An Introduction to Further Mathematics -2014

Year 12 Further Maths

November 2013

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

Planned TimelineTerm 1

Weeks 1-8 Core Chapter 1- 8

Term 2Weeks 1-2 SAC for Core

Weeks 3-8 1st module

Weeks 9-10 SAC End of Unit 3

Weeks 11-12 Start of Unit 4 2nd Module

Term 3Weeks 1-4 2nd Module continued

Weeks 4-5 SAC

Weeks 6-9 3rd Module

Week 10 SAC End of Unit 4

November Exams 1 & 2

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

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

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 80% 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: Essential Further Maths 3 &4 CAS (Enhanced 4th edition – Evans)

A CAS calculator A 20 page Display FolderOne binder book for class notesSeveral binder books for completion of set

exercises from text book

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- 4 Ex 1B (Categorical Data display) – Nos 1 - 8 Ex 1C (Displaying Numerical Data) – Nos 1 - 9 Ex 1D (Histograms) – Nos 1 - 4

Ex 1E (Dot plots and Stem & leaf plots) – No 1 - 8

Ch 1 – Organising & Displaying

DataCLASSIFYING 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.

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.