qcaa general maths assignment

General Mathematics 2019 v1.2 - IA1: High-level annotated sample response September 2021 - Queensland ...

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Formula Book

Explore the QCAA General Mathematics Syllabus to search for specific topics and find relevant questions and insights seamlessly

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Unit 1: Money, measurement and relations

Topic 1: consumer arithmetic.

Applications of rates, percentages and use of spreadsheets

Unit 1: Money, measurement and relations > Topic 1: Consumer arithmetic > Applications of rates, percentages and use of spreadsheets

• Review definitions of rates and percentages
• Calculate weekly or monthly wages from an annual salary, and wages from an hourly rate, including situations involving overtime and other allowances and earnings based on commission or piecework
• Calculate payments based on government allowances and pensions, such as youth allowances, unemployment, disability and study
• Prepare a personal budget for a given income, taking into account fixed and discretionary spending
• Compare prices and values using the unit cost method
• Apply percentage increase or decrease in various contexts, e.g. determining the impact of inflation on costs and wages over time, calculating percentage mark-ups and discounts, calculating GST, calculating profit or loss in absolute and percentage terms, and calculating simple and compound interest
• Use currency exchange rates to determine the cost in Australian dollars of purchasing a given amount of a foreign currency, such as US$1500, or the value of a given amount of foreign currency when converted to Australian dollars, such as the value of 2050 euros in Australian dollars
• Calculate the dividend paid on a portfolio of shares, given the percentage dividend or dividend paid per share, for each share; and compare share values by calculating a price-to-earnings ratio
• Use a spreadsheet to display examples of the above computations when multiple or repeated computations are required, e.g. preparing a wage sheet displaying the weekly earnings of workers in a fast-food store where hours of employment and hourly rates of pay may differ, preparing a budget or investigating the potential cost of owning and operating a car over a year.

Topic 2: Shape and measurement

Pythagoras' theorem

Unit 1: Money, measurement and relations > Topic 2: Shape and measurement > Pythagoras' theorem

• Review Pythagoras' theorem and use it to solve practical problems in two dimensions and simple applications in three dimensions.

Mensuration

Unit 1: Money, measurement and relations > Topic 2: Shape and measurement > Mensuration

• Solve the problem regarding the calculation of perimeters and areas of circles, sectors of circles, triangles, rectangles, trapeziums, parallelograms and composites
• Calculate the volumes and capacities of standard three-dimensional objects, including spheres, rectangular prisms, cylinders, cones, pyramids and composites in practical situations, such as the volume of water contained in a swimming pool
• Calculate the surface areas of standard three-dimensional objects, e.g. spheres, rectangular prisms, cylinders, cones, pyramids and composites in practical situations, such as the surface area of a cylindrical food container.

Similar figures and scale factors

Unit 1: Money, measurement and relations > Topic 2: Shape and measurement > Similar figures and scale factors

• Review the conditions for similarity of two-dimensional figures, including similar triangles
• Use the scale factor for two similar figures to solve linear scaling problems
• Obtain measurements from scale drawings, such as maps or building plans, to solve problems
• Obtain a scale factor and use it to solve scaling problems involving the calculation of the areas of similar figures, including the use of shadow sticks, calculating the height of trees, use of a clinometer
• Obtain a scale factor and use it to solve scaling problems involving the calculation of surface areas and volumes of similar solids.

Topic 3: Linear equations and their graphs

Linear equations

Unit 1: Money, measurement and relations > Topic 3: Linear equations and their graphs > Linear equations

• Identify and solve linear equations, including variables on both sides, fractions, non-integer solutions
• Develop a linear equation from a description in words.

Straight-line graphs and their applications

Unit 1: Money, measurement and relations > Topic 3: Linear equations and their graphs > Straight-line graphs and their applications

• Construct straight-line graphs using \( y = a + bx \) both with and without the aid of technology
• Determine the slope and intercepts of a straight-line graph from both its equation and its plot
• Interpret, in context, the slope and intercept of a straight-line graph used to model and analyse a practical situation
• Construct and analyse a straight-line graph to model a given linear relationship, such as modelling the cost of filling a fuel tank of a car against the number of litres of petrol required.

Simultaneous linear equations and their applications

Unit 1: Money, measurement and relations > Topic 3: Linear equations and their graphs > Simultaneous linear equations and their applications

• Solve a pair of simultaneous linear equations in the format \( y = mx + c \), using technology when appropriate; they must solve equations algebraically, graphically, by substitution and by the elimination method
• Solve practical problems that involve finding the point of intersection of two straight-line graphs, such as determining the break-even point where cost and revenue are represented by linear equations.

