Download Chapter 1 Earning money

1
MATHS QUEST
General
Mathematics:
Preliminary
Course
2
Chapter 1: Earning money
FM1: Financial mathematics
Section
Content
Calculating salary payments (page 2)
WE 1, 2, 3
Ex 1A Calculating salary payments (page 3)
Calculating salary payments
 Dividing an annual salary from a
periodical amount
 Calculating an annual salary from a
periodical amount
Calculating wage payments
 Calculating wages from an hourly rate
 Including overtime and special
allowances
Calculating commissions and royalties
 Calculation as a straight percentage
 Calculating part commission and part
retainer
Payment by piece
Calculating wages (page 5)
WE 4, 5, 6
Ex 1B Calculating wages (page 7)
Computer application 1: Spreadsheets (page 9)
Commission and royalties (page 10)
WE 7, 8, 9, 10
Ex 1C Commission and royalties (page 13)
Payment by piece (page 15)
WE 11, 12, 13
Ex 1D Payment by piece (page 16)
Working overtime (page 18)
WE 14, 15, 16, 17
Ex 1E Working overtime (page 20)
Computer application 2: Wages (page 22)
Fixed incomes (page 23)
Investigating government payments (page 23)
Additions to and deductions from gross pay
(page 24)
WE 18, 19, 20, 21
Calculating overtime rates
 Using time-and-a-half and double time to
calculate wages
 Completing time sheets
Calculating income based on government
payments
 Students to investigate government
payments
Additions and deductions from gross pay
 Students to calculate net pay given the
amount of each deduction from gross pay
Prescribed skills, knowledge and
understanding
 calculating monthly, fortnightly, weekly,
daily and hourly payments from salary


calculating wages; incorporating hourly
rates and penalty rates like overtime and
special allowances (wet work, confined
spaces, toxic substances, heat, heights)
calculating earnings based on
commission, piecework, royalties

calculating earnings based on
commission, piecework, royalties

calculating wages; incorporating hourly
rates and penalty rates like overtime and
special allowances (wet work, confined
spaces, toxic substances, heat, heights)
calculating income based on government
allowances such as the youth allowance
and pensions


determining deductions such as union
fees, superannuation contributions, health
fund instalments and tax instalments
3
Ex 1F Additions to and deductions from gross
pay (page 26)
Computer application 3: Wages template
(page 28)
Costs of banking (page 29)
Examining bank fees and taxes (page 29)
Budgeting (page 30)
WE 22, 23, 24, 25
Ex 1G Budgeting (page 34)
Summary (page 39)
Chapter review (page 40)
Practice examination questions (page 42)

Students to calculate the size of various
deductions
Calculating annual leave loading


calculating annual leave loading
calculating net pay following deductions
Costs of banking
 Students to investigate the costs
associated with maintaining accounts at
financial institutions
Calculating personal budgets
Reading household bills
 Questions relating to electricity, gas,
telephone bills, etc

calculating and comparing user costs
associated with maintaining accounts at
financial institutions


creating and managing budgets
reading information from household
bills, including those for electricity, gas,
telephone, council rates and water rates

4
Chapter 2: Units of measurement
M1: Measurement
Section
Content
Units of measurement (page 44)
WE 1, 2, 3, 4, 5
Ex 2A Units of measurement (page 47)
Units of measurement
 Converting between common units
 Choosing the most appropriate units to
use in practical situations
Errors in measurement
 Determining maximum possible error
 Calculating relative error in a variety of
contexts
 Determining percentage error
Relative error (page 49)
WE 6, 7, 8, 9
Ex 2B Relative error (page 51)
Measuring heights (page 53)
Prescribed skills, knowledge and
understanding
 determining the appropriate units to use
when measuring physical attributes
 converting between commonly used units
of measurement using standard prefixes
 determining possible sources of error
 recognising that accuracy of physical
1
measurement is limited to  of the
2


Significant figures (page 54)
WE 10, 11, 12
Ex 2C Significant figures (page 57)
Rates (page 59)
WE 13, 14, 15, 16, 17, 18,
Ex 2D Rates (page 62)
Significant figures
 Explaining the most practical degree of
accuracy
 Rounding off measurements to the
required accuracy, including questions
involving scientific notation
Working with rates
 Simplifying rates
 Converting from km/h to m/s and other
similar exercises
 Calculations involving medicine and
chemicals in agriculture





