3. Equations And Inequalities Flashcards
Quadratic and linear simultaneous equations if both equal y
Make them equal to each other
Rearrange to find a quadratic
Solve that quadratic and then find y for each x
If both simultaneous equations don’t equal x or y when 1 is linear and one quadratic
Rearrange the linear to get y= or x=
Substitute that in place of y or x in the equation
Expand and rearrange to get a quadratic
Solve and find x for each y or y for each x
What are the solutions to graphical simultaneous equations?
The intersections
How to solve simultaneous equations when given them as two graphical equations
Make them equal and rearrange
How to see how many times 2 lines intersect if there is a quadratic?
Use the discriminant after rearranging to equal 0
What is a set?
A collection of values such that:
a) the order does not matter
b) there are no duplicates
A ⋃ B
Values that belong to A or B, no duplicates
A ⋂ B
Values that belong to A and B
Empty set
∅
N
All natural numbers (positive integers)
Z
All integers
R
All real numbers
A ∈ R
A is member of the real numbers
How to produce a set?
{expression | condition} or {expression : condition}
e.g. {2x : x ∈ Z} - all even numbers
{x : x < 3} - all real numbers less than 3
Quadratic inequalities
1) Get 0 on one side
2) Factorise
3) Sketch the graph and reason
