11–12Mathematics Advanced 11–12 Syllabus

Use Venn diagrams in practical situations to represent and interpret sets that may intersect in various ways within a universal set

Use Venn diagrams to represent the relationship between events within the same sample space, including mutually exclusive events, that is, events that as subsets of the sample space are disjoint

Use arrays and tree diagrams to determine the outcomes and probabilities for multistage events

Examine conditional probability by restricting the sample space and event spaces in a Venn diagram, using a two-way table, a tree diagram and other arrays

Define two events to be independent if the occurrence of one event does not affect the probability that the other event occurs

Solve practical problems involving independent events

Define a random variable as a variable whose value is the outcome of a random experiment

Compare discrete random variables with continuous random variables, describe their differences, and give practical examples of each

Organise finite datasets using a table or a spreadsheet, listing the values, frequency, relative frequency, cumulative frequency, and cumulative relative frequency

Graph the frequency, relative frequency, and cumulative frequency histograms and polygons of datasets, using spreadsheets or graphing applications, and identify the mode and median from the graphs, and from tables

Use the relative frequency to estimate the probability of results in experiments