Mathematics: Applications and Interpretation SL

Functions

Linear, quadratic, exponential, and logarithmic models with graphical and contextual interpretation.

Model with linear functions Build, use, and interpret linear models in applied contexts. Model with quadratic functions Use quadratic models to interpret maximum, minimum, intercepts, and contextual restrictions. Model with exponential functions Use exponential models for growth, decay, and repeated percentage change. Interpret logarithmic scales Interpret logarithmic models and scales in applied measurement contexts. Compare models using technology Choose and justify a suitable model using fit, context, and prediction behaviour. Use domain and range in models State practical domain and range restrictions for applied models. Read values from a linear graph Read a coordinate directly off a straight-line graph on a grid, then state the y-value at a given x. Builds graph-interpretation skill where the value must be extracted from the diagram, not given in the text. Read the gradient of a linear graph Read the coordinates of two points off a straight-line graph, then calculate the gradient as rise over run. Builds the skill of extracting values from a diagram and combining them, not just reading a single value. Read values from a curve Read a coordinate off a curved (parabola) graph on a grid, then state the y-value at a given x. Extends graph reading from straight lines to curves, where the height changes at different rates. Find a flow rate from a volume-time graph Read two points off a volume-time graph and find the constant flow rate as volume over time (the gradient). Find an hourly rate from a pay graph Read two points off a pay vs hours-worked graph and find the hourly rate of pay as pay over hours (the gradient). Find a unit price from a cost graph Read two points off a total-cost vs number-of-items graph and find the price per item as cost over quantity (the gradient). Solve simultaneous equations from a graph Read the x-coordinate of the point where two straight lines cross - the solution of the pair of simultaneous equations. Find the speed of part of a travel graph Read the speed of one part of a journey from a travel graph (distance-time), where a flat section means stopped and a steeper section means a faster speed.