Piece-wise linear graphs and step graphs

Unit 1: Money, measurement and relations > Topic 3: Linear equations and their graphs > Piece-wise linear graphs and step graphs

• Sketch piece-wise linear graphs and step graphs, using technology where appropriate
• Interpret piece-wise linear and step graphs used to model practical situations.

Unit 2: Applied trigonometry, algebra, matrices and univariate data

Topic 1: applications of trigonometry.

Applications of trigonometry

Unit 2: Applied trigonometry, algebra, matrices and univariate data > Topic 1: Applications of trigonometry > Applications of trigonometry

• Review the use of the trigonometric ratios to find the length of an unknown side or the size of an unknown angle in a right-angled triangle
• Determine the area of a triangle given two sides and an included angle by using the rule \( area=\frac{1}{2}bc \sin A \), or given three sides by using Heron's rule \( A = \sqrt{s(s-a)(s-b)(s-c)} \), where \( s = \frac{a+b+c}{2} \), and solve related practical problems
• Solve two-dimensional problems involving non-right-angled triangles using the sine rule (ambiguous case excluded) and the cosine rule
• Solve two-dimensional practical problems involving the trigonometry of right-angled and non-right-angled triangles, including problems involving angles of elevation and depression and the use of true bearings.

Topic 2: Algebra and matrices

Linear and non-linear relationships

Unit 2: Applied trigonometry, algebra, matrices and univariate data > Topic 2: Algebra and matrices > Linear and non-linear relationships

• Substitute numerical values into linear algebraic and simple non-linear algebraic expressions, and evaluate, e.g. order two polynomials, proportional, inversely proportional
• Find the value of the subject of the formula, given the values of the other pronumerals in the formula
• Transpose linear equations and simple non-linear algebraic equations, e.g. order two polynomials, proportional, inversely proportional
• Use a spreadsheet or an equivalent technology to construct a table of values from a formula, including two-by-two tables for formulas with two variable quantities, e.g. a table displaying the body mass index (BMI) of people with different weights and heights.

Matrices and matrix arithmetic

Unit 2: Applied trigonometry, algebra, matrices and univariate data > Topic 2: Algebra and matrices > Matrices and matrix arithmetic

• Use matrices for storing and displaying information that can be presented in rows and columns, e.g. tables, databases, links in social or road networks
• Recognise different types of matrices (row matrix, column matrix (or vector matrix), square matrix, zero matrix, identity matrix) and determine the size of the matrix
• Perform matrix addition, subtraction, and multiplication by a scalar
• Perform matrix multiplication (manually up to a 3 x 3 but not limited to square matrices)
• Determining the power of a matrix using technology with matrix arithmetic capabilities when appropriate
• Use matrices, including matrix products and powers of matrices, to model and solve problems, e.g. costing or pricing problems, squaring a matrix to determine the number of ways pairs of people in a communication network can communicate with each other via a third person.

Topic 3: Univariate data analysis

Making sense of data relating to a single statistical variable

Unit 2: Applied trigonometry, algebra, matrices and univariate data > Topic 3: Univariate data analysis > Making sense of data relating to a single statistical variable

• Define univariate data
• Classify statistical variables as categorical or numerical
• Classify a categorical variable as ordinal or nominal and use tables and pie, bar and column charts to organise and display the data, e.g. ordinal: income level (high, medium, low); or nominal: place of birth (Australia, overseas)
• Classify a numerical variable as discrete or continuous, e.g. discrete: the number of rooms in a house; or continuous: the temperature in degrees Celsius
• Select, construct and justify an appropriate graphical display to describe the distribution of a numerical dataset, including dot plot, stem-and-leaf plot, column chart or histogram
• Describe the graphical displays in terms of the number of modes, shape (symmetric versus positively or negatively skewed), measures of centre and spread, and outliers and interpret this information in the context of the data
• Determine the mean, \(\bar{x}\), and standard deviation (using technology) of a dataset and use statistics as measures of location and spread of a data distribution, being aware of the significance of the size of the standard deviation.

Comparing data for a numerical variable across two or more groups

Unit 2: Applied trigonometry, algebra, matrices and univariate data > Topic 3: Univariate data analysis > Comparing data for a numerical variable across two or more groups

• Construct and use parallel box plots (including the use of the \(Q_1 - 1.5 \times IQR \leq x \leq Q_3 + 1.5 \times IQR\) criteria for identifying possible outliers) to compare datasets in terms of median, spread (IQR and range) and outliers to interpret and communicate the differences observed in the context of the data
• Compare datasets using medians, means, IQRs, ranges or standard deviations for a single numerical variable, interpret the differences observed in the context of the data and report the findings in a systematic and concise manner.

Unit 3: Bivariate data, sequences and change, and Earth geometry

Topic 1: bivariate data analysis.

