Algebra I Flashcards
GEDMAS
Order of operations
Grouping, exponents, division/multiplication, addition/subtraction
Real numbers
Represent real values. Can be rational or irrational or negative. Whatever
Natural Numbers vs. Whole Numbers
Natural numbers are integers that start with 1
Whole numbers are integers that starte with 0
Integers can be negative
Rational Numbers
Can be any number that can be represented by a fraction made up of two integers (can have results that are forever repeating, as long as there is a pattern)
Irrational Numbers
Numbers that cannot be expressed as a fraction of two integers. Go on forever and don’t have any repeated patterns
Prime vs. Composite
Prime numbers are numbers that can only be evenly divided by itself and 1. The first prime number is 2, and it is the only even one. Composite numbers are any number that isn’t prime
Factorial definition
n! = n*(n-1)*(n-2)*(n-3)…3*2*1
And 0! = 1
Communitive property
Order doesn’t matter
a+b=b+a
Associative Property
Grouping doesn’t matter:
(a+b)+c = a+(b+c)
Distributive Property
a (b + c) = ab + ac
Structure of a fraction
Numerator / Denominator
What is an improper fraction
The numerator is greater than the denominator
What is a mixed number
Integer plus a fraction
What is a least common multiple
The smallest number that two numbers can evenly go into
Sum of a finite arithmetic series
where a1 is the first term, an is the last term
Sum of an infinite geometric sequence
a is the first term, r is the ratio (0 to 1)
Sum of a finite geometric sequence
a is the first term, r is the ratio 0 to 1
The 5 rules of exponents
Keep in mind the bottom two apply to radicals
Rules for radical expressions (same as the rules of exponents, but a good visual)
Fractional radical notation
What is prime factorization?
prime factorization of a number is the unique product of prime numbers that results in the given number
How do you determine what the smallest number is that a group of numbers can evenly go into?
Do prime factorization on all the numbers, and multiply the prime numbers by each other for a final product (the catch is, don’t repeat values if the prime factor is already listed)
How to simplify fractions to solve an equation
The key here is to multiply both sides of the equation by the least common denominator, not just one side!
Rules of Divisibility (2-6)
2: number is even
3: sum of digits is a number divisibile by 3
4: last two digits form a number divisible by 4
5: 5 or 0 last digit
6: the number is divisible by 2 and 3
Rules of Divisibility (7-12)
7: take the last digit, double it, and subtract it from the rest of the number. If you get an answerdivisible by 7 (including zero), then the original number is divisible by seven. If you don’t know the new number’s divisibility, you can apply the rule again.
8: Last three digits form a number divisible by 8
9: the sum of the digits is a number divisible by 9
11: The difference between the sums of the alternating digits is divisible by 11
12: the number is divisible by 3 and 4
What is a GCF
Greatest common factor is the largest possible number that evenly divides each term of an expression containing two or more terms (or evenly divides the numerator and denominator of a fraction)
The largest number that divides evenly into all the numbers. GCF of 15 and 25 is 5.
The expression becomes “prime” when it cannot be factored anymore
What is a binomial?
An algebraic expression with 2 terms in it.
Polynomial is the general term
GCF / Difference of Squares / Sum or Difference of Cubes
(Factoring Binomials)
GCF / Un-Foil / Factoring by Grouping
(Factoring Trinomials)
Perfect square trinomial quickie
Is (a2+b2) == (a+b)2
NO
Qaudratic Formula
What is the remainder theorem
When you divide a polynomial by some linear binomial, the remainder resulting from the division is the same number as you’d get if you evaluated the polynomial using the opposite of the constant in the binomial
The best way to accomplish this is synthetic division
(if you use 2 in syn div, then the linear binomial is (x-2))
What is the rational roots theorem
The rational roots theorem is a very useful theorem. It tells you that given a polynomial function with integer or whole number coefficients, a list of possible solutions can be found by listing the factors of the constant, or last term, over the factors of the coefficient of the leading term. These potential solutions can be quickly tested with synthetic division to verify.
How to accomplish synthetic division
Be sure to put zeros for any coefficients that are not present. You are adding…
What does cubic and quadratic equation mean
Power of three and power of two
A cubic equation can have up to 3 solutions
Interval notation for inequalities
(x,y) is noninclusive of x and y
[x,y] is inclusive of x and y
if infinity, use a “)”, not a ]
How inequalities are affected by operators
Adding subtracting stays the same
If you divide or multiply by a negative number, the sign flips
And don’t multiply or divide by 0
How to solve absolute value equations
Write as two seperate problems, where the absolute value stuff either equals positive or negative
Formula for simple interest
I = Prt
Where I equals interest, P is start amount, r is interest rate, t is time
Formula for compound interest
n is the number of times it’s compounded each time unit, t
Difference between combinations and permutations
In permutations, order matters
Equation for Combination
n is how many items are available
r is how many are to be chosen per iteration
Think “niccer”, n always greater than or equal to r
Has the extra r in the denominator to make smaller (because smaller than a permutation)
Equation for Permutation
Where n is total number of items and r is the number per iteration
Think “nipper”, n always greater than or equal r
Linear system of equations by substitution
Can be solved into either equation
Slope intercept form and point-slope form equations for a line
y = mx + b
y - y1 = m( x - x1 )
Midpoint Formula
Standard form for a line
Ax + By = C