smallest unit of which the measuring
instrument is capable of
calculating the percentage error of a
measurement
repeating and averaging measurements to
reduce the likelihood of error
determining the significant figures to be
used when recording measurements, in
relation to the accuracy of the measuring
instrument being used
using positive and negative powers of ten
to express numbers in scientific notation
calculating rates (pay, speeds, flow rates)
converting between units for rates, eg.
km/h to m/s
calculating concentrations expressed as
weight/weight, weight/volume or
volume/volume
5
Percentage change (page 64)
WE 19
Ex 2E Percentage change (page 65)
Using ratios (page 66)
WE 20, 21, 22
Ex 2F Using ratios (page 69)
Summary (page 71)
Chapter review (page 72)
Practice examination questions (page 73)
Percentage change
 Exercises on increasing and decreasing a
certain quantity by given percentages
 Calculating repeated discounts
Ratios
 Simplifying ratios
 Applying ratios to practical situations
 Dividing a quantity in a given ratio

determining overall change in a quantity
following repeated percentage changes

finding the ratio of two quantities in
familiar contexts
dividing quantities in a given ratio
using a unitary method to solve problems


6
Chapter 3: Applications of area and volume
M2: Measurement
Section
Content
Review of area (page 76)
WE 1, 2, 3, 4
Ex 3A Review of area (page 78)
Maximising an area of land (page 81)
Calculating irregular areas from a field
diagram (page 82)
WE 5
Land survey (page 83)
Ex 3B Calculating irregular areas from a field
diagram (page 84)
Solid shapes (page 86)
WE 6, 7, 8
Ex 3C Solid shapes (page 88)
Basic areas
 Review of calculating areas of triangles
and quadrilaterals
 Applying this to practical applications
Areas from surveys
 Calculating areas using traverse surveys
leading to field diagrams
 Performing a survey and using the results
to produce a field diagram and calculate
an area
Solid shapes
 Naming solids
 Matching solids with nets
 Drawing nets of solids
 Using isometric paper to draw solid
shapes
Surface area (page 90)
WE 9, 10, 11
Ex 3D Surface area (page 92)
Volume of a prism (page 95)
Exploring the volume of a prism (page 95)
WE 12, 13, 14, 15, 16
Ex 3E Volume of a prism (page 97)
Areas of solids
 Calculating surface areas of prisms and
pyramids
Volume of prisms
 Calculating volumes of prisms and
cylinders
Prescribed skills, knowledge and
understanding
 calculating the area of triangles and
quadrilaterals (review only)

using a field diagram to calculate the area
of irregularly-shaped blocks of land

classifying polyhedra into prisms (named
with respect to their constant crosssection), pyramids or other
constructing nets of solids and matching
nets to solids
sketching 3D solids using isometric
paper and vanishing points
using appropriate formulae when
calculating the surface area of right
prisms, square and rectangular pyramids
using appropriate formulae when
calculating the volume of right prisms
and cylinders
applying the relationship between units
of capacity and units of volume





7
Volume of other solids (page 101)
WE 17, 18, 19
Ex 3F Volume of other solids (page 103)
Summary (page 106)
Chapter review (page 107)
Practice examination questions (page 110)
Volume of other solids
 Calculating volumes of pyramids, cones
and spheres and composite shapes
 Calculating capacity after determining
volume

using appropriate formulae when
calculating the volume of pyramids,
cones and spheres
8
Chapter 4: Basic algebraic skills
AM1: Algebraic modelling
Section
Content
General number patterns (page 112)
WE 1, 2, 3
Ex 4A General number patterns (page 114)
Number pattern notation (page 116)
WE 4, 5, 6, 7
Ex 4B Number pattern notation (page 119)
Number patterns
 Describing patterns in words
 Calculating terms in a pattern
Terms of sequences
 Calculating terms of a sequence written
in algebraic form
 Writing a sequence in algebraic form
Collecting like terms
 Simplifying algebraic expressions by
collecting like terms
Adding and subtracting like terms (page 122)
WE 8, 9, 10
Ex 4C Adding and subtracting like terms
(page 123)
Substitution (page 124)
WE 11, 12
Ex 4D Substitution (page 125)
Multiplication and division of algebraic
expressions (page 127)
WE 13, 14, 15, 16, 17
Ex 4E Multiplication and division of algebraic
expressions (page 129)
Solving linear equations (page 131)
WE 18, 19, 20, 21, 22
Ex 4F Solving linear equations (page 134)
Substitution into formulae
 Substituting into a variety of formulae to
calculate the subject
 Calculations involving practical
applications
Algebraic multiplication and division
 Multiplying algebraic expressions
including those with indices
 Dividing simple algebraic expressions
including those with indices
 Removing brackets and simplifying
 Simplifying using the three index laws
Solving equations
 Solving linear equations including those
with fractions
 Substituting solutions to verify accuracy
Prescribed skills, knowledge and
understanding
 identifying and generalising simple linear
number patterns