Identifying and describing associations between two categorical variables

Unit 3: Bivariate data, sequences and change, and Earth geometry > Topic 1: Bivariate data analysis > Identifying and describing associations between two categorical variables

• Define bivariate data
• Construct two-way frequency tables and determine the associated row and column sums and percentages
• Use an appropriately percentaged two-way frequency table to identify patterns that suggest the presence of an association
• Understand an association in terms of differences observed in percentages across categories in a systematic and concise manner, and interpret this in the context of the data.

Identifying and describing associations between two numerical variables

Unit 3: Bivariate data, sequences and change, and Earth geometry > Topic 1: Bivariate data analysis > Identifying and describing associations between two numerical variables

• Construct a scatterplot to identify patterns in the data suggesting the presence of an association
• Understand an association between two numerical variables in terms of direction (positive/negative), form (linear) and strength (strong/moderate/weak)
• Calculate and interpret the correlation coefficient (r) to quantify the strength of a linear association using Pearson's correlation coefficient.

Fitting a linear model to numerical data

Unit 3: Bivariate data, sequences and change, and Earth geometry > Topic 1: Bivariate data analysis > Fitting a linear model to numerical data

• Identify the response variable and the explanatory variable
• Use a scatterplot to identify the nature of the relationship between variables
• Model a linear relationship by fitting a least-squares line to the data
• Use a residual plot to assess the appropriateness of fitting a linear model to the data
• Interpret the intercept and slope of the fitted line
• Use, not calculate, the coefficient of determination (\( R^2 \)) to assess the strength of a linear association in terms of the explained variation
• Use the equation of a fitted line to make predictions
• Distinguish between interpolation and extrapolation when using the fitted line to make predictions, recognising the potential dangers of extrapolation.

Association and causation

Unit 3: Bivariate data, sequences and change, and Earth geometry > Topic 1: Bivariate data analysis > Association and causation

• Recognise that an observed association between two variables does not necessarily mean that there is a causal relationship between them
• Identify and communicate possible non-causal explanations for an association, including coincidence and confounding due to a common response to another variable
• Solve practical problems by identifying, analysing and describing associations between two categorical variables or between two numerical variables.

Topic 2: Time series analysis

Describing and interpreting patterns in time series data

Unit 3: Bivariate data, sequences and change, and Earth geometry > Topic 2: Time series analysis > Describing and interpreting patterns in time series data

• Construct time series plots
• Describe time series plots by identifying features such as trend (long-term direction), seasonality (systematic, calendar-related movements) and irregular fluctuations (unsystematic, short-term fluctuations), and recognise when there are outliers, e.g. one-off unanticipated events.

Analysing time series data

Unit 3: Bivariate data, sequences and change, and Earth geometry > Topic 2: Time series analysis > Analysing time series data

• Smooth time series data by using a simple moving average, including the use of spreadsheets to implement this process
• Calculate seasonal indices by using the average percentage method
• Deseasonalise a time series by using a seasonal index, including the use of spreadsheets to implement this process
• Fit a least-squares line to model long-term trends in time series data, using appropriate technology
• Solve practical problems that involve the analysis of time series data.

Topic 3: Growth and decay in sequences

The arithmetic sequence

Unit 3: Bivariate data, sequences and change, and Earth geometry > Topic 3: Growth and decay in sequences > The arithmetic sequence

• Use recursion to generate an arithmetic sequence
• Display the terms of an arithmetic sequence in both tabular and graphical form and demonstrate that arithmetic sequences can be used to model linear growth and decay in discrete situations
• Use the rule for the nth term using \( t_n = t_1 + (n - 1)d \), where \( t_n \) represents the nth term of the sequence, \( t_1 \) = first term, \( n \) = term number and \( d \) = common difference of a particular arithmetic sequence from the pattern of the terms in an arithmetic sequence, and use this rule to make predictions
• Use arithmetic sequences to model and analyse practical situations involving linear growth or decay, such as analysing a simple interest loan or investment, calculating a taxi fare based on the flag fall and the charge per kilometre, or calculating the value of an office photocopier at the end of each year using the straight-line method or the unit cost method of depreciation.

The geometric sequence

Unit 3: Bivariate data, sequences and change, and Earth geometry > Topic 3: Growth and decay in sequences > The geometric sequence

• Use recursion to generate a geometric sequence
• Display the terms of a geometric sequence in both tabular and graphical form and demonstrate that geometric sequences can be used to model exponential growth and decay in discrete situations
• Use the rule for the nth term using \( t_n = t_1(r^{n-1}) \) where \( t_n \) represents the nth term of the sequence, \( t_1 \) = first term, \( n \) = term number and \( r \) = common ratio of a particular geometric sequence from the pattern of the terms in the sequence, and use this rule to make predictions
• Use geometric sequences to model and analyse (numerically or graphically) practical problems involving geometric growth and decay (logarithmic solutions not required), such as analysing a compound interest loan or investment, the growth of a bacterial population that doubles in size each hour or the decreasing height of the bounce of a ball at each bounce; or calculating the value of office furniture at the end of each year using the declining (reducing) balance method to depreciate.

