Principles of Mathematics - 10

Course Description:

This course enables students to broaden their understanding of relationships and extend their problem-solving and algebraic skills through investigation, the effective use of technology, and abstract reasoning. Students will explore quadratic relations and their applications; solve and apply linear systems; verify properties of geometric figures using analytic geometry; and investigate the trigonometry of right and acute triangles. Students will reason mathematically and communicate their thinking as they solve multi-step problems.

Prerequisite: MPM1D - Principles of Mathematics - Grade 9 Academic

Course Outline

Unit 1: Linear Systems (10 hours)

In a simple business organization, the inputs are its employees, raw materials and factories. Its outputs are its finished products. Management decides what the interactions among the inputs should be to give the maximum output. If the business organization is represented as a linear system, then if we double the employees, raw materials and factories (the inputs) then we should expect to get double the production (the output). We can describe mathematically how the parts of a linear system relate to one another and to the input using a system of linear equations. In this unit, we will learn and explore about linear systems of equations graphically as well as algebraically. We will apply them to solve real-world problems.

1-1 Solve by Graphing
1-2 Solve by Substitution            
1-3 Solve by Elimination
1-4 Applications of Linear Systems


Unit 2: Quadratic Relations (40 hours)

Have you ever wondered why the best roller coasters are parabolic? When you're riding these coasters it feels like you're defeating the force of gravity, right? Exactly! When a coaster falls from the peak of the parabola, it is rejecting air resistance and all the bodies are falling at the same rate. The only force here is gravity. The shape of a coaster, as well as the ascent and descent, play a vital role in the rider's enjoyment. Parabolas represent the graphs of the quadratic relations. Welcome to unit 2. We will begin this unit by collecting and fitting data that is non-linear and then move into graphing simple quadratic equations using appropriate technology. Through investigation, we will learn some key features of parabolas. This leads to a study of some transformations of quadratics and sketching by hand. We will also learn to find the equation of a quadratic from a graph and solve quadratic equations that arise from realistic situations. 

2-1 Collecting And Fitting Data
2-2 Graphing Quadratic Equations
2-3 Key Features of Parabola
2-4 Transforming Parabolas
2-5 Sketching by Hand
2-6 Factoring Polynomial Expressions
2-7 Connecting Factors with x-Intercepts
2-8 Completing the Square
2-9 Quadratic Formula
2-10 Solve Quadratic Equations
2-11 Maximum or Minimum Value of a Quadratic Relation


Unit 3: Analytic Geometry (20 hours)

Architects often design buildings and structures that contain arches. Carpenters may use wooden frames to build these arches. To build a wooden frame, carpenters need to know the radius of the circle that contains the arch. In this unit, we will use analytical geometry to form a relationship between the three basic shapes namely a line segment, a circle, and a triangle. These shapes will also form the basis of some key formulas that are used in calculations.

3-1 Length and Midpoint of a Line Segment
3-2 Solve Problems using Analytic Geometry
3-3 Equation of a Circle and Applications                                           
3-4 Characteristics and Properties of Geometric Figures
3-5 Verifying Properties of Geometric Figures


Unit 4: Trigonometry (40 hours)

There is an enormous number of uses of trigonometry and trigonometric functions. For instance, the technique of triangulation is used in astronomy to measure the distance to nearby stars, in geography to measure distances between landmarks, and in satellite navigation systems or global positioning system to measure the distance between your vehicle and the point of destination. The sine and cosine functions are fundamental to the theory of periodic functions such as those that describe sound and light waves. In this unit, we will develop primary trigonometric ratios and solve trigonometric problems involving right and acute triangles.

4-1  Congruence and Similarity in Triangles
4-2 Solving Similar Triangle Problems
4-3 Similar Right Triangles
4-4 The Primary Trigonometric Ratios
4-5 Solving Right Triangles
4-6 Right Triangles in Real Life Applications
4-7 The Sine and Cosine Law
4-8 Solving Problems using Acute Triangles