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 2 Weeks 1-8 Core Chapter 1- 5 Weeks 9-12
SAC for Core
Recursion and Financial Modelling
Chapter 8 (start)
Weeks 14-17
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. Your VCE result consists of
34% from your 4 SACs
SAC 1:
Based on statistics
40 marks
SAC 2:
Financial Modelling
20 marks
SAC 3:
Application tasks: Matrices
SAC 4:
Application tasks: Networks
66% from your exams
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 student’s 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. Catch up with the lesson yourself
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. 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. Q1: Answer True or False True False
The age of my car is numerical data
True
False

19. Q2: Answer True or False The colour of my car is categorical data True

20. Q3: Answer True or False
The number of cars in the car park would be considered numerical & continuous data.
True
False

21. Q4: Answer True or False True False
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. Q5: Answer True or False Continuous numerical data can be measured

23. Q6: Answer True or False
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 12 12/35 * 100 = 34% 5 14% 15 43% 3 9% 35 100%
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 2 2/25*100 = 8% 1 4 16% 12 48% 3 7 28% 25 100%
NUMBER OF
SIBLINGS
FREQUENCY
PERCENTAGE 2
2/25*100 = 8% 1 4
16% 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 23
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. Spread
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.