identifying and generalising simple linear
number patterns

adding and subtracting like terms

evaluating the subject of a formula
through substitution of numerical values,
using a wide variety of formulae


multiplying algebraic terms
dividing single terms (linear, quadratic
and cubic)
expanding and simplifying expressions


solving linear equations involving up to
three steps (fractions with numerical
denominators only)
9
Equations arising from substitution (page 136)
WE 23, 24
Ex 4G Equations arising from substitution
(page 137)
Summary (page 139)
Chapter review (page 140)
Practice examination questions (page 141)
Substituting and solving equations
 Substituting into a variety of formulae to
calculate a pronumeral which is not the
subject

solving equations following substitution
and evaluation
10
Chapter 5: Statistics and society
DA1: Data analysis
Section
Content
Analysing data (page 144)
Why statistical investigation? (page 144)
A statistical investigation – 1 (page 144)
Statistical processes (page 145)
Posing questions (page 145)
A statistical investigation – 2 (page 145)
Analysing data
 Examining applications of data analysis
 Questions for a statistical investigation
Posing questions
 Examining situations that need prepared
questions to conduct an investigation
Collecting data (page 146)
WE 1
Ex 5A Collecting data (page 147)
A statistical investigation - 3 (page 148)
Organising data (page 148)
WE 2, 3
Ex 5B Organising data (page 150)
A statistical investigation – 4 (page 150)
Displaying data (page 151)
WE 4, 5
Exercise 5C Displaying data (page 153)
A statistical investigation - 5 (page 153)
A statistical investigation – 6 (page 153)
A statistical investigation – 7 (page 153)
Collecting information
 Examining different methods of data
collection using external/internal sources
 Preparatory work in data collection
Organising data
 Organising collected data in tables
 Selecting the most appropriate type of
table for a given set of data
Displaying data and writing a report
 Displaying data using a variety of graphs
such as column and sector graphs
 Examining data, reaching conclusions
and making recommendations
 Writing a report on a statistical inquiry
including suitable graphs
Quality control
 Explaining the need for quality control
 Practical exercises involving calculations
to measure whether quality control
guidelines are being met or not
Quality control (page 154)
WE 6, 7
Ex 5D Quality control (page 156)
Prescribed skills, knowledge and
understanding
 the importance of analysing data in
planning and decision-making by
governments and businesses
 the process of statistical inquiry
including – posing questions
 using the principles of effective
questionnaire design
 the process of statistical inquiry
including – collecting data

the process of statistical inquiry
including – organising data and
summarising data

the process of statistical inquiry
including – displaying data, analysing
data and drawing conclusions and writing
a report

the role of statistical methods in quality
control in manufacturing industries
11
Privacy and ethical issues (page 157)
Privacy issues (page 157)
Statistical organisations (page 157)
Organisations that use statistics (page 157)
Summary (page 158)
Chapter review (page 159)
Privacy and ethics in data collection
 Explanation of some ethical issues
surrounding data collection
 Examining privacy issues
Organisations that use statistics
 Information and an exercise on
organisations that require data collection
and its analysis



issues of privacy and ethics in data
collection and analysis
using the principles of effective
questionnaire design
organisations that collect and/or use
statistics, including the ABS, the UN, the
WHO
12
Chapter 6: Data collection and sampling
DA2: Data analysis
Section
Content
Target populations and sampling (page 162)
Gallup poll (page 162)
Identifying the target population (page 162)
WE 1, 2, 3
Ex 6A Target populations and sampling
(page 166)
Census or sample (page 168)
Sampling
 Identifying sections of the population for
a specific statistical investigation
 Collecting data by census or sample
 Choosing random, stratified or
systematic samples
 Using a calculator to generate random
numbers
Bias (page 169)
Biased sampling (page 169)
Biased sampling
 Examining types of bias that might occur
when sampling
Types of data (page 170)
WE 4, 5
Ex 6B Types of data (page 172)
Estimating populations (page 174)
Estimating a population (page 174)
WE 6
Ex 6C Estimating populations (page 175)
Population characteristics (page 176)
Population characteristics (page 176)
WE 7
Choosing a sample (page 177)
Types of data
 Examining data to see if it is categorical
or quantitative (discrete or continuous)
Sampling and releasing
 Estimating a total population by
sampling, releasing and sampling again
Choosing a sample
 Examining how to choose a sample so
that all appropriate sections of the
population are included
Prescribed skills, knowledge and
understanding
 identifying target populations
 determining if data for the whole
population is available or whether
sampling is necessary
 recognising that sampling provides an
estimate for a characteristic when the
entire population cannot be accessed
 distinguishing between sample types:
random, stratified, systematic
 determining which of the above sample
types is appropriate for a given situation
 generating random numbers with a table
or calculator to assist with sampling
 recognising that sampling provides an
estimate for a population characteristic
when the entire population cannot be
accessed
 classifying data as: quantitative (discrete
or continuous) or categorical

