Support · Mathematics Advanced 11–12 – Year 12 · Integral calculus
Support Use the fact that the graphs of y = a^x and y = log_ax are reflections of each other in the line y = x to solve problems involving areas between the x -axis or y -axis and a curve involving either an exponential or logarithmic function
Resources for the prerequisite content of this dot point: earlier-stage (or earlier sub-level) dot points in the same strand that students usually need first. Use these to fill gaps before or alongside the core lesson.
Prerequisite links are draft mappings generated from the syllabus structure (earlier stage, same strand, closest content). They are being reviewed by teachers. Spot a poor match? Tell us.
Prerequisite dot points
Use graphing applications to identify the graphs of y = a^x and y = log_ax as reflections of each other in the line y = x, in cases where a > 1 and 0
Mathematics Advanced 11–12 – Year 11 · Exponential and logarithmic functions Draft mapping
- Desmos Graphing CalculatorUse it for: Graph lines, parabolas and exponentials live; find intersections to solve simultaneous equations.
- Interactive toolEnrichmentGeoGebra ClassicUse it for: Dynamic geometry and graphing for constructions and proofs.
Recognise and use the logarithmic properties: log_aa^x = x for all real x, a^(log_ax) = x where x > 0
Mathematics Advanced 11–12 – Year 11 · Exponential and logarithmic functions Draft mapping
No checked resources on this prerequisite dot point yet.
Justify the logarithmic results log_aa = 1, log_a1 = 0 and log_a(1/x) = - log_ax
Mathematics Advanced 11–12 – Year 11 · Exponential and logarithmic functions Draft mapping
No checked resources on this prerequisite dot point yet.