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ACMGM084

investigate and solve practical problems to determine the shortest path between two vertices in a weighted graph (by trial-and-error methods only)

ACMGM084 | Content Descriptions | Unit 3 | General Mathematics | Mathematics | Senior secondary curriculum

ACMSM005

determine and use the formulas for finding the number of elements in the union of two and the union of three sets. 

ACMSM005 | Content Descriptions | Unit 1 | Specialist Mathematics | Mathematics | Senior secondary curriculum

ACMSM035

When two chords of a circle intersect, the product of the lengths of the intervals on one chord equals the product of the lengths of the intervals on the other chord

ACMSM035 | Content Descriptions | Unit 1 | Specialist Mathematics | Mathematics | Senior secondary curriculum

ACMSM060

establish geometric results by matrix multiplications; for example, show that the combined effect of two reflections in lines through the origin is a rotation.

ACMSM060 | Content Descriptions | Unit 2 | Specialist Mathematics | Mathematics | Senior secondary curriculum

ACMSM106

examine the position of two particles each described as a vector function of time, and determine if their paths cross or if the particles meet 

ACMSM106 | Content Descriptions | Unit 3 | Specialist Mathematics | Mathematics | Senior secondary curriculum

ACMSM112

derive the Cartesian equation of a path given as a vector equation in two dimensions including ellipses and hyperbolas

ACMSM112 | Content Descriptions | Unit 3 | Specialist Mathematics | Mathematics | Senior secondary curriculum

ACMEM106

interpret different forms of two-dimensional representations of three-dimensional objects, including nets and perspective diagrams

ACMEM106 | Content Descriptions | Unit 3 | Essential Mathematics | Mathematics | Senior secondary curriculum

ACMGM066

implement the statistical investigation process to answer questions that involve identifying, analysing and describing associations between two categorical variables or between two numerical variables; for example, is there an association between attitude …

ACMGM066 | Content Descriptions | Unit 3 | General Mathematics | Mathematics | Senior secondary curriculum

ACMEM126

interpret the point of intersection and other important features of given graphs of two linear functions drawn from practical contexts; for example, the ‘break-even’ point.

ACMEM126 | Content Descriptions | Unit 3 | Essential Mathematics | Mathematics | Senior secondary curriculum

ACMEM139

describe the association between two numerical variables in terms of direction (positive/negative), form (linear/non-linear) and strength (strong/moderate/weak).

ACMEM139 | Content Descriptions | Unit 3 | Essential Mathematics | Mathematics | Senior secondary curriculum

ACMGM053

describe an association between two numerical variables in terms of direction (positive/negative), form (linear/non-linear) and strength (strong/moderate/weak)

ACMGM053 | Content Descriptions | Unit 3 | General Mathematics | Mathematics | Senior secondary curriculum

ACMMM045

use the notation \(\begin{pmatrix}n\\r\end{pmatrix}\) and the formula \(\begin{pmatrix}n\\r\end{pmatrix}=\frac{n!}{r!\left(n-r\right)!}\) for the number of combinations of \(r\) objects taken from a set of \(n\) distinct objects

ACMMM045 | Content Descriptions | Unit 1 | Mathematical Methods | Mathematics | Senior secondary curriculum

ACMGM033

implement the statistical investigation process to answer questions that involve comparing the data for a numerical variable across two or more groups; for example, are Year 11 students the fittest in the school?

ACMGM033 | Content Descriptions | Unit 2 | General Mathematics | Mathematics | Senior secondary curriculum

ACMGM035

determine the area of a triangle given two sides and an included angle by using the rule \(Area=\frac12ab\sin C\), or given three sides by using Heron’s rule, and solve related practical problems

ACMGM035 | Content Descriptions | Unit 2 | General Mathematics | Mathematics | Senior secondary curriculum

ACMGM045

solve practical problems that involve finding the point of intersection of two straight-line graphs; for example, determining the break-even point where cost and revenue are represented by linear equations.

ACMGM045 | Content Descriptions | Unit 2 | General Mathematics | Mathematics | Senior secondary curriculum

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