International Baccalaureate Mathematics Applications and Interpretation SL
These are the statements describing what students need to learn:
- Different forms of the equation of a straight line. Gradient, intercepts, parallel lines and perpendicular lines
- concept of a function, domain, range and graph. Function notation, for example f(x), v(t), C(n). The concept of a function as a mathematical model. Informal concept that an inverse function reverses or undoes the effect of a function. Inverse function as a reflection in the line y=x, and the notation f-1(x)
- the graph of a function; its equation y=f(x). Creating a sketch from information given or a context, including transferring a graph from screen to paper. Using technology to graph functions including their sums and differences
- determine key features of graphs. Maximum and minimum values; intercepts; symmetry; vertex; zeros of functions or roots of equations; vertical and horizontal asymptotes using graphing technology. Finding the point of intersection of two curves or lines using technology.
- modelling with the following functions: Linear models. Quadratic models (including axis of symmetry, vertex, zeros and roots, intercepts on the x-axis and y-axis). Exponential growth and decay models. Equation of a horizontal asymptote. Direct/inverse variation: Cubic models: Sinusoidal models i.e. f(x)=asin(bx)+d, f(x)=acos(bx)+d
- modelling skills: Use the modelling process described in the “mathematical modelling” section to create, fit and use the theoretical models in section SL2.5 and their graphs. Develop and fit the model: Given a context recognize and choose an appropriate model and possible parameters. Determine a reasonable domain for a model. Find the parameters of a model. Test and reflect upon the model: Comment on the appropriateness and reasonableness of a model. Justify the choice of a particular model, based on the shape of the data, properties of the curve and/or on the context of the situation. Use the model: Reading, interpreting and making predictions based on the model
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