# Resources: Mathematics and Science

## Mathematics, Physics, and Chemistry

Many textbooks and internet sites are available to explain technical matters. However, what can also make a difference in tests and exams are things like:

- understanding how to
**interpret a problem statement**; - understanding how to
**check your answers**.

The first point is mainly improved by practising (learning by experience, recognising patterns). Some thoughts on the latter point are compiled in the PDF file linked above.

As discussed in the "*Checking your answers in mathematics and physics*" document, taking care to ensure consistency with **dimensions** (*e.g*. length, mass, time) and **units** (*e.g*. cm, kg, min) is extremely important to avoid mistakes, and indeed to catch accidental missteps. Therefore knowledge of units and ability to perform unit conversions are vital. The following document is focussed on metric / SI units, with brief coverage of imperial lengths; however, the basic methodology can be used for any **unit conversion**.

## Mathematics: fundamentals

In lower years of school a 'fluency' in mental arithmetic is required. Even in later years strong competency and speed in mental arithmetic is highly beneficial, as it means that the student's attention and time can be focused on the more challenging concepts, rather than the basic arithmetic.

## Mathematics: Year 11 & Year 12

There are several options that students can choose for studying mathematics in Year 11 and Year 12 in N.S.W.. The official source of detailed information on these options is the N.S.W. Education Standards Authority, supported by resources provided by your local high school.

For your convenience, a summary of the **syllabus for each mathematics offering** at Year 11 and Year 12 level in N.S.W. has been prepared, including information on options being introduced in 2018 and 2019.

Tips to sound like you know what you're talking about:

- The word "locus" sounds like "focus", with only the initial consonant changing. LOW-kus (/ˈləʊkəs/), not LOCK-us. The plural is "loci" (analogous to "foci"), pronounced LOW-kai (/ˈləʊkaɪ/).
- To "derive" means to obtain (We derived the following proof by applying Pythagoras's Theorem"); "derivation" is the process or result of deriving something.
- To "differentiate" means to obtain the so-called gradient function (an expression representing the gradient of the original function); "differentiation" is the process of differentiating a function; a "derivative" is the result of performing differentiation.

## Mathematics: Year 11

Exposition of various methods to factorise quadratic polynomials:

Methods for **factorising quadratics**.

Computation of trigonometric functions of angles in each of the four quadrants:

Trigonometric functions of **angles in each quadrant**.

Below is a short multiple-choice exam intended to test students' knowledge of material associated with the Year 11 ('*Preliminary*') "2-unit" mathematics syllabus.

Year 11 2-Unit Mathematics **review test**.

Section I is easiest, Section II is somewhat harder, and Section III is the most challenging.

Topics and some questions are adapted from *Maths in Focus. Mathematics Preliminary Course* (Margaret Grove, 2009, 2nd Edition).

Description of the problems that can arise when squaring (both sides of) an equation:

## Mathematics: Year 12 (HSC)

Exposition of four methods to find the overall outcome with the highest probability in problems involving binomial probability: