# MATHEMATICS 2T and 2P SUBJECT CURRICULUM (MAT5-02)

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### Competence aims after 2T

#### Geometry

The aims of the training are to enable the apprentice to
• elaborate on the geometric picture of vectors as arrows in a plane, and calculate sums, differences and scalar products of vectors and the product of numbers and vectors
• calculate with plane vectors written in coordinate form, calculate lengths, distances and angles using vector arithmetic and determine when two vectors are parallel or orthogonal
• draw and describe curves in parametric form and calculate intersection points between such curves

#### Combinatorics and probability

The aims of the training are to enable the apprentice to
• give an account of and use the concepts of independent and conditional probability and apply Bayes' theorem to two events, and evaluate and interpret the results
• calculate probability in the event of ordered sampling with and without repetition, and in the event of non-ordered sampling without repetition
• calculate with binomic and hypergeometric probability, recognising and modelling such spreads in different situations

#### Culture and modelling

The aims of the training are to enable the apprentice to
• analyse theoretical and practical problems, find patterns and structures in different situations and describe relationships with help from mathematical models
• explore mathematical models, compare different models, evaluate the kinds of information the models can provide and what areas of validity and limitations they have
• use digital tools for exploration, model building and presentations
• find, evaluate and present examples from the multicultural history of mathematics and discuss and elaborate on the importance of mathematics for natural science, technology, societal life and culture

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