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Inequalities:

Solve inequalities the same way you solve equations, EXCEPT that you MUST CHANGE THE SIGN when dividing or multiplying both sides by a negative number.

For example, consider the problem
-2x > -4

To solve, you divide both sides by -2.
x > 2

However, since you divided by a negative number, you MUST flip the sign.
x < 2

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solution to a system of 3 equations, 3 variables are in the order of (x,y,z)

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To solve a system of three equations, first choose one variable to eliminate. Solve for the other two variables then plug everything in at the end.

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i equals √-1 and i^2 equals -1

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Domain is x, Range is y

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When you have two equalities you can solve for one variable to substitute into the other.

Always try to isolate the variable when solving.

Don't overthink the problems and break them into blocks of work. (The numbers aren't too scary)

Good luck!!! Try to pass!

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For the i^x questions, you can take the remainder of x/4 and then just figure out the answer for that number of is.

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If it has an exponent then it is not linear.-Seth

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If you take the time to draw the line, you take the time to fill in the circle (when plotting on a number line, if the answer is less/more than or equal to, you will shade the circle in on the number line)

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Use the matrix on the calculator

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Parabolas
A parabola is a u or n shaped line that follows the equation y = ax^2 + bx + c. When the A in a equation is positive, the parabola opens up or has a minimum. When the A is negative, the parabola opens down, or has a maximum. Minimums and maximums are determined by the vertex.

Finding zeros
When finding the zeros to a parabola, make sure the equation is 0 = ax^2 + bx + c, because the y should equal zero. Then, you follow the equation (b +/- √{b^2 - 4ac})/2a, by substituting a, b, and c into their correct places and then you simplify. Simplify until you get to the +/- then you split the equation in two, where one is + and the other is -. Other than that the equations should be the same.

What if the square root cannot be simplified?
If your simplifying and you find that your square root cannot be simplified (√{11} or √{23}, then you leave it as is. You don't divide is by the 2a and you don't +/- the b. You still split it into two equations, one + and the other -, but you don't simplify anymore.
If you find that the square root can be simplified but it's a negative (√{-25} or √{-100}), then you must add the imaginary number. Remember, when you are finding the square root regularly, you use the tree method. Do the same except first get rid of the negative by separating the a imaginary number (i) and the number you started with. For example, √{-81}, you separate the numbers into i x 9 x 9 then you simplify normally.

What is i?
i is an imaginary number which really equals √{-1}. This number can be used to help solve negative square roots to be able to simplify it. But what happens when i is to the power of something? when i looks like i^2, you get -1 because remember, i = √{-1}. So when you have i^20, you split the number in half, which in this case is 10, and then you multiply -1 ten times, which, in this case, is -1.

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When absolute value is equal to a negative number it has NO SOLUTION

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Open sentence: Mathematical statement with one or more variable.

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Solution-replacement value for the variable in an open sentence

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Solution-replacement value for the variable in an open sentence

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On number 5, you have to distribute the 4 to the variables in the parenthesis. Then you can solve from there.

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Slope is y2-y1/x2-x1

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If you multiply or divide on both sides by a negative number, you have to flip the inequality sign.

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Use the elimination method to solve

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You can use the vertical line test to see if it is a function or not.

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If u take the time to draw the line you take the time to fill in the circle.

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If you draw the line, you fill in the circle

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positive and negative signs determine the parabola opening

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positive and negative signs determine the parabola opening

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-when a is negative, the parabola opens down.
-when a is positive, the parabola opens up.

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move all numbers by themselves to one side

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move all numbers by themselves to one side

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Inequality signs flip when you multiply or divide both sides by a negative number

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Inequality signs flip when you multiply or divide both sides by a negative number

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Get x by itself