Year 11
GENERAL MATHEMATICS
Program 2013
Key:
Mandatory, Notified Common Tasks (on set week)
Term 1
1
2
Topic 1
3
4
Algebraic Modelling
AM
1
5
6
7
Topic 3
Topic 2
2
3
4
Area & Volume
M
5
P6
6
DA P4
7
8
Topic 6
Topic 7
Topic 8
Displaying Data
Similar figures
Earning Money
Taxation
1
P9
M
2
Topic 10
3
P6
4
Modeling Linear
Relationships
AM P5
FM
P8
5
Topic 11
6
FM
7
Probability
PB
10
Data Collecting
Topic 5
DA
9
Topic 4
This is not the
YearTerm
11 22013
General
Maths
Term 3
Program
Calculations &
Measurement
FM, M P2, P7
P3
8
9
10
Topic 9
Right Angled
Triangles
M P2, P6
P8
8
Topic 12
9
10
Investing Money
P11
FM
Exams
P8
Year 12
GENERAL MATHEMATICS
Program 2013
Key:
Mandatory, Notified Common Tasks (on set week)
Term 4
1
2
3
Topic 13
5
Topic 22
Annuities & loan
repayments
FM
H8
P9
AM = Algebraic Modeling
FM = Financial Mathematics
PB = Probability
Statistical measurement
DA
Syllabus strands:
4
GENERAL MATHEMATICS Year 11/12
6
7
8
Topic 23
Depreciation
FM
H8
DA = Data Analysis
M = Measurement
9/10
Task 1
Financial Maths
Investigation
20%
Topic 16
Credit & borrowing
FM
page -1-
H8
Year 12
GENERAL MATHEMATICS
Program 2013
Key:
Mandatory, Notified Common Tasks (on set week)
Term 1
1
2
3
4
5
6
7
8
9/10
Task 2
Stats
Investigation
25%
Topic 17
Topic 25
Topic 26
Interpreting sets of data
DA
H9
The Normal Distribution
AM
H9
Correlation
DA
H9
Term 2
1
2
3
4
5
6
7
8
9/10
Task 3
Trial HSC Exam
35%
Topic 24
Topic 14
Topic 21
Topic 15
Topic 18
Algebraic skills &
techniques
Spherical
Geometry
Area & volume
Applications of
trig
AM
H3
M
H6
M
H6
M
H7
Linear & nonlinear
relationships
AM
H3
Term 3
1
2
3
Topic 19
4
5
Task 4
In class
Test
20%
6
7
8
9
10
Topic 20
Multi stage events
Application of
Revision of GENERAL MATHEMATICS
Probability
PB
H10
PB
H10
Syllabus strands:
AM = Algebraic Modeling
DA = Data Analysis
FM = Financial Mathematics
M = Measurement
PB = Probability
The HSC exam:
Time = 2.5 hours (plus 5 minutes reading time)
Section 1:
22 multiple-choice questions (1 mark each) = 22marks
Section 2:
6 free response questions (13 marks each) = 78 marks
No more than 30% of the exam will be based on the Preliminary course.
Lead in questions can be asked on the Prelim course. (This does NOT count as part of the 30%)
GENERAL MATHEMATICS Year 11/12
page -2-
Topic
1
Time:
1
-
3 weeks
12 hours
Introduction:
Algebraic Modelling
Text reference:
New Century
Cambridge
J&C MIS Bk 1
Ch 1
Ch 8
Ch 7
Insight Bk 1
Heinnman
Grove
Access
Ch 4
Ch 8
Ch 5
Ch 5, 2 p237-262
Syllabus Ref:
This is the first Algebra topic in the Preliminary course. Its main focus is to provide a foundation in ALGEBRAIC MODELLING
basic algebraic skills and introduce the concepts of linear functions and linear modelling. Students
should appreciate how formulas are a practical way of representing the mathematical patterns that
AM1:Basic algebraic skills
occur in society, industry and nature.
Outcome: P3
Content:
Objectives:
Students will be able to:
1. Algebraic terms
2. Formulas
3. Expanding expressions
4. Solving equations
5. Equations involving algebraic fractions
6. Equations and formulas
1. simplify algebraic expressions by adding, subtracting, multiplying and dividing
terms.
2. substituting into formulas & interpret answers
3. expand algebraic expressions
4. & 5. solve a variety of equations, including those involving brackets, letters on
both sides & fractions with numerical denominators
6. substitute into formulas to create equations & interpret answers
Teaching notes & ideas:
GENERAL MATHEMATICS Year 11/12
page -3-
Topic
2
Time:
2
-
Calculations, measurement & ratios
2 weeks
8 hours
Introduction:
Text reference:
New Century
Cambridge
J&C MIS Bk 1
Ch 2
Ch 4
Ch 3
Insight Bk 1
Heinnman
Grove
Access
Ch 2
Ch
Ch 1, 2 p45-73
Ch
Syllabus Ref:
This short topic covers the numeration skills necessary for success in the General Mathematics
course, especially in the Financial Maths strand. While parts of this topic revise concepts learned in
Years 7-10 and are not strictly part of the senior syllabus, it has been included anyway for those
classes who require work in these areas.
The theory on error will make them realise that a measurement is never exact, so measured values
must be expressed with an appropriate precision.
MEASUREMENT
M1:Scientific notation, repeated
percentage changes, calculation and
spreadsheet applications for Financial
Mathematics
M1:Units of measurement
Outcome: P2, P7
Content:
Objectives:
Students will be able to:
1. Fractions, decimals and percentages
2. Rounding off
decimal places, significant figures
3. Percentage and fraction calculation
percentage of a quantity
percentage change
successive percentage changes
the unitary method
1 a. know & use commonly used fraction & percentage equivalents
b. estimate, calculate and convert between fractions, decimals & percentages
c. express a quantity as a fraction or percentage of another
2. round a value to a given number of decimal places or significant figures
3. a. calculate a percentage of a quantity
b. increase & decrease a quantity by a percentage
c. determine overall percentage change of a quantity following successive
percentage changes
d. use the unitary method to find a whole, given the value of a part
4. Scientific notation
5. Scientific notation on the calculator
4. convert between scientific notation & normal decimal form
5. a. read scientific notation on the calculator
b. use the [EXP] key on the calculator to enter numbers in scientific notation
6. Metric measurement
Units for length, mass, time, capacity
Metric prefixes
7. Estimating in measuring
6. convert between metric units for length, mass, time & capacity
7. a. use appropriate units of measurement
b. estimate measurements of common objects
8. Precision and accuracy
8. a. understand the possible sources of error in a measurement eg. instrumental
Sources of error in measurement
(human), constant
Precision of measuring devices & measured values
b. write the precision of a measuring devices or measured value
9. Absolute error
9. find the absolute error & limits of accuracy of a measured value
10. calculate the percentage error of a measured value
10. Percentage error
11. simplify ratios, including ratios of metric quantities
11. Simplifying ratios
The ratio of two quantities
12. solve ratio problems using the unitary method
12. The unitary method
Ratio problems
13. divide a quantity in a given ratio
13. Dividing a quantity in a given ratio
14. Rates
15. Rate problems
The unitary method
Concentrations
16. Speed & fuel consumption
17. Converting rates eg. km/hr to m/s
14. calculate and simplify rates
15. a. solve rate problems, including the use of the unitary method
b. calculate concentrations expressed as weight/weight, weight/volume &
volume/volume
16. solve problems involving speed & fuel consumption
17. convert between units for rates eg. km/hr to m/s
Teaching notes & ideas:
GENERAL MATHEMATICS Year 11/12
page -4-
Topic
3
Time:
3
-
Area & Volume
Text reference:
New Century
Cambridge
J&C MIS Bk
Ch 3
Ch 2
Ch
Insight Bk 1
Heinnman
Grove
Access
2 weeks
8 hours
Introduction:
This measurement topic has three main sections: error in measurement, area, volume and surface
area. It is not a revision topic but the application of measurement skills to practical problems.