Topic 4: Earth geometry and time zones

Locations on the Earth

Unit 3: Bivariate data, sequences and change, and Earth geometry > Topic 4: Earth geometry and time zones > Locations on the Earth

• Define the meaning of great circles
• Define the meaning of angles of latitude and longitude in relation to the equator and the prime meridian
• Locate positions on Earth's surface given latitude and longitude, e.g. using a globe, an atlas, GPS and other digital technologies
• State latitude and longitude for positions on Earth's surface and world maps (in degrees only)
• Use a local area map to state the position of a given place in degrees and minutes, e.g. investigating the map of Australia and locating boundary positions for Aboriginal language groups, such as the Three Sisters in the Blue Mountains or the local area's Aboriginal land and the positions of boundaries
• Calculate angular distance (in degrees and minutes) and distance (in kilometres) between two places on Earth on the same meridian using \( D = 111.2 \times \) angular distance
• Calculate angular distance (in degrees and minutes) and distance (in kilometres) between two places on Earth on the same parallel of latitude using \( D = 111.2 \cos \theta \times \) angular distance
• Calculate distances between two places on Earth, using appropriate technology.

Unit 3: Bivariate data, sequences and change, and Earth geometry > Topic 4: Earth geometry and time zones > Time zones

• Define Greenwich Mean Time (GMT), International Date Line and Coordinated Universal Time (UTC)
• Understand the link between longitude and time
• Determine the number of degrees of longitude for a time difference of one hour
• Solve problems involving time zones in Australia and in neighbouring nations, making any necessary allowances for daylight saving, including seasonal time systems used by Aboriginal peoples and Torres Strait Islander peoples
• Solve problems involving GMT, International Date Line and UTC
• Calculate time differences between two places on Earth
• Solve problems associated with time zones, such as online purchasing, making phone calls overseas and broadcasting international events
• Solve problems relating to travelling east and west incorporating time zone changes, such as preparing an itinerary for an overseas holiday with corresponding times.

Unit 4: Investing and networking

Topic 1: loans, investments and annuities.

Compound interest loans and investments

Unit 4: Investing and networking > Topic 1: Loans, investments and annuities > Compound interest loans and investments

• Use a recurrence relation \(A_{n+1} = rA_n\), to model a compound interest loan or investment, and investigate (numerically and graphically) the effect of the interest rate and the number of compounding periods on the future value of the loan or investment, e.g. payday loan
• Calculate the effective annual rate of interest and use the results to compare investment returns and the future value when interest is paid or charged daily, monthly, quarterly or six-monthly
• Solve problems involving compound interest loans or investments, e.g. determine the future value of a loan, the number of compounding periods for an investment to exceed a given value, the interest rate needed for an investment to exceed a given value.

Reducing balance loans (compound interest loans with periodic repayments)

Unit 4: Investing and networking > Topic 1: Loans, investments and annuities > Reducing balance loans (compound interest loans with periodic repayments)

• Use a recurrence relation, \(A_{n+1} = rA_n - R\) (where \(R =\) monthly repayment) to model a reducing balance loan and investigate (numerically or graphically) the effect of the interest rate and repayment amount on the time taken to repay the loan
• With the aid of appropriate technology, solve problems involving reducing balance loans, e.g. determining the monthly repayments required to pay off a housing loan.

Annuities and perpetuities (compound interest investments with periodic payments made from the investment)

Unit 4: Investing and networking > Topic 1: Loans, investments and annuities > Annuities and perpetuities (compound interest investments with periodic payments made from the investment)

• Use a recurrence relation \(A_{n+1} = rA_n + d\) to model an annuity and investigate (numerically or graphically) the effect of the amount invested, the interest rate, and the payment amount on the duration of the annuity
• Solve problems involving annuities, including perpetuities as a special case, e.g. determining the amount to be invested in an annuity to provide a regular monthly income of a certain amount.

Topic 2: Graphs and networks

Graphs, associated terminology and the adjacency matrix

Unit 4: Investing and networking > Topic 2: Graphs and networks > Graphs, associated terminology and the adjacency matrix

• Understand the meanings of the terms graph, edge, vertex, loop, degree of a vertex, subgraph, simple graph, complete graph, bipartite graph, directed graph (digraph), arc, weighted graph and network
• Identify practical situations that can be represented by a network and construct such networks, e.g. trails connecting camp sites in a national park, a social network, a transport network with one-way streets, a food web, the results of a round-robin sporting competition
• Construct an adjacency matrix from a given graph or digraph.

Planar graphs, paths and cycles

Unit 4: Investing and networking > Topic 2: Graphs and networks > Planar graphs, paths and cycles

• Understand the meaning of the terms planar graph and face
• Apply Euler's formula, \( v + f - e = 2 \), to solve problems relating to planar graphs
• Understand the meaning of the terms walk, trail, path, closed walk, closed trail, cycle, connected graph and bridge
• Investigate and solve practical problems to determine the shortest path between two vertices in a weighted graph (by trial-and-error methods only)
• Understand the meaning of the terms Eulerian graph, Eulerian trail, semi-Eulerian graph, semi-Eulerian trail and the conditions for their existence, and use these concepts to investigate and solve practical problems, e.g. the Konigsberg bridge problem, planning a garbage bin collection route
• Understand the meaning of the terms Hamiltonian graph and semi-Hamiltonian graph and use these concepts to investigate and solve practical problems (by trial-and-error methods only), e.g. planning a sightseeing tourist route around a city, the travelling-salesman problem.

Topic 3: Networks and decision mathematics

Trees and minimum connector problems

Unit 4: Investing and networking > Topic 3: Networks and decision mathematics > Trees and minimum connector problems

• Understand the meaning of the terms tree and spanning tree
• Identify practical examples
• Identify a minimum spanning tree in a weighted connected graph, e.g. using Prim's algorithm
• Use minimal spanning trees to solve minimal connector problems, e.g. minimising the length of cable needed to provide power from a single power station to substations in several towns.

Project planning and scheduling using critical path analysis (CPA)

Unit 4: Investing and networking > Topic 3: Networks and decision mathematics > Project planning and scheduling using critical path analysis (CPA)

• Construct a network diagram to represent the durations and interdependencies of activities that must be completed during the project, e.g. preparing a meal
• Use forward and backward scanning to determine the earliest starting time (EST) and latest starting times (LST) for each activity in the project
• Use EST and LSTs to locate the critical path/s for the project
• Use the critical path to determine the minimum time for a project to be completed
• Calculate float times for non-critical activities.

Flow networks

Unit 4: Investing and networking > Topic 3: Networks and decision mathematics > Flow networks

• Solve small-scale network flow problems including the use of the maximum-flow minimum-cut theorem, e.g. determining the maximum volume of oil that can flow through a network of pipes from an oil storage tank to a terminal.

Assigning order and the Hungarian algorithm

Unit 4: Investing and networking > Topic 3: Networks and decision mathematics > Assigning order and the Hungarian algorithm

• Use a bipartite graph and its tabular or matrix form to represent an assignment/allocation problem, e.g. assigning four swimmers to the four places in a medley relay team to maximise the team's chances of winning
• Determine the optimum assignment/s for small-scale problems by inspection, or by use of the Hungarian algorithm (3 x 3) for larger problems.

Material from QCAA is © State of Queensland ( QCAA ) 2024, CC BY 4.0

QCE General Maths Resources - Units 3&4 - MegaGuide

ATAR Notes - QCE

Friday 22nd, May 2020

In this resource megaguide, we’ve listed a whole heap of resources you might find useful in your QCE General Maths studies. 💯

If you’re keen to subscribe to our regular QCE newsletter and stay on top of all of our QCE resources, your best bet is to make an ATAR Notes account:

MAKE AN ACCOUNT!

QCE GENERAL MATHS RESOURCES | NOTES

A great place to start for QCE study is our range of free notes ! Generously uploaded by those who have come before you, these notes are by students, for students.

For General Maths 3&4 notes specifically, go here . Note that you will need to be logged in to your ATAR Notes account to download the notes – otherwise you’ll just be met with a blank screen!

When the time comes, it would be amazing if you could upload your own notes , too – even through the year!

QCE GENERAL MATHS RESOURCES | REVISION VIDEOS

If you’re keen on study videos, you’re in luck! We also have a series of excellent revision videos on concepts you can brush up on. Here’s the very first video in the series:

But you can find the full series – plus videos for lots of other QCE subjects – on our free videos page . If you like, you can also subscribe to our YouTube channel to make sure you’re the first to know about new videos – we’re uploading new content all the time!

QCE GENERAL MATHS RESOURCES | Q&A

We have a dedicated section on the ATAR Notes Forums for QCE General Maths discussion , where you can get help for any content or questions you’re struggling with. Free help from current and past students – we really recommend using this as much as you can!

