Australia
Skills available for Australia year 12 maths curriculum
Objectives are in black and IXL maths skills are in dark green. Hold your mouse over the name of a skill to view a sample question. Click on the name of a skill to practise that skill.
Show alignments for:
- Australian Curriculum: Senior Secondary Essential Mathematics Australian Curriculum: Senior Secondary Essential Mathematics
- Australian Curriculum: Senior Secondary General Mathematics Australian Curriculum: Senior Secondary General Mathematics
- Australian Curriculum: Senior Secondary Mathematical Methods Australian Curriculum: Senior Secondary Mathematical Methods
- Australian Curriculum: Senior Secondary Specialist Mathematics Australian Curriculum: Senior Secondary Specialist Mathematics
Actions
11-12.1.1 Calculations, percentages and rates
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11-12. Calculations:
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11-12.ACMEM001 solve practical problems requiring basic number operations
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11-12.ACMEM002 apply arithmetic operations according to their correct order
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11-12.ACMEM003 ascertain the reasonableness of answers to arithmetic calculations
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11-12.ACMEM004 use leading-digit approximation to obtain estimates of calculations
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11-12.ACMEM005 use a calculator for multi-step calculations
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11-12.ACMEM006 check results of calculations for accuracy
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11-12.ACMEM007 recognise the significance of place value after the decimal point
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11-12.ACMEM008 evaluate decimal fractions to the required number of decimal places
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11-12.ACMEM009 round up or round down numbers to the required number of decimal places
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11-12.ACMEM010 apply approximation strategies for calculations.
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11-12. Percentages:
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11-12.ACMEM011 calculate a percentage of a given amount
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11-12.ACMEM012 determine one amount expressed as a percentage of another
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11-12.ACMEM013 apply percentage increases and decreases in situations; for example, mark-ups, discounts and GST.
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11-12. Rates:
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11-12.ACMEM014 identify common usage of rates; for example, km/h as a rate to describe speed, beats/minute as a rate to describe pulse
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11-12.ACMEM015 convert units of rates occurring in practical situations to solve problems
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11-12.ACMEM016 use rates to make comparisons; for example, using unit prices to compare best buys, comparing heart rates after exercise.
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11-12.1.2 Measurement
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11-12. Linear measure:
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11-12.ACMEM017 use metric units of length, their abbreviations, conversions between them, and appropriate levels of accuracy and choice of units
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11-12.ACMEM018 estimate lengths
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11-12.ACMEM019 convert between metric units of length and other length units
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11-12.ACMEM020 calculate perimeters of familiar shapes, including triangles, squares, rectangles, and composites of these.
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11-12. Area measure:
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11-12.ACMEM021 use metric units of area, their abbreviations, conversions between them, and appropriate choices of units
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11-12.ACMEM021 estimate the areas of different shapes
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11-12.ACMEM023 convert between metric units of area and other area units
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11-12.ACMEM024 calculate areas of rectangles and triangles.
- Area of triangles and quadrilaterals (10-W.5)
- Area of a triangle: sine formula (11-V.20)
- Area of a triangle: Law of Sines (11-V.21)
- Area of polygons and circles (11-Y.2)
- Area and perimeter in the coordinate plane (11-Y.3)
- Area of a triangle: sine formula (12-L.16)
- Area of a triangle: Heron's formula (12-L.17)
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11-12. Mass:
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11-12.ACMEM025 use metric units of mass, their abbreviations, conversions between them, and appropriate choices of units
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11-12.ACMEM026 estimate the mass of different objects.
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11-12. Volume and capacity:
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11-12.ACMEM027 use metric units of volume, their abbreviations, conversions between them, and appropriate choices of units
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11-12.ACMEM028 understand the relationship between volume and capacity
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11-12.ACMEM029 estimate volume and capacity of various objects
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11-12.ACMEM030 calculate the volume of objects, such as cubes and rectangular and triangular prisms.
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11-12. Units of energy:
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11-12.ACMEM031 use units of energy to describe consumption of electricity, such as kilowatt hours
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11-12.ACMEM032 use units of energy used for foods, including calories
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11-12.ACMEM033 use units of energy to describe the amount of energy in activity, such as kilojoules
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11-12.ACMEM034 convert from one unit of energy to another.
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11-12.1.3 Algebra
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11-12. Single substitution:
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11-12.ACMEM035 substitute numerical values into algebraic expressions; for example, substitute different values of x to evaluate the expressions 3x/5, 5(2x - 4).
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11-12. General substitution:
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11-12.ACMEM036 substitute given values for the other pronumerals in a mathematical formula to find the value of the subject of the formula.
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11-12.1.4 Graphs
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11-12. Reading and interpreting graphs:
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11-12.ACMEM037 interpret information presented in graphs, such as conversion graphs, line graphs, step graphs, column graphs and picture graphs
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11-12.ACMEM038 interpret information presented in two-way tables
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11-12.ACMEM039 discuss and interpret graphs found in the media and in factual texts.
