3.4+Solve+Equations+NCEA+Info

Here is all the information for this standard.

- 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. || **Achievement with Merit** || · Solve problems involving equations. || · Problems will involve a selection from: - optimising an objective function for a linear programming problem, which may require i forming some constraints ii forming the objective function iii 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 3x3 system of linear equations. || - 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 <span style="font-family: Symbol; mso-fareast-font-family: Symbol; mso-bidi-font-family: Symbol; msofareastfontfamily: Symbol; msobidifontfamily: Symbol; msolist: Ignore;">- giving a geometric description of the Newton-Raphson method or the bisection method. ||
 * || ======**Achievement Criteria**====== || ======**Explanatory Notes**====== ||
 * == Achievement == || <span style="font-family: Symbol; mso-fareast-font-family: Symbol; mso-bidi-font-family: Symbol; msofareastfontfamily: Symbol; msobidifontfamily: Symbol; msolist: Ignore;">· Solve equations. || <span style="font-family: Symbol; mso-fareast-font-family: Symbol; mso-bidi-font-family: Symbol; msofareastfontfamily: Symbol; msobidifontfamily: Symbol; msolist: Ignore;">·  Solving equations will involve a selection from:
 * <span style="font-size: 12pt; font-family: Arial; mso-bidi-font-size: 10.0pt; mso-fareast-font-family: 'Times New Roman'; mso-bidi-font-family: 'Times New Roman'; mso-ansi-language: EN-NZ; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;">
 * **Achievement with Excellence** || <span style="font-family: Symbol; mso-fareast-font-family: Symbol; mso-bidi-font-family: Symbol; msofareastfontfamily: Symbol; msobidifontfamily: Symbol; msolist: Ignore;">· Analyse or interpret the outcome or the process used to solve equations or linear programming problems. || <span style="font-family: Symbol; mso-fareast-font-family: Symbol; mso-bidi-font-family: Symbol; msofareastfontfamily: Symbol; msobidifontfamily: Symbol; msolist: Ignore;">·  The analysis or interpretation may include: