Mathematics Assessment Map – Sample at Level 6
Standards for Structure are introduced at Level 3.
Samples are available for the following tasks:
CAS e-activity: sums and products of two numbers
Students used the e-activity functionality of CAS to summarise their work on the solution of two simultaneous equations (linear and reciprocal) which reduces to the equivalent of a single quadratic equation.
The element of the Structure standard addressed by the task is:
(Students) solve equations of the form f(x) = k, where k is a real constant … using algebraic, numerical … and graphical methods.
The sum and product of two numbers are given. What are the two numbers? Consider this for various positive integer values of the sum and product, for example, when the sum of two numbers is 14 and their product is 36.
The following samples illustrate the kinds of responses that students produce when they have achieved the elements of the standard addressed by the task.
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Structure – Level 6
- Uses spreadsheet functionality of CAS to test the truth of the relations represented by the equations for various values of the two numbers, and identifies that the solution values will not be integers.
- Formulates the problem as a pair of equations and then uses CAS solve functionality to solve these simultaneously and obtain two pairs of solutions in surd form, with corresponding decimal approximate solution to six significant figures.
- Notes that the exact answers could not have been obtained by a ‘guess and check’ numerical method, and has checked the solutions by inspection of the points of intersection of the graphs of y = 14 – x and y = 36/x, labelling each point of intersection with its approximate coordinates.
Elements of the standard
(Students) solve equations of the form f(x) = k, where k is a real constant … using algebraic, numerical … and graphical methods.
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