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 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

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 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

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!

Catch up with the lesson yourself 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 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

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.

Q1: Answer True or False True 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

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 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

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

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 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%

Categorical Data Bar Graph / Column Graph

Percentaged Segmented Bar Chart

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 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%

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 Leaf 20 1 2 2 5 6 21 0 1 2 22 2 3 8 23 24 0 2 24 0 represents 240

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

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

Numerical Data Shape: 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.