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• NCEA on TKI
• NZQA website

Statistics and modelling 3.4 Solve equations

Achievement criteria

The level of achievement that you reach is decided by the questions that you answer correctly.

Achievement

• You solve equations.
• Solving equations will involve a selection from:
  • solving systems of three linear equations in three variables, where there is a unique solution (this may involve re-arrangement of equations and/or interpreting solutions).
• Solving equations may involve:
  • solving a non-linear equation using the Newton-Raphson method with a given starting value, or the bisection method with a given starting interval (Newton-Raphson method includes derivatives of polynomials only)
  • optimising an objective function for a situation requiring techniques of linear programming, where the constraints and the objective function for the problem are given.

Achievement with Merit

• You need to reach Achievement.
• You solve problems involving equations.
• Problems will involve a selection from:
  • optimising an objective function for a linear programming problem, where you are expected to form your own constraints and objective function, and round the solution in relation to the context
  • using a suitable method to find an approximate solution to a non-linear equation (graphical, table, graphics calculator etc)
  • finding appropriate solutions to a non-linear equation using either the Newton-Raphson method or the bisection method to improve the approximation to a stated precision or for a specified number of iterations. Derivatives of functions other than polynomials will be given
  • forming and solving a 3x3 system of linear equations.

Achievement with Excellence

• You need to reach Achievement with Merit.
• You analyse or interpret the outcome, or the process used to solve equations or linear programming problems.
• The analysis or interpretation may include:
  • discussing consistency or non-independence of 3x3 systems of linear equations, including geometric representations
  • determining the effect of varying the constraints or objective function of a linear programming problem
  • considering the possibility of multiple solutions to a linear programming problem
  • giving advantages and disadvantages of the Newton-Raphson method or the bisection method for the problem
  • giving a geometric description of the Newton-Raphson method or the bisection method.

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