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11-12. Drawing graphs:
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11-12.ACMEM040 determine which type of graph is best used to display a dataset
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11-12.ACMEM041 use spreadsheets to tabulate and graph data
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11-12.ACMEM042 draw a line graph to represent any data that demonstrate a continuous change, such as hourly temperature.
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11-12.2.1 Representing and comparing data
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11-12. Classifying data:
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11-12.ACMEM043 identify examples of categorical data
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11-12.ACMEM044 identify examples of numerical data.
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11-12. Data presentation and interpretation:
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11-12.ACMEM045 display categorical data in tables and column graphs
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11-12.ACMEM046 display numerical data as frequency distributions, dot plots, stem and leaf plots, and histograms
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11-12.ACMEM047 recognise and identify outliers
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11-12.ACMEM048 compare the suitability of different methods of data presentation in real-world contexts.
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11-12. Summarising and interpreting data:
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11-12.ACMEM049 identify the mode
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11-12.ACMEM050 calculate measures of central tendency, the arithmetic mean and the median
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11-12.ACMEM051 investigate the suitability of measures of central tendency in various real-world contexts
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11-12.ACMEM052 investigate the effect of outliers on the mean and the median
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11-12.ACMEM053 calculate and interpret quartiles, deciles and percentiles
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11-12.ACMEM054 use informal ways of describing spread, such as spread out/dispersed, tightly packed, clusters, gaps, more/less dense regions, outliers
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11-12.ACMEM055 calculate and interpret statistical measures of spread, such as the range, interquartile range and standard deviation
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11-12.ACMEM056 investigate real-world examples from the media illustrating inappropriate uses, or misuses, of measures of central tendency and spread.
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11-12. Comparing data sets:
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11-12.ACMEM057 compare back-to-back stem plots for different datasets
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11-12.ACMEM058 complete a five number summary for different datasets
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11-12.ACMEM059 construct box plots using a five number summary
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11-12.ACMEM060 compare the characteristics of the shape of histograms using symmetry, skewness and bimodality.
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11-12.2.2 Percentages
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11-12. Percentage calculations:
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11-12.ACMEM061 review calculating a percentage of a given amount
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11-12.ACMEM062 review one amount expressed as a percentage of another.
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11-12. Applications of percentages:
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11-12.ACMEM063 determine the overall change in a quantity following repeated percentage changes; for example, an increase of 10% followed by a decrease of 10%
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11-12.ACMEM064 calculate simple interest for different rates and periods.
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11-12.2.3 Rates and ratios
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11-12. Ratios:
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11-12.ACMEM065 demonstrate an understanding of the elementary ideas and notation of ratio
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11-12.ACMEM066 understand the relationship between fractions and ratio
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11-12.ACMEM067 express a ratio in simplest form
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11-12.ACMEM068 find the ratio of two quantities
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11-12.ACMEM069 divide a quantity in a given ratio
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11-12.ACMEM070 use ratio to describe simple scales.
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11-12. Rates:
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11-12.ACMEM071 review identifying common usage of rates such as km/h
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11-12.ACMEM072 convert between units for rates; for example, km/h to m/s, mL/min to L/h
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11-12.ACMEM073 complete calculations with rates, including solving problems involving direct proportion in terms of rate.
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11-12.ACMEM074 use rates to make comparisons
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11-12.ACMEM075 use rates to determine costs; for example, calculating the cost of a tradesman using rates per hour, call-out fees.
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11-12.2.4 Time and motion
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11-12. Time:
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11-12.ACMEM076 use units of time, conversions between units, fractional, digital and decimal representations
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11-12.ACMEM077 represent time using 12-hour and 24-hour clocks
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11-12.ACMEM078 calculate time intervals, such as time between, time ahead, time behind
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11-12.ACMEM079 interpret timetables, such as bus, train and ferry timetables
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11-12.ACMEM080 use several timetables and electronic technologies to plan the most time-efficient routes
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11-12.ACMEM081 interpret complex timetables, such as tide charts, sunrise charts and moon phases
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11-12.ACMEM082 compare the time taken to travel a specific distance with various modes of transport.
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11-12. Distance:
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11-12.ACMEM083 use scales to find distances, such as on maps; for example, road maps, street maps, bushwalking maps, online maps and cadastral maps
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11-12.ACMEM084 optimise distances through trial-and-error and systematic methods; for example, shortest path, routes to visit all towns, and routes to use all roads.
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11-12. Speed:
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11-12.ACMEM085 identify the appropriate units for different activities, such as walking, running, swimming and flying
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11-12.ACMEM086 calculate speed, distance or time using the formula speed = distance/time
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11-12.ACMEM087 calculate the time or costs for a journey from distances estimated from maps
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11-12.ACMEM088 interpret distance-versus-time graphs
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11-12.ACMEM089 calculate and interpret average speed; for example, a 4-hour trip covering 250 km.
