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# AS 3.15 Apply Simultaneous Eqns to Solve Problems

### Possible Lesson Sequence for AS 3.15 Simultaneous Equations(AS 91587)

STARTERS with Answers (Powerpoint version) (Web version)

1. Achievement Criteria
2. Review of SOLVING 2 variable simultaneous equations
3. Forming 2D equations and determining / describing geometric situations
4. Equations in 3 variables investigating planes using software or Graphing calculator 3D
5. Solving 3 variable simultaneous equations by Elimination
6. Elimination Practice
7. Form equations then solve them in context
8. Form equations then solve them in context
9. Infinite Solutions and Dependent Equations
10. No solutions, inconsistent equations
11. Practice of different situations
12. Determining Linear combinations
13. Revision
15. Assessment

### For Teachers

* Be familiar with the Achievement Standard AS3.15 #91587 (link to NZQA)

* Check the latest information on the NZQA clarifications page as things change all the time, and the exemplars in NZQA may be out of date

* Look over the NZQA Exemplars on AS3.15 Simultaneous Equations. Note: these exemplars may not reflect the latest information or the end of year exam... but we can only hope. Link to NZQA Sample Exemplar A | Exemplar B

* Material available on the mathstatsfacilitators web site AS 3.15 page

* AS 3.15 section on Nayland Web site updated: Sept 2014

### AS 3.15 'Apply systems of simultaneous equations in solving problems' is a 3 credit internally assessed topic AS 91587

Form and use systems of simultaneous equations, including three linear equations and three variables, and interpret the solutions in context

Methods include a selection from those related to:
- forming systems of simultaneous equations
- solving systems of simultaneous equations
- The nature of solutions to systems

Great free 2D & 3D grapher Excellent 3D graphing freeware that has to be installed.

Graph Calc Great 2D & 3D graphing freeware that can be run of a USB - no installation required