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Year 11: QCE General Mathematics

Listed Mathematics syllabus sub-topics at Units 1 and 2, in the words of the Queensland Curriculum and Assessment Authority (QCAA), with the practice on this site that covers it. Checked against the source on 4 September 2026.

2025 syllabus, version 1.3. Queensland numbers its units and topics but gives the content itself no codes, so each entry here is a sub-topic and its text is the sub-topic's own bullet list. Mathematical notation is flattened out of the syllabus PDF.

  • 13syllabus sub-topics
  • 38skills mapped
  • 100%have practice

Coverage is the percentage of listed syllabus sub-topics with at least one linked practice skill; it does not measure how fully every part of an entry is practised. A skill can practise more than one syllabus sub-topic, so some appear more than once below.

Unit 1: Money, measurement, algebra and linear equations

  1. Topic 1 · Applications of rates, percentages and use of spreadsheetsUnderstand the meaning of rates and percentages. Calculate weekly, fortnightly 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 income support payments based on government allowances and pensions. 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. inflation of costs and wages, percentage mark-ups and discounts, percentage profit and loss, GST, simple interest. 𝐼 = 𝑃𝑖𝑛 where 𝐼 is simple interest, 𝑃 is principal, 𝑖 is interest rate per year and 𝑛 is number of years Use currency exchange rates to convert between the Australian dollar and foreign currencies. Calculate the dividend paid on a portfolio of shares, given the dividend yield or dividend paid per share, and compare share values by calculating a price-to-earnings (P/E) ratio. dividend yield = (dividend/share price) × 100; P/E ratio = (market price per share)/(annual earnings per share). 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 an organisation, preparing a budget, investigating the potential cost of owning and operating a car over a year.

  2. Topic 2 · Pythagoras’ theoremUnderstand and use Pythagoras’ theorem to solve practical problems in two dimensions and simple applications in three dimensions. 𝑐2 = 𝑎2 + 𝑏2 where 𝑐 is length of the hypotenuse and 𝑎 and 𝑏 are lengths of the two perpendicular sides

  3. Topic 2 · MensurationCalculate perimeters, 𝑃, of standard two-dimensional objects in practical situations, including circles, sectors, triangles, rectangles, trapeziums, parallelograms and composites. circle: 𝐶 = 2𝜋𝑟 where 𝐶 is circumference and 𝑟 is radius sector: 𝑃 = 2𝑟 + 𝜃 𝜋𝑟 where 𝜃 is central angle and 𝑟 is radius

  4. Topic 3 · Similar figures and scale factorsUnderstand the conditions for similarity of two-dimensional figures, including similar triangles. Use the scale factor for two similar figures to solve linear scaling problems. Determine measurements from scale drawings (e.g. maps and building plans) to solve problems. Determine a scale factor and use it to solve scaling problems, e.g. calculating lengths and areas of similar figures; and calculating surface areas, volumes and capacities of similar solids.

  5. Topic 4 · Linear and non-linear relationshipsSubstitute numerical values into linear and simple non-linear algebraic expressions, and evaluate. Find the value of a pronumeral in linear and simple non-linear equations given the values of the other pronumerals, transposing equations where necessary. 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.

  6. Topic 5 · Linear equationsSolve linear equations, including equations with variables on both sides and equations with rational solutions. Develop a linear equation from a description in words. Solve practical problems involving linear equations.

  7. Topic 5 · Straight-line graphsUnderstand and use the slope-intercept form of a linear function, 𝑦 = 𝑚𝑥 + 𝑐 where 𝑚 is slope (gradient) and 𝑐 is 𝑦-intercept. Construct a straight-line graph using a linear function of the form, 𝑦 = 𝑚𝑥 + 𝑐 where 𝑚 is slope (gradient) and 𝑐 is 𝑦-intercept. Determine the slope (gradient), 𝑥-intercept and 𝑦-intercept of a straight line from both its equation and its graph. Interpret, in context, the slope (gradient) and intercept of a linear function used to model and analyse a practical situation. Construct and analyse a straight-line graph to model a given linear relationship, e.g. modelling the cost of filling a fuel tank of a car against the number of litres of petrol required.

Unit 2: Applications of linear equations and trigonometry, matrices and univariate data analysis

  1. Topic 1 · Simultaneous linear equations and their applicationsSolve a pair of simultaneous linear equations, algebraically using substitution and elimination, and graphically. Solve practical problems involving simultaneous linear equations.

  2. Topic 1 · Piece-wise linear graphs and step graphsSketch piece-wise linear graphs and step graphs. Interpret piece-wise linear graphs and step graphs used to model practical situations.

  3. Topic 2 · Applications of trigonometryUnderstand and use the trigonometric ratios to find the size of an unknown angle, 𝜃, or the length of an unknown side in a right-angled triangle. cos 𝜃 = adjacent/hypotenuse, sin 𝜃 = opposite/hypotenuse, tan 𝜃 = opposite/adjacent. Calculate the area of a non-right-angled triangle, △𝐴𝐵𝐶, and solve related practical problems. area = (1/2)𝑏𝑐 sin 𝐴, given two sides, 𝑏 and 𝑐, and an included angle, 𝐴 Heron’s rule: area = √𝑠(𝑠 − 𝑎)(𝑠 − 𝑏)(𝑠 − 𝑐) where 𝑠 = (𝑎+𝑏+𝑐)/2, given three sides, 𝑎, 𝑏 and 𝑐 Solve two-dimensional problems involving a non-right-angled triangle, △𝐴𝐵𝐶, with sides, 𝑎, 𝑏 and 𝑐, and corresponding angles, 𝐴, 𝐵 and 𝐶. sine rule: 𝑎/sin 𝐴 = 𝑏/sin 𝐵 = 𝑐/sin 𝐶 (ambiguous case excluded); cosine rule: 𝑐^2 = 𝑎^2 + 𝑏^2 − 2𝑎𝑏 cos 𝐶 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.

  4. Topic 3 · Matrices and matrix arithmeticUse 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, including row matrix, column matrix, square matrix, zero matrix and identity matrix, and determine the size of the matrix. Perform matrix addition, subtraction and multiplication by a scalar. Perform matrix multiplication manually up to 3 × 3 matrices but not limited to square matrices. Determine 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.

  5. Topic 4 · Making sense of data relating to a single statistical variableUnderstand the meaning of univariate data. Classify a statistical variable 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); nominal: place of birth (Australia, overseas). Classify a numerical variable as discrete or continuous, e.g. discrete: the number of people in a room; 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 and histogram. Describe a graphical display 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. Understand and calculate the mean, median, mode, range and interquartile range (IQR) of a dataset, with and without technology. mean: 𝑥̅ = (∑ 𝑥)/𝑛; median: ((𝑛+1)/2)th data value. Understand and calculate the (sample) standard deviation, 𝑠_𝑥, of a dataset, using technology only. Use statistics as measures of centre and spread of a data distribution, being aware of their limitations.

  6. Topic 5 · Comparing data for a single numericalvariable across two or more groupsConstruct and use parallel box plots, including identifying possible outliers, to compare datasets in terms of median, spread (range and IQR) and outliers to interpret and communicate the differences observed in the context of the data. outliers (identifying): Q1 − 1.5 × IQR ≤ 𝑥 ≤ Q3 + 1.5 × IQR where Q1 is lower quartile and Q3 is upper quartile Compare datasets in terms of mean, median, range, IQR and standard deviation, interpret the differences observed in the context of the data, and report the findings in a systematic and concise manner.

Other Year 11 skills

Year 11 skills not currently linked to an entry on this page. These may include revision, extension practice, or skills still awaiting a curriculum mapping.

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