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External links

• NCEA on TKI
• NZQA website

Achievement criteria

This achievement standard involves demonstrating an understanding of equations and expressions when solving problems.

Note: Candidates cannot use credit for both this achievement standard and either AS90637 or AS90638 (Calculus 3.3 and 3.4) towards a national qualification including a National Certificate of Educational Achievement.

Achievement

• You need to demonstrate an understanding of equations and expressions when solving problems.
• Equations and expressions will be selected from:
  • polynomial with real and complex roots
  • exponential, such as 2^3x+1 = 5
  • logarithmic, such as log(x + 5) = 1.34 (any base)
  • trigonometric, such as y= A trig B(x + C) + D
  • surds
  • complex numbers such as zⁿ = r cisθ ,
    zⁿ = a + b i where a, b are real and n is a positive integer.
• General solution and solutions within a specified domain may be required for trigonometric situations and families of functions.

Achievement with Merit

• You need to reach Achievement.
• You need to demonstrate a deeper understanding of equations and expressions when solving problems.
• Candidates will be expected to have a knowledge of:
  • the remainder and factor theorem
  • the process of completing the square
  • sine and cosine rules.

Achievement with Excellence

• You need to reach Achievement with Merit.
• You need to demonstrate a comprehensive understanding of equations and expressions when solving problems.
• Candidates will be required to form an equation or expression to model and solve the problems.
• Problem solving may include:
  • manipulation of algebraic or trigonometric expression and equations
    • reciprocal relationships
    • Pythagorean identities
    • compound angle formulae
    • double angle formulae
    • sum and product formulae
    • conversion between polar and rectangular forms of real and complex numbers
    • simplification of sums, differences, products, and quotients of surds or complex numbers
  • use of De Moivre’s theorem
  • geometric representation of complex numbers eg loci
  • 3-D trigonometric problems
  • modelling and evaluation
  • identifying and rectifying a flaw in reasoning
  • proof
  • binomial expansions for small positive integer exponents.

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