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A “Novel” approach to polynomial division…

During the last few weeks I have been working with some Year 11 students from a local private school that has a fairly good reputation. These students have been working, in particular, on cubic and quartic functions, including the use of polynomial division. The students in question are taught by two different teachers at the school, including their school’s Head of Mathematics, a highly experienced and long serving teacher by all accounts. All of these students are certainly above average students, but like most of their peers, have had little exposure to the long division method in primary school, mostly due to the prevalence of handheld calculators.

Whilst working with these students, each of them has independently demonstrated to me a short-cut method taught to them at school for polynomial division. This short-cut method is well known and quite useful when applied correctly. Unfortunately, when originally demonstrated to the students (judging by each of their theory books), their respective teachers each made the same monumental error and taught the students a technique that would work only in certain circumstances. The following are some of the examples given to these students in class:

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Exam Advice

Exams are a fact of life and there is nothing you can do to avoid them. The following are some of the things you can do to make them easier on you:

  1. Prepare summary notes as you go
  2. For those students, particularly in VCE mathematics, who are allowed to take in notes to an exam, preparing them early is the biggest key to exam success. As you finish an exercise in a textbook or finish a topic, you should immediately summarise what you have learned. This will make it easier to do your pre-exam revision.

  3. Use your summary notes to do revision exercises
  4. A key test of whether or not your summary notes are complete is in attempting revision exercises. If you are unable to complete a question using your summary notes it means that they are incomplete. You should therefore go back and update your summary notes to cover the missing material.

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