11–12Mathematics Advanced 11–12 Syllabus

Implementation from 2026

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Content

Year 11

Teaching advice

Examples

Probability and data

MAO-WM-01
develops understanding and fluency in mathematics through exploring and connecting mathematical concepts, choosing and applying mathematical techniques to solve problems, and communicating their thinking and reasoning coherently and clearly
MAV-11-09
solves problems involving probability in a variety of contexts
MAV-11-10
displays and analyses datasets using summary statistics and graphical representations

Probability and data

Sets and set notation

Define a set as a collection of objects, called the elements of the set, and represent a set using notation such as $\{2,3,5,7\}$ and ${0,2,4,6, \dots}$
Use the notation $n (A)$ or $|A|$ to represent the number of elements in a finite set $A$
Define the empty set as the set with no elements, denoted in set notation as $\emptyset$
Use the notation $\bar{A}$ , $A'$ or $A^{c}$ to represent the complement of a set $A$ with respect to some universal set $U$
Define $A$ to be a subset of $B$ if all the elements of $A$ are elements of $B$
Define the intersection $A \cap B$ of sets $A$ and $B$ to be the set of elements that are in $A$ and in $B$
Define the union $A \cup B$ of sets $A$ and $B$ to be the set of elements that are in $A$ or in $B$
Define sets $A$ and $B$ to be disjoint if $A \cap B = \emptyset$ , that is, they have no elements in common
Use Venn diagrams in practical situations to represent and interpret sets that may intersect in various ways within a universal set
Establish and use the rule $|A \cup B| = |A| + |B| - |A \cap B|$

Probability

Define an experiment or a trial to be any procedure that can be infinitely repeated and has a well-defined set of possible outcomes known as the sample space, denoted $S$
Identify an event $A$ as a subset $A$ of the sample space $S$
Define the probability of each outcome to be $\frac{1}{|S|}$ when all the outcomes are equally likely and the probability of the event $A$ to be $P (A) = \frac{|A|}{|S|}$
Interpret the notation $\bar{A}$ to be the event ‘ $A$ does not occur’, interpret $A \cap B$ to be the event ‘ $A$ and $B$ both occur’, and interpret $A \cup B$ to be the event ‘ $A$ or $B$ occurs’
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
Establish and use the rules $P (\bar{A}) = 1 - P (A)$ and $P (A \cup B) = P (A) + P (B) - P (A \cap B)$
Use arrays and tree diagrams to determine the outcomes and probabilities for multistage events

Conditional probability

Define conditional probability as the probability that an event $A$ occurs given that another event $B$ has already occurred, and use the notation $P (A |B)$
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
Establish that $P (A | B) = \frac{|A \cap B|}{|B|}$ when all outcomes are equally likely by restricting the sample space and event space, and hence $P (A | B) = \frac{P (A \cap B)}{P (B)}$ , provided $|B| \neq 0$
Use the formulas for $P (A | B)$ to solve practical problems involving conditional probability
Define two events to be independent if the occurrence of one event does not affect the probability that the other event occurs
Explain that two events $A$ and $B$ are independent means $P (A| B) = P (A)$ and $P (B| A) = P (B)$ , and show algebraically that if one of these formulas is true, then the other is also true
Use the formula $P (A | B) = \frac{P (A \cap B)}{P (B)}$ , and the test $P (A| B) = P (A)$ for independence to prove that if two events are independent, then $P (A \cap B) = P (A) \times P (B)$ , and to prove conversely that if $P (A \cap B) = P (A) \times P (B)$ , then $A$ and $B$ are independent
Solve practical problems involving independent events

Data

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

Related files

Year 12