Academic Mathematics Strands and Subgroups in the Grade 10 Course

  • Quadratic Relations of the Form y = ax2 + bx + c
              - Investigating the Basic Properties of Quadratic Relations
              - Relating the Graph of y = x2 and Its Transformations
              - Solving Quadratic Equations
              - Solving Problems Involving Quadratic Relations
  • Analytic Geometry
              - Using Linear Systems to Solve Problems
              - Solving Problems Involving Properties of Line Segments
              - Using Analytic Geometry to Verify Geometric Properties
  • Trigonometry
              - Investigating Similarity and Solving Problems Involving Similar Triangles
              - Solving Problems Involving the Trigonometry of Right Triangles
              - Solving Problems Involving the Trigonometry of Acute Triangles

Table of Contents by Nelson

Chapter 1: Using Linear Systems to Solve Problems

1.1: Modelling with Linear Equations
1.2: Exploration: Tables of Values and Linear Systems
1.3: Solving Linear Systems: Graphing by Hand
1.4: Technology: Graphing Lines Using the TI-83 Plus Calculator
1.5: Investigating Ways That Two Lines Can Intersect
1.6: Technology: Determining the Point of Intersection
1.7: Solving a Linear System Using Graphing Technology
1.8: Solving a Linear System Algebraically: Substitution
1.9: Solving a Linear System Algebraically: Elimination
1.10: Technology: Linear Regression Using the TI-83 Plus Calculator
1.11: Modelling Using Linear Systems

CHAPTER 2: Coordinates and Geometry: Where Shapes Meet Symbols

2.1: Exploration: Graphical Images: Combining Symbolic and Visual Models
2.2: Technology: Using The Geometer's Sketchpad
2.3: Distance on the Plane—Part I: Distance From the Origin
2.4: The Equation of a Circle
2.5: Distance on the Plane—Part II
2.6: Technology: The Geometer's Sketchpad: The Midpoint of a Line Segment
2.7: Finding the Midpoint of a Line Segment
2.8: Classifying Shapes on a Coordinate Plane
2.9: Technology: The Geometer's Sketchpad: The Point of Intersection
2.10: Using the Point of Intersection to Solve Problems
2.11: Verifying Geometric Properties

CHAPTER 3: Analyzing and Applying Quadratic Models

3.1: Quadratic Relations
3.2: Properties of Quadratic Relations
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
3.5: Exploration: Multiplying Binomials Using Algebra Tiles
3.6: Technology: Using Quadratic Regression to Find the Curve of Best Fit with a TI-83 Plus Calculator
3.7: Standard Form of a Quadratic Relation
3.8: Extending Algebra Skills: Factoring Quadratic Expressions
3.9: Solving Problems with Quadratic Equations

CHAPTER 4: Quadratic Relations: Using The Model to Ask and Answer Questions

4.1: Exploration: Quadratic Dental Models
4.2: The Vertex Form of a Quadratic Relation
4.3: Using Technology to Investigating Transformations of Quadratics
4.4: Using Symmetry to Relate Standard Form to Vertex Form
4.5: Technology: Finding the Maximum or Minimum Values of a Quadratic Relation
4.6: Determining Maximum and Minimum Values Algebraically: Completing the Square
4.7: Solving Quadratic Equations: The Quadratic Formula
4.8: Investigating Quadratic Relations

CHAPTER 5: Introduction to Trigonometry

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
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

CHAPTER 6: Investigating Non-Right Triangles as Models for Problems

6.1: Exploration: Quadratic Dental Models
6.2: The Vertex Form of a Quadratic Relation
6.3: Using Technology to Investigating Transformations of Quadratics
6.4: Using Symmetry to Relate Standard Form to Vertex Form
6.5: Technology: Finding the Maximum or Minimum Values of a Quadratic Relation
6.6: Determining Maximum and Minimum Values Algebraically: Completing the Square
6.7: Solving Quadratic Equations: The Quadratic Formula

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Table of Contents by McGraw Hill

Chapter 1: Linear Systems

1.1 Connect English With Mathematics and Graphing Lines
1.2 The Method of Substitution
1.3 Investigate Equivalent Linear Relations and Equivalent Linear Systems
1.4 The Method of Elimination
1.5 Solve Problems Using Linear Systems

CHAPTER 2: Analytic Geometry

2.1: Midpoint of a Line Segment
2.2: Length of a Line Segment
2.3: Apply Slope, Midpoint, and Length Formulas
2.4: Equation for a Circle

CHAPTER 3: Geometric Properties

3.1: Investigate Properties of Triangles
3.2: Verify Properties of Triangles
3.3: Investigate Properties of Quadrilaterals
3.4: Verify Properties of Quadrilaterals
3.5: Properties of Circles

CHAPTER 4: Quadratic Relations

4.1: Investigate Non-Linear Relations
4.2: Quadratic Relations
4.3: Investigate Transformations of Quadratics
4.4: Graph y = a(x – h)2 + k
4.5: Quadratic Relations of the Form y = a(x – r)(x – s)
4.6: Negative and Zero Exponents

CHAPTER 5: Quadratic Expressions

5.1: Multiply Polynomials
5.2: Special Products
5.3: Common Factors
5.4: Factor Quadratic Expressions of the Form x2 + bx + c
5.5: Factor Quadratic Expressions of the Form ax2 + bx + c
5.6: Factor a Perfect Square Trinomial and a Difference of Squares

CHAPTER 6: Quadratic Equations

6.1: Maxima and Minima
6.2: Solve Quadratic Equations
6.3: Graph Quadratics Using the x-Intercepts
6.4: The Quadratic Formula
6.5: Solve Problems Using Quadratic Equations

CHAPTER 7: Trigonometry of Right Triangles

7.1: Investigate Properties of Similar Triangles
Use Technology
Create Designs With Similar and Congruent Figures Using Dynamic Geometry Software
7.2: Use Similar Triangles to Solve Problems
7.3: The Tangent Ratio
7.4: The Sine and Cosine Ratios
7.5: Solve Problems Involving Right Triangles

CHAPTER 8: Trigonometry of Acute Triangles

8.1: The Sine Law
8.2: The Cosine Law
8.3: Find Angles Using the Cosine Law
Use Technology
Program a Graphing Calculator
Use Technology
Program a TI-89 Calculator
8.4: Solve Problems Using Trigonometry

Strictly Ontario Curriculum

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