Algebra

Question 1

What is a linear equation?

Answer 1

An algebraic equation without exponents or roots

Question 2

Whats one way to simplify an equation that contains a fraction?

Answer 2

Multiply the entire fraction by the denominator of the fraction. The fraction will cancel out

If its two denominators choose their LCD

Question 3

How can you simplify an equation of two fractions?

Answer 3

Cross multiply

Question 4

When do you flip a sign when working with inequalities?

Answer 4

When dividing or multiplying an inequality by a negative number

Question 5

Why should you never multiply an inequality by a variable?

Answer 5

You dont know if the variable is negative or positive; thus you dont know if you need to flip the sign

Question 6

What is the equation for translating graphs for absolute value

Answer 6

|x - (midpoint)

Question 7

How do you find a midpoint

Answer 7

Average of the two endpoints

Question 8

How do you do problems with absolute value on both sides of the equation?

Answer 8

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)

Question 9

The product of two numbers with different signs is always …?

Answer 9

Negative

And less than 0

Question 10

The product of two numbers with identical signs is always …?

Answer 10

Positive

I.e. more than 0

Question 11

What do you call an equation with a fraction raised to both the first power and the second power?

Answer 11

A quadratic equation

Question 12

-x^2 =7x + 3. Is what type of equation?

Answer 12

Quadratic

Question 13

Whats an easy way to solve quadratic equations?

Answer 13

Factoring

Question 14

How do you factor a quadratic equation?

Answer 14

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

Question 15

What are the solutions to quadratic equations?

Answer 15

Roots

Question 16

How can you get the roots of a quadratic equation?

Answer 16

Set each factor equal to zero

Question 17

How do you solve a quadratic equation that cant be factored?

Answer 17

You use the quadratic formula

Question 18

What is the discriminant?

Answer 18

b^2 - 4ac

Its the portion under the square root symbol in the quadratic formula

Question 19

What can the discriminant show you?

Answer 19

The number of solutions a quadratic has

Question 20

Describe what each of the values of a discriminant tell you?

Answer 20

>

0. The equation has two solutions

=0. The equation has one solution

<0. The equation has no solutions

Question 21

What is the sq root of -7

Answer 21

Its an imaginary number

You cant take a sq root of a negative number

Question 22

What are some tricks for substitution?

Answer 22

If asked to solve for a specific variable always isolate the other variable.

I.e. if asked to solve for x isolate y

Question 23

When using the elimination method what do you do to your equations

Answer 23

Stack them
Arrange the variables
Add the equations

Question 24

What happens when you plug an equation that contains addition or subtraction into an equation that contains multiplication?

Answer 24

You produce a quadratic equation

Question 25

If two equations provide the same info, it is impossible to solve for either variable.

Answer 25

I.e.

If 5m - n =3 and 10m - 2n = 6

0=0

Answer : indeterminable

Question 26

How do you combine inequalities and equations?

Answer 26

Isolate the variable in common

Substitute the equation into the inequality

Question 27

What must be in order to add two inequalities?

Answer 27

Their inequality signs must point in the same direction

Question 28

How do you do the elimination method?

Answer 28

Add two equations

Question 29

What do you do if inequalities cant be added?

Answer 29

Combine them by adding them and giving them a common term

Question 30

What is the smallest number that can be squared

Answer 30

0

Question 31

What is the smallest possible value of any expression within AV brackets?

Answer 31

0

Question 32

How do you factor?

Answer 32

Determine the maximum factor in common to both terms

And thus,

The factored element x the expression left behind should equal the original element

Question 33

How can you factor c-b to make it b-c

Answer 33

-1(b-c)

Question 34

Whats a good thing to do when factoring?

Answer 34

Put like terms together

I.e. make pq + rs + qs + pr read

pq + pr + qs + rs = 10

Question 35

Given one equation with two or more variables when might it be possible to solve for those variables?

Answer 35

If those variables MUST be integers

Question 36

If you have two integers and are asked to solve for one how can you do that?

Answer 36

Solve for the variable you are not asked for and plug in answer choices to find your answer

Question 37

How many modes can a list of numbers have ?

Answer 37

Many, there can be more than 1

Question 38

What is frequency distribution?

Answer 38

Its a list of numbers and a list of how frequent each number is in the set

Question 39

What do you call two sets that have no elements in common?

Answer 39

Disjoint or

Mutually exclusive