Senior Secondary 2021 Pathways Information

General Mathematics - Units 1 & 2

Is this the right maths for me?

Watch the following brief video that explains all of the different mathematics subjects and suggests some possible mathematical pathways for you to consider before making your final choice.

Disclaimer: Changes to the VCAA Maths Studies in 2023

There are currently proposed changes to the Course Design for all VCE Mathematics subjects which may come into effect in 2023. One of the proposals is to change the name of Unit 3,4 Further Maths, to Unit 3,4 General Maths, so it is more clearly the logical pathway to follow Unit 1,2 General Maths.

It is also proposed that an additional Unit 3,4 subject, Foundation Maths be introduced so this may be an option for you. This is intended to be a more practical subject covering topics that "have a strong emphasis on providing students with the mathematical knowledge, skills and understanding to solve problems in real contexts for a range of workplace, personal, further learning, community and global settings relevant to contemporary society". However, as this is not yet confirmed, we would recommend that if you want to continue the study of maths into year 12 in 2023, it would be best to choose General Maths in Year 11 (rather than Foundation) with the expectation that it may lead to either General Maths in Year 12 or Foundation Maths in Year 12.

General Mathematics - Units 1 & 2

Rationale

This study is designed to provide access to worthwhile and challenging mathematical learning in a way which takes into account the interests, needs, dispositions and aspirations of a wide range of students, and introduces them to key aspects of the discipline. It is also designed to promote students’ awareness of the importance of mathematics in everyday life in a technological society, and to develop confidence and the disposition to make effective use of mathematical concepts, processes and skills in practical and theoretical contexts.

Structure

The study is made up of the following units:

General Mathematics Units 1 and 2

Each unit deals with specific content contained in areas of study and is designed to enable students to achieve a set of three outcomes for that unit. Each outcome is described in terms of key knowledge and key skills.

General Mathematics Units 1 and 2 provide for a range of courses of study involving non-calculus based topics for a broad range of students and may be implemented in various ways to reflect student interests in, and applications of, mathematics. They incorporate topics that provide preparation for various combinations of studies at Units 3 and 4 and cover assumed knowledge and skills for those units.

Entry

There are no prerequisites for entry to Units 1, 2 and 3. Students must undertake Unit 3 prior to undertaking Unit 4. Units 1 to 4 are designed to a standard equivalent to the final two years of secondary education. All VCE studies are benchmarked against comparable national and international curriculum.

General Mathematics Units 1 and 2

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.

Assessment

Satisfactory completion

The award of satisfactory completion for a unit is based on the teacher’s decision that the student has demonstrated achievement of the set of outcomes specified for the unit. Demonstration of achievement of outcomes and satisfactory completion of a unit are determined by evidence gained through the assessment of a range of learning activities and tasks. Teachers must develop courses that provide appropriate opportunities for students to demonstrate satisfactory achievement of outcomes. The decision about satisfactory completion of a unit is distinct from the assessment of levels of achievement. Schools will report a student’s result for each unit to the VCAA as S (Satisfactory) or N (Not Satisfactory).

Levels of achievement

Units 1 and 2

Procedures for the assessment of levels of achievement in Units 1 and 2 are a matter for school decision. Assessment of levels of achievement for these units will not be reported to the VCAA. Schools may choose to report levels of achievement using grades, descriptive statements or other indicators.

Study Design Mathematics

Click on the link to take you to the VCAA site.

Resources

Computation and practical arithmetic

This topic includes:

review of computation: order of operations, directed numbers, scientific notation, estimation, exact and approximate answers, rounding correct to a given number of decimal places or significant figures
efficient mental and by-hand estimation and computation in relevant contexts
effective use of technology for computation
orders of magnitude, units of measure that range over multiple orders of magnitude and their use and interpretation, and the use and interpretation of log to base 10 scales, such as the Richter scale
use of ratios and proportions, and percentages and percentage change to solve practical problems
the unitary method and its use to make comparisons and solve practical problems involving ratio and proportion.

Investigating and comparing data distributions

This topic includes:

- types of data, including categorical (nominal or ordinal) or numerical (discrete or continuous)
- display and description of categorical data distributions using frequency tables and bar charts; and the mode and its interpretation
- display and description of numerical data distributions in terms of shape, centre and spread using histograms, stem plots (including back-to-back stem plots) and dot plots and choosing between plots
- measures of centre and spread and their use in summarising numerical data distributions, including use of and calculation of the sample summary statistics, median, mean, range, interquartile range (IQR) and standard deviation; and choosing between the measures of centre and spread
- the five-number summary and the boxplot as its graphical representation and display, including the use of the lower fence (Q₁– 1.5 × IQR) and upper fence (Q₃+ 1.5 × IQR) to identify possible outliers
- use of back-to-back stem plots or parallel boxplots, as appropriate, to compare the distributions of a single numerical variable across two or more groups in terms of centre (median) and spread (IQR and range), and the interpretation of any differences observed in the context of the data.