describing and using the ‘capturerecapture’ technique for estimating the
size of populations

relating sample selection to population
characteristics
recognising the effect of a sample size in
estimating the nature of a population

13
Summary (page 178)
Chapter review (page 179)
Practice examination questions (page 180)
14
Chapter 7: Modelling linear relationships
AM2: Algebraic modelling
Section
Content
Graphing linear functions (page 184)
WE 1, 2, 3
Ex 7A Graphing linear functions (page 186)
Graph of height versus age (page 187)
Graphing linear functions
 Explaining a function including the terms
independent and dependent variables
 Drawing linear graphs based on real-life
situations – recognising that in some
cases the model is limited
 Drawing conversion graphs
 Constructing a line of best fit
Gradient and intercept (page 188)
WE 4, 5, 6
Ex 7B Gradient and intercept (page 192)
Gradient and y intercept
 Calculating gradient from a graph
 The significance of the y intercept and
calculating it from a graph
Drawing graphs using gradient and intercept
(page 194)
WE 7, 8, 9, 10
Drawing graphs
 Drawing graphs of lines when given the
gradient and intercept on the vertical axis
Prescribed skills, knowledge and
understanding
 sketching graphical representations of
quantities that vary over a period of time
or in relation to each other
 identifying independent and dependent
variables in practical contexts
 graphing of linear functions derived from
everyday situations (eg. the cost of an
excursion = fixed cost + cost per student
 number of students) by plotting ordered
pairs from tables of values
 recognising the limitations of such
models, eg. a person’s height as a
function of age may be approximated by
a straight line for a limited number of
years, but not over a complete lifetime
 using graphs to convert from one
measurement to another ($AUD – Euros)
 drawing a line of best fit on a graphed set
of ordered pairs with a ruler and pencil
 calculating the gradients of such graphs
with a ruler and pencil
 establishing a meaning for the gradient in
the given context
 establishing a meaning for the intercept
on the vertical axis in the given context
 sketching graphs of linear functions
expressed in the form: y = mx + b
15
Ex 7C Drawing graphs using gradient and
intercept (page 197)
Graphing variations (page 199)
WE 11, 12
Ex 7D Graphing variations (page 200)
Currency conversions (page 201)
Proportional graphs
 Drawing graphs of direct proportion or
variation
 Finding the equation of proportion by
graphing data




Step and piecewise functions
WE 13, 14
Ex 7E Step and piecewise functions (page 203)
Step graphs
 Drawing step graphs
 Drawing graphs of piecewise function

Simultaneous equations (page 204)
WE 15
Ex 7F Simultaneous equations (page 205)
Graphing simultaneous equations
 Drawing graphs of simultaneous linear
equations based on practical examples,
and using these to solve problems

Summary (page 206)
Chapter review (page 207)
Practice examination questions (page 208)
developing a linear graph of the form:
y = ax from a description of a situation in
which one quantity varies in a direct
linear fashion with another, given one
ordered pair
using the above graph to establish the
value of a (the gradient) and to solve
problems related to the given variation
context
interpreting linear functions as models of
physical phenomena
using graphs to make conversions from
one measurement to another
(eg. $AUD to Euros)
using stepwise and piecewise linear
functions to model situations encountered
in daily life, eg. parking charges, taxi
fares, tax payments, mobile phone bills
interpreting the graphical solution of
simultaneous linear equations drawn
from practical situations
16
Chapter 8: Investing money
FM2: Financial mathematics
Section
Content
Calculation of simple interest (page 212)
WE 1, 2, 3, 4
Ex 8A Calculation of simple interest
(page 215)
Simple interest
 Calculating simple interest on
investments over various time periods
 Finding values other than I in I=Prn
Graphing simple interest functions (page 217)
WE 5, 6
Ex 8B Graphing simple interest functions
(page 219)
Computer application 1: Simple interest
spreadsheets (page 221)
Calculation of compound interest (page 222)
WE 7, 8, 9
Ex 8C Calculation of compound interest
(page 225)
Computer application 2: Compound interest
spreadsheets (page 227)
Calculating compound interest from a table of
compounded values (page 229)
WE 10, 11, 12
Ex 8D Calculating compound interest from a
table of compounded values (page 232)
Graphing compound interest functions (p 234)
WE 13, 14
Ex 8E Graphing compound interest functions
(page 236)
Simple interest graphs
 Completing simple interest tables
 Using these tables to graph interest and
investment values against time
 Using a simple interest spreadsheet
Prescribed skills, knowledge and
understanding
 calculating simple interest using I = Prn,
where P = principal, r = percentage
interest rate per period expressed as a
decimal (eg. rate of 8.2% means r =
0.082), and n = the number of periods
 calculating monthly, quarterly and
six-monthly interest rates based on
quoted rates per annum (pa)
 for fixed values of P, using tables of
values and hence drawing and describing
graphs of A against n for differing values
of r
Compound interest
 Calculating Future Value when interest is
compounded over various time periods
 Calculating the interest on investments
 Using a compound interest spreadsheet