Students will be exposed to a variety of situations in which they rely on their measurement
knowledge.
Ch 6
Ch 5
Ch 8, 6
Ch 4, 9, 10
Syllabus Ref:
MEASUREMENT
M2:Applications of area and volume
Outcome: P6
Content:
Objectives:
1. Metric units for area
Square cm, square metre, hectare, square km
2. Areas of plane figures - square, rectangle, triangle,
trapezium, parallelogram, circle, Composite
figures
3. Field diagrams
Traverse survey, offsets
4. Sketching solids
5. Vanishing points
6. Nets of solids
1. convert the metric units for area
7. Metric units for volume, cubic cm, cubic metre
Students will be able to:
2. calculate the areas of quadrilaterals, triangle, circle & composite shapes
3. use a field diagrams to calculate areas of irregularly shaped blocks of land
4-5 sketch prisms & pyramids using isometric paper & vanishing points
6. a. classify prisms, pyramids & other solids
b. construct nets of solids & match nets to solids
7. convert between metric units for volume
8. Volumes of solids Prism, cylinder, pyramid, cone, 8. calculate volumes of prisms, cylinders, pyramids, cones, spheres & composite
sphere, Composite solids
solids
9. Surface area Prism, cylinder, pyramid, cone, sphere, 9. calculate surface area of prisms, square & rectangular pyramids
Composite solids
10. Problems involving volume & surface area
10. solve problems involving volume & surface area
3
3
11. Volume & capacity 1cm = 1 mL, 1m = 1000L 11. apply the relationship between volume & capacity
Teaching notes & ideas:
GENERAL MATHEMATICS Year 11/12
page -5-
Topic
4
Time:
4
-
Data Collecting
Text reference:
New Century
Cambridge
J&C MIS Bk 1
Ch 5
Ch 3
2 weeks
Ch 4
8 hours
Ch 7
Introduction:
Syllabus Ref:
DATA ANALYSIS
There are two Statistics topics in the Preliminary course. This first one looks at the various types of DA1:Statistics & society
statistical sampling and graphs. Some of the material in this topic was introduced in Years 9-10 DA2:Data collection & sampling
but needs to be revised and consolidated here.
Outcome: P4
Content:
1. Statistical investigations
The process of statistical inquiry
2. Interpreting graphs
3. Types of data
Categorical data
Quantitative data: discrete Vs continuous
4. Sample types
Sample Vs population
Random sample, systematic sample, stratified
sample
5. Sampling techniques
Random numbers
Capture-recapture techniques
Eliminating bias
6. Designing a questionnaire
Effective questionnaire design
Ch 4
Ch 5
Ch 9
Insight Bk 1
Heinnman
Grove
Access
Objectives: Students will be able to:
1. a. understand the importance of analysing data in planning & decision making by
governments & business
b. understand the stages of a statistical investigation: collecting & organising data,
summarising & displaying data, analysing & interpreting data
2. read & interpreting a variety of statistical graphs: column, sector, line, divided bar
3. classify data as being categorical or quantitative, and if quantitative, discrete or
continuous
4. a. understand the difference between a sample & population
b. recognise the purpose of a sample is to provide an estimate for a particular
population characteristic when the entire population cannot be accessed
c. understand & use the different types of sampling : random, systematic, stratified
- and determine which is best for a particular situation
5. a. generate random numbers using technology or a table & use them to select items
for a sample
b. use the capture-recapture method to estimate the size of a population
c. understand the meaning of bias & the rationale for eliminating bias in sampling
6. use the principles of good questionnaire design: simple language, unambiguous
questions, respect for privacy, freedom from bias, consideration of a number of
choices
Teaching notes & ideas:
Topic
5
Time:
5
-
Displaying Data
Text reference:
New Century
Cambridge
J&C MIS Bk 1
Ch 7
Ch 3
2 weeks
Ch 4
8 hours
Ch 7
Introduction:
Syllabus Ref:
DATA ANALYSIS
There are two Statistics topics in the Preliminary course. This second one covers statistical
DA3:Displaying single data sets
calculations (measures of central tendency and dispersion). Some of the material in this topic was
introduced in Years 9-10 but needs to be revised and consolidated here.
Outcome: P9
Content:
Objectives: Students will be able to:
1. a. construct a variety of statistical graphs: sector, line, divided bar
1. Constructing graphs
b. understand the features of a good graph & select a suitable scale for each axis of
Features of a graph: labels, scale
a graph
Selecting the best display/graph
c. determine which is the best graph for a particular type of data, describing the
strengths & weaknesses of each graph
2. Misleading graphs
2. detect misrepresentation of data in graphs, particularly in the selection of the scale
Incorrect scales and sizes
used on the axes
3. Frequency histograms and polygons
3. create frequency histograms and polygons, paying attention to the scale on each
axis
4. Dot plots
4-5
Outliers
a. create dot plots & stem-and-leaf plots for small sets of data
5. Stem-and-leaf plots
b. note outlier scores in these displays
6. Radar charts
6. draw radar charts to display data for a cycle, such as sales figures, temperature or
rainfall readings
Teaching notes & ideas:
GENERAL MATHEMATICS Year 11/12
Ch 4
Ch 5
Ch 9
Insight Bk 1
Heinnman
Grove
Access
page -6-
Topic
6
Time:
6
-
Similar figures
Text reference:
New Century
Cambridge
J&C MIS Bk 1
2 weeks
8 hours
Introduction:
Insight Bk 1
Heinnman
Grove
Access
Ch 5
Ch 14
Ch 6
Ch 12
Ch 7
Ch 2 p74-87, Ch 8 p425-461
Ch 13
Syllabus Ref:
This short Measurement topic examines similar figures, their properties and their applications in the MEASUREMENT
form of scale drawings and building plans. This is a fairly practical topic so there are many
opportunities for outdoor projects and geometrical constructions.
M3:Similarity of two-dimensional
figures
Outcome: P6
Content:
Objectives:
1. Scale factors & centre of enlargement
Similar figures
1. a. understand the meaning of similarity & recognise its applications
b. find scale factors of similar figures
c. enlarge & reduce an original figure to create an image
2. a. understand the angle & side properties of similar figures
b. use scale factors to calculate actual dimensions
2. Properties of similar figures
Properties of angles & sides
Calculating missing sides
3. Using shadows & similar triangles
4. Scale drawings
5. Floor plans & elevations
Reading building plans
6. Symbols & calculations from house plans
Interpreting house plans
Calculating lengths & areas
Students will be able to:
3. use scale factor to solve problems
4. a. read & interpret scales on scale drawings, plane & maps
b. calculate real & scaled lengths on a scale drawing
5. read & interpret floor plans & elevations (north, south, east, west)
6. a. obtain measurements & information from plans of buildings & rooms
b. calculate lengths & areas from a floor plan
c. interpret commonly used symbols on house plans
Teaching notes & ideas:
Topic
7
Time:
7
-
Earning money
3 weeks
12 hours
Introduction:
Text reference:
New Century
Ch 5
Cambridge
Ch 1, 9
J&C MIS Bk 2 Ch 1 p1-20 Access
Insight Bk 1
Ch 3
Heinnman
Ch 1
Grove
Ch 3 p88-123, Ch 12 p613-622
Ch 3, 12 p386-396
Syllabus Ref:
This Financial Mathematics topic examines the mathematics of earning an income and paying taxes. FINANCIAL MATHEMATICS
Some of the content will have been met before but it is revised here in greater detail. Students will
become competent in performing calculations involving wages, salaries, overtime and allowances. As FM1:Earning money
well as the calculations, there is also considerable financial terminology to be covered.
Outcome: P8
Content:
Objectives:
1. Wages, salary & overtime
Time-and-a-half, double time
2. Commission, piecework & royalties
3. Bonuses & allowances
Work allowances, annual leave loading
Government allowances
1. a. calculate monthly, fortnightly, weekly, daily and hourly payments from salary
b. calculate wages including overtime
2. calculate earnings based on commission, piecework & royalties
3. a. calculate special work allowances such as for wet work, confined spaces, toxic
substances, heat, height
b. calculate income based on government allowances, such as youth allowances &
pension
c. calculate annual leave loading
4. calculate gross & net pays after considering deductions such as union fees,
superannuation contributions, health fund installments & tax installments
4. Gross & net pay
Deductions from gross pay
5. Household bills
Electricity, gas, telephone, council, water rates
6. Budgeting
Students will be able to:
5. read information from household bills
6. create & manage a budget
Teaching notes & ideas:
GENERAL MATHEMATICS Year 11/12
page -7-
Topic
8
Time:
8
-
Taxation
Text reference:
New Century
Ch 5
Cambridge
Ch 1, 9
J&C MIS Bk 2 Ch 1 p1-20 Access
Insight Bk 1
Ch 10
Heinnman
Ch 1
3 weeks
Grove
Ch 3 p88-123, Ch 12 p613-622
12 hours
Ch 3, 12 p386-396
Introduction:
Syllabus Ref:
FINANCIAL MATHEMATICS
This Financial Mathematics topic examines the detail and processes behind income tax and the GST.
As well as the calculations, there is also considerable financial terminology to be covered.
FM3:Taxation
Outcome: P8
Content:
Objectives:
Students will be able to:
1. Income tax
Tax deductions, taxable income, Medicare levy,
PAYE, tax refund or tax owing
1. a. calculate allowable (tax) deductions from gross income & find taxable income
b. calculate income tax payable & Medicare levy
c. calculate tax refund or tax debt
2. Goods and Services tax (GST)
Value added tax (VAT) in different countries
3. Graphs of tax rates
2. calculate GST for Australian goods and services & VAT for items in other
countries
3. read & construct line graphs illustrating different tax rates
Teaching notes & ideas:
Topic
9
Time:
9
-
Right Angled Triangles
3 weeks
12 hours
Introduction:
Text reference:
New Century
Cambridge
J&C MIS Bk 1
Ch 7
Ch 12
Ch 12
Insight Bk 1
Heinnman
Grove
Access
Ch 14
Ch 6
Ch 7
Ch 14
Syllabus Ref:
This single Trigonometry topic of the Preliminary course covers elementary right angled
MEASUREMENT
trigonometry and Pythagoras' theorem. The sine and cosine rules and their applications will be
covered next year. Although the sine, cosine and tangent ratios have been introduced to Intermediate M4:Right angled triangles
(but not Standard) students in Years 9-10, the following topic should not be rushed as the emphasis is
upon applying trigonometry to practical situations. Spend considerable time teaching the concepts of Outcome: P2, P6
bearings and angles of elevation/depression.
Content:
Objectives: Students will be able to:
1. Pythagoras' theorem
Finding unknown sides
Proving a triangle is right angled
2. Applications of Pythagoras' theorem
3. Investigating the tangent ratio
4. Using tan to find a missing side
Degrees, minutes, seconds
5. Using tan to find a missing angle
To the nearest minute
6. The sine ratio
7. The cosine ratio
8. Mixed problems
9. Bearings
10. Applications of trigonometry
Bearings
Angles of elevation & depression
Teaching notes & ideas:
GENERAL MATHEMATICS Year 11/12
1. a. understand the convention for labeling the sides (a, b, c) and angles (A, B, C) of
a triangle
b. use Pythagoras' theorem to calculate the hypotenuse or a shorter side in any right
angled triangle
c. use Pythagoras' theorem to prove that a triangle is right angled
2. use Pythagoras' theorem to solve a variety of real life problems involving right
angled triangles, including perimeters of irregularly shaped blocks of land
3-4. a. identify the tangent ratio for a right angled triangle and on the calculator
b. use the degrees-minutes-seconds key on a calculator to enter angle sizes
c. use the tan ratio to calculate unknown lengths
5. a. round an angle size to the nearest degree or minute
b. use the tan ratio to calculate unknown angles to the nearest degree, decimal
degree or minute
6-7. a. identify the sine and cosine ratios for a right angled triangle and on the
calculator
b. use the sin and cos ratio to calculate unknown lengths including the hypotenuse
c. use the sin & cos ratios to calculate unknown angles
8. select the correct trigonometric ratio to calculate an unknown side or angle in a
right angled triangle
9. understand & use the concept of true bearings (three figure bearings measured
clockwise from North)
10. a. solve trigonometry problems involving bearings
b. solve trigonometry problems involving angles of elevation & depression,
given the appropriate diagram
page -8-
Topic
10
Time:
10
-
Modelling Linear Relationships
3 weeks
12 hours
Introduction:
Text reference:
New Century
Cambridge
J&C MIS Bk 1
Ch 8
Ch 13
Ch 8
Insight Bk 1
Heinnman
Grove
Access
Ch 13
Ch 9
Ch 7
Ch 8 p263-286
Syllabus Ref:
This Algebraic Modeling topic revises and develops the theory on linear functions introduced in
MEASUREMENT
Topic 1. It is a fairly detailed topic involving graphing work and analysis of practical situations. New
content includes concentration as variation, lines of best fit and stepwise linear functions.
AM2:Modelling linear relationships
Outcome: P5
Content:
Objectives:
1. Linear functions
gradient
vertical intercept
graphing linear functions
2. The gradient as a rate of change
finding y=mx+b
horizontal & vertical lines
1. a. understand the meaning of gradient and vertical intercept(y-intercept) &
calculate their values given the graph of a straight line
b. graph a linear function of the form y=mx+b
3. Linear modeling
dependent and independent variables
applying y=mx+b
4. Graphing linear functions
Graphing y=mx+b
The graphical solution of simultaneous linear
equations
5. Direct linear variation y=kx
Constant of variation
Graph of linear variation
Applications of direct linear variation
6. Conversion graphs
7. Linear modeling
Applications of linear functions
Line of best fit
8. Intersection of lines
Applications
9. Stepwise & piecewise linear functions
Parking charges, taxi fares, tax payments, mobile
phone bills
Teaching notes & ideas:
GENERAL MATHEMATICS Year 11/12
Students will be able to:
2. a. understand that the gradient measures a rate of change
b. given a linear function expressed as a table of values, find its equation in the
form y=mx+b
c. graph horizontal (y=b) and vertical lines (x=c)
3. a. identify the dependent and independent variables in a linear function
b. interpret linear functions as models of physical phenomena and solve problems
involving linear models
4. a. understand the meaning of gradient, vertical intercept, dependent & independent
variables & identify them in a linear function
b. graph y=mx+b
