Unit 3 Specialist Mathematics
Unit 3 of Specialist Mathematics contains three topics: ‘Vectors in three dimensions’, ‘Complex numbers’ and ‘Functions and sketching graphs’. The study of vectors was introduced in Unit 1 with a focus on vectors in two-dimensional space. In this unit, …
Unit 3 | Specialist Mathematics | Mathematics | Senior secondary curriculum
Unit 1 Specialist Mathematics
Unit 1 of Specialist Mathematics contains three topics – ‘Combinatorics’, ‘Vectors in the plane’ and ‘Geometry’ – that complement the content of Mathematical Methods. The proficiency strand, Reasoning, of the F–10 curriculum is continued explicitly in …
Unit 1 | Specialist Mathematics | Mathematics | Senior secondary curriculum
Structure of Specialist Mathematics Specialist Mathematics
Specialist Mathematics is structured over four units. The topics in Unit 1 broaden students’ mathematical experience and provide different scenarios for incorporating mathematical arguments and problem solving. The unit provides a blending of algebraic …
Structure of Specialist Mathematics | Specialist Mathematics | Mathematics | Senior secondary curriculum
Links to Foundation to Year 10 Specialist Mathematics
For all content areas of Specialist Mathematics, the proficiency strands of the F–10 curriculum are still very much applicable and should be inherent in students’ learning of the subject. The strands of Understanding, Fluency, Problem solving and Reasoning …
Links to Foundation to Year 10 | Specialist Mathematics | Mathematics | Senior secondary curriculum
Rationale Specialist Mathematics
Rationale Mathematics is the study of order, relation and pattern. From its origins in counting and measuring it has evolved in highly sophisticated and elegant ways to become the language now used to describe much of the modern world. Statistics is concerned …
Rationale | Specialist Mathematics | Mathematics | Senior secondary curriculum
ACMSM093
find the composition of two functions
ACMSM093 | Content Descriptions | Unit 3 | Specialist Mathematics | Mathematics | Senior secondary curriculum
ACMSM092
determine when the composition of two functions is defined
ACMSM092 | Content Descriptions | Unit 3 | Specialist Mathematics | Mathematics | Senior secondary curriculum
ACMSM104
use vector equations of curves in two or three dimensions involving a parameter, and determine a ‘corresponding’ Cartesian equation in the two-dimensional case
ACMSM104 | Content Descriptions | Unit 3 | Specialist Mathematics | Mathematics | Senior secondary curriculum
ACMSM013
use the triangle rule to find the sum and difference of two vectors.
ACMSM013 | Content Descriptions | Unit 1 | Specialist Mathematics | Mathematics | Senior secondary curriculum
ACMSM021
examine properties of parallel and perpendicular vectors and determine if two vectors are parallel or perpendicular
ACMSM021 | Content Descriptions | Unit 1 | Specialist Mathematics | Mathematics | Senior secondary curriculum
ACMSM105
determine a vector equation of a straight line and straight-line segment, given the position of two points, or equivalent information, in both two and three dimensions
ACMSM105 | Content Descriptions | Unit 3 | Specialist 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