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Unit 2 Specialist Mathematics

Unit 2 of Specialist Mathematics contains three topics – ‘Trigonometry’, ‘Real and complex numbers’ and ‘Matrices’… ‘Trigonometry’ contains techniques that are used in other topics in both this unit and Unit 3. ‘Real and complex numbers’ provides a continuation …

Unit 2 | Specialist Mathematics | Mathematics | Senior secondary curriculum

Units 1 and 2 Specialist Mathematics Achievement Standard

demonstrates knowledge and understanding of the concepts of vectors, combinatorics, geometry, matrices, trigonometry and complex numbers in routine and non-routine problems in a variety of contexts synthesises information to select and apply techniques …

Units 1 and 2 | Achievement standards | Specialist Mathematics | Mathematics | Senior secondary curriculum

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

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

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

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

Representation of General capabilities Specialist Mathematics

The seven general capabilities of Literacy, Numeracy, Information and Communication technology (ICT) capability, Critical and creative thinking, Personal and social capability, Ethical understanding, and Intercultural understanding are identified where …

Representation of General capabilities | Specialist Mathematics | Mathematics | Senior secondary curriculum

ACMSM121

integrate expressions of the form \(\frac{\pm1}{\sqrt[{}]{a^2-x^2}}\) and \(\frac a{a^2+x^2}\)

ACMSM063

prove irrationality by contradiction for numbers such as \(\sqrt[{}]2\) and \(\log_25\)

ACMSM067

define the imaginary number i as a root of the equation \(x^2=-1\)

ACMSM131

examine slope (direction or gradient) fields of a first order differential equation

ACMSM066

prove divisibility results, such as \(3^{2n+4}-2^{2n}\) is divisible by 5 for any positive integer n.

ACMSM065

prove results for sums, such as \(1+4+9\dots+n^2=\frac{n(n+1)(2n+1)}6\) for any positive integer n

ACMSM036

When a secant (meeting the circle at \(A\) and \(B\)) and a tangent (meeting the circle at \(T\)) are drawn to a circle from an external point \(M\), the square of the length of the tangent equals the product of the lengths to the circle on the secant. …

ACMSM055

define and use basic linear transformations: dilations of the form \((\mathrm x,\mathrm y)\longrightarrow({\mathrm\lambda}_1\mathrm x,{\mathrm\lambda}_2\mathrm y)\) , rotations about the origin and reflection in a line which passes through the origin, …

ACMSM086

identify subsets of the complex plane determined by relations such as \(\left|z-3i\right|\leq4\) \(\frac\pi4\leq Arg(z)\leq\frac{3\pi}4\), \(Re\left(z\right)>Im(z)\) and \(\left|z-1\right|=2\vert z-i\vert\)

ACMSM136

consider and solve problems involving motion in a straight line with both constant and non-constant acceleration, including simple harmonic motion and the use of expressions \(\frac{dv}{dt}\), \(v\frac{dv}{dx}\) and \(\frac{d(\frac12v^2)}{dx}\) for a …

ACMSM130

solve simple first-order differential equations of the form \(\frac{dy}{dx}=f(x)\), differential equations of the form \(\frac{dy}{dx}=g\left(y\right)\) and, in general, differential equations of the form \(\frac{dy}{dx}=f\left(x\right)g\left(y\right)\) …

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