An Introduction to Further Mathematics -2016
Year 12 Further Maths
November 2015
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
Planned TimelineTerm 1
Weeks 1-8 Core Chapter 1- 5
Term 2Weeks 9-12 Core Chapter 6-7
Week 13 SAC for CoreRecursion and Financial
Modelling
Chapter 8 (start)
Weeks 14-17 Recursion and Financial Modelling
Chapter 8 -10
Weeks 18 SAC for Recursion and Financial Modelling
Semester 2 Timeline
Term 3 Start of Unit 41st Module Matrices
2nd Module Networks and decision Mathematics
End of Unit 4:
November Exams 1 & 2 Tech active
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 20 marks
SAC 4: Application tasks: Networks 20 marks
66% from your examsTech active
Exam 1 Multiple choice
Exam 2 Short answer and extended response
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.
Want an “S” not “N”?
Complete all outcome questions. Pass 40% on each outcome test. Have at least 90% of attendance.
Failure to satisfy the outcome requirements above
Letters sent home
Resit the tests
May cause you to drop out of the
subject!
Absent from a lesson?
Catch up with the lesson yourself
Miss a SAC or an outcome test?
Bring A medical certificate
Do the test at an arranged time
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 referenceSeveral binder books for completion of set
exercises from text book
Bound Reference
Bound Reference
Any questions?
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
Ch 1 – Organising & Displaying
DataCLASSIFYING 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
Numerical Data
Two types of numerical dataDiscrete: 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.
Q1: Answer True or False
The age of my car is numerical data
True
False
Q2: Answer True or False
The colour of my car is categorical data
True
False
Q3: Answer True or False
The number of cars in the car park would be considered numerical & continuous data.
True
False
Q4: Answer True or False
If I rate my driving experience of some test cars between one and ten, this is considered numerical & discrete data.
True
FalseThis is an example of categorical data
Q5: Answer True or False
Continuous numerical data can be measured
True
False
Q6: Answer True or False
If 1 = satisfied, 2 = indifferent & 3 = dissatisfied, I am collecting categorical data
True
False
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 kgsEg: weight recorded as 1 = underweight,
2 + normal weight, etc
Univariate Data
Summarising dataFrequency 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.
Categorical Data
FAVOURITE TEAM
FREQUENCY % FREQUENCY
Collingwood 12 12/35 * 100 = 34%
Essendon 5 14%Bulldogs 15 43%
Carlton 3 9%TOTAL 35 100%
Categorical DataBar Graph / Column Graph
Preferred Football Team
0
2
4
6
8
10
12
14
16
Collingwood Essendon Bulldogs Carlton
Team
Fre
qu
ency
Percentaged Segmented Bar Chart
Percentaged Segmented Barchart of Favourite Teams
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
Team
Per
cen
tag
e F
req
uen
cy
Collingwood
Essendon
Bulldogs
Carlton
Describing a Bar Chart
We focus on 2 things:The presence of a DOMINANT Category
in the distribution – given by the ModeThe order of Occurrence of each
category and its relative importanceREPORT – where you comment on
features. Use percentages to support any conclusions
Organising & Displaying Numerical Data
Group the DATA
Guidelines for choosing the number of Intervals:Usually use between 5 and 15 intervals
Numerical Data
NUMBER OF SIBLINGS
FREQUENCY PERCENTAGEFREQUENCY
0 2 2/25*100 = 8%
1 4 16%
2 12 48%
3 7 28%
25 100%
How has forming a Frequency Table helped?
Orders the dataDisplays the data in compact formShows a pattern – way the data values
are distributedHelps us to identify the mode
Numerical DataHistogram
There are no spaces between the columns of a histogram
Numerical DataStem 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
Numerical DataStem and Leaf Plots
Stem Leaf20 1 2 2 5 621 0 1 222 2 3 82324 0 2
24 0 represents 240
Numerical DataDescribing a distribution
ShapeGenerally one of three types
SymmetricPositively SkewedNegatively Skewed
Numerical DataShape Symmetric
Symmetric (same shape either
side of the centre)
Numerical DataShape: Positively Skewed
Positively skewed : tails off to the right
Numerical Data Shape: Negatively Skewed
Negatively skewed : tails off to the left
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
Spread
The maximum and minimum values should be used to calculate the range.
Range = Maximum Value – Minimum Value
Outliers
Outliers are extreme values well away from the majority of the data
Outlier
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
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.