Linear Relations

Area of Study- Functions and Graphs (Unit 1)

From the VCAA 2016-2020 Mathematics Study Design

In this area of study students cover the graphical representation of simple algebraic functions (polynomial and power functions) of a single real variable and the key features of functions and their graphs such as axis intercepts, domain (including the concept of maximal, natural or implied domain), co-domain and range, stationary points, asymptotic behaviour and symmetry. The behaviour of functions and their graphs is explored in a variety of modelling contexts and theoretical investigations.

Key skills and knowledge (outlined from the VCAA Study Design for Outcome 1)

These essentially serve a Learning Goals and Success Criteria for the topic.

• the equation of a straight line, gradient and axis intercepts, midpoint of a line segment, distance between two points, and parallel and perpendicular lines
• determine by hand the length of a line segment and the coordinates of its midpoint, the equation of a straight line given two points or one point and gradient, and the gradient and equation of lines parallel and perpendicular to a given line through some other point
• re-arrange and solve simple algebraic equations and inequalities by hand
• expand and factorise linear and simple quadratic expressions with integer coefficients by hand
• set up and solve systems of simultaneous linear equations involving up to four unknowns, including by hand for a system of two equations in two unknowns
• sketch by hand graphs of linear, quadratic and cubic polynomial functions, and quartic polynomial functions in factored form (approximate location of stationary points only for cubic and quartic functions), including cases where an x-axis intercept is a touch point or a stationary point of inflection

Outcome 2 (namely modelling) and 3 (CAS) will also be part of the topic.

Assessment Overview

Topic tests will assess:

• key knowledge and skills,
• ability to problem-solve and use the mathematics in context,
• use of the CAS, to assist problem-solving