Join the community, get involved, and see your marks improve. 📈 The forum also has a heap of useful content guides and discussions, such as:

→  QCE General Maths questions thread →  Sample solutions to QCAA’s sample papers →  A quick glossary of graph/network concepts →  Smoothing a time series: full example of a 4-point-mean case →  A quick glossary of statistics concepts →  Examples of arithmetic vs. geometric sequences →  Modelling reducing balance loans (simple example)

Qce general maths resources | articles.

We’re always publishing new QCE articles for you to sink your teeth into. Here are some of our favourite QCE General Maths-related articles from time gone by:

→  How NOT to study for your mathematics subjects! →  QCE maths – should you be studying every night? →  Common ways of studying QCE maths →  Three little things to consider whilst studying maths →  QCE mathematics and the battle with forgetfulness →  My experience studying maths →  QCE General Maths Units 1&2 resources

Qce general maths resources | course notes.

We recommend checking out our QCE study guides for a range of subjects, but particularly for General Maths 3&4 if you’re looking for a helping hand!

Our QCE General Maths 3&4 Complete Course Notes contain everything you need to know for your assessment tasks and exams, written from the perspective of a past high-achieving student.

With a summary of key concepts, and clear explanations of every section of the syllabus, this book focuses on clarifying your understanding of all the examinable material, so you can focus on maximising your marks.

STILL WANT MORE QCE GENERAL MATHS RESOURCES?

We hear you! We’ll be offering  heaps  of new (and varied – very exciting!) QCE General Maths resources, and we’d love for you to be the first to know. If you haven’t already, the first step is simply to make an ATAR Notes account . 😍

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How to Structure Your PSMT Report for QCAA Mathematical Methods

Feeling a little overwhelmed and aren’t sure how you’re meant to approach your problem-solving and modelling task (PSMT) for QCAA Maths Methods ?

It may seem a little out of left field that you need to write a report instead of complete an exam that covers different mathematical topics, but don’t worry — we’ll guide you through how to structure it!

What are you waiting for? Let’s get started on familiarising ourselves with the QCAA Methods PSMT.

What is a Problem-Solving and Modelling Task (PSMT)? Structure of a PSMT for Maths Methods Tips for Writing a PSMT Breaking Down the Instrument-Specific Marking Guide (ISMG)

What is a Problem-Solving and Modelling Task (PSMT)?

A PSMT is an assessment task designed to evaluate your ability to respond to an investigative mathematical scenario or stimulus . The specific task provided will be related to the mathematical concepts and techniques you have been learning in class.

You will be required to create a written report, no longer than 10 pages and 2000 words , to address the following assessment objectives:

• Selecting, recalling and using facts, rules, definitions and procedures 
• Comprehending mathematical concepts and techniques 
• Communicating using mathematical, statistical and everyday language and conventions 
• Evaluating the reasonableness of solutions 
• Justifying procedures and decisions by explaining mathematical reasoning 
• Solving problems by applying mathematical concepts and techniques 

The other key features of this report include providing a response that addresses the real-life application of mathematics, using technology, using tables/graphs/diagrams, and following the structure of a report (past tense and third person) . Now that you know what a PSMT is all about, let’s find out how to set it out and what each section needs!

Struggling your way through the PSMT? Here’s how to decide whether to drop down to General Maths for your QCE or not!

Structure of a PSMT for Maths Methods

#1: title page.

Should include: the title of the report, your name, the year, and a relevant image.

#2: Contents Page

A clear table of contents that correlates with the different sections of the report is required. Learn how to create a table of contents page on Microsoft Word here.  

#3: Introduction (100 words)

Explain the purpose of your QCAA Methods PSMT  (what is the scenario/context) and list the contents of the report (each step that was taken to develop and evaluate your solution).

Example: This report consists of the formulation, evaluation and justification of a pendant design. Factors, such as, target consumer, size, weight, hole for stringing, materials and aesthetic, will be utilised to guide the decision choices made. The pendant will consist of a variety of types of functions, including logarithmic, parabolic, cubic and circular. The mathematical feasibility and practicality of the pendant will also be considered by utilizing both technological and mathematical methods and procedures, including transformations and graphing of functions, simultaneous equations and Desmos. Strengths, limitations and recommendations will also be given about the pendant.

#4: Background (50-150 words)

Discuss any considerations or research you had to do in order to address the task

Example: Research was conducted on currently existing pendants, which were used to support the design of the new pendant. Both fashion jewellery and fine jewellery were investigated in order to determine appropriate materials, dimensions and designs.

#5: Observations and Assumptions (200-350 words)

Observations .

These are the things you may have come across while researching (so you’ll have a few in-text references here). It can be effective to use diagrams and statistics . Aim for at least four. 

