Algebra Basics

Question 2

topic

manipulating equations

Answer 2

1. solving for one variable
2. solving equations with fractions
3. solving for two or more variables

Question 3

topic

Simulatneous equations

Answer 3

given two equations, solve for the value of an expression as opposed to the value of the variables

Question 4

topic

inequalities

Answer 4

statements much like those with = signs. can be manipulated by the same rules, with the notable expection of flipping the direction of the < or > when you multiple or divide by a negative number

Question 5

topic

quadratic equations

Answer 5

1. expanded quadratic equations
2. fully factored quadratic equations
3. FOIL
4. common quadratic equations

Question 6

topic

exponents

Answer 6

1. multiplying exponents
2. dividing exponents
3. exponents raised to a power
4. negative exponents
5. zero exponents
6. factoring exponents

Question 7

topic

square roots

Answer 7

1. adding and subtracting square roots
2. multiplying and dividing square roots
3. simplifying square roots

Question 8

golden rule of manipulating equations

Answer 8

whatever you do to one side of the equation, you must do to the other side of the equation

Question 9

operation pairs

Answer 9

addition– subtraction
division– multiplication
power– square root

Question 10

solving equations with fractions

Answer 10

1. clear the fraction by multiplying the fraction by the value in the denominator
2. perform the same operation (multiplication by whatever the denominator was) to each other term in the expression

Question 11

equations with more than one variable

Answer 11

1. given two equations, find a way to match at least one of the coefficients by multiplying or dividing
2. subtract the newly formed equation from the first original equation to find one of the variable values
3. plug in the variable value into one of the original equations to solve for the other variable

Question 12

simultaneous equations

Answer 12

apply same method as two variable equations, end up with an expression instead of a value for the variables

Question 13

combining ranges

Answer 13

consider all possible combinations of x and y (and then all possible combinations of x and y in the defined expression)
Calculate: (example x-y)
1. the greatest x minus the greatest y
2. the greatest x minus the least y
3. the least x minus the greatest y
4. the least x minus the least y

the greatest value from the above calculation and the least consitutes the range of x-y

Question 14

fully expanded quadratic equations

Answer 14

example: x^2 + 10x + 24
contains a squared variable, a variable multiplied by some number, and an additional number

Question 15

factoring an expanded quadratic

Answer 15

goal: break the equation apart to find the values for the variables that make the equation true. these are referred to as the roots of the equation, and the roots of a quadratic equation are the variables that make the expression equal to 0

Question 16

steps to factoring

Answer 16

1. seperate the x^2 into two cvalues of x and place them inside their own parantheses
2. consider the second and third terms in the equation and find the factor pair of the third term that, when added or subtracted, yields the second term
3. determine the operations that are inside the parentheses
4. once the parentheses have been filled in, solve for the roots of the equation

Question 17

fully factored quadratic equations

Answer 17

in order to expand a fully factored quadratic equation into the fully expanded standard form, employ the FOIL tactic

Question 18

difference of squares

Answer 18

x^2-y^2=(x+y)(x-y)

Question 19

common quadratics

Answer 19

1. difference of squares
2. (x+y)2=x^2+2xy+y^2
3. (x-y)2=x^2-2xy+y^2

Question 20

exponents

Answer 20

shorthand for repeated multiplation, composed of a base and a “power”. The power tells you how many times to multiply the base by itself

Question 21

MADSPM

Answer 21

First three rules of exponents.
1. Multiply– Add
2. Divide– Subtract
3. Power– Multiply

Question 22

negative exponent

Answer 22

any term raised to a negative power is equal to the reciprocal of that term raised to the positive power. 8^-2 = 1/8^2 = 1/64

Question 23

zero exponent

Answer 23

any nonzero number raised to apower of 0 is equal to 1.

Question 24

exponent tip 1:

Answer 24

if none of the bases in an exponent equation match up, search for a way to rewrite the bases so they do match

Question 25

exponent tip 2:

Answer 25

if you get stuck on an exponent question, try to factor the expression to produce values that can be manipulated by one of the five rules

Question 26

base greater than 1 to a power greater than one

Answer 26

always results in a greater number

Question 27

base between 0 and 1 to a power greater than 1

Answer 27

results in a smaller number

Question 28

negative number raised to an even power

Answer 28

results in a positive number

Question 29

negative number raised to an odd power

Answer 29

results ina negative number

Question 30

a number raised to the first power

Answer 30

always results in the number itself

Question 31

square root

Answer 31

a square root of a number, x, is the number, y, for which y^2 = x. taking the square root is the opposite of finding the square of a number. the square root of a number is always non-negative

Question 32

adding and subtracting square roots

Answer 32

add or subtract only if the values under the radical sign are equal

Question 33

multiplying and dividing square roots

Answer 33

any square root can be multiplied or divided– no restrictions. multiplying square roots is as simple as multiplying the terms outside square roots together and the terms underneath the radical signs togather

Question 34

simplifying square roots

Answer 34

simplify a square root by looking for ways to factor the number under the root that results in at least one perfect square