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Solving Equations

This achievement standard involves solving equations and interpreting solutions.linear

  • 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 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.
  • Solve problems involving equations.

  • Problems will involve a selection from:

    • optimising an objective function for a linear programming problem, which may require

      1. forming some constraints

      2. forming the objective function

      3. rounding 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 3×3 system of linear equations.
  • 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 3×3 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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