Algebraic and Graphical Techniques Coursework Portfolio

1 Reports of at least two investigations including use of:
a) different functions as models
b) key features of graphs
c) algebraic techniques.

These should show working in full (especially when calculators have been used) and evidence of estimation and checking to ensure accuracy.

In totality the reports should include:

a) use of 2 different types of functions to model the same data set, either
• one function for the full data set and another for part of it, or
• two different functions for different sections of the data
where
• at least 1 set of data is plotted using a graphic calculator or computer
• the effectiveness of each model is considered
• predictions are made for cases where there is no data
• explanations are given of how the functions are related to basic functions of their type
• errors or inaccuracies in the data are considered and the way in which these may affect the functions used.

b) use of key features of graphs including:
(i) intercepts with axes
(ii) gradients
(iii) changes and trends in gradients
(iv) local maximum and minimum points for functions that model real situations in order to solve problems and explain how the function relates to the real situation.


c) use of algebraic techniques to solve problems for:
(i) a polynomial model
(ii) one other model which may be trigonometric, exponential or logarithmic.

(8 hours i.e. 4 hours for each investigation)

Linearising Data

2 Report of a piece of work in which a function is fitted to non-linear data using logarithmic or other techniques to determine parameters by plotting a linear function.

Include clear explanation of method, correct algebraic notation and clearly labelled, accurate graphs. (4 hours)

(Total for Coursework Portfolio = 12 hours)