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11-12.3.1 Measurement
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11-12. Linear measure:
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11-12.ACMEM090 review metric units of length, their abbreviations, conversions between them, estimation of lengths, and appropriate choices of units
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11-12.ACMEM091 calculate perimeters of familiar shapes, including triangles, squares, rectangles, polygons, circles, arc lengths, and composites of these.
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11-12. Area measure:
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11-12.ACMEM092 review metric units of area, their abbreviations, and conversions between them
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11-12.ACMEM093 use formulas to calculate areas of regular shapes, including triangles, squares, rectangles, parallelograms, trapeziums, circles and sectors
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11-12.ACMEM094 find the area of irregular figures by decomposition into regular shapes
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11-12.ACMEM095 find the surface area of familiar solids, including cubes, rectangular and triangular prisms, spheres and cylinders
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11-12.ACMEM096 find the surface area of pyramids, such as rectangular- and triangular-based pyramids
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11-12.ACMEM097 use addition of the area of the faces of solids to find the surface area of irregular solids.
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11-12. Mass:
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11-12.ACMEM098 review metric units of mass (and weight), their abbreviations, conversions between them, and appropriate choices of units
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11-12.ACMEM099 recognise the need for milligrams
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11-12.ACMEM100 convert between grams and milligrams.
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11-12. Volume and capacity:
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11-12.ACMEM101 review metric units of volume, their abbreviations, conversions between them, and appropriate choices of units
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11-12.ACMEM102 recognise relations between volume and capacity, recognising that 1cm³ = 1mL and 1m³ = 1kL
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11-12.ACMEM103 use formulas to find the volume and capacity of regular objects such as cubes, rectangular and triangular prisms and cylinders
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11-12.ACMEM104 use formulas to find the volume of pyramids and spheres.
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11-12.3.2 Scales, plans and models
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11-12. Geometry:
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11-12.ACMEM105 recognise the properties of common two-dimensional geometric shapes and three-dimensional solids
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11-12.ACMEM106 interpret different forms of two-dimensional representations of three-dimensional objects, including nets and perspective diagrams
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11-12.ACMEM107 use symbols and conventions for the representation of geometric information; for example, point, line, ray, angle, diagonal, edge, curve, face and vertex.
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11-12. Interpret scale drawings:
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11-12.ACMEM108 interpret commonly used symbols and abbreviations in scale drawings
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11-12.ACMEM109 find actual measurements from scale drawings, such as lengths, perimeters and areas
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11-12.ACMEM110 estimate and compare quantities, materials and costs using actual measurements from scale drawings; for example, using measurements for packaging, clothes, painting, bricklaying and landscaping.
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11-12. Creating scale drawings:
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11-12.ACMEM111 understand and apply drawing conventions of scale drawings, such as scales in ratio, clear indications of dimensions, and clear labelling
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11-12.ACMEM112 construct scale drawings by hand and by using software packages.
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11-12. Three dimensional objects:
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11-12.ACMEM113 interpret plans and elevation views of models
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11-12.ACMEM114 sketch elevation views of different models
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11-12.ACMEM115 interpret diagrams of three-dimensional objects.
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11-12. Right-angled triangles:
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11-12.ACMEM116 apply Pythagoras' theorem to solve problems
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11-12.ACMEM117 apply the tangent ratio to find unknown angles and sides in right-angled triangles
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11-12.ACMEM118 work with the concepts of angle of elevation and angle of depression
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11-12.ACMEM119 apply the cosine and sine ratios to find unknown angles and sides in right-angled triangles
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11-12.ACMEM120 solve problems involving bearings
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11-12.3.3 Graphs
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11-12. Cartesian plane:
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11-12.ACMEM121 demonstrate familiarity with Cartesian coordinates in two dimensions by plotting points on the Cartesian plane
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11-12.ACMEM122 generate tables of values for linear functions, including for negative values of x
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11-12.ACMEM123 graph linear functions for all values of x with pencil and paper and with graphing software.
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11-12. Using graphs:
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11-12.ACMEM124 interpret and use graphs in practical situations, including travel graphs and conversion graphs
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11-12.ACMEM125 draw graphs from given data to represent practical situations
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11-12.ACMEM126 interpret the point of intersection and other important features of given graphs of two linear functions drawn from practical contexts; for example, the 'break-even' point.