c. given a linear function expressed as a table of values, find its equation in the
form y=mx+b
d. find the solution of two simultaneous equations graphically by locating their
point of intersection
5. a. understand the concept of direct linear variation & its related terminology
b. evaluate the constant of variation
c. solve problems involving linear variation
d. graph y=kx from a description of linear variation
6. use graphs to make conversions from one measurement to another eg. AUD$ to
Euros
7. a. interpret linear functions as models of physical phenomena
b. draw a line of best fit for a graphed set of ordered pairs, find its equation & use
it to interpolate or extrapolate results
8. interpret the graphical solution of simultaneous equations drawn from practical
situations
9. use stepwise & piecewise linear functions to model situations encountered in daily
life
page -9-
Topic
11
Time:
3 weeks
12 hours
Introduction:
11
-
Probability
Text reference:
New Century
Cambridge
J&C MIS Bk 1
Ch 9
Ch 3, 11
Ch 11
Insight Bk 1
Heinnman
Grove
Access
Ch 9
Ch 10
Ch 11
Ch 11
Syllabus Ref:
This topic is an introduction to probability-the language of chance, counting sample spaces,
PROBABILITY
experimental probability and simple probability problems-and in many ways similar to the
Probability topic met in Years 9-10 Intermediate course. More formal treatment of probability theory PB1:The language of chance
(multi-stage problems, counting techniques, addition and product rules, tree diagrams) will take place
in the HSC topic Probability next year.
PB2:Relative frequency & probability
The practical section of this topic allows comparisons to be made between experimental and
theoretical probabilities. Probability is often a difficult concept for students to grasp. Better
Outcome: P11
understanding can be reinforced through careful practice with a variety of applied problems. Reliance
upon formal "theory" should be kept to a minimum.
Content:
Objectives: Students will be able to:
1. The language of probability
Ordering events on a probability scale
1. a. understand & use the language of chance
b. order everyday events from the very unlikely to the almost certain
2. a. understand the meaning of outcome, event, equally likely outcomes & sample
2. Outcomes & sample spaces
space
Counting using lists & tables
b. use a list or table to identify the sample space of a simple experiment or game
3. a. determine the number of outcomes for a multi-stage event by multiplying the
number of choices at each stage
3. Multi-stage events
b. use systematic lists to verify the total number of outcomes for simple multi-stage
The fundamental counting principle: multiplication
events
rule
4-5 a. perform simple experiments to obtain relative frequencies from recorded
results
4. Performing simple experiments
b. use relative frequencies to obtain approximate probabilities
5. Experimental probability
6. a. understand & use the definition of (theoretical) probability, knowing that its
Probability as relative frequency
values ranges from 0(impossible) to 1(certain)
b. calculate probabilities as a fraction, decimal or percentage
6. Theoretical probability
7. a. compare calculated probabilities with experimental results
b. illustrate the results of experiments through statistical graphs & displays
P(E)= number of favourable outcomes
8. a. understand the definition of a complementary event
total number of outcomes
b. solve probability problems involving complementary events
7. Using expected & calculated probabilities
Comparing theory with experimental results
8. Complementary events
P(Ñ) = 1 - P(N)
Teaching notes & ideas:
GENERAL MATHEMATICS Year 11/12
page -10-
Topic
12
Time:
12
-
Investing Money
3 weeks
12 hours
Introduction:
Text reference:
New Century
Ch 10
Cambridge
Ch 6
J&C MIS Bk 2 Ch 1 p20-26
Insight Bk 1
Heinnman
Grove
Access
Ch 8
Ch 2
Ch 3 p124-140, Ch 12 p596-612
Ch 6, 12 p375-385
Syllabus Ref:
This topic investigates the mathematics of investing money: in financial institutions, the stock market FINANCIAL MATHEMATICS
and in items that appreciate in value. The methods and formulas for calculating simple and
compound interest are analysed, followed by the costs and procedures involved in buying shares.
FM2:Investing money
There will be many opportunities for students to perform calculations, learn new terminology and
interpret information presented in tables and graphs.
FM1:Earning money(Account fees)
Outcome: P8
Content:
Objectives:
1. Simple Interest
I = Prn
1. a. calculate simple interest
b. calculate monthly, quarterly & six monthly interest rates based on quoted rates
per annum
c. solve problems involving simple interest
2. solve compound interest problems, calculating future value (final amount),
compound interest and present value (principal) for different compounding
periods
3. a. draw & describe simple interest graphs (Interest I Vs No. of periods n) for fixed
Principal P; this is a linear graph
b. draw & describe compound interest graphs (Final amount A Vs No. of periods
n) for fixed Principal P; this is an exponential graph
c. calculate the future and present value of an investment using a prepared table
that shows the values of (1+r)n, ie. compounded values of $1
4 calculate & compare user costs associated with maintaining accounts with financial
institutions
5. a. understand & use the language of the stock market
b. calculate the costs involved in buying & selling shares, including brokerage
c. calculate the dividend paid on a share holding & the yield dividend
2. Compound Interest
A = P(1+r)n , I = A - P
3. Interest tables & graphs
Linear relationship for simple interest
Exponential relationship for compound interest
4. Account fees & charges
5. Investing in shares
Ordinary Vs preference shares
Brokerage, dividend, dividend yield
6. Share tables & graphs
Table of share prices
Graphs of share prices over time
7. Inflation & appreciation
Students will be able to:
6. a. read & interpret information about share prices displayed in a table
b. extrapolate from the information shown on a prepared graph of share
performance to suggest possible future movement
7. a. calculate the price of goods following inflation
b. calculate the appreciated value of items such as stamp collections &
memorabilia
Teaching notes & ideas:
GENERAL MATHEMATICS Year 11/12
page -11-
Topic
13
Time:
13
-
Statistical measurement
Text reference:
New Century
Cambridge
J&C MIS Bk 1
4 weeks
16 hours
Introduction:
Ch 11
Ch 10
Ch 10
Insight Bk 1
Heinnman
Grove
Access
Ch 11
Ch 4
Ch 10
Ch
Syllabus Ref:
While the first Statistics topic of this course examined sampling and graphs, the following topic
DATA ANALYSIS
covers statistical calculations and the measures of central tendency (average) and dispersion (spread).
Students will use pen-and-paper and the statistical mode of their calculators to find the statistics of DA3:Displaying single data sets
data sets presented in different forms. This is a fairly technical topic, and a considerable amount of DA4:Summary statistics
theory will be new to the Year 11 student.
DA1:Statistics and society
Outcome: P9
Content:
Objectives:
1. Measures of central tendency
The mean, median & mode
Formulas for the mean
1. calculate the mean, median & mode for a data set, either from a list or frequency
table

