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An Introduction to Further Mathematics -2016

This guide provides an introduction to the Year 12 Further Mathematics curriculum, including core material, modules, assessment breakdown, and guidelines for success in the subject. Topics covered include data analysis, recursion, financial modeling, matrices, networks, and decision mathematics.

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An Introduction to Further Mathematics -2016

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  1. An Introduction to Further Mathematics -2016 Year 12 Further Maths November 2015

  2. 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

  3. Planned Timeline

  4. 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

  5. 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 exams Tech active Exam 1 Multiple choice Exam 2 Short answer and extended response Your VCE result consists of

  6. 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.

  7. Want an “S” not “N”? • Complete all outcome questions. • Pass 40% on each outcome test. • Have at least 90% of attendance.

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

  9. Absent from a lesson? • Catch up with the lesson yourself

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

  11. 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

  12. Bound Reference

  13. Bound Reference

  14. Any questions?

  15. 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

  16. 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 ismeasured

  17. 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.

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

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

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

  21. 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 categoricaldata

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

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

  24. 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

  25. 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.

  26. Categorical Data

  27. Categorical DataBar Graph / Column Graph

  28. Percentaged Segmented Bar Chart

  29. 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

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

  31. Numerical Data

  32. 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

  33. Numerical DataHistogram • There are no spaces between the columns of a histogram

  34. 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

  35. Numerical DataStem 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

  36. Numerical DataDescribing a distribution Shape • Generally one of three types • Symmetric • Positively Skewed • Negatively Skewed

  37. Numerical DataShape Symmetric • Symmetric (same shape either side of the centre)

  38. Numerical DataShape: Positively Skewed • Positively skewed : tails off to the right

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

  40. 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

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

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

  43. Which Graph??

  44. 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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