Embedded Files
In this internal you will concentrate on solving equations simultaneously in 3 dimensions. This isn't just a theoretical idea only to be used by maths students across the world but its actually a technique required any time you have a problem with more than one variable that needs to be solved for at any one time. Your progression in this unit will loosely follow this plan. The slideshow linked to the right here gives an brief overview of the topic and assessment format.
In this internal you will concentrate on solving equations simultaneously in 3 dimensions. This isn't just a theoretical idea only to be used by maths students across the world but its actually a technique required any time you have a problem with more than one variable that needs to be solved for at any one time. Your progression in this unit will loosely follow this plan. The slideshow linked to the right here gives an brief overview of the topic and assessment format.
- Getting to grips with Simultaneous equations in 2 variables.
It will be important to be able to solve a system of 2 x 2 manually in a number of ways before moving into 3D. Follow through the videos or slideshows for each method below and then do the questions on the red links.
2. Getting to grips with Simultaneous equations in 3 variables.
2. Getting to grips with Simultaneous equations in 3 variables.
Elimination & Substitution methods will need to be combined when solving 3 x 3 systems
Physical visualisation on cartesian plane in 3D
Not all systems have a unique solution!
This cheesy but clear video describes the possibilities well. Watch it to understand the different scenarios we could be facing and then get stuck into actually solving some systems using the video and question sheets below.
Practice solving these systems of 3 x 3 equation using a combination of Elimination and Substitution
Practice solving these systems of 3 x 3 equation using a combination of Elimination and Substitution
Answers Below:
NOTE: The answer for Q5 should be: a=-6, b=2, c=1
It may please some of you to know that your graphic calculator can be of some help in thsi standard as it will solve Simultaneous Equations in 3 dimensions for you IF there is a unique solution!
Choose MODE 8: EQTN
Choose F1: Simultaneous
Choose F2: 3 Unknowns
Enter the coefficients of your three equations assuming they are all in the form ax + by + cz = d
Hit F1: SOLVE! Yay. It is acceptable to state that this is how you have attained you solution and then answer the question in context at Achieved level.
NOTE: (If you get a MA ERROR this tells you that there are EITHER no solutions or infinite solutions which the calculator can't narrow down. At this stage you will have to get your pen and paper and your brain on to figure out what is going on.)
3. Solving Simultaneous equations in 3 variables.
Establishing if there is a unique solution.
If not, why not? Which configuration of planes do you see? How can you tell?
Try to draw the geometrical scenario once you know which it is!!
4. Forming a set of simultaneous equations from a context like this one we did in class.
Identify what the UNKNOWNS are in the scenario, they are your variables!
Once you have formed the system solve it using technology or manually until you have solved the problem.
Some astronauts capture 12 monsters and brings them to earth.pdfNulake Workbook Activities (inc Practice task towards the end) :
Animal Farm:
For further support with this standard have a look at this site, written by a colleague at St Kentigern College :)
For further support with this standard have a look at this site, written by a colleague at St Kentigern College :)
Report abuse