x
x
n

x
Students will be able to:
 fx
n
2. Finding averages form statistical displays
Mean, median & mode form graphs/plots
Mean using the calculator's statistical mode
3. Investigating averages
Selecting the best average
2. a. calculate the mean, median or mode of data displayed in a frequency histogram,
polygon, dot plot & stem-and-leaf plot
b. use the statistical functions of a calculator to calculate the mean of a data set,
either from a list or frequency table
3. select & use the appropriate average to describe the features of a data set, eg.
median house prices, modal shirt size
4. Deciles, quartiles & percentiles
4 divide data into deciles(tenths), quartiles(quarters) & percentiles(hundredths)
5. Measures of dispersion
The range & interquartile range
6. Standard deviation
The meaning of standard deviation
7. using the calculator to find summary statistics
The population standard deviation  n
The sample standard deviation  n-1
8. Box-and -whisker plots
Five number summary: lower extreme (min), lower
quartile, median, upper quartile, upper extreme
(max)
9. Cumulative frequency graphs
Cumulative frequency histogram & polygon
Median and interquartile range
10. Statistical investigations
Teaching notes & ideas:
GENERAL MATHEMATICS Year 11/12
5. calculate the range and interquartile range as measures of spread of a data set
6 understand the meaning of standard deviation & perform simple calculations to
find it
7. understand the difference between the population standard deviation  n & sample
standard deviation  n-1 and calculate them using the calculators statistical mode
8. a. develop a five number summary for a data set
b. develop a box-and-whisker plot from a five number summary
9. a. complete the cumulative frequency column in a table & construct a cumulative
frequency histogram & polygon(ogive)
b. determine the median, lower & upper quartiles of a data set from an ogive
10. investigate & analyse data from a real life situation & present conclusions in a
report
page -12-
Topic
14
Time:
14
-
Algebraic skills & techniques
4 weeks
16 hours
Introduction:
Text reference:
New Century Bk 2 Ch 1
Cambridge
Ch 5, 9
J&C MIS Bk 1
Ch 7, 8
Insight Bk 2
Heinnman
Grove
Access
Ch 3
Ch 6
Ch 1, 2 (pp 85-111)
Ch 5
Syllabus Ref:
This topic revises the algebraic concepts covered in the preliminary course, in particular, solving
ALGEBRAIC MODELLING
equations and linear modeling. New content includes power equations requiring a “guess, check and
refine” method of solution and changing the subject of a formula.
AM3: Algebraic skills and techniques
Outcome: H3
Content:
1. Revision: Algebraic expressions
Simplfiying algebraic expressions
Expanding expressions
2. Revision: Scientific notation
3. Revision: Formulas
4. Revision: Solving equations
Linear equations
Equations involving algebraic
Fractions
5. Equations involving powers and roots
Squares and cubes, square and cube roots.
Power equations and the “guess, check and
refine” method.
6. Changing the subject of formula
Objectives: Students will be able to:
1. a.Simplify algebraic expressions by adding, subtracting, multiplying and dividing
terms.
b. Expand algebraic expressions
2. Calculate with numbers in scientific notation
3. Substitute into and evaluate algebraic expressions and formulas
4. Solve equations involving brackets, terms on both sides and fractions (numerical
denominators only)
5. Solve equations involving powers, including the use of the “guess, check and
refine” method
6. Change the subject of equations and formulas involving linear and quadratic terms.
7. Substitute into formulas to solve equations and interpret answers.
7. Equations and formulas
Teaching notes & ideas:
GENERAL MATHEMATICS Year 11/12
page -13-
Topic
15
Time:
15
-
Area and Volume
Text reference:
New Century Bk 2 Ch 2
Cambridge
Ch 2
J&C MIS Bk 1
Ch 5
3 weeks
12 hours
Introduction:
Insight Bk 2
Heinnman
Grove
Access
Ch 2
Ch 3
Ch 4
Ch 1
Syllabus Ref:
This Measurement topic revises and extends area, surface area and volume concepts introduced in
MEASUREMENT
the preliminary course, and applies them to composite and irregular figures in practical situations. In
particular students examine the measurement of circles and circular figures. Simpson’s rule is
M5: Further applications of area and
introduced as an approximation method for calculating areas and volumes.
volume.
Outcome: H6
Content:
1. Revision: composite areas
Areas of basic shapes
Field diagrams
2. Parts of a circle
Length of an arc l    2r
360
Area of a sector A    r 2
Objectives: Students will be able to:
1. a. Calculate areas of basic shapes and composite figures
b. Calculate areas of irregular fields represented by field
diagrams in offset surveys
2-3. Calculate the arc length of a circle and the areas of ellipses, annuluses and parts
of a circle (quadrant, sector) using appropriate formulas.
360
Area of annulus A   ( R 2  r 2 )
3. Area of an ellipse A  ab
Semi minor and semi major axes
4. Simpson’s rule for approximating areas and
volumes A  h (d  4d  d )
3
f
m
4. Apply Simpson’s rule to approximate areas of irregular fields
l
5. Revision: surface areas of prisms and pyramids.
6. Surface area of a cylinder
7. Surface area and volume of a sphere
5. Calculate the surface areas of prisms, square pyramids and rectangular pyramids.
6. Calculate the external surface areas of open and closed cylinders
7.Calculate volumes and surface area of spheres and hemispheres
4
S  4r 2 ,V  r 3
3
8. Volumes of composite solids
9. Errors in measurement and calculations
8. Calculate volumes of prisms, pyramids, cylinders, cones and composite solids
9. a. Find the limits of accuracy and absolute error of a measurement and calculate
the percentage error.
b. Determine errors in calculations resulting from errors in measurement.
c. Calculate largest and smallest possible areas and volumes
Teaching notes & ideas:
.
GENERAL MATHEMATICS Year 11/12
page -14-
Topic
16
Time:
16
-
Credit and borrowing
2 weeks
8 hours
Introduction:
Text reference:
New Century Bk 2 Ch 3
Cambridge
Ch 1
J&C MIS Bk 2
Ch 1
Insight Bk 2
Heinnman
Grove
Access
Ch 1
Ch 1 (pp 1 –17)
Ch 5 (pp 233 – 264)
Ch 2
Syllabus Ref:
This short topic follows from the Savings and Investment topic of the Preliminary course. We now FINANCIAL MATHEMATICS
look at borrowing money. Students examine the calculations involved in credit and loans: interest,
repayments, fees and charges, interest-free periods, deferred payment, terms and conditions. The aim FM4: Credit and borrowing
of this topic is to explain and demystify the realities of personal finance so that students can make
sound financial mathematical decisions. In this topic students should use the spreadsheet to analyse, Outcome: H8
compare and chart the progress of the different loans.
Content:
1. Flat rate loans, I=Prn
2.
Buying on terms
Term payments
Deferred payment plans
3.
Reducing balance loans
Table showing progress of a loan
4.
Using published loan repayment tables
5.
Using technology to compare home loans
Using the internet
The financial mode of a graphics calculator
Constructing a spreadsheet
Credit card payments
Credit card statements
6.
Objectives: Students will be able to:
1. Calculate the principal, interest and repayments for a flat rate (simple interest)
loan
2. a. Consider borrowing money “on terms” and deferred payment plans (eg.
“nothing to pay for 6 months”)
b. Compare different options for borrowing money in relation to total
repayments, fees, interest rates and flexibility
3. a. Understand the concept of a reducing balance (reducible interest) loan and
calculate the progress of a loan
b. Construct and calculate values in a table of loan repayments (see syllabus
notes FM4 or p88 of text)
4. Use published tables to determine monthly repayments on a reducing balance
loan (see p 90 of text)
5. Use spreadsheets and graphics calculators to compare loans
6.
Calculate credit card payments involving interest free periods, interest rates, fees
and charges.
Teaching notes & ideas:
GENERAL MATHEMATICS Year 11/12
page -15-
Topic
17
Time:
17
-
3 weeks
12 hours
Interpreting sets of data
Text reference:
New Century Bk2
Cambridge
J&C MIS Bk 1
Insight Bk 1
Introduction:
Ch 4
Ch 3
Ch 9, 10
Ch 4
Insight Bk 2
Heinnman
Grove
Access
Ch 4
Ch 2 (pp 64 –93)
Ch 2
Ch 3
Syllabus Ref:
This topic builds upon the Statistical Samples and Displays and Statistical Measurement topics of DATA ANALYSIS
the preliminary course. This topic compares the data of two different distributions in order to
interpret information about them. Students will examine more closely the shape of distributions, as DA5: Interpreting sets of data
well as use area charts to illustrate the changes in two or more variables over time.
Outcome: H9
Content:
1. Revision: Collecting and displaying data
Types of data
Random sampling
2. Summary statistics
Measures of location (averages)
Outliers
Measures of spread
3. Features of a statistical display
Shape, clustering, symmetry, skewness, peaks
and modes
4.
Investigating outliers
5.
Displaying and comparing two sets of data
Double stem-and-leaf plots
Double box plots
Comparing data sets using charts
Radar chart
Area chart
Two-way tables
Using multiple displays to compare data sets
6.
7.
8.
Objectives: Students will be able to:
1. Name and use different types of data and sampling techniques
2.
Calculate measures of location (mean, median, mode) and spread (range,
interquartile range, standard deviation)
3.
a. Describe the shape of a distribution, eg smoothness, symmetry, number of
modes
b. Make judgments about data based on the shape and skewness of the
distribution
4. Investigate outliers in small data sets and their effects on the mean, median and
mode
5-6. Display and compare two data sets illustrated on double
stem-and-leaf plots, double box-and-whisker plots, radar
charts and area charts
7. Interpret data presented in two-way table form
8. Use summary statistics and multiple displays to interpret
and compare relationships between two data sets
Teaching notes & ideas:
GENERAL MATHEMATICS Year 11/12
page -16-
Topic
18
Time:
18
-
Applications of trigonometry
Text reference:
New Century Bk 2 Ch 5
Cambridge
Ch 8
J&C MIS Bk 1
Ch 12,13 Access
3 weeks
12 hours
Insight Bk 2
Heinnman
Grove
Ch 7
Ch 6
Ch 4 (pp 150-182)
Ch 8
Introduction:
Syllabus Ref:
This Trigonometry topic introduces the sine and cosine rules, which apply to all types of triangles,
not only right-angled ones. Students will use trigonometry to calculate lengths, angles and areas of
MEASUREMENT
triangles. This topic should not be rushed as the emphasis is upon applying the knowledge and skills
to practical situations. Spend considerable time on bearings and the different types of surveying
M6: Applications of trigonometry
techniques.
Outcome: H7
Content:
1. Revision: Right-angled triangle trigonometry
2. Revision: Bearings
The eight points of the compass
True bearings
3. Trigonometry with obtuse angles
Sin is positive, cos and tan are negative
4. The sine rule
Revision: The triangle-labeling convention
Objectives: Students will be able to:
1. Solve problems using trigonometric ratios in one or more right-angled triangles
2. Use compass bearings (eight points only) and true bearings (three-figure
bearings) in maps, charts and trigonometry problems
3.
4.
a
b
c


