## 数学篇Online Study Resource - Math

# MATHS RESOURCES

All resources have worked examples and there are exercises together with worked solutions for you to practise with.

### CONNECT: CALCULATIONS – ORDER OF OPERATIONS IN MATHEMATICS

Are you confused by symbols such as +, –, x and ÷? (Do brackets have you worried?) In this resource you are taken through how the conventions of mathematics organise the order in which operations are carried out.

Order of Operations in Mathematics [PDF 164kb]

### CONNECT: DIRECTED NUMBERS – SORTING THE POSITIVES FROM THE NEGATIVES

If you are not sure about how to calculate with both positive and negative numbers then have a look at this resource. Firstly, both positive and negative numbers are defined and then how to calculate with positive and negative numbers using money as an example is demonstrated.

Directed Numbers Positives and Negatives [PDF 106kb]

### CONNECT: CALCULATORS – GETTING TO KNOW YOUR SCIENTIFIC CALCULATOR

You might be worried about using a new calculator. You will find an introduction to using a Scientific Calculator in this resource. The information is based on the Casio fx82es or 100AU, and a range of operations are demonstrated, from clearing and correcting entry errors, through calculating with fractions, to using Scientific Notation.

Calculators [PDF 195kb]

### CONNECT: DECIMALS – OPERATIONS: + AND –

In this, the first of 2 resources on decimals, the importance of understanding the Decimal or Base 10 system of numbers is emphasized as this system is used as the basis for addition and subtraction using decimals.

Decimals 1 Plus Minus [PDF 74kb]

### CONNECT: DECIMALS – OPERATIONS: X AND ÷

This is the second of 2 resources on decimals. Decimals are described by their use in the Base 10 (or Decimal) system. The methods of multiplying and dividing using decimals are explained by this use, following an explanation of multiplying and dividing by 10, 100, 1 000 and so on.

Decimals 2 Times Divide [PDF 435kb]

### CONNECT: FRACTIONS – FRACTIONS 1 – MANIPULATING FRACTIONS

This is the first of a series of four resources on Fractions. Fractions are defined as well as terminology associated with them. Equivalent Fractions are explained and the method of calculating fractions that are equivalent to each other is demonstrated using algorithms and models.

Fractions 1 Manipulating fractions [PDF 162kb]

### CONNECT: FRACTIONS – FRACTIONS 2 – OPERATIONS WITH FRACTIONS: X AND ÷

Both algorithms and models of multiplication and division with fractions are explained in this resource.

Fractions 2 Times divide [PDF 191kb]

### CONNECT: FRACTIONS – FRACTIONS 3 – OPERATIONS WITH FRACTIONS: + AND –

Both algorithms and models of addition and subtraction using fractions are explained in this resource.

Fractions 3 Plus minus [PDF 314kb]

### CONNECT: FRACTIONS – FRACTIONS 4 – FRACTIONS, DECIMALS, PERCENTAGES – HOW DO THEY RELATE?

A review of the Decimal or Base 10 system is given in this resource because it is the basis of the relationship between fractions, decimals and percentages. This relationship is explained and methods and examples of working between each type of number are given.

Fractions 4 Fractions, decimals, percentages [PDF 238kb]

### CONNECT: PERCENTAGES

You will be pleasantly surprised to find out just how much you really know about percentages! In this resource you will also find demonstrations of how to find a percentage of a quantity, and how to calculate the percentage change resulting in an increase or decrease of a quantity.

Percentages 1 [PDF 190kb]

### CONNECT: WAYS OF WRITING NUMBERS – SCIENTIFIC NOTATION; SIGNIFICANT FIGURES; DECIMAL PLACES

This resource is useful to Science students in particular, and anyone who is wondering about how to write numbers in different ways, especially for scientific purposes. Our number system is the Decimal or Base 10 system – there is a review of this, followed by definitions and examples of using, firstly, a specific number of decimal places, then of using significant figures. Scientific notation is also explained.

Scientific Notation Significant Figures Decimal Places [PDF 148kb]

### CONNECT: STATISTICS – USING FORMULAS

In this resource an explanation is given of how to calculate just two statistical measurements: the mean and standard deviation, by describing how each symbol is used in each formula and how to work out the formula as a whole.

Statistics calculations [PDF 159kb]

### CONNECT: ALGEBRA – FROM THE SPECIFIC TO THE GENERAL

Here is a gentle introduction to using letters instead of numbers (Algebra). There is also a section on how to use formulas, from straightforward to complicated.

