Download Principles of Mathematics, Grade 10, Academic (MPM2D)

Correlation of the Expectations for Principles of Mathematics 10 to Nelson Mathematic 10
Page 1
Principles of Mathematics, Grade 10, Academic (MPM2D)
This course enables students to broaden their understanding of relations, extend their skills in multi-step problem solving, and continue to develop
their abilities in abstract reasoning. Students will pursue investigations of quadratic functions and their applications; solve and apply linear systems;
solve multi-step problems in analytic geometry to verify properties of geometric figures; investigate the trigonometry of right and acute triangles; and
develop supporting algebraic skills.
Quadratic Functions
Overall Expectations
By the end of this course, students will:
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QFV.01
Expectation
solve quadratic equations;
QFV.02
determine, through investigation, the relationships between the
Throughout Chapters 3 and 4
graphs and the equations of quadratic functions;
determine, through investigation, the basic properties of quadratic Throughout Chapters 3 and 4
functions;
solve problems involving quadratic functions.
Throughout Chapters 3 and 4
QFV.03
QFV.04
Nelson Mathematics 10
Throughout Chapters 3 and 4
Specific Expectations
Solving Quadratic Equations
By the end of this course, students will:
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Expectation
QF1.01
expand and simplify second-degree polynomial expressions;
QF1.02
factor polynomial expressions involving common factors,
differences of squares, and trinomials;
Nelson Mathematics 10
3.5 Exploration: Multiplying Binomials Using Algebra Tiles
3.7 Standard Form of a Quadratic Relation
3.8 Extending Algebra Skills: Factoring Quadratic Expressions
Correlation of the Expectations for Principles of Mathematics 10 to Nelson Mathematic 10
QF1.03
QF1.04
QF1.05
solve quadratic equations by factoring and by using graphing
calculators or graphing software;
solve quadratic equations, using the quadratic formula;
interpret real and non-real roots of quadratic equations
geometrically as the x-intercepts of the graph of a quadratic
function.
3.9
4.7
4.7
4.7
3.4
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Solving Problems with Quadratic Equations
Solving Quadratic Equations: The Quadratic Formula
Solving Quadratic Equations: The Quadratic Formula
Solving Quadratic Equations: The Quadratic Formula
The Role of the Zeros of a Quadratic Relation
Investigating the Connection Between the Graphs and the Equations of Quadratic Functions
By the end of this course, students will:
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Expectation
QF2.01
identify the effect of simple transformations (i.e., translations,
reflections, vertical stretch factors) on the graph and the equation
of y=x2, using graphing calculators or graphing software;
explain the role of a, h, and k in the graph of y=a(x – h)2 + k;
QF2.03
QF2.04
express the equation of a quadratic function in the form y=a(x –
h)2 + k, given it in the form y=ax2 + bx + c, using the algebraic
method of completing the square in situations involving no
fractions;
sketch, by hand, the graph of a quadratic function whose equation
is given in the form y=ax2 + bx + c, using a suitable method [e.g.,
complete the square; locate the x-intercepts if the equation is
factorable; express in the form y=ax(x – s) + t to locate two points
and deduce the vertex].
Nelson Mathematics 10
4.3 Using Technology to Investigate Transformations of
Quadratics
4.2 The Vertex Form of a Quadratic Relation
4.3 Using Technology to Investigate Transformations of
Quadratics
4.6 Determining Maximum and Minimum Values
Algebraically: Completing the Square
3.4 The Role of the Zeros of a Quadratic Relation
4.2 The Vertex Form of a Quadratic Relation
4.3 Using Technology to Investigate Transformations of
Quadratics
4.4 Using Symmetry to Relate Standard Form to Vertex Form
4.6 Determining Maximum and Minimum Values
Algebraically: Completing the Square
Investigating the Basic Properties of Quadratic Functions
By the end of this course, students will:
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Expectation
Nelson Mathematics 10
Correlation of the Expectations for Principles of Mathematics 10 to Nelson Mathematic 10
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QF3.01
collect data that may be represented by quadratic functions, from
secondary sources (e.g., the Internet, Statistics Canada), or from
experiments, using appropriate equipment and technology (e.g.,
scientific probes, graphing calculators);
3.1 Quadratic Relations
4.1 Exploration: Quadratic Dental Models
4.8 Investigating Quadratic Relations
QF3.02
fit the equation of a quadratic function to a scatter plot, using an
informal process (e.g., a process of trial and error on a graphing
calculator), and compare the results with the equation of a curve of
best fit produced by using graphing calculators or graphing
software;
QF3.03
3.6 Technology: Using Quadratic Regression to Find a Curve
of Best Fit with a TI-83 Plus Calculator
3.7 Standard Form of a Quadratic Relation
4.1 Exploration: Quadratic Dental Models
4.2 The Vertex Form of a Quadratic Relation
4.4 Using Symmetry to Relate Standard Form to Vertex Form
3.1 Quadratic Relations
3.2 Properties of Quadratic Relations
describe the nature of change in a quadratic function, using finite
differences in tables of values, and compare the nature of change
in a quadratic function with the nature of change in a linear
function;
report the findings of an experiment in a clear and concise manner, 4.1 Exploration: Quadratic Dental Models
using appropriate mathematical forms (e.g., written explanations, 4.8 Investigating Quadratic Relations
tables, graphs, formulas, calculations), and justify the conclusions
reached.
QF3.04
Solving Problems Involving Quadratic Functions
By the end of this course, students will:
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Expectation
QF4.01
determine the zeros and the maximum or minimum value of a
quadratic function, using algebraic techniques;
Nelson Mathematics 10
3.4 The Role of the Zeros of a Quadratic Relation
3.8 Extending Algebra Skills: Factoring Quadratic Expressions
4.4 Using Symmetry to Relate Standard Form to Vertex Form
4.6 Determining Maximum and Minimum Values
Algebraically: Completing the Square
Correlation of the Expectations for Principles of Mathematics 10 to Nelson Mathematic 10
QF4.02
determine the zeros and the maximum or minimum value of a
quadratic function from its graph, using graphing calculators or
graphing software;
QF4.03
solve problems related to an application, given the graph or the
formula of a quadratic function (e.g., given a quadratic function
representing the height of a ball over elapsed time, answer
questions such as the following: What is the maximum height of
the ball? After what length of time will the ball touch the ground?
Over what interval is the height of the ball greater than 3 m?).
3.3 Technology: Finding the Zeros of a Quadratic Relation
Using a TI-83 Plus Calculator
3.4 The Role of the Zeros of a Quadratic Relation
4.5 Technology: Finding the Maximum or Minimum Value of a
Quadratic Relation
4.6 Determining Maximum and Minimum Values
Algebraically: Completing the Square
Throughout Chapters 3 and 4
Analytic Geometry
Overall Expectations
By the end of this course, students will:
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Expectation
AGV.01
model and solve problems involving the intersection of two
straight lines;
Nelson Mathematics 10
Throughout Chapter 1
AGV.02
Throughout Chapter 2
AGV.03
solve problems involving the analytic geometry concepts of line
segments;
verify geometric properties of triangles and quadrilaterals, using
analytic geometry.
Throughout Chapter 2
Specific Expectations
Using Linear Systems to Solve Problems
By the end of this course, students will:
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Expectation
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Nelson Mathematics 10
Correlation of the Expectations for Principles of Mathematics 10 to Nelson Mathematic 10
AG1.01
determine the point of intersection of two linear relations
graphically, with and without the use of graphing calculators or
graphing software, and interpret the intersection point in the
context of a realistic situation;
AG1.02
solve systems of two linear equations in two variables by the
algebraic methods of substitution and elimination;
solve problems represented by linear systems of two equations in
two variables arising from realistic situations, by using an
algebraic method and by interpreting graphs.
