Læreplan i matematikk for realfag - programfag i utdanningsprogram for studiespesialisering (MAT3-01)
Utgått
Denne læreplanen har utgått.
Mathematics R1
Geometry
- use lines and circles as geometric loci together with congruence and the inscribed angle theorem in geometrical analysis and calculations
- execute and analyze constructions defined by straight lines, triangles and circles in the plane, with and without the use of dynamic software
- derive and apply the intersection theorems for the heights, angle bisectors, perpendicular bisectors and medians in a triangle
- give an account of different proofs for Pythagoras’ equation, in terms of cultural history as well as mathematics
- visualize vectors in the plane, both geometrically as arrows and analytically in co-ordinate form
- calculate and analyze lengths and angles to determine the parallelity and orthogonality by combining arithmetical rules for vectors
Algebra
- factorize polynomials with the help of zeros and polynomial division, and use this to solve equations and inequalities with polynomial and rational expressions
- transform and simplify complex rational functions and other symbolic expressions with and without the use of digital aids
- derive the basic arithmetical rules for logarithms, and use these and the power rules to simplify expressions and solve equations and inequalities
- give an account of implication and equivalence, and implement direct and contrapositive proof
Functions
- give an account of the concepts of boundedness, continuity and differentiability, and give examples of functions that are not continuous or differentiable
- use formulae for the derivative of power, exponential and logarithmic functions, and differentiate composites, differences, products, quotients and combinations of these functions
- use first derivative and second derivative to elaborate on and discuss the path of functions and interpret the derivatives in models of practical situations
- draw graphs to functions with and without digital means, and interpret the basic characteristics of a function using the graph
- find the equation for horizontal and vertical asymptotes to rational functions and draw the asymptotes
- use vector functions for a parameter presentation of curves in the plane, draw the curve and differentiate the vector function to find velocity and acceleration
Combinatorics and probability
- give an account of the concepts of statistical independence and conditional probability, and derive and apply Bayes' equation for two events
- elaborate on and discuss combinatoric problems linked to non-random selection with or without replacement and random selection without replacement, and use this to derive rules for calculating probability
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