using formulae to calculate future value,
compound interest and present value
Compound interest table
 Using a table to solve compound interest
problems
 Finding Present Value using the formula

using formulae to calculate future value,
compound interest and present value
calculating future and present values of
an investment from prepared tables
Compound interest graphs
 Completing compound interest tables
 Using these tables to draw and describe
graphs of FV against time


for fixed values of P, using tables of
values and hence drawing and describing
graphs of A against n for differing values
of r
17
Share dividends (page 238)
WE 15, 16
Ex 8F Share dividends (page 239)
Share dividends
 Calculating dividend yield for shares
 Calculating dividends on shares when
given the company profits

calculating the dividend paid on a share
holding and the dividend yield, excluding
franked dividends
Graphing share performance (page 241)
WE 17, 18
Ex 8G Graphing share performance (page 243)
Researching share prices (page 244)
Graphing shares
 Graphing the value of a share over a
certain time period and making
predictions from such graphs
 Graphing the performance of a given
share over a 6 month period
Inflation and appreciation
 Calculating the effect of inflation over
different time periods
 Using the compound interest formula in
inflation questions
 Calculating appreciation

extrapolating from the information
shown on a prepared graph of share
performance to suggest possible future
stockmarket movement

calculating the price of goods following
inflation
calculating the appreciated value of items
such as stamp collections and
memorabilia
Inflation and appreciation (page 245)
WE 19, 20, 21
Ex 8H Inflation and appreciation (page 247)
Summary (page 248)
Chapter review (page 249)
Practice examination questions (page 251)

18
Chapter 9: Displaying single data sets
DA3: Data analysis
Section
Content
Frequency tables (page 254)
WE 1, 2
Ex 9A Frequency tables (page 257)
Types of graphs (page 259)
WE 3, 4, 5, 6, 7
Ex 9B Types of graphs (page 262)
Choice of graph (page 264)
Producing graphs using technology (page 264)
Frequency tables
 Entering grouped and ungrouped data
into frequency tables
Statistical graphs
 Creating dot plots, sector graphs, line
charts, bar and column graphs and radar
charts
 Advantages and disadvantages of various
graphs
 Graphing with a spreadsheet or graphics
calculator
Statistical graphs (page 265)
WE 8, 9, 10
Ex 9C Statistical graphs (page 268)
Statistical graphs
 Creating frequency histograms and
polygons and cumulative frequency
graphs
 Working with grouped and ungrouped
data
Prescribed skills, knowledge and
understanding
 creating tally charts and frequency tables
to organise undergrouped and grouped
data
 creating dot plots, sector graphs (pie
charts), bar graphs, histograms and line
graphs, with attention being paid to the
scale on each axis
 selecting a suitable scale for graph axes
 drawing a radar chart to display data such
as sales figures, temperature or rainfall
readings (see example at end of unit)
 describing the strengths and weaknesses
of sector graphs, bar graphs, histograms,
frequency polygons and radar charts;
including suitability for data represented
 noting the capacity of statistical displays
for misrepresentation, particularly in the
selection of the scale used on the axes
 linking types of data with displays, eg.
continuous quantitative data is best
represented by a histogram; categorical
data with a bar graph or sector graph etc
 creating frequency graphs and
cumulative frequency graphs (ogives)
19
Range and interquartile range (page 273)
WE 11, 12, 13, 14, 15
Ex 9D Range and interquartile range
(page 277)
Stem-and-leaf plots (page 282)
WE 16, 17, 18
Ex 9E Stem-and-leaf plots
Five-number summaries (page 288)
WE 19, 20, 21, 22
Ex 9F Five-number summaries (page 291)
Summary (page 294)
Chapter review (page 295)
Practice examination questions (page 297)
Some statistical measures
 Calculating range, median, quartiles and
interquartile range
 Dividing data into deciles
Stem-and-leaf plots
 Creating stem-and-leaf plots
 Calculating quartiles and the median
from a stem-and-leaf plot
Five-number summaries
 Calculating the five-number summary for
a set of scores
 Using an ogive to develop five-number
summaries
 Creating box-and-whisker plots based on
these summaries


