# CURRICULUM FOR THE COMMON CORE SUBJECT OF MATHEMATICS (MAT1-04)

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### Competence aims after 1T - Vg1 education programmes for general studies

#### Numbers and algebra in practice

The aims of the training are to enable the apprentice to
• interpret, process and assess the mathematical content in various texts
• evaluate, select and use mathematical methods and tools to solve problems from different subjects and social areas and reflect on, evaluate and present solutions in a purposeful manner
• calculate with powers with rational exponents and numbers in scientific notation, algebraic expressions, formulas, expressions with brackets and alphanumerical rational and square expressions, use quadratic equations to factor algebraic expressions
• reformulate expressions and solve equations, inequalities and systems of equations of the first and second order and simple equations with exponential and logarithmic functions, using algebra and digital aids
• convert a practical problem into an equation, an inequality or an equation system, solve it with and without using digital tools, present and provide rationale for the chosen solution and assess the validity of the solution

#### Geometry

The aims of the training are to enable the apprentice to
• elaborate on the definitions of sine, cosine and tangent and use trigonometry to calculate length, angles and area of triangles
• use plane geometry to analyse and solve composite theoretical and practical problems connected to lengths, angles and areas
• make and use sketches and drawings to formulate and solve problems and to present and provide rationale for chosen solutions, with and without using digital tools

#### Probability

The aims of the training are to enable the apprentice to
• formulate, experiment with and discuss and elaborate on simple uniform and non-uniform probability models
• calculate probability by counting all favourable and all possible results based on tables and by systematising counts using cross tables, venn diagrams and the addition rule and the multiplication principle in practical contexts

#### Functions

The aims of the training are to enable the apprentice to
• explain the concept of functions and be able to convert between different representations of functions
• calculate zero, minimum gradient, intersection and average rate of change, find approximate values for instantaneous rates of change and provide practical interpretations of these aspects
• elaborate on the definition of the derivative, use the definition to deduce a rule for the derivative of polynomial functions and use this rule to discuss functions
• make, interpret and explain functions that describe practical questions, analyse empirical functions and find expressions for an approximate linear function, with and without using digital tools
• use digital aids to present and analyse combinations of polynomial functions, rational functions, exponential functions and power functions

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