Unit 3 - Holiday Homework and Course Outline

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Edit   Delete - Last Modified By: rmc at 24/11/2014 8:51:26 AM

Familiarity with sequence and series notation and related simple applications, the use of sine and cosine
rules in non-right-angled triangles and the following mathematics is assumed:
• the solution of triangles in two-dimensional situations;
• the sum of the interior angles of a triangle is 180°;
• the sum of the exterior angles of a convex polygon is 360°;
• corresponding angles of lines cut by a transversal are equal if, and only if, the lines are parallel;
• alternate angles of lines cut by a transversal are equal if, and only if, the lines are parallel;
• opposite angles of a parallelogram are equal;
• opposite sides of a parallelogram are equal in length;
• the base angles of an isosceles triangle are equal;
• the line joining the vertex to the midpoint of the base of an isosceles triangle is perpendicular to
the base;
• the perpendicular bisector of the base of an isosceles triangle passes through the opposite vertex;
• the angle subtended by an arc at the centre of a circle is twice the angle subtended by the same arc
at the circumference;
• the angle in a semicircle is a right angle;
• angles in the same segment of a circle are equal;
• the sum of the opposite angles of a cyclic quadrilateral is 180°;
• an exterior angle of a cyclic quadrilateral and the interior opposite angle are equal;
• the two tangents to a circle from an exterior point are equal in length;
• a tangent to a circle is perpendicular to the radius to the point of contact;
• the angle between a tangent to a circle and a chord through the point of contact is equal to the angle
in the alternate segment.


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Cyclic Quadrilaterals

Arcs

Isoceles Triangles

Parallel Lines


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The following websites provide some excellent interactive tools that you can use throughout the year to help you visualise and explore mathematical concepts.

Calculus Applets

Analyze Math

IntMath

Wolfram Alpha


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As part of your holiday homework you will need to ensure that you are familiar with all the content listed in the "What do you already know" section. You should familiarise yourself with the course outline too.

Additionally you are to read and complete all questions for the following excercises as homework:

  • 1.2 An introduction to the Modulus Function
  • 1.3 Sketching graphs of Reciprocal Graphs
  • 1.4 Sketching graphs of Rational Functions
  • 1.5 Sketching graphs of y = f(|x|) and y = |f(x)| from y = f(x)
  • 1.6 Circles, Ellipses and Hyperbolas

Those wanting to do well should also to read/complete up to (but not including the review) in Chapter 2: Trigonometry.

We will be using the Flip Model for learning this subject in 2016. You will need to pre-read the information for each topic before coming to class so that a focus can be made on answering your questions or addressing problems you have come across.

On the topic of Flip Learning, I have made a push with Edrolo to support the Specialist Maths course. They are cuurently investigating if it is financially viable for them to do so. Should Edrolo publish a course for Specialist Maths it is my intention to work with it as a core part of our classes.


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It is highly recommended that you take notes that you find useful (beyond those provided in the chapter summary) as you will be able to use a bound reference book in a few of your SACs and one of your exams. It is important to practice writing clear and concise notes as you will have limited time for your Exam at the end of your course and you will want to minimise time wasted huntng for what you need. The VCAA guidelines are as follows.

Mathematics examinations: use of bound references

Students are permitted to take a bound reference into designated Mathematics examinations. This resource is intended to provide students with access to mathematics-related reference material that may be of assistance during the examination. A suitably qualified member of the school teaching staff is responsible for checking that reference materials comply with specifications as students enter the examination room for Mathematics examinations where these items are permitted. The following table summarises the examinations into which the bound reference may be taken.

StudyExamination 1Examination 2
Further Mathematics Bound reference as described Bound reference as described
Mathematical Methods (CAS) None Bound reference as described
Specialist Mathematics None Bound reference as described

Specifications for bound reference

  • The bound reference must be in book format of A4 size or smaller when closed.
  • The number of pages is not specified.
  • Pages must be permanently bound and securely attached to the spine.
  • There must be a single horizontal or vertical spine.
  • The bound reference may be:
  • a textbook
  • a securely bound lecture pad
  • a permanently bound student-constructed set of notes without fold-outs
  • an exercise book.
  • The form of binding is not specified but it must be secure, and pages must not be readily detachable or designed to be removed. Binding can include cloth, glue, staple, spiral or comb binding.

Students are allowed to:

  • annotate the material
  • design their own written index
  • fold pages
  • cut page corners
  • colour code pages
  • insert dividers into their own sets of notes
  • firmly attach (for example, by glue, adhesive tape or staples) additional material to pages in the bound reference.

Bound references may be consulted during reading time and throughout the examination.

Bound references must not include:

  • pages or parts of pages that can be detached from the bound reference during the examination
  • fold-outs, maps or brochure-style components
  • removable tabs, post-it notes or other pages or material designed to be detached
  • forms of collation/binding that are designed to be non-permanent and the content modified by insertion including:
  • ring-binder folders
  • plastic A4 sleeves (permanent or removable) from which pages may be removed
  • manila and similar folders with clip, clamp, slide and metal prong binding of loose-leaf material.

If any page or part of a page is detached from the rest of the bound reference, the page will be removed by the supervisor for the duration of the examination and the incident will be reported as a potential breach of rules.