sin A sin B sin C
5.
Finding a missing side
Using the sine rule to find a missing angle
5.
Extend the trigonometric ratios and relations to obtuse angles
a. Understand the convention for labeling sides (a, b, c) and angles (A, B, C) of a
triangle
b. Calculate an unknown side of a triangle using the sine rule
calculate an unknown angle of a triangle using the sine rule
7.
2
2
2
The cosine rule c  a  b  2ab  cos C 6-7. Calculate unknown sides and angles in a triangle using the cosine rule
Finding a missing side
Using the cosine rule to find a missing angle
8.
Area of a triangle
9.
Applications of the sine and cosine rules
Which rule to use?
6.
Area 
1
ab  sin C
2
10. Surveying
Offset survey
Plane table radial survey
Compass radial survey
8. Calculate the area of a triangle given the lengths of two sides and the size of the
included angle
9. Solve a variety of practical trigonometry problems involving non-right-angled
triangles, including those involving two triangles where one is right-angled, by
selecting appropriate methods
10. Conduct offset and radial (plane table and compass) surveys to calculate lengths,
perimeters and areas
Teaching notes & ideas:
GENERAL MATHEMATICS Year 11/12
page -17-
Topic
19
Time:
19
-
Multi stage events
Text reference:
New Century Bk 2 Ch 6
Cambridge
Ch 4, 13
J&C MIS Bk 1
Ch 11
Access
Insight Bk 2
Ch 7
Heinnman
Ch 5
2 weeks
Grove
Ch 6
8 hours
Ch 4, 12
Introduction:
Syllabus Ref:
This comprehensive Probability topic examines more complex problems involving ordered and
unordered selections and the techniques for counting them. Students were introduced to basic
PROBABILITY
probability concepts in the Preliminary course and now they learn about multiplication principles of
counting and tree diagrams. Probability is a topic in which many students experience difficulty, so
PB3: Multi-stage events
spend considerable time teaching the key ideas and methods.
Outcome: H10
Content:
1.
Revision: The meaning of probability
The range of probabilities
Complementary events
Experimental probability
2.
Tree diagrams and tables
3.
Multiplication principle for counting
4.
5.
6.
Counting arrangements
Counting unordered selections
Ordered and unordered selections
7.
Probability tree diagrams
Objectives: Students will be able to:
1.
Solve simple problems involving theoretical and experimental probability,
including complementary events
2.
Construct and use tree diagrams and tables to list the sample space for multistage events
3.
Count the number of outcomes for multi-stage event by multiplying the
number of choices at each stage
4-6.
a. Count the number of ways in which n different items can be arranged,
using the formula n(n-1)(n-2)…1
b. Count the number of ordered and unordered selections of a given size
that can be made from a group of different items
b.
List ordered and unordered selections (small numbers only)
c. Calculate probabilities involving ordered and unordered selections
7. Construct and use probability tree diagrams to solve multi-stage probability
problems
Teaching notes & ideas:
Topic
20
Time:
20
-
Application of Probability
Text reference:
New Century Bk 2 Ch 6
Cambridge
Ch 4, 13
J&C MIS Bk 1
Ch 11
Ch 11
Ch 5
2 weeks
Ch 6
8 hours
Ch 4, 12
Introduction:
Syllabus Ref:
Students were introduced to basic probability concepts in the Preliminary course, but now they learn
about expectation, simulation and probability in diagnostic testing (eg. lie detectors). Probability is a PROBABILITY
topic in which many students experience difficulty, so spend considerable time teaching the key ideas
and methods.
PB4: Applications of probability
Content:
1.
Expectation
Financial expectation
2.
Probability simulations
3.
Probability in testing
Insight Bk 2
Heinnman
Grove
Access
Outcome: H10
Objectives: Students will be able to:
1. Calculate the expected number of times a particular outcome should occur over a
number of trials and the financial expectation of a game of chance
2. Carry out probability simulations to model events and analyse their results
3. Examine the use of probability in diagnostic tests and interpret tables to make
conclusions about the effectiveness of such tests
Teaching notes & ideas:
GENERAL MATHEMATICS Year 11/12
page -18-
Topic
21
Time:
21
-
Spherical Geometry
Text reference:
New Century Bk 2 Ch 7
Cambridge
Ch 14
J&C MIS Bk 2
Ch 3
Insight Bk 2
Heinnman
Grove
Access
2 weeks
8 hours
Introduction:
In this short Measurement topic, students use circle and spherical geometry to solve problems
relating to positions, distances and times on the Earth’s surface. Most of the concepts met in this
topic will be fairly new: latitude and longitude, great circle distances, nautical miles and knots,
international time zones.
Ch 10
Ch 4 (pp 182-192)
Ch 9
Ch 10
Syllabus Ref:
MEASUREMENT
M7: Spherical geometry
Outcome: H6
Content:
1. Latitude and longitude
Great circles and small circles
Objectives: Students will be able to:
1. a. Understand and use the following geographical concepts: great and small
circles, latitude and longitude, the Equator and the Greenwich meridian
b. Use latitude and longitude to describe locations on the Earth’s surface
2.
2-3. a. Convert between nautical miles and kilometres
b. Calculate distances between two points on the same great
circle, in nautical miles and kilometres
c. Understand the meaning of a knot as a measure of speed
and use it to solve problems
Great circle distances
Revision: Arc length of a circle
l

