Math Section 3 Flashcards
What is a set?
a collection of numbers, ex: {1, 2, 3}
What is an element?
a member of a set, represented by ∈
What does ∈ mean?
“belongs to”, is used to show that an element belongs to a set
What are equal sets?
sets with the same elements
What are equivalent sets?
sets with the same number of elements
What is a union of sets?
a set with all the members found in both sets you are unioning
What is ∪?
the symbol for union
What is an intersection of sets?
a set with elements both sets have in common, represented by ∩
What is ∩?
the symbol for intersection
What are integers?
the counting numbers, their negative form, and zero
What are rational numbers?
numbers written as a ratio of 2 integers
What are irrational numbers?
numbers that can’t be written as a ratio of 2 integers
What is a prime number?
a number greater than one with only 2 whole factors
What is prime factorization?
the integers that are the product of all prime factors that can be divided into the number
What is GCF? (greatest common factor)
the greatest whole numbers will divide evenly into 2 numbers
What is a base in an exponent?
the whole number that is affected by the exponent
Any number above zero raised to the power of zero will always equal what?
1
How do you make the exponent in x^-1 positive?
use the reciprocal of the original power, ex: x^-1 = 1/x^1
How do you simplify this? (x^n)^p
multiply n and p, x^np
How do you distribute this? (c/d)^n
distribute it to the numerator and denominator, c^n/d^n
How do you simplify this? x^n * x^n
add the exponents, x^n+n
What is power in an exponent?
the base and exponent together, ex: 5^3
What is base in an exponent?
the number being affected by the exponent, ex: 5 in 5^3
What is exponent in an exponent?
the number that is raising the power of the base, ex: 3 in 5^3
How do you simplify this? x^m/x^n
subtract the exponents, ex: x^m-n
What is the name of the symbol used to square root a number?
the radical sign
What is a square root?
the number that makes the original number when squared
How do you simplify this? √xy
√x * √y
How do you simplify this? √a * √a
a
How do you simplify this? √x/y
√x/√y
How do you simplify this? √a^n
(√a)^n
What is a cube root
the number that makes the original number when cubed
What is a variable?
a symbol used to represent an unknown number or value
What does sum, greater than, increased by, or more than usually indicate?
to use addition
What does difference, smaller than, decreased by, or less than usually indicate?
to use subtraction
What does product, times, or multiplied by usually indicate?
to use multiplication
What does quotient, halve, divided by, or ratio usually indicate?
to use division
What is a ratio?
a method of comparing two or more numbers or variables, and can be written as a:b or a/b
What are the 2 ways ratios can be written?
a:b or a/b
How do you read ratios?
“a is to b”
What is a proportion?
a relationship between 2 variables whose ratio is a constant
What is a proportionality constant?
the number you get when diving 2 values in a proportion
What is a monomial?
an algebraic expression that has only one term
How do you add monomials?
combine the coefficients and combine like terms, leave variables the same if they are not alike
How do you multiply monomials?
add the exponents of the same bases and multiply the coefficients
How do you divide monomials?
subtract the exponents with the same bases and divide the coefficients
What is a binomial?
an algebraic expression with 2 monomial terms
What type of algebraic expression is x + y?
binomial
What is a trinomial?
an algebraic expression with 3 terms
What type of algebraic expression is x + y + z?
trinomial
What type of algebraic expression is y^2 + 9y + 8?
trinomial
What is a linear equation?
an equation whose solution(s) create a straight line
What is the FOIL method?
a way two multiply 2 binomials
What is slope?
the steepness of a line
What is an equation?
a mathematical sentence, or a relationship between numbers and variables
What is slope formula?
(y2-y1)/(x2-x1)
What mnemonic device is used to remember the order of operations?
PEMDAS
What does PEMDAS stand for?
P = Parenthesis
E = Exponents
M/D = * and /, left to right
A/S = + and -, left to right
What does FOIL stand for?
F = first terms
O = outer terms
I = inner terms
L = last terms
What is factoring?
a method to find the two or more polynomials whose product equals the original value
What are the steps to factoring?
factor out the GCF, look for a factor pattern like binomial squares, differences of 2 squares, etc, and check your answer by multiplying them
What is the difference of 2 squares strategy?
it works when you factor out common factors and have 2 perfect squares subtracted from each other, ex: a^2 - b^2 would be (a - b)(a + b)
What is the binomial squares strategy?
when you have 2 positive perfect squares for the first and last terms and the middle term is 2x the square root of the first and last term, middle term can be positive or negative
What is a quadratic equation?
an equation with a variable that is squared and is usually in this form: ax^2 + bx + c = 0
What is an inequality?
a statement where the relationships between the numbers are not equal
What does < mean?
less than
What does > mean?
greater than
What does ≤ mean?
less than or equal to
What does ≥ mean?
greater than or equal to
What does ≠ mean?
not equal to