AG1.03
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1.3 Solving Linear Systems: Graphing by Hand
1.5 Investigating the Ways That Two Lines Can Intersect
1.6 Technology: Determining the Point of Intersection
1.7 Solving a Linear System Using Graphing Technology
1.11 Modelling Using Linear Systems
1.8 Solving a Linear System Using Algebra: Substitution
1.9 Solving a Linear System Using Algebra: Elimination
Throughout Chapter 1
2.10 Using the Point of Intersection to Solve Problems
Solving Problems Involving the Properties of Line Segments
By the end of this course, students will:
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Expectation
AG2.01
determine formulas for the midpoint and the length of a line
segment and use these formulas to solve problems;
AG2.02
AG2.03
AG2.04
determine the equation for a circle having centre (0, 0) and radius
r, by applying the formula for the length of a line segment;
identify the radius of a circle of centre (0, 0), given its equation;
and write the equation, given the radius
solve multi-step problems, using the concepts of the slope, the
length, and the midpoint of line segments (e.g., determine the
equation of the right bisector of a line segment, the coordinates of
whose end points are given; determine the distance from a given
point to a line whose equation is given; show that the centre of a
given circle lies on the right bisector of a given chord);identify the
radius of a circle of centre (0, 0), given its equation; and write the
equation, given the radius;
communicate the solutions to multi-step problems in good
mathematical form, giving clear reasons for the steps taken to
reach the solutions.
Nelson Mathematics 10
2.3 Distance on the Plane—Part I: Distance from the Origin
2.5 Distance on the Plane—Part II
2.7 Finding the Midpoint of a Line Segment
2.4 The Equation of a Circle
2.7 Finding the Midpoint of a Line Segment
2.8 Classifying Shapes on a Coordinate Plane
2.10 Using the Point of Intersection to Solve Problems
2.11 Verifying Geometric Properties
Throughout Chapters 1 and 2
Correlation of the Expectations for Principles of Mathematics 10 to Nelson Mathematic 10
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Using Analytic Geometry to Verify Geometric Properties
By the end of this course, students will:
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Expectation
AG3.01
determine characteristics of a triangle whose vertex coordinates
are given (e.g., the perimeter; the classification by side length; the
equations of medians, altitudes, and right bisectors; the location of
the circumcentre and the centroid);
AG3.02
determine characteristics of a quadrilateral whose vertex
coordinates are given (e.g., the perimeter; the classification by
side length; the properties of the diagonals; the classification of a
quadrilateral as a square, a rectangle, or a parallelogram);
AG3.03
verify geometric properties of a triangle or quadrilateral whose
vertex coordinates are given (e.g., the line joining the midpoints of
two sides of a triangle is parallel to the third side; the diagonals of
a rectangle bisect each other).
Nelson Mathematics 10
2.7 Finding the Midpoint of a Line Segment
2.8 Classifying Shapes on a Coordinate Plane
2.10 Using the Point of Intersection to Solve Problems
2.8 Classifying Shapes on a Coordinate Plane
2.11 Verifying Geometric Properties
Trigonometry
Overall Expectations
By the end of this course, students will:
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Expectation
TRV.01
develop the primary trigonometric ratios, using the properties of
similar triangles;
Nelson Mathematics 10
First Half of Chapter 5
5.1 Technology: Constructing Triangles with The Geometer’s
Sketchpad
5.2 Investigating and Comparing Triangles
5.3 Technology: Enlarging or Reducing a Triangle with The
Geometer’s Sketchpad
5.4 Modelling with Similar Triangles
Correlation of the Expectations for Principles of Mathematics 10 to Nelson Mathematic 10
TRV.02
solve trigonometric problems involving right triangles;
TRV.03
solve trigonometric problems involving acute triangles.
