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COURSE GUIDE
Maths Quest
General Mathematics:HSC Course
Financial Mathematics 4
FM4: Credit and borrowing (Chapter 1)
This unit of work focuses on the mathematics involved in borrowing money, the different types of loans available and credit cards.
Outcomes addressed
A student:
H1 appreciates the importance of mathematics in her/his own life and its usefulness in contributing to society
H2 integrates mathematical knowledge and skills from different content areas in exploring new situations
H5 makes predictions about the behaviour of situations based on simple models
H8 makes informed decisions about financial situations
H11 uses mathematical argument and reasoning to evaluate conclusions drawn from other sources, communicating his/her position clearly to others
Students learn and acquire the following skills, knowledge and understanding
Skills, knowledge and understanding / Exercises/Investigations· calculation of principal, interest and repayments for flat-rate loans / Ex 1A Flat rate interest (page 4)
· calculation of values in a table of home loan repayments / Ex 1B Home loans (page 10)
Researching home loans (page 18)
· comparison of different options for borrowing money in relation to total repayments, fees, interest rates and flexibility / Ex 1C The cost of a loan (page 16)· calculation of credit-card payments, incorporating fees, charges, rates and interest-free periods / Ex 1D Credit cards (page 22)
Researching credit cards (page 24)
· use of published tables from financial institutions to determine monthly repayments on a reducing balance loan / Ex 1E Loan repayments (page 27)Terminology introduced in this unit
Syllabus/glossary terms / PageFlat rate loan / 14
Reducing balance loan / 7
Term of loan / 2
Further activities
Computer application 1: Flat rate interest loan calculator (page 6)
Computer application 2: Home loan calculator (page 8)
Investigation – Researching home loans (page 18)
Graphics calculator tip – Loan repayment function (page 18)
Computer application 3: Loan repayments (page 29)
Financial Mathematics 5
FM5: Annuities and loan repayments (Chapter 8)
The key focus of this unit is the nature and maths of annuities; the processes by which they accrue and ways of maximising their value as investments. Stress should be placed on using formulae and tables.
Outcomes addressed
A student:
H1 appreciates the importance of mathematics in her/his own life and its usefulness in contributing to society
H2 integrates mathematical knowledge and skills from different content areas in exploring new situations
H5 makes predictions about the behaviour of situations based on simple models
H8 makes informed decisions about financial situations
H11 uses mathematical argument and reasoning to evaluate conclusions drawn from other sources, communicating his/her position clearly to others
Students learn and acquire the following skills, knowledge and understanding
Skills, knowledge and understanding / Exercises/Investigations· recognition that an annuity is a form of investment involving periodical and equal contributions to an account, with interest compounding at the conclusion of each period / Ex 8A Calculating the future value of an annuity (page 227)
· calculating the future value (A) of an annuity
(or the contribution per period), using:
where M = contribution per period, paid at
the end of the period / Ex 8A Calculating the future value of an annuity (page 227)
· calculating the present value (N) of an annuity (or the contribution per period), using:
/ Ex 8B Present value of an annuity
(page 234)
· using tables to solve problems with annuities / Ex 8C Future and present value tables
(page 239)
· use the present value formula for annuities to calculate loan instalments, and therefore the total amount paid over the term of a loan / Ex 8D Loan repayments (page 243)
· investigate various processes for loan repayment / Types of loan arrangements (page 245)
· calculate the fees and charges which apply to different options for borrowing money in order to make a purchase / Types of loan arrangements (page 245)
Terminology introduced in this unit
Syllabus/glossary terms / PageAnnuity / 224
Future value of an annuity / 225
Present value of an annuity / 231
Further activities
Computer application 1: Annuity calculator (page 230)
Computer application 2: Future value of $1 (page 235)
Computer application 3: Present value table (page 237)
Investigation – Types of loan arrangements (page 245)
Computer application 4: Graphs of annuities and loans (page 245)
Financial Mathematics 6
FM6: Depreciation (Chapter 10)
The focus of this unit is to investigate situations involving the depreciation of an asset over time.
