiplying
by -1 to cancel a negative coefficient for x
6.3
Graphing by using intercepts
o identify the y-intercept and x-intercept as the intersection of the line with the y and x
axes respectively, or the coordinate produced by substituting x=0 and y=0
respectively into the equation of the line
o

use the formula of slope m 
 Page 4

6.4
Slopes and Equations of Lines: Special Cases
o
recognize and state equations in the form y  # as representing a horizontal line with
slope 0
recognize and state equations in the form x # as representing a vertical line with
undefined slope
o use the fact that parallel lines have the same slope and/or the fact that perpendicular
lines have slopes that are negative reciprocals of one another (“negative and flipped”)
to determine equations of lines based on a description involving parallel and/or
perpendicular lines
6.5-6 Finding equations of lines
o determine equations of lines based on two points, e.g., find slope, use the formula of
o

slope m 
o
o
o

6.7
o
o
o

5.3
o
o
o
o
o

o
y  y1
and cross-multiply to determine the equation of a line by solving
x  x1
for y (for y=mx+b) or emptying one side (for standard form)
solve for the value of a variable in a linear equation, e.g, substitute x=# into an
equation and solve for y
solve for the value of a variable in a linear equation based on a description
Solving a linear system
solve a linear system by graphing
verify the solution by substituting the coordinates of the point of intersection into each
equation
make comparisons by locating and interpreting the meaning of the location of the
point of intersection, e.g., which company is cheaper, under what circumstances…
Distance-Time Graphs Movement
interpret various sections of a graph representing “real-life” data such as motion and
identifying the rate of change
relate the rate of motion (speed/velocity) of object as the slope of its distance time
graph
relate a distance-time graph with y-intercept as initial position and slope as speed
interpret and create graphs to represent forward and reverse directions, increase and
decreases in speed/rate of change
demonstrate understanding of a slope of zero as a duration of no change
Finding the equation of Line of Best Fit
determine the equation of a line of best fit from a scatter plot by selecting two points
along the line and make predictions based on substitution of x or of y into the equation
Two-Dimensional Geometry



7.1-2 Angles Associated with Triangles and Quadrilaterals
o determine missing interior and exterior angles involving triangles by recognizing the
sum of the interior angles of a triangle as 1800, quadrilaterals as 360o and/or the sum
of the exterior angles of a polygon as 3600
7.3
Angles and Polygons
o determine missing angles involving polygons with the sum of the interior angles of a
polygon as (n-2)x1800 and/or the sum of the exterior angles of a polygon as 3600
7.4-5 Midpoints and Medians
o use and identify angle, perpendicular bisectors, altitudes and medians to locate the,
circumcentre, centroid for triangles
o describe the ways in which diagonals can help us classify quadrilaterals
 Page 5
Third Term
Three-Dimensional Geometry

These formulae should be reviewed to solve problems involving containers, e.g., determine the
dimensions, surface area and volume of containers given a description of its contents, such as
a box of golf balls, a canister of tennis balls, a 6-pack of soup cans, etc. Other combinations
and variations may also be required as explained in class notes, e.g., surface area of a prism.
Circumference of a circle
Area of a circle
Area of a triangle
Area of a rectangle
Pythagoras’ Theorem
Surface area of a sphere
Lateral surface area of a cylinder
Lateral surface area of a cone
Volume of a sphere
Volume of a regular prism or cylinder
Volume of a pyramid or cone
o
o
o
o
o
o
 Page 6
8.1
C  d
A  r 2
1
A  lw
2
A  lw
H 2  A2  B 2
SA  4r 2
SA  Ch
SA  rl
4
V  r 3
3
V  Ah
1
V  Ah
3
Pythagoras
 finding the length of the hypotenuse or either of the two other sides
8.2
Area of Composite Figures and Regular Polygons
 determine the area of a rectangle, triangle, circle and regular polygon
 determine the perimeter of polygons or circumference of a circle
8.3
Surface Area and Volume of Prisms, Cylinder and Pyramids
 determine the volume of polygonal prisms and cylinder as the product of the
area of its base times its height
 determine the dimensions of a prism or cylinder given its volume
 determine the volume of pyramid as one-third the volume of the
corresponding polygonal prism
 determine the surface area of a prism as the sum of its surfaces
 determine the dimensions of a pyramid given its volume
 use the Pythagorean Theorem to determine the slant height of a
cone/pyramid given its height and apothem/radius
 determine the surface area of a pyramid or cone
8.4-7 Surface Area and Volume of a Sphere and Cone
 determine the volume given circumference, diameter or radius
 determine the dimensions of sphere given its volume
 determine the surface area of a sphere
9.5
Surface Area of a cylinder
determine the lateral surface of a cylinder as the area of a rectangle whose length is
the circumference of the circle and width is the height of the cylinder