General Mathematics provides for different combinations of student interests and preparation for study of VCE Mathematics at the Unit 3 and 4 level. The areas of study for General Mathematics Unit 1 and Unit 2 are ‘Algebra and structure’, ‘Arithmetic and number’, ‘Discrete mathematics’, ‘Geometry, measurement and trigonometry’, ‘Graphs of linear and non-linear relations’ and ‘Statistics’.

For Units 1 and 2, to suit the range of students entering the study, content must be selected from the six areas of study using the following rules:

for each unit, content covers four or more topics in their entirety, selected from at least three different areas of study
courses intended as preparation for study at the Units 3 and 4 level should include a selection of topics from areas of study that provide a suitable background for these studies
topics can also be selected from those available for Specialist Mathematics Units 1 and 2
content covered from an area of study provides a clear progression in knowledge and skills from Unit 1 to Unit 2.

In undertaking these units, students are expected to be able to apply techniques, routines and processes involving rational and real arithmetic, sets, lists and tables, diagrams and geometric constructions, algebraic manipulation, equations and graphs with and without the use of technology. They should have facility with relevant mental and by-hand approaches to estimation and computation. The use of numerical, graphical, geometric, symbolic, financial and statistical functionality of technology for teaching and learning mathematics, for working mathematically, and in related assessment, is to be incorporated throughout each unit as applicable.

OUTCOMES

For each unit the student is required to demonstrate achievement of three outcomes. As a set these outcomes encompass all of the selected areas of study for each unit. For each of Unit 1 and Unit 2, the outcomes apply to the content from the areas of study selected for that unit.

Area of Study 1 - Algebra and structure

Linear relations and equations

Key skills

solve linear equations including literal linear equations
construct tables of values from a given formula
solve, algebraically and/or graphically, simultaneous linear equations in two variables
solve word problems that involve the setting up and solving of a linear equation or a pair of simultaneous linear equations.

Area of Study 2 - Arithmetic and number

Computation and practical arithmetic

Key skills

distinguish between exact and approximate answers and write approximate answers correct to a given number of decimal places or significant figures
use efficient mental and by-hand estimation and computation
use technology effectively for computation
use a log scale (base 10) to represent quantities that range over several orders of magnitude
solve practical problems involving the use of ratios, proportions, percentages, percentage change, rates and the unitary method.

Financial arithmetic

Key skills

apply ratio and proportion, and percentage and percentage change, to solve problems in a range of financial contexts
apply simple interest to analyse cash flow in common savings and credit accounts
apply compound interest to solve problems involving compound interest investments and loans
compare the costs of a range of purchase options such as cash, credit and debit cards, personal loans, and time payments (hire purchase).

Area of Study 3 - Discrete mathematics

Matrices

Key skills

use matrices to store and display information that can be presented in rows and columns
identify row, column, square, zero, and identity matrices and determine their order
add and subtract matrices, multiply a matrix by a scalar or another matrix, raise a matrix to a power and determine its inverse, using technology as applicable
use matrix sums, difference, products, powers and inverses to model and solve practical problems.

Graphs and networks

Key skills

describe a planar graph in terms of the number of faces (regions), vertices and edges and apply Euler’s formula to solve associated problems
apply the concepts of connected graphs: trails, paths, circuits, bridges and cycles to model and solve practical problems related to traversing a graph
find the shortest path in a weighted graph (solution by inspection only)
apply the concepts of trees and minimum spanning trees to solve practical problems using Prim’s algorithm when appropriate.

Number patterns and recursion

Key skills

use a given recurrence relation to generate an arithmetic or a geometric sequence, deduce the rule for the nth term from the recursion relation and evaluate
use a recurrence relation to model and analyse practical situations involving discrete linear and geometric growth or decay
formulate the recurrence relation to generate the Fibonacci sequence and use this sequence to model and analyse practical situations.

Area of Study 4 - Geometry, measurement and trigonometry

Shape and measurement

Key skills

solve practical problems involving the use of Pythagoras’ theorem in two and three dimensions
calculate the perimeter and areas of triangles, quadrilaterals, circles and composites in practical situations
calculate the volumes and surface areas of solids (spheres, cylinders, pyramids and prisms and their composites) in practical situations
use a linear scale factor to scale lengths, areas and volumes of similar figures and shapes in practical situations.

Applications of trigonometry

Key skills

use trigonometric ratios sine, cosine and tangent to find the length of an unknown side or the size of an unknown angle, in a right-angled triangle
solve practical problems involving right-angled triangles including the use of angles of elevation and depression, and the use of three-figure (true) bearings in navigation
calculate the areas of triangles in practical situations using Heron’s formula
solve practical problems requiring the calculation of side lengths or angles in non-right angled triangles using the sine rule or the cosine rule as appropriate
identify sufficient sets of information to determine a triangle

Area of Study 5 - Graphs of linear and non-linear relations

Linear graphs and models

Key skills

develop a linear model to represent and analyse a practical situation and specify its domain of application
interpret the slope and the intercept of a straight-line graph in terms of its context and use the equation to make predictions with consideration of limitations of extrapolation
fit a linear model to data by finding a line fitted by eye and use piecewise linear (line-segment) graphs to model and analyse practical situations.

Inequalities and linear programming

Key skills

graph linear inequalities in one and two variables and use to solve practical problems
construct the constraints of a linear programming problem (with two decision variables) as a set of linear inequalities
construct the feasible region of a linear programming problem by graphing its constraints
determine the optimum value of the objective function using the corner-point principle.

Area of Study 6 - Statistics

Investigating and comparing data distributions

Key skills

construct and interpret graphical displays of data, and describe the distributions of the variables involved and interpret in the context of the data
calculate the values of appropriate summary statistics to represent the centre and spread of the distribution of a numerical variable and interpret in the context of the data
construct and use parallel boxplots or back-to-back stem plots (as appropriate) to compare the distribution of a numerical variable across two or more groups in terms of centre (median), spread (IQR and range) and outliers, interpreting any observed differences in the context of the data.

Investigating relationships between two numerical variables

Key skills

use a scatterplot to describe an observed association between two numerical variables in terms of direction, strength and form
estimate the value of the correlation coefficient r from a scatterplot and calculate its value from the data using technology
identify the explanatory variable and use the equation of the least squares line fitted to the data to model an observed linear association
calculate the intercept and slope correct to a specified number of decimal places or significant figures, and interpret the slope and intercept of the model in the context of data
use the model to make predictions, being aware of the limitations of extrapolation.