## Mathematics Advanced: Graphs and Equations

Module 3 for Mathematics Advanced (HSC)

Module 2 for Mathematics Advanced (HSC)

## Mathematics Advanced: Sequences and Series

Module 1 for Mathematics Advanced (HSC)

Table of Contents Radians Radians Mnemonic Sine and Cosine Rule Sine Rule Cosine Rule Radians Radians are a fundamental component of year 11 and 12 Trigonometry They are another unit for angle, like degrees They can be calculated from degrees using the following formula: $$\color{lightblue}{Radians = Degrees\cdot \frac{180}{\pi}}$$
Roots of multiplicity r A root of a polynomial is a value of $$x$$ for which $$P(x)=0$$ For example, $$P(x)=x^2+6x+9$$ can be expressed as $$(x+3)^2$$ In this case, $$-3$$ is a root of multiplicity 2 of $$P(x)$$ Roots of multiplicity 1 are also known as “single roots” Roots of multiplicity 2 are also known as “double roots” Roots of multiplicity 2 are also known as “triple roots” Curve Sketching Graphs with multiple roots have specific rules for sketching Rules for Leading Coefficient and Degrees The table below explains what happens as a graph approaches infinity and negative infinity, based on the leading coefficient and degree: Degree: OddDegree: EvenLeading Coefficient: PositiveUp Arrow: 1st Quadrant