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Understanding Year 10 Maths Advanced: Australian Curriculum Edition

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This book has been written to broadly follow both the Australian and the NSW Year 10 Mathematics Curriculum (5.3). It is intended to be a very thorough and concise summary of most major core topics which are taught and covered in Year 10 Advanced classes throughout Australia.

Please keep in mind that this curriculum is based on the work covered in 2 years of high school (Year 9 and Year 10 ) which implies that different schools may teach the topics in a different order throughout the two year period. Therefore if you cannot find a particular topic summary in this Year 10 book (for example: measurement), then you will almost certainly find it explained in the Understanding Year 9 book.

This book will prove to be very beneficial to students, teachers and coaches in all states. It has primarily been developed to be used as an additional learning aid to the conventional school text book, but it could also be used as a class text on its own account.

Features of Benefits

  1. Firstly, the book has been split up into the 15 MAJOR IMPORTANT TOPICS.
  2. Each of these major topics has been broken down into a number of simpler ideas and rules, thus saving educators and students valuable TIME in research.
  3. Most pages explain only one idea or rule, thus giving students CLARITY.
  4. Each concept is thoroughly, but simply, explained for UNDERSTANDING.
  5. Each formula, rule or set of steps is highlighted in larger print for ease of MEMORISING.
  6. Each formula and page contains at least one fully worked example. This not only reinforces understanding, but also shows the student how to APPLY each formula to typical questions.
  7. At the end of each chapter, there are usually at least 4 comprehensive graded exercises for PRACTICE, which cover all the ideas in the topic. If a student is not sure how to do a particular problem, all they need to do is turn back to the page number shown in order to find a very similar example.
  8. In addition, the text presentation is well spaced out, in order to make the subject matter more APPEALING and USER FRIENDLY to this age group.
  9. The opening contents page of each chapter contains CURRICULUM REFERENCES which will prove helpful and beneficial to teachers.
  10. At the end of each chapter there is a CONDENSED SUMMARY of the complete chapter. These chapter summaries give all the formulas and rules that students must memorise before sitting for a test or exam.

The exercises in the book are carefully graded into 5 levels to provide confidence and success to lower ability students, while at the same time offering more difficult levels to extend students who have a good grasp of the basic concepts:

These questions given in level 1 (sometimes also in level 2) are intended to build up confidence and ensure that all the basic concepts have been understood. Most of the questions are almost identical to the examples given throughout the chapter – except with the numbers changed. If the student does have difficulty, then he/she can easily refer back to a similar example on the page number shown in the margin.

The questions in Level 2 are of average difficulty level, and will give all students (average & gifted) a good opportunity to practise and consolidate the ideas and rules given throughout most of the chapter. Once again, if a student does have difficulty with a particular problem, then he/she can quickly refer back to a similar example on the page number shown. All students should try to complete and understand the questions in the first 2 levels.

The questions in this level are usually more difficult than the ones in level 1 and 2 and some of the more difficult ideas in the topic are tested. Reference page numbers have NOT been included in the margin, in order to make students who reach this level more skilful in researching through the chapter for their own information. Level 3 should be done by more capable students, or those students who have found earlier levels straightforward.

This more difficult level has been included to challenge those students who are more gifted at Maths. Usually the questions are more sentence and problem oriented, and therefore they involve more reading and comprehension skills. It is unlikely that any of the questions in this level can be done mentally, because several different ideas, rules or steps are usually required. Because ‘problem solving’ is becoming very important in examinations, we have tried to include at least 1 exercise at the end of each chapter.


  • Further Algebra and Factorisation [Number & Algebra strand]
  • Simultaneous Equations [Number & Algebra strand]
  • Further Financial Mathematics [Number & Algebra strand]
  • Quadratic Equation [Number & Algebra strand]
  • Graphs of Parabolas, Curves and Regions [Number & Algebra strand]
  • Surface Area and Volume [Measurement & Geometry strand]
  • Simultaneous Equations and Graphs [Number & Algebra strand]
  • Statistics [Statistics & Probability strand]
  • Probability [Statistics & Probability strand]
  • Similarity [Measurement & Geometry strand]
  • Further Trigonometry [Measurement & Geometry strand]
  • Circle Geometry [Measurement & Geometry strand]
  • Logarithms [Number & Algebra strand]
  • Polynomials [Number & Algebra strand]
  • Functions [Number & Algebra strand]
  • Solutions to graded exercises (worked solutions to the more difficult exercises)
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