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Elaboration ACMNA241

using a variety of techniques to solve quadratic equations, including grouping, completing the square, the quadratic formula and choosing two integers with the required product and sum

Elaboration ACMMG242

investigating and determining the volumes and surface areas of composite solids by considering the individual solids from which they are constructed

Elaboration ACMMG243

applying an understanding of relationships to deduce properties of geometric figures (for example the base angles of an isosceles triangle are equal)

distinguishing between a practical demonstration and a proof (for example demonstrating triangles are congruent by placing them on top of each other, as compared to using congruence tests to establish that triangles are congruent)

Elaboration (1) ACMMG244

performing a sequence of steps to determine an unknown angle giving a justification in moving from one step to the next.

Elaboration (2) ACMMG244

communicating a proof using a sequence of logically connected statements

Elaboration ACMMG245

applying Pythagoras' Theorem and trigonometry to problems in surveying and design

Elaboration ACMSP246

recognising that an event can be dependent on another event and that this will affect the way its probability is calculated

Elaboration ACMSP247

using two-way tables and Venn diagrams to understand conditional statements

Elaboration (1) ACMSP247

using arrays and tree diagrams to determine probabilities

Elaboration ACMSP248

finding the five-number summary (minimum and maximum values, median and upper and lower quartiles) and using its graphical representation, the box plot, as tools for both numerically and visually comparing the centre and spread of data sets

Elaboration ACMSP249

understanding that box plots are an efficient and common way of representing and summarising data and can facilitate comparisons between data sets

Elaboration (1) ACMSP249

using parallel box plots to compare data about the age distribution of Aboriginal and Torres Strait Islander people with that of the Australian population as a whole

Elaboration ACMSP250

investigating data in different ways to make comparisons and draw conclusions

Elaboration ACMSP251

using authentic data to construct scatter plots, make comparisons and draw conclusions

Elaboration ACMSP252

investigating biodiversity changes in Australia since European occupation

Elaboration (1) ACMSP252

constructing and interpreting data displays representing bivariate data over time

Elaboration ACMSP253

investigating the use of statistics in reports regarding the growth of Australia's trade with other countries of the Asia region

Elaboration (1) ACMSP253

evaluating statistical reports comparing the life expectancy of Aboriginal and Torres Strait Islander people with that of the Australian population as a whole

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