determining the range and interquartile
range as measures of a data set spread
dividing data into deciles and quartiles

creating a stem-and-leaf plot to illustrate
a small data set

establishing a five-number summary for
a data set (lower extreme, lower quartile,
median, upper quartile, upper extreme)
developing a box-and-whisker plot from
a five-number summary
determining the median and upper and
lower quartiles of a data set from a
cumulative frequency polygon


20
Chapter 10: Summary statistics
DA4: Data analysis
Section
Content
Prescribed skills, knowledge and
understanding
 calculating the mean of small data sets,
x
fx
using the formulae: x 
,
, x
n
f
where x is the mean of the sample
 determining the mean for larger data sets
of grouped or ungrouped data using the
statistical functions of a calculator
 calculating the means of a range of
samples from a population
 an informal description of standard
deviation as a measure of the spread of
data in relation to the mean
 determining the population standard
deviation using the  n button of a
calculator and the sample standard
deviation as an estimate of the population
measure, using the  n 1 button
Calculating the mean (page 300)
Average – what does it mean? (page 300)
WE 1, 2, 3, 4
Ex 10A Calculating the mean (page 304)
The mean
 Calculating the mean of small sets of
data and tabulated data using formulae
 Using a calculator in statistics mode to
calculate the mean
Standard deviation (page 309)
WE 5, 6, 7, 8
Ex 10B Standard deviation (page 312)
Standard deviation
 Calculating population and sample
standard deviation – small sets and
tabulated data
Median and mode (page 316)
WE 9, 10, 11, 12, 13
Ex 10C Median and mode (page 319)
Best summary statistics (page 324)
WE 14
Ex 10D Best summary statistics (page 325)
Wage rise (page 328)
Best summary statistics and comparison of
samples (page 328)
Median and mode
 Calculating median and mode

Mean, median and mode
 Calculating and comparing relevance of
mean, median and mode
 Examining statistics to decide on the
most appropriate summary statistic


determining the median and mode(s) of a
data set, either from a list or from a
frequency table
selecting and using the appropriate
statistic (mean, median or mode) to
describe features of a data set, eg. median
house prices, modal shirt size etc
comparing the summary statistics of
various samples from the same
population
21
Summary (page 329)
Chapter review (page 330)
Practice examination questions (page 335)
22
Chapter 11: Similarity of two-dimensional figures
M3: Measurement
Section
Content
Similar figures and scale factors (page 338)
WE 1, 2, 3, 4
Ex 11A Similar figures and scale factors
(page 340)
Enlarging a figure (page 342)
Investigating scale factors (page 342)
Solving problems using similar figures
(page 343)
WE 5, 6, 7
Ex 11B Solving problems using similar figures
(page 344)
Scale drawing of the classroom (page 345)
House plans (page 346)
WE 8, 9
Ex 11C House plans (page 348)
House plans (page 350)
Similar figures
 Testing figures for similarity
 Calculating scale factors of similar
figures
 Drawing similar figures using an
enlargement factor
Using similar figures
 Solving practical problems using
similarity
 Drawing a scale diagram
Summary (page 351)
Chapter review (page 352)
Practice examination questions (page 354)
Working with house plans
 Calculating dimensions and areas from
scale drawings of land and buildings
 Interpreting house plans
 Calculations from elevations
Prescribed skills, knowledge and
understanding
 establishing properties of similar figures
 recognising similarity in everyday life
 finding scale factors of similar figures
 recognising that similar figures related by
a scale factor of 1 are said to be
congruent
 using relevant enlargement or reduction
factors to calculate actual dimensions
 developing scale drawings of objects and
images
 using scale factor to solve problems
involving similar figures
 obtaining measurements from plans of
buildings and rooms
 calculating lengths and areas from a floor
plan
 interpreting commonly used symbols on
house plans
23
Chapter 12: Taxation
FM3: Financial mathematics
Section
Content
Calculating allowable deductions (page 356)
WE 1, 2, 3, 4
Ex 12A Calculating allowable deductions
(page 359)
Taxable income (page 361)
WE 5, 6
Ex 12B Taxable income (page 363)
Computer application 1: Calculating taxable
income (page 364)
Tax deductions
 calculating a variety of tax deductions
including exercises involving repeated
depreciation
Calculating taxable income
 Calculating gross incomes, deductions
and then taxable income
 Using a prepared spreadsheet to calculate
taxable income
Medicare levy (page 367)
WE 7
Ex 12C Medicare levy (page 367)
Medicare levy (page 367)
Calculating tax (page 368)
WE 8, 9, 10, 11
Ex 12D Calculating tax (page 372)
Computer application 2: Tax calculation
(page 374)
Calculating GST and VAT (page 375)
WE 12, 13, 14, 15
Ex 12E Calculating GST and VAT (page 377)
Graphing tax functions (page 379)
Ex 12F Graphing tax functions
Prescribed skills, knowledge and
understanding
 calculating the amount of allowable
deductions from gross income

