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CAS Calculus 3.4 Demonstrate an understanding of mathematical concepts without the use of electronic technology

Achievement criteria

This achievement standard involves demonstrating an understanding of mathematical concepts without the use of electronic technology (including calculators).

Note: Candidates cannot use credit for both this achievement standard and either AS90635, AS90636, AS 90637, AS90638 or AS90639 (Calculus 3.1 - 3.5) towards a national qualification including a National Certificate of Educational Achievement.

Achievement

• You need to demonstrate an understanding of calculus concepts without the use of electronic technology.
• Mathematical concepts will be selected from:
  • limits and continuity
  • differentiation
    • from first principles for polynomial functions of degree ≤3
    • differentiability
    • chain rule, product rule, quotient rule, and their application
    • parametric functions
    • implicit.
  • Integration
    • polynomial functions of degree ≤3
    • exponential functions of the form ae^{bx + c}
    • rational functions of the type or .
    • trigonometric functions relating to exact values.

Achievement with Merit

• You need to reach Achievement.
• You need to demonstrate a deeper understanding of calculus concepts without the use of electronic technology.
• In addition to the requirements for achievement problems may involve:
  • areas under and between functions
  • rates of change
  • optimisation and turning points
  • simple volumes of revolution
  • area approximations
  • proof
  • modelling

Achievement with Excellence

• You need to reach Achievement with Merit.
• You need to demonstrate a comprehensive understanding of calculus concepts when solving problems which would typically include a solution of a problem, and may involve the linking of different representation of concepts and generalisation.
• Problems may include:
  • equation solving and algebraic manipulation
    • surds
    • complex numbers.
  • using graphs
    • write equations for and sketch graphs of conic sections
    • transformations of equations and their graphs.

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