Grade 11 General Maths
Semester 1 (Unit 1)
Topic 1: Consumer arithmetic
Applications of rates and percentages:
review rates and percentages (ACMGM001)
calculate weekly or monthly wage from an annual salary, wages from an hourly rate including situations involving overtime and other allowances and earnings based on commission or piecework (ACMGM002)
calculate payments based on government allowances and pensions (ACMGM003)
prepare a personal budget for a given income taking into account fixed and discretionary spending (ACMGM004)
compare prices and values using the unit cost method (ACMGM005)
apply percentage increase or decrease in various contexts; for example, 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 (ACMGM006)
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 in Australian dollars (ACMGM007)
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. (ACMGM008)
Use of spreadsheets:
use a spreadsheet to display examples of the above computations when multiple or repeated computations are required; for example, 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. (ACMGM009)
Topic 2: Algebra and matrices
Linear and non-linear expressions:
substitute numerical values into linear algebraic and simple non-linear algebraic expressions, and evaluate (ACMGM010)
find the value of the subject of the formula, given the values of the other pronumerals in the formula (ACMGM011)
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; for example, a table displaying the body mass index (BMI) of people of different weights and heights. (ACMGM012)
Matrices and matrix arithmetic:
use matrices for storing and displaying information that can be presented in rows and columns; for example, databases, links in social or road networks (ACMGM013)
recognise different types of matrices (row, column, square, zero, identity) and determine their size (ACMGM014)
perform matrix addition, subtraction, multiplication by a scalar, and matrix multiplication, including determining the power of a matrix using technology with matrix arithmetic capabilities when appropriate (ACMGM015)
use matrices, including matrix products and powers of matrices, to model and solve problems; for example, 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. (ACMGM016)
Topic 3: Shape and measurement
Pythagoras Theorem:
review Pythagoras’ Theorem and use it to solve practical problems in two dimensions and for simple applications in three dimensions. (ACMGM017)
Mensuration:
solve practical problems requiring the calculation of perimeters and areas of circles, sectors of circles, triangles, rectangles, parallelograms and composites (ACMGM018)
calculate the volumes of standard three-dimensional objects such as spheres, rectangular prisms, cylinders, cones, pyramids and composites in practical situations; for example, the volume of water contained in a swimming pool (ACMGM019)
calculate the surface areas of standard three-dimensional objects such as spheres, rectangular prisms, cylinders, cones, pyramids and composites in practical situations; for example, the surface area of a cylindrical food container. (ACMGM020)
Similar figures and scale factors:
review the conditions for similarity of two-dimensional figures including similar triangles (ACMGM021)
use the scale factor for two similar figures to solve linear scaling problems (ACMGM022)
obtain measurements from scale drawings, such as maps or building plans, to solve problems (ACMGM023)
obtain a scale factor and use it to solve scaling problems involving the calculation of the areas of similar figures (ACMGM024)
obtain a scale factor and use it to solve scaling problems involving the calculation of surface areas and volumes of similar solids. (ACMGM025)
Unit 2
Topic 1: Univariate data analysis and the statistical investigation process
The statistical investigation process:
review the statistical investigation process; for example, identifying a problem and posing a statistical question, collecting or obtaining data, analysing the data, interpreting and communicating the results. (ACMGM026)
Making sense of data relating to a single statistical variable:
classify a categorical variable as ordinal, such as income level (high, medium, low), or nominal, such as place of birth (Australia, overseas), and use tables and bar charts to organise and display the data (ACMGM027)
classify a numerical variable as discrete, such as the number of rooms in a house, or continuous, such as the temperature in degrees Celsius (ACMGM028)
with the aid of an appropriate graphical display (chosen from dot plot, stem plot, bar chart or histogram), describe the distribution of a numerical dataset in terms of modality (uni or multimodal), shape (symmetric versus positively or negatively skewed), location and spread and outliers, and interpret this information in the context of the data (ACMGM029)
determine the mean and standard deviation of a dataset and use these statistics as measures of location and spread of a data distribution, being aware of their limitations. (ACMGM030)
Comparing data for a numerical variable across two or more groups:
construct and use parallel box plots (including the use of the ‘Q1 – 1.5 x IQR’ and ‘Q3 + 1.5 x IQR’ criteria for identifying possible outliers) to compare groups in terms of location (median), spread (IQR and range) and outliers and to interpret and communicate the differences observed in the context of the data (ACMGM031)
compare groups on a single numerical variable using medians, means, IQRs, ranges or standard deviations, as appropriate; interpret the differences observed in the context of the data; and report the findings in a systematic and concise manner (ACMGM032)
implement the statistical investigation process to answer questions that involve comparing the data for a numerical variable across two or more groups; for example, are Year 11 students the fittest in the school? (ACMGM033)
Topic 2: 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 (ACMGM034)
determine the area of a triangle given two sides and an included angle by using the rule Area=12absinCArea=12absinC, or given three sides by using Heron’s rule, and solve related practical problems (ACMGM035)
solve problems involving non-right-angled triangles using the sine rule (ambiguous case excluded) and the cosine rule (ACMGM036)
solve 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 bearings in navigation. (ACMGM037)
Topic 3: Linear equations and their graphs
Linear equations:
identify and solve linear equations (ACMGM038)
develop a linear formula from a word description (ACMGM039)
Straight-line graphs and their applications:
construct straight-line graphs both with and without the aid of technology (ACMGM040)
determine the slope and intercepts of a straight-line graph from both its equation and its plot (ACMGM041)
interpret, in context, the slope and intercept of a straight-line graph used to model and analyse a practical situation (ACMGM042)
construct and analyse a straight-line graph to model a given linear relationship; for example, modelling the cost of filling a fuel tank of a car against the number of litres of petrol required. (ACMGM043)
Simultaneous linear equations and their applications:
solve a pair of simultaneous linear equations, using technology when appropriate (ACMGM044)
solve practical problems that involve finding the point of intersection of two straight-line graphs; for example, determining the break-even point where cost and revenue are represented by linear equations. (ACMGM045)
Piece-wise linear graphs and step graphs:
sketch piece-wise linear graphs and step graphs, using technology when appropriate (ACMGM046)
interpret piece-wise linear and step graphs used to model practical situations; for example, the tax paid as income increases, the change in the level of water in a tank over time when water is drawn off at different intervals and for different periods of time, the charging scheme for sending parcels of different weights through the post. (ACMGM047)