360
 2r
3.
Nautical miles and knots
1 M = 1.852 km
1° on a great circle = 60 M
4. Longitude and time differences
15° = 1 hour, 1° = 4 minutes time differences
5. International time zones
The international date line
Daylight saving
4.
5.
Calculate (local) time differences using differences in
longitude
Use standard time zones, the International Date Line and
daylight saving to solve problems involving travel and
communication
Teaching notes & ideas:
* There is a lot of terminology in this topic so a student-generated glossary would be a useful study aid.
GENERAL MATHEMATICS Year 11/12
page -19-
Topic
22
Time:
22
-
Annuities & Loan repayments
Text reference:
New Century
Cambridge
J&C MIS Bk 2
Ch 5
Ch 1 (pp 18-52)
2 weeks
Ch 5 (pp 265-293)
8 hours
Ch 6, 8
Introduction:
Syllabus Ref:
This long and complex topic examines the financial mathematics of long term investing. Annuities,
depreciation and their associated terminology are entirely new to students so spend considerable time FINANCIAL MATHEMATICS
introducing the concepts, calculations and formulas. The use of graphs, tables and technology (such as
spreadsheets) is essential if students are to understand the processes involved in calculating annuities, FM5: Annuities and loan repayments
long term loans and depreciation. This is probably the most difficult topic of the General Mathematics
course.
Outcome: H8
Content:
Objectives: Students will be able to:
1. Interest calculations
1. a. Calculate the final amount and interest earned in a compound interest problem
n
Revision: Compound interest
b. Use the formula E = (1 + r) – 1 to convert between stated interest rate and
Extension: Effective interest rates
effective interest rate
n
2.
E = (1 + r) – 1
Future value of an annuity
Meaning of annuity
Future value formula
2.
 (1  r ) n  1
A M

r


3.
4.
Sinking funds
Present value an annuity
Present value formula
Superannuation funds
Using tables for annuity calculations
Future value table
Present value table
 (1  r ) n  1
N  M
n 
 r (1  r ) 
Contribution table
5. Loan repayments
Teaching notes & ideas:
Topic
23
Time:
23
-
Ch 8
Ch 6, 10
Ch 1
Insight Bk 1
Heinnman
Grove
Access
a. Understand the meaning of an annuity
b. Calculate the future value of an annuity or the contribution per period using
the future value formula
c. Construct and calculate values in a table/spreadsheet of the progress of an
annuity (see specimen exam question 25b)
3.
Calculate the present value of an annuity or the contribution per period using the
present value formulas
4.
Use tables to solve problems involving annuities (see syllabus FM5 p54)
5.
a. Use the present value formula for annuities to calculate loan repayments and,
hence, the total amount paid over the term of a loan
b. Investigate various processes for the repayment of loans
Depreciation
Text reference:
New Century
Cambridge
J&C MIS Bk 2
Ch 9
Ch 1 (pp 18-52)
2 weeks
Ch 5 (pp 265-293)
8 hours
Ch 6, 8
Introduction:
Syllabus Ref:
This long and complex topic examines the financial mathematics of long term investing. Annuities,
depreciation and their associated terminology are entirely new to students so spend considerable time FINANCIAL MATHEMATICS
introducing the concepts, calculations and formulas. The use of graphs, tables and technology (such as
spreadsheets) is essential if students are to understand the processes involved in calculating annuities, FM6: Depreciation
long term loans and depreciation.
Outcome: H8
Content:
1. Straight line method of depreciation
Meaning of depreciation
Purchase price, salvage value
S=Vo-Dn
2.
Depreciation schedules
Declining balance method of depreciation
S=Vo(1-r)n
3.
Calculating tax deductions
Ch 8
Ch 6, 10
Ch 1
Insight Bk 1
Heinnman
Grove
Access
Objectives: Students will be able to:
1-2. a. Understand the meaning of depreciation and its
associated terminology
b. Use the straight line and declining balance methods of
depreciation
c. Model depreciation using appropriate formulas, graphs
and tables
d. Calculate the value of a depreciating item over time using
a depreciation schedule
e. Compare depreciation tables
3. Calculate tax deductions based on depreciation of assets
Teaching notes & ideas:
GENERAL MATHEMATICS Year 11/12
page -20-
Topic
20
Time:
24
-
Linear & non-linear relationships
Text reference:
New Century
Cambridge
J&C MIS Bk 1
Ch 9
Ch 11
Ch 7
Insight Bk 1
Heinnman
Grove
Access
2 weeks
8 hours
Introduction:
In this final Algebraic modeling topic, non-linear functions are examined as further models for
representing the mathematical patterns and relationships occurring in nature and society. Students
will examine the following functions and investigate their properties and graphs : the quadratic,
cubic, exponential and hyperbolic functions. This is followed by a detailed analysis of direct and
inverse variation, a concept first met in the Preliminary course.
Ch 12
Ch 7 (NOT pp 321-336)
Ch 2 (pp 112-144)
Ch 13
Syllabus Ref:
ALGEBRAIC MODELLING
AM4: Modeling linear and non-linear
relationships
Outcome: H3
Content:
Objectives:
1. Revision: Linear functions
1. Graph y=mx+b
Interpret linear functions as models of physical phenomena
Draw a line of best fit to a set of empirical data and find its equation
Linear models
Line of best fit
2. Intersection of lines
Break even points
3.
The quadratic function
Features of a parabola
Students will be able to:
2. Interpret the point of intersection of the graphs of two linear functions drawn from
practical contexts, eg. break even points.
3.
a. Generate tables of values and graph quadratic functions
b. Note that different forms of a quadratic expression produce identical graphs
4.
Use a quadratic graph to find maximum and minimum values in practical
contexts
2
4.
Graphing y = ax + bx + c
Maximum and minimum problems
Maximum/minimum value of a quadratic
Extension: The vertex formula
x
b
2a
5.
The cubic function
6.
Graphing y = ax
The exponential function
3
x
7.
6.
Graphing y = b(a )
The size of a and b
Exponential growth and decay
The hyperbolic function
5-8 a. Generate tables of values and graph cubic, exponential and hyperbolic
functions
x
b. Recognise exponential growth and decay by the value of a in y = b(a )
c. Apply the different types of functions to model and solve real life problems
d. Use functions as models of physical phenomena and recognise their
limitations when interpolating and extrapolating
a
Graphing y = /x
The sign and size of a
8. More applications of functions
9. Direct variation
Revision: Linear variation
Variation to the square, cube, root
10. Inverse variation
Meaning of inverse variation
Linear, square, cube, root
Teaching notes & ideas:
GENERAL MATHEMATICS Year 11/12
9-10 a. Understand the meanings and relationships involved in direct and inverse
variation
b. Form a variation equation and evaluate the constant of variation
c. Solve problems involving direct and inverse variation, including variation to the
square, cube and square root of a variable
page -21-
Topic
25
Time:
25
-
The Normal Distribution
Text reference:
New Century
Cambridge
J&C MIS Bk 1
Ch 8
Ch 2 (pp94-100),7 (pp321-336)
2 weeks
Ch 7
8 hours
Ch 9, 11
Introduction:
Syllabus Ref:
In this Data Analysis (Statistics) topic students examine the normal curve. This topic builds upon the
Statistical Distributions work introduced at the start of the HSC course. Most of the concepts
DATA ANALYSIS
covered in this chapter will be entirely new to students – Z-scores, scatter plots – although lines of
best fit have been covered in both the Preliminary and HSC courses.
DA6: The normal distribution
Ch 10
Ch 7, 12
Ch 10
Insight Bk 2
Heinnman
Grove
Access
Outcome: H9
Content:
1. The normal distribution
Standard deviation and the normal curve
Areas under the normal curve: the 68%, 95%,
99.7% limits
2. Z-scores
z
xx

Objectives: Students will be able to:
1. a. Use a normal curve to model continuous data
b. Investigate the percentages of scores in a normal distribution that are within 1,
2 and 3 standard deviations of the mean and use them to make judgments in
individual cases
2. a. Understand the meaning of a Z-score to indicate the position of a score
relative to the mean
b. Calculate Z-scores
3. Comparing normal distributions
Comparing using Z-scores
Properties of a normal distribution
3.
a. Use calculated Z-scores to compare scores from different data sets
b. Identify the properties of data that are normally distributed (equality of mean,
median, mode; bell-shaped)
4.
4.
Plot ordered pairs of data onto a scatter plot and recognise any patterns
Scatter plots
Teaching notes & ideas:
Topic
26
Time:
26
-
Correlation
Text reference:
New Century
Cambridge
J&C MIS Bk 1
Ch 13
Ch 2 (pp94-100),7 (pp321-336)
2 weeks
Ch 7
8 hours
Ch 9, 11
Introduction:
Syllabus Ref:
In this final Data Analysis (Statistics) topic students examine correlation. This topic builds upon the
Statistical Distributions work introduced at the start of the HSC course. The concept covered in this DATA ANALYSIS
chapter will be entirely new to students although lines of best fit have been covered in both the
Preliminary and HSC courses. The construction of the median regression line is a fairly detailed
DA7: Correlation
process so spend considerable class time practising the technique.
Outcome: H9
Content:
Objectives: Students will be able to:
1. a. Interpret the sign and size of a given correlation coefficient
1. Correlation
b. Recognise correlation patterns shown on a scatter plot
Positive, negative, high, low and perfect
c. Recognise that a high degree of correlation does not necessarily imply a
correlation
casual relationship
Correlation and causality
The correlation coefficient: sign and size
2. a. Construct a median regression line to give a line of best fit on a scatter plot
2. Regression lines
b. Find the equation of the median regression line and use it to make predictions
Line of best fit
Median regression line
Making predictions
Ch 10
Ch 7, 12
Ch 10
Insight Bk 2
Heinnman
Grove
Access
Teaching notes & ideas:
GENERAL MATHEMATICS Year 11/12
page -22-
General Mathematics Stage 6 Syllabus
Objectives
Objectives and Outcomes
Preliminary Outcomes
HSC Outcomes
Students will develop:
A student:
A student:

appreciation of the relevance of
mathematics
P1
develops a positive attitude to
mathematics and appreciates its
capacity to provide enjoyment and
recreation
H1
appreciates the importance of
mathematics in her/his own life and
its usefulness in contributing to
society

the ability to apply
mathematical skills and
techniques to interpret practical
situations
P2
applies mathematical knowledge
and skills to solving problems within
familiar contexts
H2
integrates mathematical knowledge
and skills from different content
areas in exploring new situations
P3
develops rules to represent patterns
arising from numerical and other
sources
H3
develops and tests a general
mathematical relationship from
observed patterns
P4
represents information in symbolic,
graphical and tabular forms
H4
analyses representations of data in
order to make inferences,
predictions and conclusions
P5
represents the relationships between
changing quantities in algebraic and
graphical form
H5
makes predictions about the
behaviour of situations based on
simple models
P6
performs calculations in relation to
two-dimensional and threedimensional figures
H6
analyses two-dimensional and
three-dimensional models to solve
practical and mathematical
problems
P7
determines the degree of accuracy
of measurements and calculations
H7
interprets the results of
measurements and calculations and
makes judgements about
reasonableness


skills, knowledge and
understanding in algebraic
modelling
skills, knowledge and
understanding in measurement
GENERAL MATHEMATICS Year 11/12
page -23-
Objectives
Preliminary Outcomes
HSC Outcomes
Students will develop:
A student:
A student:

P8
models financial situations using
appropriate tools
H8
makes informed decisions about
financial situations
P9
determines an appropriate form of
organisation and representation of
collected data
H9
develops and carries out statistical
processes to answer questions
which she/he and others have
posed
P10
performs simple calculations in
relation to the likelihood of familiar
events
H10
solves problems involving
uncertainty using basic principles of
probability
P11
justifies his/her response to a given
problem using appropriate
mathematical terminology
H11
uses mathematical argument and
reasoning to evaluate conclusions
drawn from other sources,
communicating his/her position
clearly to others
skills, knowledge and
understanding in financial
mathematics
 skills, knowledge and
understanding in data analysis
 skills, knowledge and
understanding in probability
 the ability to communicate
mathematics in written and/or
verbal form
GENERAL MATHEMATICS Year 11/12
page -24-
DRAFT PERFORMANCE BANDS
GENERAL MATHEMATICS
The typical performance in this band:
Band 6








uses a wide- variety of problem-solving strategies to solve mathematics problems
successfully applies mathematical skills and processes across a wide range of topic areas
communicates mathematical ideas and reasoning clearly and effectively using symbols, numbers, words,
diagrams and graphs
analyses representations of data and makes predictions, inferences and conclusions
constructs and uses diagrams to solve mathematical problems in familiar and unfamiliar contexts
makes and justifies informed decisions about financial situations based on appropriate models
carries out statistical processes to analyse, interpret and compare data
solves problems involving uncertainty using the basic principles of probability
















uses a variety of problem-solving strategies to solve mathematical problems
uses mathematical skills and processes accurately and can apply these in different contexts
communicates mathematical ideas and reasoning using symbols, numbers, words, diagrams and graphs
analyses data in symbolic, graphical or tabular forms and makes predictions, inferences and conclusions
constructs and uses diagrams to solve mathematical problems in familiar contexts
makes informed decisions about financial situations based on mathematical models
carries out statistical processes to analyse and compare data
solves familiar problems involving uncertainty using the basic principles of probability
uses some problem-solving strategies to solve familiar mathematical problems
uses mathematical skills and processes accurately in familiar contexts
communicates mathematics using symbols, numbers, words, diagrams and graphs
uses information in graphs, tables or symbols to make predictions, inferences and conclusions
draws diagrams and graphs to solve familiar mathematical problems
performs calculations in financial mathematics such as substituting into appropriate formulae
calculates summary statistics, such as mean and standard deviation
performs probability calculations to solve familiar problems







uses mathematical skills and processes to solve familiar problems
communicates mathematical results using numbers, words, diagrams and graphs
uses given diagrams, tables and graphs to make some predictions, inferences and conclusions
draws simple diagrams when given clear instructions to help solve familiar mathematical problems
performs basic calculations in financial mathematics
calculates basic summary statistics, such as mode and range
performs simple probability calculations to solve familiar problems





uses basic mathematical skills and processes to solve simple familiar problems with limited accuracy
communicates mathematical results using numbers, words simple diagrams and graphs
uses given diagrams, tables and graphs to help solve some simple mathematical problems
performs some basic calculations in financial mathematics with limited accuracy
recognises language of probability
Band 5
Band 4
Band 3
Band 2
Band 1
GENERAL MATHEMATICS Year 11/12
page -25-