We Love Maths!

Love Maths?

Did you know?

  • 111,111,111 multiplied by 111,111,111 gives 12,345,678,987,654,321
  • 2520 is the smallest number that can be exactly divided by all the number 1 to 10

Sodoku helps with your maths?

Article on benefits of Sodoku for strengthening core logic skills needed to solve Maths problems… Give your struggling student a small challenge in the holidays!


Finish this simple Soduku – rules: the consecutive numbers 1 to 4(a set) must fill the remaining empty boxes BUT there can only be 1 set (in any order) per row(s), column(s) or box(es)

Sites to visit if you want to practice over the holidays:

Primary and up to yr 11:




For Year 12:


http://www.harderhscmaths.com/ (videos to watch of harder maths being completed)

Do boys like maths more than girls?

Article about Maths and gender?


Probability Pandemonium

Crazy Kids:

Imagine that you know a family has 2 children (that aren’t twins). Later, you discover that one of the children is a girl, what then is the probability that the other one is a girl?

Hint: it’s not 1/2!

Answer see below…


Devious Doors:

There was a games show which included a section in which you could win a car by correctly selecting which door it was behind. It went like this:

  1. The host would ask you to pick and stand in front of 1 out of 3 closed doors, 1 of which had a car behind it, the other 2 with nothing
  2. The host would then reveal a door that you hadn’t chosen that had nothing behind it, leaving two unopened doors, one of which you were still standing in front of.
  3. The host would then ask, would you like to stick with the door you’re currently with, or would you like to switch to the other remaining unopened door?

If you wish to maximise your probability of winning the car, what should you do?

Answer see below…



Solution Crazy Kids:

You have to consider the possible combinations of the children’s genders and how the information came to you.

When you knew that they had 2 children there were 4 possibilities:

Older:                   Boy        Boy        Girl         Girl

Younger:              Boy        Girl         Boy        Girl

When you discover that one is a girl it eliminates the possibility that they’re both boys, it also leaves only 1 of the remaining 3 that has the second child as a girl.

Therefore the answer is 1/3!

Solution Devious Doors:

You should switch!

When you first chose your door there was a 2/3 chance that it contained nothing. Despite the host eliminating one of the nothing outcomes it is still more likely that you are currently standing in front of a nothing outcome because of when you made your selection.

Therefore since it’s more likely that you have nothing and the other nothing option is gone you have a 2/3 chance of winning if you switch to the remaining door! Deal or No Deal works on the same concept to a much larger scale.


Mathematics (formerly 2 Unit Mathematics)

The current calculus-based mathematics courses will remain unchanged in the introductory years of the New Higher School Certificate. During this time the course content and internal assessment arrangements of 2 Unit Mathematics , 3 Unit Mathematics and 4 Unit Mathematics will be maintained. However, under the new HSC structure, the courses will be called Mathematics, Mathematics Extension 1 and Mathematics Extension 2, respectively.

The HSC results of students studying these Mathematics courses will be reported using the standards-referencing procedures in place for all Board developed courses under the new structure.

Following are the outcomes developed for the preliminary course for Mathematics. The outcomes have been derived from the content of the courses, and together with the content, determine the breadth and depth of study to be undertaken by students.

Common problems that students encounter in the HSC Mathematics syllabus revolve around Applications of Calculus to the Physical World, Logarithmic and Exponential Functions, Max and Min Problems, Trigonometry and Applications of Geometrical Properties. If your performance is suffering in these or any of the other topics in HSC Mathematics, our professional tutors can help you rectify your problems and fine-tune your answers to maximise your marks. HSC and Primary tutoring in Maths is available at Smart Moves One-on-One Tutoring. For many students, mathematics proves to be a challenging and rewarding experience.

Objectives Preliminary Outcomes
Students will develop:  A student:
appreciation of the scope, usefulness, beauty and elegance of maths
  • demonstrates confidence in using maths to obtain realistic solutions to problems
the ability to reason in a broad range of math contexts
  • provides reasoning to support conclusions which are appropriate to the context
skills in applying math techniques to the solution of practical problems
  • performs routine arithmetic and algebraic manipulation involving surds, simple rational expressions and trigonometric identities
  • chooses and applies appropriate arithmetic, algebraic, graphical, trigonometric and geometric techniques
understanding of the key concepts of calculus and the ability to differentiate and integrate a range of functions
  • understands the concept of a function and the relationship between a function and its graph
  • relates the derivative of a function to the slope of its graph
  • determines the derivative of a function through routine application of the rules of differentiation
the ability to interpret and communicate maths in a variety of forms
  • understands and uses the language and notation of calculus

Can you answer the following question from the Board of Studies 2006 HSC Mathematics Exam?


maths q 2k6 hsc

A HSC Smart Moves tutor can provide valuable help in any of the following Maths Topic Areas:

• Basic Arithmetic and Algebra
• Plane Geometry
• Probability
• Real Functions
• Trigonometry
• Linear Functions and lines
• Series and Applications
• The Tangent to a Curve and the Derivative of a Function
• The Quadratic Polynomial and the Parabola
• Geometrical Applications of Differentiation
• Integration
• Logarithmic and Exponential Functions
• Applications of Calculus to the Physical World

 If you have any questions or queries about our HSC Maths tutors at Smart Moves One-on-One Tutoring, please do not hesitate to contact us. We welcome all enquiries!

Top 10 Exam Tips

Generally speaking, the top ten things you should keep in mind as you do your exam:

  • Exam tip #1: Make it easy for the marker.
  • Exam tip #2: Use a black pen.
  • Exam tip #3: Write on one side of the page only.
  • Exam tip #4: Try to avoid writing extra pieces in margins that are linked by asterisks, arrows, etc.
  • Exam tip #5: Read and follow all key instructions. For example, if you are asked to provide a title to a response, than make sure you do.
  • Exam tip #6: Write in the correct genre/form and sustain it throughout. For example, if you are asked to write a speech, make sure it is clearly a speech from beginning to end. If you are asked to write a letter, make sure it has a salutation and address at the start, reads like a letter throughout the response and has a farewell or something similar at the end.
  • Exam tip #7: Try, as much as you can, to write clearly and legibly. Perhaps leave a line between paragraphs. Don’t be afraid of white space – it makes reading easier.
  • Exam tip #8: Practice the key conventions that demonstrate mastery of English: the correct use of apostrophe, the correct title conventions (either underlining or using inverted commas), the full use of a text’s title at least once and the correct spelling of key character names and composer’s names (at least).
  • Exam tip #9: If you have time during the exam, quickly proofread your work and check the pages are in the right order and that as many mistakes as you can find are corrected. (Examiners understand you are under pressure and that this is a first draft but demonstration of control of the key conventions is the mark of a more sophisticated response).
  • Exam tip #10: You may also be required to write a more personal response, which includes your ability to demonstrate you have reflected personally on the effect of studying a particular module or area of study. Think through how to do this.

This exam advice is general in nature and may need to be adapted for different subjects.

General Mathematics

Finding it difficult to gain real motivation to study for HSC General Mathematics? Formulas don’t make sense? Or plainly you just can’t see the point? Think about it – General Mathematics, Topic 1: Financial Mathematics. Face it, it doesn’t matter who you are – any one and everyone is affected by the world of money – Credit and Borrowing; Annuities and Loans (FM4 & FM5 sub-topics of the HSC Financial Mathematics course). For example, what about that car you want? Mum and Dad won’t get it for you, so you decide to look into loans, but, are unfamiliar just what a loan does and is. You’ll learn all about this through the HSC General Mathematics course. This is the true definer of the General Mathematics HSC course. It provides students with a firm understanding of the applicability and necessity of general mathematics in the real world.

