Mathematics S2
Algebra
The aims of the training are to enable the apprentice to- find patterns in numerical series and use them to sum finite arithmetical and geometrical series and other series, with and without digital means
- determine whether an infinite geometric series is convergent and calculate the sum of the series
- use series to solve practical problems related to savings, loans and hire-purchase
- factorize polynomials using zero points and polynomial division, and use the result to solve equations with polynomial and rational functions
- model practical problems using systems of linear equations with several unknowns, and solve them with and without digital means
Functions
The aims of the training are to enable the apprentice to- derive polynomial functions, power functions, exponential functions and logarithmic functions, and sums, differences, products and quotients of these functions, and use the chain rule to derive combined functions
- elaborate on and discuss the path of functions and interpret the derivative in practical contexts by using first and second derivatives
- interpret the basic characteristics of a function using the graph
- solve economic optimization problems in connection with income, cost and demand functions, and calculate and use marginal costs and income in simple models
- model exponential and logistical growth rate by using exponential functions and logarithmic functions
- calculate the area under graphs by digital means and interpret this in practical situations
Probability and statistics
The aims of the training are to enable the apprentice to- give an account of the concepts distribution and stochastic variable for finite probability spaces, and find expectation, variance and standard deviation for a stochastic variable
- give an account of the significance of the normal distributions and calculate probabilities linked to these
- give an account of the central limit theorem and use it to calculate probabilities for sums of independent stochastic variables and binomial distributions
- carry out simple hypothesis testing using p-values and interpret results
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