Power functions y = a · xⁿ
Even or odd, positive or negative: y = a · xⁿ changes with every exponent, and only a few points always stay the same.
Mathematics – grade 11
Introductory phase of upper secondary (G9: grade 11). The letters A and G are the curriculum’s labels for the content areas; the numbers of the focal points are our own. Core curriculum for upper secondary of 2026, in force from 1 August 2027, starting with the introductory phase; the 2023 core curriculum is being phased out and is not shown here.
Unit EF-AFunctions and calculus (A)
Power functions and polynomial functions, transformations, the step from average to instantaneous rate of change and analysing graphs with the derivative.
EF-A.1Functions
Power functions with integer exponents and polynomial functions; solving polynomial equations by factoring out.
Polynomial functions: zeros, multiplicity and end behaviour
Does the graph cross the x-axis or only touch it? The multiplicity of the zero decides, the highest power decides what happens far out.
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.
EF-A.2Properties of functions
Shape of the graph, domain and range, zeros, symmetry and behaviour for large x.
Polynomial functions: zeros, multiplicity and end behaviour
Does the graph cross the x-axis or only touch it? The multiplicity of the zero decides, the highest power decides what happens far out.
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.
EF-A.3Transformations
Reflecting, shifting and stretching along both axes, including the sine function; interpreting parameters.
Shifting, stretching and reflecting graphs
Shift, stretch, reflect: every move of the graph leaves its mark in the function's equation.
General sine function
Change the amplitude, period and shift of a sine curve with sliders or by dragging.
EF-A.4Basic understanding of the derivative
Average and instantaneous rate of change, secant and tangent, sketching the derivative graphically.
From secant to tangent
Let a point Q move towards P: the secant becomes the tangent, and the average slope becomes the derivative.
The derivative function graphically
A tangent slides along the graph and draws its slope as a new graph: the derivative function.
EF-A.5Differential calculus
Power, sum and constant-multiple rules, monotonicity, local and global extrema, curvature and points of inflection.
Monotonicity, extrema and inflection points
Analyse a graph step by step: zeros, maximum and minimum points, inflection points and where it rises or falls.
The derivative function graphically
A tangent slides along the graph and draws its slope as a new graph: the derivative function.
Unit EF-GAnalytic geometry and linear algebra (G)
Points and vectors in a three-dimensional coordinate system, calculating with vectors, lines in parametric form and their relative positions.
EF-G.1Coordinates in space
Points, position vectors and vectors in a three-dimensional coordinate system.
Points and solids in 3D coordinates
Place points in 3D coordinates, rotate the view and calculate distances with Pythagoras' theorem.
Adding and scaling vectors (3D)
Drag vector arrows in space, add them and multiply them by numbers. The calculation is shown alongside in column form.
EF-G.2Vector operations
Addition and multiplication by a scalar.
Adding and scaling vectors (3D)
Drag vector arrows in space, add them and multiply them by numbers. The calculation is shown alongside in column form.
EF-G.3Properties of vectors
Length and distance using Pythagoras’ theorem, collinearity.
Points and solids in 3D coordinates
Place points in 3D coordinates, rotate the view and calculate distances with Pythagoras' theorem.
Adding and scaling vectors (3D)
Drag vector arrows in space, add them and multiply them by numbers. The calculation is shown alongside in column form.
EF-G.4Lines and segments
Parametric form and interpreting the parameters in context.
Lines and planes in space
A point travels along a line through space, two vectors span a plane. Parametric, normal and coordinate forms all describe the same thing.
EF-G.5Relative position of lines
Identical, parallel, skew or intersecting.
Relative positions and distances in space
Do the lines meet, run parallel or pass each other by? In a 3D space you can turn, intersections, angles and distances become visible.
EF-G.6Points of intersection
Intersections of lines using systems of linear equations.
Relative positions and distances in space
Do the lines meet, run parallel or pass each other by? In a 3D space you can turn, intersections, angles and distances become visible.
The summaries describe the curriculum in our own words. The original text is authoritative. Original text (German): Kernlehrplan, Gymnasium, Mathematics, grade 11