# Extension 2 HSC (Year 12) Mathematics – New South Wales (NSW)

### NSW Extension 2 HSC (Year 12) Mathematics

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

1 | Study Plan | Study plan – Year 12 – Stage 6 – HSC Mathematics Extension 2 | |

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

2 | Number theory – sets | Number sets and their members | |

Objective: On completion of the lesson the student will understand the notation used with sets and the subsets of the real number system. | |||

3 | Logarithms-Complex numbers | Imaginary numbers and standard form | |

Objective: On completion of the lesson the student will use the a+bi form of complex numbers for addition and subtraction. | |||

4 | Logarithms-Complex numbers | Complex numbers – multiplication and division | |

Objective: On completion of the lesson the student will use the a+bi form of complex numbers for multiplication and division. | |||

5 | Logarithms-Complex numbers | Plotting complex number and graphical representation | |

Objective: On completion of the lesson the student will use the argand diagram to assist in the addition and subtraction of complex numbers. | |||

6 | Logarithms-Complex numbers | Absolute value | |

Objective: On completion of the lesson the student will use the absolute value or modulus of complex numbers | |||

7 | Logarithms-Complex numbers | Trigonometric form of a complex number | |

Objective: On completion of the lesson the student will write complex numbers in trigonometric or polar form. This may also be known as mod-ard form. | |||

8 | Logarithms-Complex numbers | Multiplication and division of complex numbers in trig form (Stage 2) | |

Objective: On completion of the lesson the student will use the trig form of complex numbers for multiplication and division. | |||

9 | Logarithms-Complex numbers | DeMoivre’s theorem (Stage 2) | |

Objective: On completion of the lesson the student will use DeMoivre’s theorem to find powers of complex numbers in trig form. | |||

10 | Logarithms-Complex numbers | The nth root of real and complex numbers (Stage 2) | |

Objective: On completion of the lesson the student will use DeMoivre’s theorem to find roots of complex numbers in trig form. | |||

11 | Logarithms-Complex numbers | Fundamental theorem of algebra (Stage 2) | |

Objective: On completion of the lesson the student will recognise and use the fundamental theorem of algebra to find factors for polynomials with real coefficients over the complex number field. | |||

12 | Polar coordinates | Plotting polar coordinates and converting polar to rectangular | |

Objective: On completion of the lesson the student will understand the polar coordinate system and relate this to the rectangular coordinate system. | |||

13 | Polar coordinates | Converting rectangular coordinates to polar form | |

Objective: On completion of the lesson the student will understand the polar coordinate system and report these from rectangular coordinates. | |||

14 | Polar coordinates | Write and graph points in polar form with negative vectors (Stage 2) | |

Objective: On completion of the lesson the student will be using negative angles and negative vector lengths. | |||

15 | Conic sections | Introduction to conic sections and their general equation | |

Objective: On completion of the lesson the student will identify the conic section from the coefficients of the equation. | |||

16 | Conic sections | Ellipses | |

Objective: On completion of the lesson the student will identify focus, vertices and axes of an ellipse. | |||

17 | Conic sections | Hyperbola | |

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

18 | Functions | Polynomial addition etc in combining and simplifying functions (Stage 2) | |

Objective: On completion of the lesson the student will have multiple techniques to understand and construct graphs using algebra. | |||

19 | Functions | Parametric functions (Stage 2) | |

Objective: On completion of the lesson the student will understand some standard parametric forms using trigonometric identities, appreciate the beauty of the the graphs that can be generated and an application to projectile motion. | |||

20 | Exam | Exam – Year 12 – Stage 6 – HSC Mathematics Extension 2 | |

Objective: Exam |