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Elaboration ACMNA238

solving problems using the fact that parallel lines have the same gradient and conversely that if two lines have the same gradient then they are parallel

Elaboration (1) ACMNA238

solving problems using the fact that the product of the gradients of perpendicular lines is –1 and conversely that if the product of the gradients of two lines is –1 then they are perpendicular

Elaboration ACMNA240

solving a wide range of linear equations, including those involving one or two simple algebraic fractions, and checking solutions by substitution

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 (1) ACMSP247

using arrays and tree diagrams to determine probabilities

Elaboration (1) ACMNA239

applying translations, reflections and stretches to parabolas and circles

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 ACMMG245

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

Elaboration ACMNA236

representing word problems with simple linear inequalities and solving them to answer questions

Elaboration ACMNA237

associating the solution of simultaneous equations with the coordinates of the intersection of their corresponding graphs

Elaboration (1) ACMNA230

understanding the relationship between factorisation and expansion

Elaboration ACMNA231

applying knowledge of index laws to algebraic terms, and simplifying algebraic expressions using both positive and negative integral indices

Elaboration ACMNA232

expressing the sum and difference of algebraic fractions with a common denominator

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 ACMSP246

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

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 ACMNA235

representing word problems with simple linear equations and solving them to answer questions

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