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• NCEA on TKI
• NZQA website

CAS Mathematics 2.1 Demonstrate an understanding of mathematical relationships

Key tips

• Revise basic algebra skills used in CAS Algebra 1.1 and CAS Graphs 1.2
• You may choose numerical, algebraic or graphical techniques to solve the problems.
• When using graphical techniques, you may be expected to consider the sensibility of the domain or range when relating the graph to the context.
• Attempt all questions, since evidence from higher level questions can be used towards gaining Achievement.
• Set solutions out logically, using correct mathematical statements.
• Do not round until the end of the problem.
• Be careful to copy terms correctly from step to step.
• Show all working as credit may be given for a minor slip or a term that has been incorrectly transferred, if the assessor can see what you have done.
• Check that you have answered the question asked.
• Be certain that you can use and apply the quadratic formula correctly.
• When solving a quadratic equation to answer a question in context, check that you have selected or used the correct solution. Both answers may not be relevant in the context given.
• You should know how to model a situation using an equation, so practice selecting variables and writing equations to solve word problems.
• The key features of graphs may be x and y intercept(s), turning points, axis of symmetry, horizontal and vertical asymptotes, or centre and radius of circle.
• Practise using the specific mathematical language to identify each of the features of a graph.
• For Achievement with Merit, interpreting features of a graph requires you to relate features, such as intercepts and turning points, to the real-life situations that the graph represents.
• Knowledge of sine, cosine, and tangent forms of trigonometric equations and graphs is required.
• When solving trigonometric equations, check that your calculator is in the correct mode (degrees or radians) for each question.
• Give your answers within the domain that is given in the question. The domain will tell you if your answers should be in degrees or radians. You will not be given credit if your answer is in radians and the question requires degrees.
• There is usually more than one solution for a trigonometric equation. All solutions within the given domain are required to gain credit for a problem.
• Where the context involves arithmetic or geometric sequences, list the first few terms to ensure that you use the correct approach. Look for key words. arithmetic progressions are indicated by extra, less, shorter, longer, etc. geometric progressions are indicated by times, percentage increase, ratio, etc.
• For Achievement with Merit and Achievement with Excellence, you are expected to show evidence of the techniques used. You may be required to use correct mathematical statements and should present your work in a logical manner.
• Computer Algebraic Systems (CAS) technology may be used.

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