Title: Simultaneous Equations
You should hopefully recognise these as straight line graphs. If you take the first equation on its own you can see that if x = 4 then y = 3x4 + 2 = 14 and indeed whatever value of x I give you, you can calculate a value of y. We can do the same for the second equation.
In solving these simultaneous equations we are looking for a value of x and y that works for both equations. When drawn as graph this is the point where the two graphs cross.
Below I have used Wolfram Alpha to plot these two graphs and find the solution (the coordinates of where they cross).
Hopeful this gives you an idea of what you might be asked to do in the exam (although they would ask you to draw the graphs).
Note: the answers are on the last page.
Book Review
Homework
Target Question
What are you trying to achieve when solving simultaneous equations?
Learning Objectives
Beginning
What are you trying to achieve when solving simultaneous equations?
Learning Objectives
Beginning
To be able to demonstrate solving a pair of
linear simultaneous equations from their graphs.
Developing
To be able to explain a method for solving two simultaneous linear equations.
Mastering
To be able to explain how to find the equation of linear graphs parallel and perpendicular to other linear graphs, that pass through specific points.
Developing
To be able to explain a method for solving two simultaneous linear equations.
Mastering
To be able to explain how to find the equation of linear graphs parallel and perpendicular to other linear graphs, that pass through specific points.
Resources
Today you are going to remind yourself how to solve simultaneous equations (and hopefully expand on your understanding).
Today you are going to remind yourself how to solve simultaneous equations (and hopefully expand on your understanding).
Beginning
There are a number of ways to do this however lets start with the easiest to visualise (but not always the quickest) method - drawing graphs.
Lets take these two equations:
1) y = 3x + 2
2) y = 5x - 1
There are a number of ways to do this however lets start with the easiest to visualise (but not always the quickest) method - drawing graphs.
Lets take these two equations:
1) y = 3x + 2
2) y = 5x - 1
You should hopefully recognise these as straight line graphs. If you take the first equation on its own you can see that if x = 4 then y = 3x4 + 2 = 14 and indeed whatever value of x I give you, you can calculate a value of y. We can do the same for the second equation.
In solving these simultaneous equations we are looking for a value of x and y that works for both equations. When drawn as graph this is the point where the two graphs cross.
Below I have used Wolfram Alpha to plot these two graphs and find the solution (the coordinates of where they cross).
Hopeful this gives you an idea of what you might be asked to do in the exam (although they would ask you to draw the graphs).
Developing
We are now going to look at solving simultaneous equations without drawing graphs. Watch this video to remind yourself how to do Elimination.
Simultaneous Equations (from MEP 10.8)*
Note: the answers are on the last page.
We are now going to look at solving simultaneous equations without drawing graphs. Watch this video to remind yourself how to do Elimination.
Simultaneous Equations (from MEP 10.8)*
Note: the answers are on the last page.
Here you will find a few more questions on solving Simultaneous Equations by Elimination - watch this video for an extra helping hand.
Simultaneous Equations (from TEN Ticks 7-8, 4)*
Simultaneous Equations (from TEN Ticks 7-8, 4)*
Mastering
Now check your understanding using these exam questions.
Book Review
Homework
Further & Additional
Title: Inequalities
Challenge Question
What effect does a quadratic have on the inequality sign?
Learning Targets
Developing
Be able to illustrate linear inequalities in two variables (a).
Mastering
Be able to use graphs of linear inequalities to solve 2-dimensional maximisation and minimisation problems, know the definition of objective function and be able to find it in 2-dimensional cases (a).
Resources
Start today's lesson by solving this puzzle on the NRich website (a solution can be found on this website but try to solve the puzzle first in your own way).
Inequality - Starter
Today you are going to look at Inequalities in a little more detail. Work on this topic can be found between pages 111-120 in the Additional book (I am working from memory on this so please check the page number on the contents page).
If you complete this work please start have a go at this puzzle (again a solution is provided).
Inner Inequality - challenge from NRich
If you complete this work, challenge yourself using the UKMT test questions linked below:
Challenge Yourself
Homework