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11-12.3.4 Data collection
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11-12. Census:
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11-12.ACMEM127 investigate the procedure for conducting a census
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11-12.ACMEM128 investigate the advantages and disadvantages of conducting a census
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11-12. Surveys:
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11-12.ACMEM129 understand the purpose of sampling to provide an estimate of population values when a census is not used
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11-12.ACMEM130 investigate the different kinds of samples; for example, systematic samples, self-selected samples, simple random samples
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11-12.ACMEM131 investigate the advantages and disadvantages of these kinds of samples; for example, comparing simple random samples with self-selected samples.
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11-12. Simple survey procedure:
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11-12.ACMEM132 identify the target population to be surveyed
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11-12.ACMEM133 investigate questionnaire design principles; for example, simple language, unambiguous questions, consideration of number of choices, issues of privacy and ethics, and freedom from bias.
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11-12. Sources of bias:
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11-12.ACMEM134 describe the faults in the collection of data process
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11-12.ACMEM135 describe sources of error in surveys; for example, sampling error and measurement error
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11-12.ACMEM136 investigate the possible misrepresentation of the results of a survey due to misunderstanding the procedure, or misunderstanding the reliability of generalising the survey findings to the entire population
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11-12.ACMEM137 investigate errors and misrepresentation in surveys, including examples of media misrepresentations of surveys.
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11-12. Bivariate scatterplots:
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11-12.ACMEM138 describe the patterns and features of bivariate data
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11-12.ACMEM139 describe the association between two numerical variables in terms of direction (positive/negative), form (linear/non-linear) and strength (strong/moderate/weak).
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11-12. Line of best fit:
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11-12.ACMEM140 identify the dependent and independent variable
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11-12.ACMEM141 find the line of best fit by eye
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11-12.ACMEM142 use technology to find the line of best fit
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11-12.ACMEM143 interpret relationships in terms of the variables
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11-12.ACMEM144 use technology to find the correlation coefficient (an indicator of the strength of linear association)
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11-12.ACMEM145 use the line of best fit to make predictions, both by interpolation and extrapolation
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11-12.ACMEM146 recognise the dangers of extrapolation
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11-12.ACMEM147 distinguish between causality and correlation through examples.
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11-12.4.1 Probability and relative frequencies
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11-12. Probability expressions:
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11-12.ACMEM148 interpret commonly used probability statements, including 'possible', 'probable', 'likely', 'certain'
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11-12.ACMEM149 describe ways of expressing probabilities formally using fractions, decimals, ratios, and percentages.
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11-12. Simulations:
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11-12.ACMEM150 perform simulations of experiments using technology
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11-12.ACMEM151 recognise that the repetition of chance events is likely to produce different results
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11-12.ACMEM152 identify relative frequency as probability
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11-12.ACMEM153 identify factors that could complicate the simulation of real-world events.
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11-12. Simple probabilities:
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11-12.ACMEM154 construct a sample space for an experiment
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11-12.ACMEM155 use a sample space to determine the probability of outcomes for an experiment
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11-12.ACMEM156 use arrays or tree diagrams to determine the outcomes and the probabilities for experiments.
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11-12. Probability applications
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11-12.ACMEM157 determine the probabilities associated with simple games
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11-12.ACMEM158 determine the probabilities of occurrence of simple traffic-light problems.
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11-12.4.2 Earth geometry and time zones
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11-12. Location:
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11-12.ACMEM159 locate positions on Earth's surface given latitude and longitude using GPS, a globe, an atlas, and digital technologies
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11-12.ACMEM160 find distances between two places on Earth on the same longitude
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11-12.ACMEM161 find distances between two places on Earth using appropriate technology.
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11-12. Time:
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11-12.ACMEM162 understand the link between longitude and time
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11-12.ACMEM163 solve problems involving time zones in Australia and in neighbouring nations, making any necessary allowances for daylight saving
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11-12.ACMEM164 solve problems involving Greenwich Mean Time and the International Date Line
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11-12.ACMEM165 find time differences between two places on Earth
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11-12.ACMEM166 solve problems associated with time zones; for example, internet and phone usage
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11-12.ACMEM167 solve problems relating to travelling east and west, incorporating time zone changes.
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11-12.4.3 Loans and compound interest
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11-12. Compound interest:
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11-12.ACMEM168 review the principles of simple interest
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11-12.ACMEM169 understand the concept of compound interest as a recurrence relation
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11-12.ACMEM170 consider similar problems involving compounding; for example, population growth
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11-12.ACMEM171 use technology to calculate the future value of a compound interest loan or investment and the total interest paid or earned
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11-12.ACMEM172 use technology to compare, numerically and graphically, the growth of simple interest and compound interest loans and investments
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11-12.ACMEM173 use technology to investigate the effect of the interest rate and the number of compounding periods on the future value of a loan or investment.
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11-12. Reducing balance loans (compound interest loans with periodic repayments):
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11-12.ACMEM174 use technology and a recurrence relation to model a reducing balance loan
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11-12.ACMEM175 investigate the effect of the interest rate and repayment amount on the time taken to repay a loan.
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