Algebra woooo Section III

Sets Set – a collection of unique objects, such as {1,2,3} Element – a member contained in a set. To say that 2 is an element of {1,2,3}, we would write 2∈{1,2,3} Equal Sets – have the same exact elements, {1,2,3} = {3,2,1} Equivalent Sets – have the same number of elements, {1,2,3} ~ {4,5,6} Union of Sets – contains all elements from two sets, denoted by ∪  Intersection of sets – contains all common elements from two sets, denoted by ∩ Sets

Set Problems True or False: 4∈{3,6,9,12} True or False: {a,b,c} = {a,d,e} True or False: {a,b,c} ~ {a,d,e} What is {1,2,3,4}∪{3,4,5,6}? What is {1,2,3,4}∩{3,4,5,6}? Set Problems

Types of Numbers Integers: ...-3,-2,-1,0,1,2,3... Rational Numbers – numbers that can be expressed in the form of a fraction, or by repeating or terminating decimals Irrational Numbers – numbers that cannot be expressed as a fraction, and whose decimal expansion does not repeat or terminate Prime Numbers – numbers divisible only by themselves and 1 Composite Numbers – numbers with factors other than themselves and 1 Types of Numbers

We use a factor tree to continually divide a number smaller and smaller until it is represented completely by prime numbers. The prime factorization of 36 is 3^2+2^2. A greatest common factor is the largest number evenly divisible by two numbers. Prime Factorization

Exponent Rules https://www.mcckc.edu/tutoring/docs/bt/exp_rad_log/Exponent_Rules_&_Practice.pdf

Square Root Rules (and Cube Root)

Expressions are solved using PEMDAS (Parentheses, Exponents, Multiplication/Division, Addition/Subtraction) To evaluate an expression, replace the variable with the given value and solve. Expressions

Use properties of equivalency to solve equations Use properties of equivalency to solve equations. What you do to one side, you must do to the other. Literal equation – an equation with no values, only letters Linear equation – an equation with no exponents greater than 1, which produces a straight line when graphed Slope - rise/run https://cdn.kutasoftware.com/Worksheets/Alg1/Two- Step%20Equations.pdf Equations

Ratios and Proportions Ratio – a:b or a/b Proportion – a relationship between two variables with a constant ratio Proportionality constant – that ratio If it takes 4 eggs to make 48 cookies, then how many cookies could be made with 5 eggs? Ratios and Proportions

'Nomials Monomial – a single term, such as 9x or 4a^2 Binomial – two monomials added or subtracted, such as x+y or y^2+2y Trinomial – Three monomials Polynomial – all of these FOIL – first, outer, inner, last (a+b)(c+d) 'Nomials

To find a GCF, find the GCF of all variables, exponents, and integers Difference of two squares – a^2-b^2=(a+b)(a-b) Quadratic Factoring is more complicated. Factoring

Quadratic – an equation that can be written as ax^2+bx+c=0 The point of a quadratic is to factor and find the zeroes of the equation. Quadratic Equation

Inequalities are very similar to equations, but have a < or > symbol rather than an equals sign. They are solved like equations as well. The one difference is that when multiplying by a negative number, the sign is flipped. Inequalities

Algebra is enough of a quiz.