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An Introduction to Further Mathematics Year 12 Further Maths November 2013

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Further Maths 3 & 4 includes Core material (unit 3) 3 modules selected from the 6 modules below Module 1:Number Patterns & Applications Module 2:Geometry and Trigonometry Module 3:Graphs & Relations Module 4:Business Mathematics Module 5:Networks & Decision Mathematics Module 6:Matrices & Applications

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Planned Timeline Term 1 Weeks 1-8CoreChapter 1- 8 Term 2 Weeks 1-2SAC for Core Weeks 3-81 st module Weeks 9-10SACEnd of Unit 3 Weeks 11-12Start of Unit 42 nd Module Term 3 Weeks 1-42 nd Module continued Weeks 4-5SAC Weeks 6-93 rd Module Week 10SACEnd of Unit 4 November Exams 1 & 2

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Your VCE result consists of 34% from your 4 SACs SAC 1 : Based on Core material 40 marks SAC 2 : Application tasks 20 marks SAC 3: Application tasks 20 marks SAC 4 : Application tasks 20 marks 66% from your exams Exam 1 Exam 2

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Exams 1 & 2 (1 bound book permitted & a CAS calculator is required) Exam 1 40 multiple choice questions (13 core, 9 from each of 3 modules) Total 40 marks Exam 2 1 set of questions from each of the Core and 3 modules Each set of questions worth 15 marks Total 60 marks

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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.

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Want an “S” not “N”? Complete all outcome questions. Pass 40% on each outcome test. Have at least 80% of attendance.

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Failure to satisfy the outcome requirements above Letters sent home Resit the tests May cause you to drop out of the subject!

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Absent from a lesson? Catch up with the lesson yourself

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

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What to prepare? A textbook : Essential Further Maths 3 &4 CAS (Enhanced 4 th edition – Evans ) A CAS calculator A 20 page Display Folder One binder book for class notes Several binder books for completion of set exercises from text book

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Any questions?

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Holiday Homework Complete the following questions from your textbook: All working out must be shown Ex 1A (Categorical and Numerical Data) – Nos 1- 4 Ex 1B (Categorical Data display) – Nos Ex 1C (Displaying Numerical Data) – Nos Ex 1D (Histograms) – Nos Ex 1E (Dot plots and Stem & leaf plots) – No 1 - 8

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Ch 1 – Organising & Displaying Data CLASSIFYING DATA Categorical: a category is recorded when the data is collected. Examples of categorical data include gender, nationality, occupation, shoe size. Numerical: when data is collected a number is recorded. The data is measured or counted.

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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.

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Q1: Answer True or False The age of my car is numerical data True False

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

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

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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

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

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Q6: Answer True or False If 1 = satisfied, 2 = indifferent & 3 = dissatisfied, I am collecting categorical data True False

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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

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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.

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Categorical Data FAVOURITE TEAMFREQUENCY% FREQUENCY Collingwood 1212/35 * 100 = 34% Essendon 514% Bulldogs 1543% Carlton 39% TOTAL 35100%

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Categorical Data Bar Graph / Column Graph

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Percentaged Segmented Bar Chart

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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

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

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Numerical Data NUMBER OF SIBLINGS FREQUENCYPERCENTAGE FREQUENCY 022/25*100 = 8% 1416% 21248% 3728% 25100%

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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

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

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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

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Numerical Data Stem and Leaf Plots Stem Leaf represents 240

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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)

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Numerical Data Shape: Positively Skewed Positively skewed : tails off to the right

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Numerical Data Shape: Negatively Skewed Negatively skewed : tails off to the left

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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

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Spread The maximum and minimum values should be used to calculate the range. Range = Maximum Value – Minimum Value

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Outliers Outliers are extreme values well away from the majority of the data Outlier

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Which Graph?? TYPE OF DATAGRAPHWHEN TO USE CATEGORICALBar Chart Segmented Bar ChartNot too many Categories Max 4-5 NUMERICALHistogramMed to Large Stem PlotSmall to Medium Dot PlotOnly small data sets

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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.

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