# Principles Of Mathematics – Grade 10

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.

From: $500.00

### Overall Curriculum Expectations

**Quadratic Relations of the Form y = ax2 + bx + c**

By the end of this course the student will:

- Determine the basic properties of quadratic relations.
- Relate transformations of the graph of y = x2 to the algebraic representation y = a (x – h)2 + k.
- Solve quadratic equations and interpret the solutions with respect to the corresponding relations.
- Solve problems involving quadratic relations.

**Analytic Geometry**

By the end of this course the student will:

- Model and solve problems involving the intersection of two straight lines.
- Solve problems using analytic geometry involving properties of lines and lines segments.
- Verify geometric properties of triangles and quadrilaterals, using analytic geometry.

**Trigonometry**

By the end of this course the student will:

- Use their knowledge of ratio and proportion to investigate similar triangles and solve problems related to similarity.
- Solve problems involving right triangles, using the primary trigonometric ratios and the Pythagorean theorem.
- Solve problems involving acute triangles, using the sine law and the cosine law.

### Course Details

Course Code | MPM2D |

Course Type | Academic |

Format | Online School Course |

Prerequisite | MPM1D or MFM1P |

Tuition Fee | 650 – 1300 |

Department | Mathematics |

Course Title | Principles of Mathematics |

Grade | Grade 10 |

Credit Value | 1.0 |

### Outline of Course Content

Unit |
Title |
Time |

1 | Linear Systems | 13 hours |

2 | Analytic Geometry | 11 hours |

3 | Geometric Properties | 14 hours |

4 | Quadratic Relations | 15 hours |

5 | Quadratic Expressions | 15 hours |

6 | Quadratic Equations | 15 hours |

7 | Trigonometry of Right Triangles | 13 hours |

8 | Trigonometry of Acute Triangles | 12 hours |

Final Examination |
2 hours | |

Total |
110 hours |

### Course Details

Course Code | MPM2D |

Course Type | Academic |

Format | Online School Course |

Prerequisite | MPM1D or MFM1P |

Tuition Fee | 650 – 1300 |

Department | Mathematics |

Course Title | Principles of Mathematics |

Grade | Grade 10 |

Credit Value | 1.0 |

### Overall Curriculum Expectations

**Quadratic Relations of the Form y = ax2 + bx + c**

By the end of this course the student will:

- Determine the basic properties of quadratic relations.
- Relate transformations of the graph of y = x2 to the algebraic representation y = a (x – h)2 + k.
- Solve quadratic equations and interpret the solutions with respect to the corresponding relations.
- Solve problems involving quadratic relations.

**Analytic Geometry**

By the end of this course the student will:

- Model and solve problems involving the intersection of two straight lines.
- Solve problems using analytic geometry involving properties of lines and lines segments.
- Verify geometric properties of triangles and quadrilaterals, using analytic geometry.

**Trigonometry**

By the end of this course the student will:

- Use their knowledge of ratio and proportion to investigate similar triangles and solve problems related to similarity.
- Solve problems involving right triangles, using the primary trigonometric ratios and the Pythagorean theorem.
- Solve problems involving acute triangles, using the sine law and the cosine law.

### Outline of Course Content

Unit |
Title |
Time |

1 | Linear Systems | 13 hours |

2 | Analytic Geometry | 11 hours |

3 | Geometric Properties | 14 hours |

4 | Quadratic Relations | 15 hours |

5 | Quadratic Expressions | 15 hours |

6 | Quadratic Equations | 15 hours |

7 | Trigonometry of Right Triangles | 13 hours |

8 | Trigonometry of Acute Triangles | 12 hours |

Final Examination |
2 hours | |

Total |
110 hours |