Matrices

This topic includes:

- use of matrices to store and display information that can be presented in a rectangular array of rows and columns such as databases and links in social and road networks
- types of matrices (row, column, square, zero and identity) and the order of a matrix
- matrix addition, subtraction, multiplication by a scalar, and matrix multiplication including determining the power
- of a square matrix using technology as applicable
- use of matrices, including matrix products and powers of matrices, to model and solve problems, for example costing or pricing problems, and squaring a matrix to determine the number of ways pairs of people in a network can communicate with each other via a third person
- inverse matrices and their applications including solving a system of simultaneous linear equations.

Linear relations and equations

This topic includes:

- substitution into, and transposition of linear relations, such as scale conversion
- solution of linear equations, including literal linear equations
- developing formulas from word descriptions and substitution of values into formulas and evaluation
- construction of tables of values from a given formula
- linear relations defined recursively and simple applications of these relations
- numerical, graphical and algebraic solutions of simultaneous linear equations in two variables
- use of linear equations, including simultaneous linear equations in two variables, and their application to solve practical problems.

Investigating relationships between two numerical variables

This topic includes:

- response and explanatory variables
- scatterplots and their use in identifying and qualitatively describing the association between two numerical variables in terms of direction, form and strength
- the Pearson correlation coefficient r, calculation and interpretation, and correlation and causation
- use of the least squares line to model an observed linear association and the interpretation of its intercept and
- slope in the context of the data
- use of the model to make predictions and identify limitations of extrapolation.

Linear graphs and models

This topic includes:

- review of linear functions and graphs
- the concept of a linear model and its specification
- the construction of a linear model to represent a practical situation including domain of application
- the interpretation of the parameters of a linear model and its use to make predictions, including the issues of interpolation and extrapolation
- fitting a linear model to data by using the equation of a line fitted by eye
- use of piecewise linear (line segment) graphs to model and analyse practical situations.

Inequalities and linear programming

This topic includes:

- linear inequalities in one and two variables and their graphical representation
- the linear programming problem and its purpose
- the concepts of feasible region, constraint and objective function in the context of solving a linear programming problem
- use of the corner-point principle to determine the optimal solution/s of a linear programming problem
- formulation and graphical solution of linear programming problems involving two variables.

Number patterns and recursion

This topic includes:

Number patterns and sequences

- the concept of a sequence as a function
- use of a first-order linear recurrence relation to generate the terms of a number sequence
- tabular and graphical display of sequences.

The arithmetic sequence

- generation of an arithmetic sequence using a recurrence relation, tabular and graphical display; and the rule for the n^thterm of an arithmetic sequence and its evaluation
- use of a recurrence relation to model and analyse practical situations involving discrete linear growth or decay such as a simple interest loan or investment, the depreciating value of an asset using the unit cost method; and the rule for the value of a quantity after n periods of linear growth or decay and its use.

The geometric sequence

- generation of a geometric sequence using a recurrence relation and its tabular or graphical display; and the rule for the n^thterm and its evaluation
- use of a recurrence relation to model and analyse practical situations involving geometric growth or decay such as the growth of a compound interest loan, the reducing height of a bouncing ball, reducing balance depreciation; and the rule for the value of a quantity after n periods of geometric growth or decay and its use.

The Fibonacci sequence

- - generation of the Fibonacci and similar sequences using a recurrence relation, tabular and graphical display
  - use of Fibonacci and similar sequences to model and analyse practical situations.

Financial arithmetic

This topic includes:

- percentage increase and decrease applied to various financial contexts such as the price to earnings ratios of shares and percentage dividends, determining the impact of inflation on costs and the spending power of money over time, calculating percentage mark-ups and discounts, and calculating GST
- applications of simple interest and compound interest
- cash flow in common savings and credit accounts including interest calculation
- compound interest investments and loans
- comparison of purchase options including cash, credit and debit cards, personal loans, and time payments

Outcome 1

On completion of this unit the student should be able to define and explain key concepts as specified in the selected content from the areas of study, and apply a range of related mathematical routines and procedures.

Outcome 2

On completion of each unit the student should be able to select and apply mathematical facts, concepts, models and techniques from the topics covered in the unit to investigate and analyse extended application problems in a range of contexts.

Outcome 3

On completion of this unit the student should be able to select and use numerical, graphical, symbolic and statistical functionalities of technology to develop mathematical ideas, produce results and carry out analysis in situations requiring problem-solving, modelling or investigative techniques or approaches.

Report abuse