Examples: The density of the materials used can heavily impact the weight and durability of the pendant Pendants sizes average between 9.5-25.4mm  Fashion pendants on average cost between $10-$99 (Lovisa, 2020) All measurements must be positive values, so when graphing, pendant must entirely be in the first quadrant to avoid negative values 

Assumptions 

As the task can be somewhat vague, some assumptions will have to be made in order to make it more specific . Aim for at least four.

Ensure you justify the reasons for/implications of each assumption. 

Examples: The pendant is for the average adult consumer, and will be considered ‘fine jewellery’ and so will have dimensions, weight and cost as such  The entire area of the pendant will have the same depth (meaning that the pendant will be flat), as creating variety in depth will make the volume of the pendant difficult to calculate  The domains and ranges of the functions will correlate to the dimensions of the pendant (i.e. 1 unit = 1cm) The cost calculated is the estimated cost for the materials of the pendant, not including the construction cost

#6: Developing a Solution (300-400 words)

Design/model considerations and decisions .

Discuss the design choices you made using mathematical concepts and techniques to justify . Reference other designs/models and how they have impacted your design choices.

Refer to your observations and assumptions and how they have influenced your design choices.   

Example: As circles are a common shape of pendant, it was decided that this pendant should have a similar shape. Along with the observations taken about pendant size, it was decided that this pendant should have both a length and width of 2cm. Instead of using just a circle function, however, in order to make it more unique, the pendant’s shape was made of two logarithmic functions and a parabola. When the first logarithmic function was created, the second one was the same but translated vertically (across the y-axis). This meant that they intersected perfectly at (1,2) – the top middle of the pendant. The logarithmic functions ranged from 0.5 to 2. As both functions would continue straight down as the range decreased, a parabola was required to create the ‘bottom half’ of the ‘circle’. To make sure it was equal, the parabola had a minimum at (2,0)…

Calculations (few words, insert screenshots of calculations instead)

This section can have multiple subdivisions within and differ widely depending on what exactly the task is. Generally, however, the use of technology must be demonstrated, the mathematical concepts used should be explained and appropriate and accurate mathematical concepts and techniques should be applied .

Note that in the main body of the report, you should include only one of each type of calculation; include the rest in the appendix.

For the pendant-designing task used in the examples, the subdivision consisted of Determining Functions, Determining Points of Intersection, Determining Area, Determining Volume, and Calculating the Weight and Cost of Materials.  

Completed Design/Model 

Include the completed design/model here and make sure that it is appropriately labelled (points of intersection could also be labelled on example below).

#7: Evaluation of Results (500-600 words)

Reasonableness .

Discuss which aspects of your design/model are reasonable and which aspects are unreasonable and provide justification. Explain how the unreasonable aspects could be improved.

Include aspects that were not taken into account and may have an effect on the design/model. Also, revisit the assumptions and consider any revisions that could be made to improve your design/model. 

Example: The dimensions, materials and the domains and ranges of the functions that make up the pendant are reasonable as they are based on current pendant designs. The reasonableness of the results has been assessed by both plotting the functions on Desmos and simultaneous equations. Although Desmos was generally informative, it was not quite accurate, as some functions did not appear to intersect… It is important to note that the construction cost of the pendant was not taken into account, and therefore the overall cost of designing and creating the pendant is likely to be much higher. 

Discuss the strengths of your design/model, such as the design choices, development process, calculations and practicality in terms of the real world.  

Example: The main strength of the pendant is that all the functions intersect perfectly, as all the points of intersection were successfully solved for. In terms of the real world, this means that the pendant can be built accurately according to these calculations with no gaps between portions of the pendant. This also meant that the area and volume of the pendant could be calculated accurately using integration. Another strength of the pendant is that there is a loop that is big enough for a chain of 5mm width to go through. These factors, along with the estimated cost and weight being $628.35 and 16.5g respectively, mean that this pendant is suitable for the average adult consumer. 

Limitations 

Discuss the limitations of the design/model of your QCAA Methods PSMT, such as the design choices, development process, calculations and practicality in terms of the real world. Explain how you would address these limitations (further calculations, more research, other considerations etc.)

Example: A limitation of this report is that the physical construction of the pendant was not considered. If and how the materials can be cut/shaped into the designed format is unknown. Although the materials were chosen according to existing pendants, the weight and costs of the materials are only estimations and based on little research. More research needs to be conducted about the density, weight and construction costs of the materials. Another restriction is that the surface of the pendant is flat, as although practical, it gives a 2D element to the pendant, thus reducing its appeal. Therefore, it is recommended that further research is conducted into the physical construction of the pendant to make sure it is practical.  

#8: Conclusion (50 words)

Sum up the report by producing a final response to the task. Discuss the k ey findings of the process and evaluation, as well as how it could be improved at the end of your QCAA Methods PSMT.