Outcomes addressed
A student:
H1 appreciates the importance of mathematics in her/his own life and its usefulness in contributing to society
H2 integrates mathematical knowledge and skills from different content areas in exploring new situations
H5 makes predictions about the behaviour of situations based on simple models
H8 makes informed decisions about financial situations
H11 uses mathematical argument and reasoning to evaluate conclusions drawn from other sources, communicating his/her position clearly to others
Students learn and acquire the following skills, knowledge and understanding
Skills, knowledge and understanding / Exercises/Investigations· modelling depreciation by using appropriate graphs, tables and functions / Ex 10A Modelling depreciation (page 285)
· using formulae for depreciation:
a) the straight line method
b) the declining balance method
/ Ex 10B Straight line depreciation (page 289)
Ex 10C Declining balance method of depreciation (page 292)
Rates of depreciation (page 293)
· preparing tables of values and hence developing graphs of n for different values of r / Ex 10A Modelling depreciation (page 285)
Ex 10D Depreciation tables (page 299)
· comparing the results obtained through each method / Ex 10C Declining balance method of depreciation (page 292)
· using the above formulae to create and compare depreciation tables / Ex 10D Depreciation tables (page 299)
· calculating tax deductions based on the depreciation of assets / Ex 10D Depreciation tables (page 299)
Terminology introduced in this unit
Asset / 282
Declining balance method / 282
Depreciation / 282
Salvage value / 288
Straight line method / 282
Further activities
Investigation – Depreciation of motor vehicles (page 282)
Investigation – Rates of depreciation (page 293)
Computer application 1: Depreciation table (page 294)
Data Analysis 5
DA5: Interpreting sets of data (Chapter 4)
The principal focus of this unit is the use of data displays, measures of location, and measures of spread to summarise and interpret one or more sets of data.
Outcomes addressed
A student:
H1 appreciates the importance of mathematics in her/his own life and its usefulness in contributing to society
H2 integrates mathematical knowledge and skills from different content areas in exploring new situations
H4 analyses representations of data in order to make inferences, predictions and conclusions
H5 makes predictions about the behaviour of situations based on simple models
H9 develops and carries out statistical processes to answer questions which she/he and others have posed
H11 uses mathematical argument and reasoning to evaluate conclusions drawn from other sources, communicating his/her position clearly to others
Students learn and acquire the following skills, knowledge and understanding
Skills, knowledge and understanding / Exercises/Investigations· identifying measures of location as mean and median / Ex 4A Measures of location and spread (page 125)
· identifying measures of spread as range, inter- quartile range and standard deviation / Ex 4A Measures of location and spread (page 125)
· investigating outliers in small data sets and their effects on the mean, median and mode / Ex 4A Measures of location and spread (page 125)
· describing a graph or display which represents a given data set, eg. smoothness, symmetry, modes / Ex 4B Skewness (page 130)
· making judgements about the data based on observed features of the display such as shape and skewness / Ex 4B Skewness (page 130)
Examining exam results (page 135)
· displaying data in double (back-to-back) stem-and-leaf plots / Ex 4C Displaying multiple data sets
(page 138)
· displaying data in two box-and-whisker plots drawn on the same scale / Ex 4C Displaying multiple data sets
(page 138)
· displaying two sets of data on a radar chart / Ex 4C Displaying multiple data sets
(page 138)
· preparing an area chart to illustrate and compare different sets of data over time / Ex 4D Comparison of data sets (page 144)
· using multiple displays to describe and interpret the relationships between data sets / Ex 4D Comparison of data sets (page 144)
· interpreting data presented in two-way table form eg. male / female versus exercise / no exercise / Ex 4D Comparison of data sets (page 144)
Developing a two-way table (page 148)
· comparing summary statistics from two data sets / Ex 4D Comparison of data sets (page 144)
Terminology introduced in this unit
Syllabus/glossary terms / PageArea chart / 137
Outlier / 123
Skewness / 130
Further activities
Investigation – Examining exam results (page 135)
Computer application 1: Displaying statistical data (page 141)
Graphics calculator tip – Displaying statistical data and statistical graphs (page 141)
Investigation – Developing a two-way table (page 148)
Data Analysis 6
DA6: The normal distribution (Chapter 11)
In this unit, students will apply the properties of the standard normal distribution to the solution of real problems.
