AC9M10A05 Year 10 Mathematics

Content descriptor experiment with functions and relations using digital tools, making and testing conjectures and generalising emerging patterns

Elaborations

• • Elaboration applying the graphing zoom functionality of digital tools and systematically refining intervals to identify approximate location of points of intersection of the graphs of 2 functions, such as x^2=2^x
• • Elaboration applying a bisection algorithm to determine the approximate location of the horizontal axis intercepts of the graph of a quadratic function such as f(x)=2x^2-3x-7
• • Elaboration applying transformations to the graph of x^2+y^2=1
• • Elaboration identifying the coordinates of any points of intersection of the graph of a linear function with the graph of a quadratic function or a circle
• • Elaboration identifying intervals on the real number line over which a given quadratic function is positive or negative
• • Elaboration using a table of values to determine when an exponential growth or decay function exceeds or falls below a given value, such as monitoring the trend in value of a share price in a context of exponential growth or decay
• • Elaboration investigating how functions and relations serve as the mathematical underpinnings of machine learning, allowing data to be transformed, models to be defined and optimisation to occur