calculating taxable income
Medicare levy
 Calculating the Medicare levy

calculating the Medicare levy (basic levy
only – see Tax Pack for details)
Calculating income tax
 Calculating income tax using a tax table
 Calculating refunds or tax owing
 Using a prepared spreadsheet to calculate
tax
Calculating GST
 Calculating a new price after adding
VAT or GST
 Calculating the pre-tax price

calculating the PAYE (Pay As You Earn)
tax payable or refund owing, using
current tax scales

Graphing tax functions
 Drawing piecewise linear graphs to show
tax payable on different incomes

calculate the Value Added Tax (VAT)
payable on a range of goods and services,
given the tax rates of various countries
calculating the goods and services tax
(GST) payable on a range of goods and
services
creating graphs to illustrate and describe
different tax rates

24
Summary (page 380)
Chapter review (page 381)
Practice examination questions (page 383)
25
Chapter 13: Right-angled triangles
M4: Measurement
Section
Content
History of Mathematics – Pythagoras of Samos
(page 386)
Pythagoras’ theorem (page 387)
WE 1, 2, 3, 4, 5
Ex 13A Pythagoras’ theorem (page 390)
Pythagoras
 Historical information on Pythagoras
Using the theorem of Pythagoras
 using Pythagoras’ theorem to find an
unknown side in a right-angled triangle
 Calculating sides in right-angled triangles
 Testing if a triangle is right-angled
 applying Pythagoras’ theorem to:
- determine whether or not a triangle is
 Applying Pythagoras to practical
right-angled
problems
- solve problems based on single
right-angled triangles
- calculate perimeters of irregularly
shaped blocks of land
Introductory trigonometry
 defining sine, cosine and tangent ratios
 Using a calculator to find trigonometric
ratios of acute angles, including degrees
and minutes
 Finding an acute angle using
trigonometry
Calculating trigonometric ratios (page 392)
Looking at the tangent ratio (page 392)
WE 6
Looking at the sine ratio (page 394)
WE 7
Looking at the cosine ratio (page 395)
WE 8, 9, 10
Ex 13B Calculating trigonometric ratios
(page 397)
Finding an unknown side (page 399)
WE 11, 12, 13, 14
Ex 13C Finding an unknown side (page 402)
Finding angles (page 406)
WE 15, 16, 17
Ex 13D Finding angles (page 408)
Using trigonometry to find sides
 Finding the sides of right triangles using
trigonometry
 Solving practical problems using trig.
Using trigonometry to find angles
 Finding angles in right triangles using
trigonometry and applying this to
practical problems
Prescribed skills, knowledge and
understanding

using trigonometric ratios to find the
length of an unknown side in a
right-angled triangle

using trigonometric ratios to find the size
of an unknown angle in a right-angled
triangle and using a calculator to find this
angle to the nearest minute
26
Angles of elevation and depression (page 411)
WE 18, 19, 20, 21
Ex 13E Angles of elevation and depression
(page 414)
Calculation of heights (page 415)
Proportional diagrams (page 416)
Checking with a proportional diagram
(page 416)
Using proportional diagrams (page 416)
Summary (page 417)
Chapter review (page 418)
Practice examination questions (page 420)
Elevation and depression
 Solving practical problems involving
depression and elevation
 Calculating heights of objects around the
school
Scale diagrams in trigonometry
 Checking accuracy using scale diagrams

solving problems involving angles of
elevation and depression, when given the
appropriate diagram

