Formulas

Topic 1 Mathematical modelling

Topic 2 Financial mathematics

      Earning money (Preliminary)

Salary and wages

Casual employment

Part-time employment

Commission

Piecework

Overtime

Penalty rates

Holiday pay

Holiday loading

      Budgeting (Preliminary)

      Taxation (Preliminary)

PAYE, PAYG

Gross income

Deductions

Tax payable

      Credit and borrowing (HSC)

Simple interest

Compound interest                                

Annuities and loan repayments     (HSC)

Future value of an annuity

Present value of an annuity

      Depreciation (HSC)

      Spreadsheet applications (HSC)

Calculation of compound and simple interest

Calculation of annuities

Tax calculations

Spreadsheet formulas

Topic 3 Data analysis

      Graphs (Preliminary)

Picturegrams

Pie charts

Column graphs

Dot plots

Stem-and-leafplots

Line graphs

Histograms and polygons

      Data collection, sorting and display

Random variables

Frequency

Cumulative frequency

Relative frequency

Distribution tables

      Interpreting sets of data (HSC)

Measures of central tendency

Measures of dispersion: range, variance,

Deviations, interquartile range

Box-and-whisker plots

      Uses of the standard deviation (HSC)

Normal distribution

z-scores

     Correlation using scatter plots (HSC)

Positive correlation

Negative correlation

Topic 4 Measurement

      Units of measurement (Preliminary)

Units and symbols

Time and calendar

Measuring instruments

Measuring angles

Rounding

Scientific notation

Ratio

Rates and conversions

Solid shapes

Nets

Scale drawing

Plans

Perspective drawing

      Applications of area and volume

Similarity

Calculation of sides

Pythagoras' theorem (right-angled triangles)

Trigonometry

Angles of elevation and depression

The field notebook

Scale diagrams

Parts of a circle

Mensuration (HSC)

Perimeter

Area

Volume

Capacity

Mass

Surface area

Formulas for perimeter and area of 2D figures

Formulas for surface area and volume of 3D figures

Composite figures

Simpson's rule

      Applications of trigonometry (HSC)

Bearings

Angles of any magnitude

Non-right-angled triangles: sine and cosine rules

Area of a triangle

Radial survey

      Spherical geometry (HSC)

The earth as a sphere

The earth's axis and the equator

            Parallels of latitude and distances

Topic 5 Probability

      Definitions

Likely outcomes

Experimental probability

Theoretical probability

Probability that an event does not occur

The multiplication principle

      Counting techniques (HSC)

Box-filling technique

Tree diagrams

Grid diagrams

Sets: intersection, union, notation

Venn diagrams

      Multi-stage events (HSC)

The addition theorem of probability

Mutually-exclusive events

The product theorem of probability

Independent events

Dependent events:

      Applications of probability (HSC)

Probability trees

            Permutations

Topic 6 Algebraic modelling

      Basic algebraic skills (Preliminary)

Pronumerals

Algebraic abbreviations

Like and unlike terms .

Simplifying algebraic  expressions

Removing grouping symbols

Binomial products

Perfect squares

Reduction

Multiplication and division

Addition and subtraction

Substitution

      Algebraic skills and techniques

Solving equations

Solving inequations and graphing solutions on the number line

Formulas

      Modelling linear relationships

The number plane

Plotting points

Graphing linear equations

Gradient and distance of an interval joining two points

Equations of lines

Lines of best fit

Equations with square roots

Intersection of two lines

Simultaneous equations

Graphs

Curves

Variation