Chapter 3 Equations And Inequalities - Year 1 Flashcards
How do you prove that 2 lines never meet?
They will never intercept each other and therefore it will have no solution if they never meet
So we put the two equations of the lines equal to each other and make it in the form of a quadratic
Then we know that the discriminant will be less than 0 because they will have no solutions if they don’t meet
Your final line should be -x<0 so b^2-4ac<0 so the lines will never meet
What do you need to know when you plot a graph?
When it crosses the x axis
The y intercept
Sometimes the turning point
If you get 1 equation with unknowns and another normal equation and are told that they meet exactly once ::: and you are asked to solve the equation, what do you do?
Put the equations equal to each other
Make it =0
You know that the discriminant will equal 0
Solve for the value of the unknown
Substitute your value back into the combined equation
Solve it and substitute your value(s) back into one of the initial equations to find the corespondent y value
What trick may exams use to narrow down the answer?
They may say that x is a positive number
What type of brackets are used in set notation?
{ }
What does this mean:
Union
(Or)
What does this mean?
The intersection
(And)
What is the symbol for an empty set?
Write down two examples of example of set notation
How do you solve 2 inequalities graphically?
You plot them both separately
If you are solving for x then the values of x will be the x co-ordinate where the 2 lines meet
What are the two ways to solve inequalities?
Graphically
Algebraically
How do you solve an inequality?
Put it equal to 0 and solve the quadratic as normal
Then sketch a graph
If x^2is greater/less than OR EQUAL to 0 then the answer will have the ≤/≥ sign
If you know the turning point and where it crosses the x axis how do you find the equation of a quadratic?
Substitute it into the complete the square format
y=a(x+-b)^2+c
Then solve for a
And substitute a into the complete the square format equation
Does a graphical region need to be finite?
No
How do you calculate the equation of a linear line if you are given the y intercept and 2 points on the line?
Use the equation y=mx+c
Since you know two points you can use the equation rise/run to calculate the gradient
Then substitute it back into the equation
