Exponential growth and decay
Water lilies on a pond, compound interest and decay: exponential growth compared with linear growth.
Mathematics – grade 10
The curriculum assigns these units to exactly this grade (Saxony, Gymnasium up to grade 12). The unit numbers are the curriculum’s; optional areas (“Wahlbereiche”) are labelled W1–W3 here.
Unit 1Growth and periodic processes
Describing growth and decay with exponential functions, parameters and regression; periodic processes with the sine function in degrees and radians.
General sine function
Change the amplitude, period and shift of a sine curve with sliders or by dragging.
Unit circle
Sine, cosine and tangent on the unit circle, and how the sine curve grows out of it.
Shifting, stretching and reflecting graphs
Shift, stretch, reflect: every move of the graph leaves its mark in the function's equation.
Unit 2Discrete random variables
Probability distributions in bar charts and histograms, expected value, variance and standard deviation, and fair games.
Galton board
Left or right at every pin, purely by chance. Yet every time the balls pile up into the same bell shape.
Unit 3Solving geometric problems algebraically
Deriving the laws of sines and cosines and applying them to triangles, pyramids and cones.
Law of sines and law of cosines
Calculate sides and angles in any triangle with the law of sines and the law of cosines. A helper shows which law fits your problem.
Pyramid, cone and sphere
Pour three times and the prism is full: a pyramid holds exactly one third. Cones and spheres can be turned and measured in 3D.
Unit 4Functional relationships
Inverse functions and logarithms, exponential equations, combining and composing functions, key graphs by hand, and sequences with limits.
Inverse functions: reflecting in y = x
Reflect the graph in y = x and the inverse function appears. It only works if no function value occurs twice.
Logarithms as the inverse of exponentiation
The logarithm answers the question: to what power do I raise the base to get this number? With graphs, rules and exponential equations.
Limits and asymptotes
What happens to a graph when x gets very large? A point runs outwards and a magnifier shows how close it gets to the asymptote.
Function plotter with custom terms
Up to three of your own functions at once, with a table of values, zeros and intersections. The tool for anything that can be a graph.
Unit 5Connections: interest
Simple and compound interest, loans and repayment.
Exponential growth and decay
Water lilies on a pond, compound interest and decay: exponential growth compared with linear growth.
Unit W1Complex numbers (optional)
The complex plane and calculating with complex numbers.
No separate simulation is planned for this.
Unit W2Logistic growth (optional)
The logistic growth model, explicit and recursive, and its limits.
No separate simulation is planned for this.
Unit W3Parametric curves and polar coordinates (optional)
Describing curves with parameters and polar coordinates.
No separate simulation is planned for this.
The summaries describe the curriculum in our own words. The original text is authoritative. Original text (German): Lehrplan, Gymnasium, Mathematics, grade 10