# Year 12 Applied 6: Probability and Simulation Mathematics – South Australia

### SA Year 12 Applied 6: Probability and Simulation Mathematics

# | TOPIC | TITLE | |
---|---|---|---|

1 | Study Plan | Study plan – Year 12 Applied 6: Probability and Simulation | |

Objective: On completion of the course formative assessment a tailored study plan is created identifying the lessons requiring revision. | |||

2 | Percentages | Changing percentages to fractions and decimals | |

Objective: On completion of the lesson the student will be able to change percentages to fractions and know how to change percentages to decimals. | |||

3 | Percentages | One quantity as a percentage of another | |

Objective: On completion of the lesson the student will be able to find a percentage of an amount and how to express one quantity as a percentage of another. | |||

4 | Lines and angles | Mapping and grid references | |

Objective: On completion of the lesson the student will be able to identify specific places on a map and use regions on a grid to locate objects or places. | |||

5 | Lines and angles | Informal coordinate system | |

Objective: On completion of the lesson the student will be able to use an informal coordinate system to specify location, and locate coordinate points on grid paper. | |||

6 | Data | Pictograms | |

Objective: On completion of the lesson the student will be able to organise, read and summarise information in picture graphs. | |||

7 | Data | Bar Charts | |

Objective: On completion of the lesson the student will be able to organise, read and summarise information in column graphs. | |||

8 | Data | Line graphs. | |

Objective: On completion of the lesson the student will be able to organise, read and summarise information in line graphs. | |||

9 | Data | Pie and bar graphs. | |

Objective: On completion of the lesson the student will be able to organise, read and summarise information in pie and bar graphs. | |||

10 | Statistics | Frequency distribution table | |

Objective: On completion of the lesson the student will be able to construct a frequency distribution table for raw data and interpret the table. | |||

11 | Statistics | Frequency histograms and polygons | |

Objective: On completion of the lesson the student will be able to construct and interpret frequency histograms and polygons. | |||

12 | Statistics | Relative frequency | |

Objective: On completion of the lesson the student will be able to collect, display and make judgements about data. | |||

13 | Statistics | The range. | |

Objective: On completion of the lesson the student will be able to determine the range of data in either raw form or in a frequency distribution table. | |||

14 | Statistic-probability | The mode | |

Objective: On completion of the lesson the student will understand how to find the mode from raw data, a frequency distribution table and polygon. | |||

15 | Statistic-probability | The mean | |

Objective: On completion of the lesson the student will be able to calculate means from raw data and from a frequency table using an fx column. | |||

16 | Statistic-probability | The median | |

Objective: On completion of the lesson the student will be able to determine the median of a set of raw scores | |||

17 | Statistic-probability | Cumulative frequency | |

Objective: On completion of the lesson the student will be able to construct cumulative frequency columns, histograms and polygons. | |||

18 | Statistic-probability | Calculating the median from a frequency distribution | |

Objective: On completion of the lesson the student will be able to determine the median from a cumulative frequency polygon. | |||

19 | Statistics – grouped data | Calculating mean, mode and median from grouped data | |

Objective: On completion of the lesson the student will be capable of identifying class centres, get frequency counts and determine the mean and mode values. | |||

20 | Statistics using a calculator | Statistics and the student calculator | |

Objective: On completion of the lesson the student will be capable of using a scientific calculator in statistics mode to calculate answers to statistical problems. | |||

21 | Statistics – Range and dispersion | Range as a measure of dispersion | |

Objective: On completion of the lesson the student will be able to determine the range and using it in decision making. | |||

22 | Statistics – Spread | Measures of spread | |

Objective: On completion of the lesson the student will be able to find the standard deviation, using a data set or a frequency distribution table and calculator. | |||

23 | Statistics – Standard deviation | Standard deviation applications | |

Objective: On completion of the lesson the student will be able to use standard deviation as a measure of deviation from a mean. | |||

24 | Statistics – Standard deviation | Normal distribution | |

Objective: On completion of the lesson the student will be able to use the standard deviation of a normal distribution to find the percentage of scores within ranges. | |||

25 | Statistics – Interquartile range | Measures of spread: the interquartile range | |

Objective: On completion of the lesson the student will be able to find the upper and lower quartiles and the interquartile range | |||

26 | Statistics | Stem and Leaf Plots along with Box and Whisker Plots | |

Objective: On completion of the lesson the student will be familiar with vocabulary for statistics including quartiles, mode, median, range and the representation of this information on a Box and Whisker Plot. | |||

27 | Statistic-probability | Probability of Simple Events | |

Objective: On completion of the lesson the student will be able to understand the probability of simple events. | |||

28 | Statistic-probability | Rolling a pair of dice | |

Objective: On completion of the lesson the student will be capable of ascertaining the probability of certain results when 2 dice are thrown simultaneously. | |||

29 | Statistic-probability | Experimental probability | |

Objective: On completion of this lesson the student will be able to find the probabilities in an experimental trial. | |||

30 | Statistic-probability | Tree diagrams – not depending on previous outcomes | |

Objective: On completion of the lesson the student will be confident in drawing tree diagrams to list outcomes of a multi stage probability problem and then finding probabilities of certain events not depending on previous outcomes. | |||

31 | Statistic-probability | Tree diagrams – depending on previous outcomes | |

Objective: On completion of the lesson the student will be confident in drawing tree diagrams to list outcomes of other multi stage probability problems and then finding probabilities of certain events depending on previous outcomes. | |||

32 | Statistic-probability | The complementary result .. | |

Objective: On completion of the lesson the student will be capable of ascertaining the probability of certain results where the complementary event is involved. | |||

33 | Statistic-probability | P[A or B] When A and B are both mutually and NOT mutually exclusive | |

Objective: On completion of this lesson the student will be able to distinguish between mutually exclusive and non mutually exclusive events and be able to find the probabilities of both. | |||

34 | Statistic-probability | Binomial Theorem – Pascal’s Triangle | |

Objective: On completion of this lesson the student will use Pascal’s triangle and the binomial theorem to write the expansion of binomial expressions raised to integer powers. | |||

35 | Statistic-probability | Binomial probabilities using the Binomial Theorem | |

Objective: On completion of the lesson the student will be able to solve certain types of probability questions using the binomial theorem | |||

36 | Statistic-probability | Counting techniques and ordered selections – permutations | |

Objective: On completion of this lesson the student will be competent in using some new counting techniques used for solving probability. | |||

37 | Statistic-probability | Unordered selections – combinations | |

Objective: On completion of the lesson the student will be able to use the formula, n c r both with and without a calculator and be able to use it to solve probability problems where unordered selections happen. | |||

38 | Exam | Exam – Year 12 Applied 6: Probability and Simulation | |

Objective: Exam |