Outcomes addressed
A student:
H2 integrates mathematical knowledge and skills from different content areas in exploring new situations
H4 analyses representations of data in order to make inferences, predictions and conclusions
H5 makes predictions about the behaviour of situations based on simple models
H9 develops and carries out statistical processes to answer questions which she/he and others have posed
H11 uses mathematical argument and reasoning to evaluate conclusions drawn from other sources, communicating his/her position clearly to others
Students learn and acquire the following skills, knowledge and understanding
Skills, knowledge and understanding / Exercises/Investigations· describing the z-score (standardised score) corresponding to a particular score in a set of scores as a number indicating the position of that score relative to the mean / Ex 11A z-scores (page 310)
· using the formula to calculate z-scores, where is the standard deviation ( for a population, for a sample) / Ex 11A z-scores (page 310)
· using calculated z-scores to compare scores from different data sets / Ex 11B Comparison of scores (page 314)
Comparison of subjects (page 316)
· identifying the properties of data that are normally distributed, ie:
- the mean, median and mode are equal
- if represented by a histogram, the resulting frequency graph is bell-shaped / Ex 11A z-scores (page 310)
· using collected data to illustrate that, for normally distributed data:
- approximately 68% of scores will have
z-scores between -1 and 1
- approximately 95% of scores will have
z-scores between -2 and 2
- approximately 99.7% of scores will have z-scores between -3 and 3 / Ex 11C Distribution of scores (page 320)
Examining a normal distribution (page 322)
· using these measures to make judgements in individual cases / Ex 11C Distribution of scores (page 320)
Examining a normal distribution (page 322)
Terminology introduced in this unit
Syllabus/glossary terms / PageNormal distribution / 308
Standardised score / 308
z-score / 308
Further activities
Investigation – Comparison of subjects (page 316)
Investigation – Examining a normal distribution (page 322)
Data Analysis 7
DA7: Correlation (Chapter 12)
In this unit, students investigate the strength of data association by examining a scatterplot of ordered pairs. Where appropriate, students find the equation of a line of fit and use this equation to make predictions.
Outcomes addressed
A student:
H1 appreciates the importance of mathematics in her/his own life and its usefulness in contributing to society
H2 integrates mathematical knowledge and skills from different content areas in exploring new situations
H4 analyses representations of data in order to make inferences, predictions and conclusions
H5 makes predictions about the behaviour of situations based on simple models
H9 develops and carries out statistical processes to answer questions which she/he and others have posed
H11 uses mathematical argument and reasoning to evaluate conclusions drawn from other sources, communicating his/her position clearly to others
Students learn and acquire the following skills, knowledge and understanding
Skills, knowledge and understanding / Exercises/Investigations· plotting ordered pairs of data onto a scatterplot / Ex 12A Scatterplots (page 333)
· recognising from the scatterplot:
- whether the points appear to form a mathematical pattern
- whether the pattern appears to be linear / Ex 12A Scatterplots (page 333)
Collecting bivariate data (page 335)
· establishing a median regression line, to give a line of fit on a scatterplot, with a ruler and pencil / Ex 12B Median regression lines (page 339)
· measuring the gradient of the line of fit drawn, with a ruler and pencil / Ex 12B Median regression lines (page 339)
· noting the vertical intercept of the line of fit / Ex 12B Median regression lines (page 339)
· establishing the equation of the resulting line of fit in the form: / Ex 12B Median regression lines (page 339)
· using this equation to make predictions / Ex 12B Median regression lines (page 339)
Relationship between variables (page 344)
· interpreting the strength of association using a given correlation coefficient / Ex 12C Correlation (page 349)
Causality (page 347)
· interpreting the sign of a given correlation coefficient / Ex 12C Correlation (page 349)
· recognising that a high degree of correlation does not necessarily imply causality, eg. there is a very high correlation between the sizes of left and right feet, but one does not cause the other / Ex 12C Correlation (page 349)
Terminology introduced in this unit
Syllabus/glossary terms / PageCausality / 347
Correlation / 345
Correlation coefficient / 346
Line of best fit / 336
Median regression line / 336
Scatterplot / 330
Further activities