The opportunities for creative thinking, communication and contextualised problem-solving within the Preliminary General Mathematics course, the HSC General Mathematics 2 course and the HSC General Mathematics 1 course assist students in finding solutions for the broad range of problems encountered in life beyond secondary schooling. The purpose of the courses is to provide an appropriate mathematical background for students who wish to enter occupations that require the use of a variety of general mathematical and statistical techniques. As well as introducing some new mathematical content, the various Focus Studies within the courses give students the opportunity to apply, and develop further, the knowledge, skills and understanding initially developed in the various Strands: Financial Mathematics, Data and Statistics, Measurement, Probability, and Algebra and Modelling. Through the Focus Studies, students develop the capacity to integrate their knowledge, skills and understanding across the Strands in contemporary contexts chosen for their ongoing relevance to the students’ everyday lives and likely vocational pathways.

The HSC General Mathematics course covers five major topics

• Financial Mathematics

• Data Analysis

• Measurement

• Probability

• Algebraic Modeling

What is important is that every student has the best opportunity to establish a firm foundation of the General Mathematics language, skills, and ideas for each of the five topics covered in General Mathematics. At Smart Moves our HSC Tutors provide personalised teaching, so that even you to can figure out the point to Algebra. Let our personable HSC Tutors guide you one-on-one through the HSC General Mathematics course – because we all need a bit of motivation.

Extension 1 (E1 Maths) or Extension 2 (E2 Maths)

Extension 1 Maths – The Must Haves

When one considers to journey through the domain of extension one maths, three key skills are needed in order to be successful. Firstly a logical and creative thought process of thinking must be developed. Secondly a speed and accuracy in problem solving, and thirdly an interest and initiative in independent work.


Developing Logical and Creative Thinking

In this high level of maths, there will always be numerous methods in obtaining solutions to problems. However, selecting the most efficient and effective method will optimise exam time and consequently maximise marks. Developing a creative form of thinking will allow you to discover several approaches to the problem and a choice in the specific scheme for the required problem. In taking the steps to find the solution a logical and systematic form of thinking is also needed to ensure the accuracy of the solution. This is where Smart Moves HSC tutoring comes in. With our specialised tutors, both creative and logical forms of thinking are fostered and students realise hey, these aren’t so difficult after all.


Speed and Accuracy

No doubt we have all heard the saying “practice makes perfect”. However in maths, there’s a catch to this statement. Selecting the correct problems and practising them is the key to achieving speed and accuracy. If the selection of the problems are done incorrectly and say the problems are too easy, the student wastes their time in setting themselves up for questions that will probably not show in their exams and assessments. Alternatively if the questions are too difficult, there is also a low chance of them occurring in the assessments. All Smart Moves HSC tutors have an in depth knowledge of the syllabus and are able to select problems which maximise the student’s potential in speed and accuracy just right to cater for the student and their learning. “Don’t work hard, work efficient”- Homer Simpson


Interest and Initiative

Lets face it, its difficult to do any subject without interest in it. The key to maintaining interest is motivation. With motivational techniques a student is able to study longer and more independently. One such technique is simply doing your maths while listening to the radio. Weird as it sounds it works! Hypothetical. Imagine yourself driving 3 or 4 hours in a car alone to the sound of the radio. Contrast this with driving 3 or 4 hours in dead silence only listening to the sound of other cars. Which would you enjoy? Smart Moves HSC tutors have knowledge of other motivational techniques that can enhance concentration and in turn foster interest and independent learning.

Leonard Koh


Extension 2 Maths

Are you finding yourself struggling with intense integration, vicious volumes, problematic polynomials, complicated conics, messy mechanics, graphs and complex numbers?

Extension 2 Maths is a particularly hard and challenging subject. It is therefore necessary that students receive as much help and support as possible, so that they can find this subject both enjoyable and rewarding!

The following topics are studied in the current HSC Extension 2 syllabus

• Complex Numbers
• Conics
• Integration
• Volumes
• Graphs
• Mechanics
• Polynomials
• Harder 3U

Our HSC Extension Maths tutoring team can help in all of the above topics, to ensure maximum results. We use past HSC Extension 2 Maths exam papers and worked solutions to help guide our students to success. At Smart Moves, there is a relaxed and fun environment to aid the learning experience. If you have any queries, contact Smart Moves coaching. We look forward to hearing from you.