Example: Through the evaluation of other pendants, consideration of all observations and assumptions and accurate application of mathematical processes, a pendant was successfully designed. Although there are some areas of improvement and further investigation into the physical construction of the pendant is recommended, overall, the pendant is unique, practical and visually appealing.

#9: Bibliography

List all of your references here. Check which style of referencing your teacher wants.

#10: Appendix

All your tables, graphs, diagrams and calculations that weren’t in the main body of the report should be here . This section is not marked and does not count towards the word or page count.  

Still stuck? Check out our local team of Brisbane Maths Methods tutors !

Tips for Writing a PSMT for QCAA Maths Methods + A Breakdown of the ISMG 

Not sure what mark you should be aiming for in the PSMT? Here’s what mark you need to be on track for an ATAR above 90 !

#1: Experiment with different designs/models before choosing one — and it’s okay if your design/model is not perfect, you can talk about its limitations in the evaluation section. #2: The graphing calculator on Desmos is a great way to graph functions and test the reasonableness of your design. #3: The WolframAlpha calculator is a great tool to help solve or double check any complex calculations. #4: Ensure all tables, graphs, images and diagrams are appropriately labelled. #5: Aim for at least four observations and four assumptions. #6: Ensure that your report can be understood independently of the task sheet and that it is presented as a real report and not a school assignment. #7: See the table below for what is and isn’t included in the page and word count for this assessment.

Breaking Down the Instrument-Specific Marking Guide ( ISMG ) 

The ISMG is split into four distinct criteria: Formulate, Solve, Evaluate and Verify, and Communicate . Let’s explore what each of them is about!

This criterion is all about your ability to effectively plan. This includes: 

• Considering all the different aspects of the task and addressing them in your observations and assumptions 
• Your observations and assumptions being accurate and relevant to the task 
• Not only stating, but documenting (supporting with evidence) your observations and assumptions 
• Effectively translating the task from a real-world problem to a mathematical scenario by identifying the mathematical concepts, processes and techniques required to develop your design/model 

This criterion is all about how effectively you apply mathematical concepts and techniques to develop your design/model. This includes: 

• Utilising technology 
• Using complex, not basic, mathematical concepts and techniques that are relevant to the task 

Evaluate and Verify

This criterion is all about your ability to apply mathematical concepts and techniques to develop your design/model. This includes: 

• Utilising the results, assumptions and observations to justify your evaluation 
• Discussing how limitations can be improved 

Communicate

This criterion is all about the flow and presentation of your report. This includes: 

• Correct spelling, grammar and referencing 
• Appropriate and accurate use of mathematical language 
• Coherent structure 

If you’re studying General Maths, check out our guide to writing a PSMT here!

Once you’ve received your marks from this PSMT, you should see how you’re tracking for your goal ATAR with our QCE Cohort Comparison Tool !

Completing this assessment at the start of Year 11? Here’s why you might be struggling in Year 11 !

On the hunt for other QCAA Maths Methods resources?

We’ve created a bunch of helpful articles and practice questions for studying QCAA Maths Methods. Check them out!

• Unit 3 IA2 Short Answer Practice Questions
• Unit 4 IA3 Short Answer Practice Questions
• Download QCAA Maths Methods Practice Exam for External Assessment Revision
• QCAA Practice Questions for Unit 3 & 4 Maths Methods External Assessment
• The Ultimate Guide to QCAA Maths Methods Unit 3: Further Calculus
• The Ultimate Guide to QCAA Maths Methods Unit 4: Further Functions and Statistics

Stuck completing this PSMT at the end of Year 11 because you’re school’s trying to get ahead? Don’t fall behind with these tips !

Are you looking for some extra guidance with the QCAA Maths Methods PSMT?

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We can help you master the QCAA Maths Methods syllabus and ace your upcoming Maths Methods assessments with personalised lessons conducted one-on-one in your home or online!

We’ve supported over  8,000 students over the last 11 years , and on average our students score mark improvements of over 20%!

We support Maths tutoring on the Gold Coast ! Live regional? We also tutor in the Townsville area .

To find out more and get started with an inspirational QLD tutor and mentor,   get in touch today  or give us a ring on  1300 267 888!

Yalindi Binduhewa is an Art of Smart tutor based in Queensland and was part of the very first cohort to go through the ATAR system, so she knows exactly how fun and enjoyable it can be. She is currently studying a Bachelor of Medical Imaging (Honours) at QUT and is loving it. When she’s not doing uni-related stuff or tutoring, she’s hanging out with her friends, rewatching a show for the 100th time, or trying out new crafty projects and discovering that she doesn’t have a talent for everything. 

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