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Clarification of Unit Standards in Mathematics
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Level 3
The following notes provide clarification of the assessment requirements for the commonly used level 3 unit standards and need to be read in conjunction with the unit standard.
5258 Version 3 Use expected values to solve problems
- Problems may be real or simulated but should be in context.
- A suitable question for mean and variance for the sum of independent random variables might be: "A bag contains 10 dice. Each die has a mean of 6 g and standard deviation 2 g. What is the mean and variance of the 10 dice?"
- A suitable question for mean and variance of a linear function of a random variable might be: "The cost of making a die is 2 cents plus 10 cents per gram. What is the variance of the cost of making a die?"
5259 Version 3 Use probability models to solve problems
- The distribution needs to be chosen by the student.
- The first performance criterion is interpreted as selection of the correct model.
- The inverse case for each situation should be assessed. Questions could include approximations - normal approximation to binomial and Poisson approximation to binomial.
5262 Version 3 Use linear systems to solve problems
Element one
- Students need to solve at least one problem.
- The solution needs to satisfy the given constraints.
Element two
- The solution must be interpreted in context so use of units is expected.
5264 Version 3 Use numerical methods to solve problems
- Students must show the use of two of the identified methods, one of which may be calculator or computer.
- The equations that are solved must be non-linear and appropriate for the curriculum level and the method chosen.
- For bisection and Newton Raphson the starting point(s) can be given in the question.
- The result of each iteration must be shown.
5265 Version 4 Differentiate functions and use differentiation to solve problems
Element two
- The derived function needs to be given as part of the student response.
5267 Version 4 Use complex numbers to solve problems
Element one
- Conversion both ways is required, i.e. rectangular to polar and polar to rectangular.
20905 Version 1 Integrate functions and use integration to solve problems
Element two
- The integrated function needs to be given as part of the student response.
Last updated: 12 May 2009