# Year 11 – 11: Coordinate Geometry – South Australia

### SA Year 11 – 11: Coordinate Geometry

# | TOPIC | TITLE | |
---|---|---|---|

1 | Study Plan | Study plan – Year 11 – 11: Coordinate Geometry | |

Objective: On completion of the course formative assessment a tailored study plan is created identifying the lessons requiring revision. | |||

2 | Lines and angles | Informal coordinate system | |

Objective: On completion of the lesson the student will be able to use an informal coordinate system to specify location, and locate coordinate points on grid paper. | |||

3 | Coordinate Geometry-the plane | Distance formula. | |

Objective: On completion of the lesson the student will be able to calculate the distance between any two points on the number plane and interpret the results. | |||

4 | Coordinate Geometry-midpoint, slope | Mid-point formula | |

Objective: On completion of the lesson the student will be able to understand the mid point formula and use it practically. | |||

5 | Coordinate Geometry-gradient | Gradient | |

Objective: On completion of the lesson the student will be able to calculate the gradient of a line given its inclination, or angle to the positive direction of the x-axis; or its rise and run. | |||

6 | Coordinate Geometry-gradient | Gradient formula. | |

Objective: On completion of the lesson the student will be able to calculate the gradient of a line given any two points on the line and also be capable of checking whether 3 or more points lie on the same line and what an unknown point will make to parallel lines. | |||

7 | Coordinate Geometry-straight line | The straight line. | |

Objective: On completion of the lesson the student will be able to draw a line which is parallel to either axis and comment on its gradient, where that gradient exists. | |||

8 | Coordinate Geometry-slope, etc. | Lines through the origin. | |

Objective: On completion of the lesson the student will be able to draw a line which passes through the origin of the form y=mx and comment on its gradient compared to the gradients of other lines through the origin and use the information to solve problems. | |||

9 | Coordinate Geometry-equation of line | General form of a line and the x and y Intercepts. | |

Objective: On completion of the lesson the student will be able to change the equation of a straight line from the form, written as y=mx+c, into the general form and vice versa. | |||

10 | Coordinate Geometry-intercept | Slope intercept form of a line. | |

Objective: On completion of the lesson the student will be able to find the slope and intercept given the equation and given the slope and intercept, derive the equation. | |||

11 | Coordinate Geometry-point slope | Point slope form of a line | |

Objective: On completion of the lesson the student will understand how to derive the equation of a straight line given the gradient and a point on the line. | |||

12 | Graphing-polynomials | General equation of a circle: determine and graph the equation | |

Objective: On completion of the lesson the student will be able to solve these types of problems. Working with circles will also help the student in the topic of circle geometry, which tests the student’s skills in logic and reasoning. | |||

13 | Conic sections | Circles | |

Objective: On completion of the lesson the student will identify the radius of a circle given in standard form. | |||

14 | Rect.hyperbola | The rectangular hyperbola. | |

Objective: On completion of the lesson the student will be able to analyse and graph a rectangular hyperbola and describe its important features. | |||

15 | Functions | Definition, domain and range | |

Objective: On completion of this lesson the student will be able to select functions from relations by referring to the domain and range. | |||

16 | Conic sections | Hyperbola | |

Objective: On completion of the lesson the student will identify focus, vertices, axes and asymptotes of a hyperbola. | |||

17 | Linear systems | Optimal solutions (Stage 2) – Vectors | |

Objective: On completion of the lesson the student will understand the process of linear programming to find optimal solutions. | |||

18 | Geometry-locus | Constructions and loci – single condition | |

Objective: On completion of the lesson the student will understand the term locus and describe several using a single condition. | |||

19 | Geometry-locus | Constructions and loci – multiple conditions | |

Objective: On completion of the lesson the student will describe a locus that satisfies multiple conditions on a number plane. | |||

20 | Co-ordinate Geometry-Two point formula | Two point formula: equation of a line which joins a pair of points. | |

Objective: On completion of the lesson the student will be able to calculate the equation of a line given any two named points on the line. | |||

21 | Co-ordinate Geometry-Intercept form | Intercept form of a straight line: find the equation when given x and y | |

Objective: On completion of the lesson the student will have an effective and efficient method for calculating the equation of a straight line. | |||

22 | Co-ordinate Geometry-Parallel lines equations | Parallel lines: identify equation of a line parallel to another | |

Objective: On completion of the lesson the student will be able to decide if two or more lines are parallel or not and to solve problems involving parallel lines. | |||

23 | Co-ordinate Geometry-Perpendicular lines | Perpendicular lines. | |

Objective: On completion of the lesson the student will be able to derive the equation of a line, given that it is perpendicular to another stated line. | |||

24 | Co-ordinate Geometry-Inequalities | Inequalities on the number plane. | |

Objective: On completion of the lesson the student will be able to derive the expression for an inequality given its graph. The student will also be able to solve some problems using inequalities. | |||

25 | Co-ordinate Geometry-Theorems | Perpendicular distance | |

Objective: On completion of the lesson the student will be able to derive the formula to calculate the distance between a given point and a given line. The student will also be able to calculate the distance between parallel lines. | |||

26 | Co-ordinate Geometry-Theorems | Line through intersection of two given lines | |

Objective: On completion of the lesson the student will be able to calculate the equation of a line which goes through the intersection of two given lines and also through another named point or satisfies some other specified condition. | |||

27 | Co-ordinate Geometry-Theorems | Internal and external division of an interval | |

Objective: On completion of the lesson the student will be able to divide an interval according to a given ratio and to calculate what point divides an interval in a given ratio for both internal and external divisions. | |||

28 | Exam | Exam – Year 11 – 11: Coordinate Geometry | |

Objective: Exam |