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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

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

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 \(x^2=-1\)

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 …

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