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Second Half of Chapter 5
5.5 Exploration: Slopes and Angles of Ramps
5.6 Investigating the Connection Between Slope and Angle
5.7 The Primary Trigonometric Ratios
5.8 Solving Problems Using Right Triangle Models and
Trigonometry
Throughout Chapter 6
Specific Expectations
Developing the Primary Trigonometric Ratios
By the end of this course, students will:
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Expectation
TR1.01
determine the properties of similar triangles (e.g., the
correspondence and equality of angles, the ratio of corresponding
sides, the ratio of areas) through investigation, using dynamic
geometry software;
TR1.02
describe and compare the concepts of similarity and congruence;
TR1.03
solve problems involving similar triangles in realistic situations
(e.g., problems involving shadows, reflections, surveying);
TR1.04
define the formulas for the sine, the cosine, and the tangent of
angles, using the ratios of sides in right triangles.
Nelson Mathematics 10
5.2 Investigating and Comparing Triangles
5.4 Modelling with Similar Triangles
5.7 The Primary Trigonometric Ratios
6.2 Similar-Triangle Models
5.2 Investigating and Comparing Triangles
5.2 Investigating and Comparing Triangles
5.4 Modelling with Similar Triangles
5.6 Investigating the Connection Between Slope and Angle
6.2 Similar-Triangle Models
5.6 Investigating the Connection Between Slope and Angle
5.7 The Primary Trigonometric Ratios
Solving Problems Involving the Trigonometry of Right Triangles
By the end of this course, students will:
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TR2.01
Expectation
determine the measures of the sides and angles in right triangles,
using the primary trigonometric ratios;
Nelson Mathematics 10
5.7 The Primary Trigonometric Ratios
5.8 Solving Problems Using Right Triangle Models and
Trigonometry
Correlation of the Expectations for Principles of Mathematics 10 to Nelson Mathematic 10
TR2.02
solve problems involving the measures of sides and angles in right
triangles (e.g., in surveying, navigation);
TR2.03
determine the height of an inaccessible object in the environment
around the school, using the trigonometry of right triangles.
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5.7 The Primary Trigonometric Ratios
5.8 Solving Problems Using Right Triangle Models and
Trigonometry
6.7 Solving Measurement Problems Modelled by Triangles
5.4 Modelling with Similar Triangles
5.7 The Primary Trigonometric Ratios
5.8 Solving Problems Using Right Triangle Models and
Trigonometry
6.2 Similar-Triangle Models
Solving Problems Involving the Trigonometry of Acute Triangles
By the end of this course, students will:
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TR3.01
TR3.02
Expectation
determine, through investigation, the relationships between the
angles and sides in acute triangles (e.g., the largest angle is opposite
the longest side; the ratio of side lengths is equal to the ratio of the
sines of the opposite angles), using dynamic geometry software;
calculate the measures of sides and angles in acute triangles, using
the sine law and cosine law;
TR3.03
describe the conditions under which the sine law or the cosine law
should be used in a problem;
TR3.04
solve problems involving the measures of sides and angles in acute
triangles;
TR3.05
describe the application of trigonometry in science or industry.
Nelson Mathematics 10
6.2 Similar-Triangle Models
6.3 Investigating the Sine Law
6.4 Proving and Using the Sine Law
6.6 Adjusting the Pythagorean Theorem: The Cosine Law
6.3 Investigating the Sine Law
6.4 Proving and Using the Sine Law
6.6 Adjusting the Pythagorean Theorem: The Cosine Law
6.7 Solving Measurement Problems Modelled by Triangles
6.4 Proving and Using the Sine Law
6.6 Adjusting the Pythagorean Theorem: The Cosine Law
6.7 Solving Measurement Problems Modelled by Triangles
6.3 Investigating the Sine Law
6.4 Proving and Using the Sine Law
6.6 Adjusting the Pythagorean Theorem: The Cosine Law
6.7 Solving Measurement Problems Modelled by Triangles
Throughout Chapters 5 and 6