Transcript An Introduction to Further Mathematics -2011

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 Timeline
Term 1
Weeks 1-8
Core
Chapter 1- 5
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
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
Your VCE result consists of
34% from your 4 SACs

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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 exams
Tech 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 reference
 Several 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
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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
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

Numerical Data
Two types of numerical data

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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.
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
False
This 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 kgs
 Eg: weight recorded as 1 = underweight,
2 + normal weight, etc

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.

Categorical Data
FAVOURITE TEAM FREQUENCY
% FREQUENCY
Collingwood
12
Essendon
5
15
12/35 * 100 =
34%
14%
43%
3
35
9%
100%
Bulldogs
Carlton
TOTAL
Categorical Data
Bar Graph / Column Graph
Preferred Football Team
16
14
Frequency
12
10
8
6
4
2
0
Collingwood
Essendon
Bulldogs
Team
Carlton
Percentaged Segmented Bar
Chart
Percentaged Segmented Barchart of Favourite Teams
100%
Carlton
Percentage Frequency
90%
80%
Bulldogs
70%
60%
50%
40%
Essendon
30%
20%
Collingwood
10%
0%
Team
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

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
PERCENTAGE
FREQUENCY
0
2
1
2
3
4
12
7
25
2/25*100 =
8%
16%
48%
28%
100%
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

Numerical Data
Histogram

There are no spaces between the
columns of a histogram
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
Numerical Data
Stem and Leaf Plots
Stem
 20
 21
 22
 23
 24
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Leaf
12256
012
238
02
24 0
represents 240
Numerical Data
Describing a distribution
Shape
 Generally one of three types
Symmetric
 Positively Skewed
 Negatively Skewed
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Numerical Data
Shape Symmetric
Symmetric (same shape either
side of the centre)

Numerical Data
Shape: Positively Skewed
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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
CATEGORICAL
Bar Chart
NUMERICAL
WHEN TO USE
Segmented Bar Chart
Not too many
Categories Max 4-5
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.