Chapter 3: Equations and Inequalities

In alevel how do we refer to the answer(s) to equation

The solution sets- could have 0, 1, 2 …or infinite solutions

What are the two methods to solve simultaneous equations

Elimination and Substitution

Elimination

Match up variables ( x or y) then take away

What do you do if variables ( x or y) ,which you have matched, have opposite signs e.g -3y and 3y

You add them ( equations )to cancel (y) out instead

Substitution

You make x or y subject( if not already) and substitute in to other equation

When should you definitely use substitution

When equations are non linear( at least one)

Simultaneous equations and graphs

The satisfactory solutions for both equations represent the point of intersection on a graph

How does discriminant come into simultaneous equations and graphs

If you solve / combine the equations you get a new equation which represents the x solutions (for intersection)

• use the discriminant of this to test for how many intersections there are

What is the outline R symbol

All real number

What is the outline N symbol

All natural numbers ( positive integers)

What is the outlined Z symbol

All integers including negatives and zero

{2x: x € _}

All possible values of 2x if x is…( a positive integer e.g)

Using notation what do we place solutions inside of

Curly/ wavy brackets { }

Linear inequalities

• they behave like equations

what do we do if we multiply or divide by a negative

switch the inequality sign round

How do we combine inequalities

create an inequality that satisfies both inequalities

Quadratic inequalities

they involve a quadratic expression and can be solved by finding the regions where the expression is greater than or less than zero.

How do we deal with quadratic inequalities

-get 0 on one side(if not already)

-solve/factorise for critical values

-sketch the corresponding parabola and determine where it is positive or negative(greater than or less than 0)

-decide whether to combine the two inequalities or seperate

When do we combine the solutions of quadratic inequalities

when sketch shows the region we are interested in is the semi circle curve bit

What do we need to be careful about when dealing with unknowns in inequalities

We need to consider when multiplying or dividing will reverse the inequality sign as we are not sure if its a negative or not

-instead multiply or divided by the unknown squared as that will always be positive.

what does each point on a line represent

a solution to the equation , the values that satisfy the equation

inequalities on graphs

are regions that represent the set of solutions for a given inequality. Each region is defined based on whether the inequality is greater than or less than a specific line.