Algebra Flashcards
What is a linear equation?
An algebraic equation without exponents or roots
Whats one way to simplify an equation that contains a fraction?
Multiply the entire fraction by the denominator of the fraction. The fraction will cancel out
If its two denominators choose their LCD
How can you simplify an equation of two fractions?
Cross multiply
When do you flip a sign when working with inequalities?
When dividing or multiplying an inequality by a negative number
Why should you never multiply an inequality by a variable?
You dont know if the variable is negative or positive; thus you dont know if you need to flip the sign
What is the equation for translating graphs for absolute value
|x - (midpoint)
How do you find a midpoint
Average of the two endpoints
How do you do problems with absolute value on both sides of the equation?
Set up two scenarios
1 scenario where both brackets are positive
Another scenario where the first bracket is positive and the second is negative
(If its an equation w = sign then just set up scenario two w a negative; if its an equality flip the sign for scenario 2)
The product of two numbers with different signs is always …?
Negative
And less than 0
The product of two numbers with identical signs is always …?
Positive
I.e. more than 0
What do you call an equation with a fraction raised to both the first power and the second power?
A quadratic equation
-x^2 =7x + 3. Is what type of equation?
Quadratic
Whats an easy way to solve quadratic equations?
Factoring
How do you factor a quadratic equation?
Set the equation equal to 0
Make sure the x^2 term is positive
Set up brackets (x )(x )
Choose two numbers that multiply to the last term and add to the coefficient of the middle term
What are the solutions to quadratic equations?
Roots
How can you get the roots of a quadratic equation?
Set each factor equal to zero
How do you solve a quadratic equation that cant be factored?
You use the quadratic formula
What is the discriminant?
b^2 - 4ac
Its the portion under the square root symbol in the quadratic formula
What can the discriminant show you?
The number of solutions a quadratic has
Describe what each of the values of a discriminant tell you?
>
- The equation has two solutions
=0. The equation has one solution
<0. The equation has no solutions
What is the sq root of -7
Its an imaginary number
You cant take a sq root of a negative number
What are some tricks for substitution?
If asked to solve for a specific variable always isolate the other variable.
I.e. if asked to solve for x isolate y
When using the elimination method what do you do to your equations
Stack them
Arrange the variables
Add the equations
What happens when you plug an equation that contains addition or subtraction into an equation that contains multiplication?
You produce a quadratic equation
If two equations provide the same info, it is impossible to solve for either variable.
I.e.
If 5m - n =3 and 10m - 2n = 6
0=0
Answer : indeterminable
How do you combine inequalities and equations?
Isolate the variable in common
Substitute the equation into the inequality
What must be in order to add two inequalities?
Their inequality signs must point in the same direction
How do you do the elimination method?
Add two equations
What do you do if inequalities cant be added?
Combine them by adding them and giving them a common term
What is the smallest number that can be squared
0
What is the smallest possible value of any expression within AV brackets?
0
How do you factor?
Determine the maximum factor in common to both terms
And thus,
The factored element x the expression left behind should equal the original element
How can you factor c-b to make it b-c
-1(b-c)
Whats a good thing to do when factoring?
Put like terms together
I.e. make pq + rs + qs + pr read
pq + pr + qs + rs = 10
Given one equation with two or more variables when might it be possible to solve for those variables?
If those variables MUST be integers
If you have two integers and are asked to solve for one how can you do that?
Solve for the variable you are not asked for and plug in answer choices to find your answer
How many modes can a list of numbers have ?
Many, there can be more than 1
What is frequency distribution?
Its a list of numbers and a list of how frequent each number is in the set
What do you call two sets that have no elements in common?
Disjoint or
Mutually exclusive
