Australian Curriculum Mathematics/Mathematical Methods/Functions and Graphs

Australian Curriculum ContentSource: Australian Curriculum, Assessment and Reporting Authority (ACARA), downloaded from the Australian Curriculum website on (5 October 2015). Lines and linear relationships: determine the coordinates of the midpoint of two points examine examples of direct proportion and linearly related variables recognise features of the graph of , including its linear nature, its intercepts and its slope or gradient find the equation of a straight line given sufficient information; parallel and perpendicular lines solve linear equations. Review of quadratic relationships: examine examples of quadratically related variables recognise features of the graphs of , , and , including their parabolic nature, turning points, axes of symmetry and intercepts solve quadratic equations using the quadratic formula and by completing the square find the equation of a quadratic given sufficient information find turning points and zeros of quadratics and understand the role of the discriminant recognise features of the graph of the general quadratic . Inverse proportion: examine examples of inverse proportion recognise features of the graphs of and , including their hyperbolic shapes, and their asymptotes. Powers and polynomials: recognise features of the graphs of for , and , including shape, and behaviour as and identify the coefficients and the degree of a polynomial expand quadratic and cubic polynomials from factors recognise features of the graphs of , and , including shape, intercepts and behaviour as and factorise cubic polynomials in cases where a linear factor is easily obtained solve cubic equations using technology, and algebraically in cases where a linear factor is easily obtained. Graphs of relations: recognise features of the graphs of and , including their circular shapes, their centres and their radii recognise features of the graph of including its parabolic shape and its axis of symmetry. Functions: understand the concept of a function as a mapping between sets, and as a rule or a formula that defines one variable quantity in terms of another use function notation, domain and range, independent and dependent variables understand the concept of the graph of a function examine translations and the graphs of and examine dilations and the graphs of and recognise the distinction between functions and relations, and the vertical line test. __TOC__ Linear Equations Identify the slope and intercepts of the following equations: Graph the following linear equations: Lines and Linear Relationships Midpoints Say we have two points and . The midpoint between these points is given by: Example Find the midpoint between the points and Find the coordinate: Find the coordinate: The coordinates of the midpoint are: Find the coordinates of the midpoint between the following points: and and and and and and and and and Linear Functions Sketch the graph of the following linear functions showing all key features: Hyperbolic functions Sketch the graphs of the following hyperbolic functions, including all key details including asymptotes: Solutions 1.1 and and and and and and References