determining whether an answer seems
reasonable by using a diagram drawn
roughly in proportion
27
Chapter 14: The language of chance
P1: Probability
Section
Content
Informal description of chance (page 424)
WE 1, 2, 3, 4, 5
Ex 14A Informal description of chance
(page 427)
Common descriptions of chance (page 429)
Sample space (page 429)
WE 6, 7, 8
Ex 14B Sample space (page 431)
Matching actual and expected results (page 432)
Tree diagrams (page 434)
WE 9, 10, 11
Ex 14C Tree diagrams (page 437)
Two stage experiments (page 438)
Language of chance
 Appropriate probability terms and their
use in ordering everyday events
Equally likely outcomes (page 439)
WE 12, 13
Ex 14D Equally likely outcomes (page 441)
Using the fundamental counting principle
(page 443)
WE 14, 15, 16
Ex 14E Using the fundamental counting
principle (page 446)
Summary (page 448)
Chapter review (page 449)
Practice examination questions (page 451)
Prescribed skills, knowledge and
understanding
 ordering everyday events from the very
unlikely to the almost certain
Recording sample spaces
 Listing sample spaces
 Listing favourable outcomes

using a list or table to identify the sample
space (set of all possible outcomes) of a
simple experiment or game
Drawing and using tree diagrams
 Listing sample spaces using tree
diagrams
 Determining some possible combinations
using tree diagrams

Equally likely outcomes
 Calculating if outcomes are equally
likely
Multi-stage events
 Calculating the number of different ways
separate events can occur

using a list or table to identify the sample
space (set of all possible outcomes) of a
simple experiment or game
using systematic lists to verify the total
number of outcomes for simple multistage events
performing experiments and determining
whether the outcomes are equally likely
or not
determining the number of outcomes for
a multi-stage event by multiplying the
number of choices at each stage
using systematic lists to verify the total
number of outcomes for simple multistage events



28
Chapter 15: Relative frequency and probability
P2: Probability
Section
Content
Relative frequency (page 454)
WE 1, 2, 3
Ex 15A Relative frequency (page 456)
Researching relative frequencies (page 458)
Using relative frequencies
 Calculating relative frequencies
 Using relative frequencies to draw
conclusions
 Obtaining relative frequencies from
recorded information
Calculating simple probabilities
 Calculating probabilities of simple
single-event experiments
 Comparing results in an activity with
expected results
Single event probability (page 459)
WE 4, 5, 6, 7, 8
Ex 15B Single event probability (page 461)
Comparing probabilities with actual results
(page 464)
Prescribed skills, knowledge and
understanding
 estimating the relative frequency of
events from recorded data
 performing simple experiments to obtain
relative frequencies from recorded results
 using relative frequencies to obtain
approximate probabilities
 using the probability formula of an event
where outcomes are equally likely:
P(event) 

Writing probabilities as decimals and
percentages (page 466)
WE 9, 10
Ex 15C Writing probabilities as decimals and
percentages (page 467)
Range of probabilities (page 469)
WE 11, 12, 13
Ex 15D Range of probabilities (page 471)
Graphing results (page 473)
Probabilities written in different forms
 Determining probabilities and expressing
answers as fractions, decimals and
percentages
Complementary events (page 474)
WE 14, 15, 16
Ex 15E Complementary events (page 476)
Complementary events
 Calculating the probabilities of
complements of events

Range of probabilities

 Matching answers to probability
questions with their informal descriptions


number of favourable outcomes
total number of outcomes
comparing calculated probabilities with
experimental results
calculating probabilities in terms of the
fractional, decimal, or percentage chance
demonstrating the range of possible
probabilities, 0  P(E)  1, by examining
a variety of results
illustrating the results of experiments
through statistical graphs and displays
defining and using the relationship
between complementary events
P(an event does not occur)
= 1  P(the event does occur)
29
Summary (page 479)
Chapter review (page 480)
Practice examination questions (page 481)
Glossary (page 483)
SKILLSHEETS
Skillsheet 1 – Converting fractions to decimals (page 489)
Skillsheet 2 – Converting decimals to fractions (page 490)
Skillsheet 3 – Converting a fraction to a percentage (page 491)
Skillsheet 4 – Converting percentages to fractions (page 491)
Skillsheet 5 – Converting decimals to percentages (page 492)
Skillsheet 6 – Converting percentages to decimals (page 492)
Skillsheet 7 – Finding a percentage of a quantity (page 493)
Skillsheet 8 – Increase or decrease by a percentage (page 494)
Skillsheet 9 – Writing one quantity as a percentage of another (page 495)
Skillsheet 10 – Unitary method of percentages (page 496)
Skillsheet 11 – Simplifying fractions (page 497)
Answers (page 499 – 533)