Algebra 1 Calculating using Algebra [PDF 277kb]

### CONNECT: ALGEBRA – ALGEBRAIC EXPRESSIONS – LIKE OR UNLIKE?

In this second resource on Algebra, the meaning of Algebraic Terms is explained, as well as how to distinguish between them. Calculating with algebra and simplifying algebraic expressions is also demonstrated.

Algebra 2 Algebraic Expressions [PDF 124kb]

### CONNECT: ALGEBRA – SOLVING EQUATIONS

In this resource (the third in a series on Algebra), firstly an explanation is given of what an equation is. A demonstration is given of the technique of backtracking as a process used in solving an equation. The widely-used technique of "balancing both sides", which builds on the backtracking process, is also demonstrated as a well-known method of solving equations.

Algebra 3 Solving equations [PDF 528kb]

### CONNECT: ALGEBRA – REARRANGING FORMULAE

The fourth resource on Algebra proceeds directly from the third. "Balancing both sides" is explained to enable you to solve equations with other variables involved.

Algebra 4 Rearranging formulae [PDF 148kb]

### CONNECT: GRAPHS – STRAIGHT LINES (LINEAR GRAPHS)

In this resource, you are taken through some scenarios in which two variables are related to each other. You are shown how to calculate one variable when you know the other, and then how to plot a graph of the relationship.

Linear graphs [PDF 180kb]

### CONNECT: CURRENCY, CONVERSIONS, RATES – CHANGING FROM ONE TO THE OTHER

In this handout, you are shown how to convert between currencies (for example from Australian dollars to New Zealand dollars, and vice versa), between different systems of measurement (such as Imperial to/from Metric) and between units of measurement within the Metric system itself.

Currency Conversions Rates [PDF 213kb]

### CONNECT: POWERS AND LOGS – POWERS, INDICES, EXPONENTS, LOGARITHMS – THEY ARE ALL THE SAME!

Firstly, an explanation is given of the meaning of powers and then how to calculate with them. Operations with powers, the zero power and negative powers are looked at. Logarithms are then explained and examples given of calculating with them. An explanation of powers expressed as fractions is given and of their use with logarithms.

Powers and logs 1 [PDF 212kb]

### CONNECT: POWERS AND LOGS 2 – USES AND RULES OF LOGARITHMS

In this resource, the ways in which logarithms may be manipulated are discussed.

Powers and logs 2 [PDF ??kb]

### CONNECT: ALGEBRA – REARRANGING FORMULAE TO ISOLATE POWERS

When rearranging formulae, often the wanted variable is a power. In this resource a demonstration is given of how to use logarithms to change the formula so that the power can be isolated.

Algebra 5 Rearranging formulae to isolate powers [PDF 137kb]

### CONNECT: AREAS, PERIMETERS – 1. AREAS OF PLANE SHAPES

Plane shapes are defined. Tessellations and the units used to measure area are discussed. Methods of calculating areas of rectangles, triangles and circles are demonstrated.

Areas [PDF 388kb]

### CONNECT: AREAS, PERIMETERS – 2. PERIMETERS OF PLANE SHAPES

The second in a series of 2 resources about areas and perimeters of plane shapes, the resource begins with defining "perimeter" and then demonstrates how to calculate the perimeters of circles, triangles, rectangles and shapes that are made up of combinations of other shapes.

Perimeters [PDF 179kb]

### CONNECT: PYTHAGORAS' THEOREM

This resource describes right-angled triangles, defines the "hypotenuse" of a right-angled triangle, shows how to calculate the hypotenuse or another side of a triangle and discusses Pythagorean Triads.

Pythagoras [PDF 172kb]

### CONNECT: VOLUME, SURFACE AREA – 1. VOLUMES OF SOLIDS

In this resource, the definition of a solid is given as well as the definition of volume and capacity. The definitions of prisms and pyramids are also given with demonstrations of methods of calculating their volumes and capacities. Converting between volumes and capacities is also discussed. The use of correct units is emphasised.

Volumes [PDF 267kb]

### CONNECT: VOLUME, SURFACE AREA – 2. SURFACE AREAS OF SOLIDS

In this resource, the definition of surface area is given. Methods of calculating the surface areas of various solids are given. The use of correct units is emphasised.

Surface Areas [PDF 191kb]