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## An Introduction to Further Mathematics -2016

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Title: An Introduction to Further Mathematics -2016

1
An Introduction to Further Mathematics -2016
• Year 12 Further Maths
• November 2015

2
Further Maths 3 4 includes
• Core material (unit 3)Data analysis and recursion
and Financial Modelling
• 2 modules (unit 4) selected from the 4 modules
below

Module 1 Matrices Applications
Module 2 Networks Decision Mathematics
Module 3 Geometry and Measurement
Module 4 Graphs Relations

3
Planned Timeline
Term 1 Term 1 Term 1
Weeks 1-8 Core Chapter 1- 5
Term 2 Term 2 Term 2
Weeks 9-12 Core Chapter 6-7
Week 13 SAC for Core Recursion and Financial Modelling Chapter 8 (start)
Weeks 14-17 Recursion and Financial Modelling Chapter 8 -10
Weeks 18 SAC for Recursion and Financial Modelling
4
Semester 2 Timeline
• Term 3 Start of Unit 4
• 1st Module Matrices
• 2nd Module Networks and decision Mathematics
• End of Unit 4
• November Exams 1 2 Tech active

5
• 34 from your 4 SACs
• SAC 1
• Based on statistics
• 40 marks
• SAC 2
• Financial Modelling
• 20 marks
• SAC 3
• 20 marks
• SAC 4
• 20 marks
• Tech active
• Exam 1 Multiple choice
• Exam 2 Short answer and extended response

6
Outcome tests
• There are 4 x 45 minutes outcome tests in class.
• Each is done before a SAC.
• They provide feedback on students progress.
• They will be good practices before SACs.

7
Want an S not N?
• Complete all outcome questions.
• Pass 40 on each outcome test.
• Have at least 90 of attendance.

8
Failure to satisfy the outcome requirements
above
• Letters sent home
• Resit the tests

May cause you to drop out of the subject!
9
Absent from a lesson?
• Catch up with the lesson yourself

10
Miss a SAC or an outcome test?
• Bring
• A medical certificate
• Do the test at an arranged time

11
What to prepare?
• A textbook Further Maths 3 4 Cambridge new
edition
• A CAS calculator
• One binder book for class notes see VCAA site
for bound reference
• Several binder books for completion of set
exercises from text book

12
Bound Reference
13
Bound Reference
14
Any questions?
15
Holiday Homework
• Complete the following questions from your
textbook  All working out must be shown
• Ex 1A (Categorical and Numerical Data) Nos 1-
6
• Ex 1B (Categorical Data display) Nos 1 - 8
• Ex 1C (Displaying Numerical Data) Nos 1 - 9
• Ex 1D completed in term 1 in class
• Ex 2A (Dot plots and Stem leaf plots) Nos 1
5
• Ex 2B(Median, Range and IQR)- Nos 1-8
• Ex 2C( 5 number summary and boxplot)- Nos 1-10
• Ex 2D (relating boxplot to shape)- No 1
• Ex 2E (Describing and comparing
distributions)-Nos 1-3
• Complete booklet on Moodle

16
Ch 1 Organising Displaying
Data
• CLASSIFYING DATA
• Categorical a category is recorded when the data
is collected.
• Nominal group has a name eg gender,
nationality, occupation,
• Ordinal group has a name which can be ordered
eg low, medium, high shoe size
• Numerical when data is collected a number is
recorded.
• Discrete data is counted.
• Continuous data is measured

17
Numerical Data
• Two types of numerical data
• Discrete the numbers recorded are distinct
values, often whole numbers and usually the data
comes from counting. Examples include number of
students in a class, pages in a book.
• Continuous any number on a continuous line is
recorded usually the data is produced by
measuring to any desired level of accuracy.
Examples include volume of water consumed, life
of a battery.

18
• The age of my car is numerical data

True False
19
• The colour of my car is categorical data
• True
• False

20
• The number of cars in the car park would be
considered numerical continuous data.
• True
• False

21
• If I rate my driving experience of some test cars
between one and ten, this is considered numerical
discrete data.

True False
This is an example of categorical data
22
• Continuous numerical data can be measured

True False
23
• If 1 satisfied, 2 indifferent 3
dissatisfied, I am collecting categorical data

True False
24
WARNING
• It is not the Variable NAME itself that
determines whether the data is Numerical or
Categorical
• It is the WAY the DATA for the VARIABLE is
recorded
• Eg weight in kgs
• Eg weight recorded as 1 underweight,
• 2 normal weight, etc

25
Univariate Data
• Summarising data
• Frequency tables may be used with both
categorical and numerical data.
• Class intervals are used to group continuous
numerical data or to group discrete data where
there is a large range of values.

26
Categorical Data
FAVOURITE TEAM FREQUENCY FREQUENCY
Collingwood 12 12/35 100 34
Essendon 5 14
Bulldogs 15 43
Carlton 3 9
TOTAL 35 100
27
Categorical Data Bar Graph / Column Graph
28
Percentaged Segmented Bar Chart
29
Describing a Bar Chart
• We focus on 2 things
• The presence of a DOMINANT Category in the
distribution given by the Mode
• The order of Occurrence of each category and its
relative importance
• REPORT where you comment on features. Use
percentages to support any conclusions

30
Organising Displaying Numerical Data
• Group the DATA
• Guidelines for choosing the number of Intervals
• Usually use between 5 and 15 intervals

31
Numerical Data
NUMBER OF SIBLINGS FREQUENCY PERCENTAGE FREQUENCY
0 2 2/25100 8
1 4 16
2 12 48
3 7 28
25 100
32
How has forming a Frequency Table helped?
• Orders the data
• Displays the data in compact form
• Shows a pattern way the data values are
distributed
• Helps us to identify the mode

33
Numerical Data Histogram
• There are no spaces between the columns of a
histogram

34
Numerical Data Stem and Leaf Plots
• Stem and Leaf Plots display the distribution of
numerical data (both discrete and continuous) as
well as the actual data values
• An ordered stem and leaf plot is obtained by
ordering the numbers in the leaf in ascending
order.
• A stem and leaf plot should have at least 5
numbers in the stem

35
Numerical Data Stem and Leaf Plots
• Stem Leaf
• 20 1 2 2 5 6
• 21 0 1 2
• 22 2 3 8
• 23
• 24 0 2
• 24 0 represents 240

36
Numerical Data Describing a distribution
• Shape
• Generally one of three types
• Symmetric
• Positively Skewed
• Negatively Skewed

37
Numerical Data Shape Symmetric
• Symmetric (same shape either
• side of the centre)

38
Numerical Data Shape Positively Skewed
• Positively skewed tails off to the right

39
Numerical Data Shape Negatively
Skewed
• Negatively skewed tails off to the left

40
Centre
• The centre as measured by the Median is the value
which has the same number of scores above as
below.
• The centre as measured by the Mean is the value
which is equal to the sum of the data divided by
n
• The centre as measured by the Mode is the value
which has the highest frequency

41
• The maximum and minimum values should be used to
calculate the range.
• Range Maximum Value Minimum Value

42
Outliers
• Outliers are extreme values well away from the
majority of the data

Outlier
43
Which Graph??
TYPE OF DATA GRAPH WHEN TO USE
CATEGORICAL Bar Chart
Segmented Bar Chart Not too many Categories Max 4-5
NUMERICAL Histogram Med to Large
Stem Plot Small to Medium
Dot Plot Only small data sets
44
Good luck with your holiday homework
• It is a good idea to do this before school
finishes so if you get stuck you can ask us.