Study Flashcards
Set of real numbers symbol
ℝ
ℝ
Set of real numbers symbol
If a and b are in ℝ so is
a+b and a•b
Commutative property
a+b = b+a / a•b = b•a
a+b = b+a / a•b = b•a
Commutative property
Associative property
(a+b)+c = a+(b+c) / (a•b)•c = a•(b•c)
(a+b)+c = a+(b+c) / (a•b)•c = a•(b•c)
Associative property
Additive identities
Real # 0 such that a+0=a for all a
Real # 0 such that a+0=a for all a
Additive identities
Multiplicative identitity
Real # 1 that a•1=a for all a
Real # 1 that a•1=a for all a
Multiplicative identitity
Additive inverses
For any a in ℝ, there is a # -a in ℝ that a+(-a)=0
For any a in ℝ, there is a # -a in ℝ that a+(-a)=0
Additive inverses
Multiplicative inverses
For any a≠0, there is a # 1/a in ℝ that a•1/a=1
For any a≠0, there is a # 1/a in ℝ that a•1/a=1
Multiplicative inverses
Distributive property
a•(b+c)=a•b+a•c for all a,b,c in ℝ
a•(b+c)=a•b+a•c for all a,b,c in ℝ
Distributive property
Term
Any number, constant, variable, or parenthetical group
Any number, constant, variable, or parenthetical group
Term
Expression
Combination of terms using additional, subtraction, multiplication, division, exponents, or roots
Combination of terms using additional, subtraction, multiplication, division, exponents, or roots
Expression
Equation
Statement that two expressions are equal
Statement that two expressions are equal
Equation
Define expression “a^n”
a^0=1 if a≠0 / a^-n=1/a^n
a^0=1 if a≠0 / a^-n=1/a^n
a^n
(a•b)^n =
a^n • b^n
a^n • b^n =
(a•b)^2
(a/b)^n =
a^n/b^n (b≠0)
Does zero have a degree?
No
Does not have a degree
Zero
Polynomial with one term
Monomial
Monomial
Polynomial with one term
Polynomial with two terms
Binomial
Binomial
Polynomial with two terms
Polynomial with three terms
Trinomial
Trinomial
Polynomial with three terms
5x^2 y^4
What is the degree of this term?
6
A^2-B^2 =
(A-B)(A+B)
(A-B)(A+B)
A^2-B^2
(A-B)^2 =
A^2-2AB+B^2
A^2-2AB+B^2
(A-B)^2
A^3-B^3 =
(A-B)(A^2+AB+B^2)
(A-B)(A^2+AB+B^2)
A^3-B^3
A^3+B^3 =
(A+B)(A^2-AB+B^2)
(A+B)(A^2-AB+B^2)
A^3+B^3
Rational number is a
Ratio of integers like 3/4
Ratio of integers
Rational number
Rational expression
Ratio of polynomials like x+3/2
Ratio of polynomials
Rational expression
Let a>0. To say b= √ a means:
- ) b^2=a
- ) b>0
This is principal square root of a
For any real x, √ x^2 =
|x|
If a>0 , n√a = b if
b^2=a and b>0
If a<0 and n is odd n√a=b if
b^n=a
If a<0 and n is even n√a is
Not real
n√x
What is index and what is radicand?
n is index and x is radicand
How do you rationalize 3√9?
Multiply by 3√9^2 because 1/3 + 2/3 = 1
Multiply by 3√9^2 because 1/3 + 2/3 = 1
Rationalizing 3√9
An equation whose solutions set is all ℝ is an
Identity
Identity
An equation whose solutions set is all of ℝ
An equation whose solution set is empty is
Inconsistent
Inconsistent
An equation whose solution set is empty
An equation with non-empty solution set that is not all of ℝ is
Conditional
Conditional
An equation with non-empty solution set that is not all of ℝ
Quadratic equation standard form
ax^2+bx+c
ax^2+bx+c
Quadratic equation standard form
b^2-4ac > 0
b^2-4ac = 0
b^2-4ac < 0
Two real solutions
One real solution
No real solutions
A combination of one or more inequalities is a
Compound inequality
Compound inequality
A combination of one or more inequalities is a
|2x-3| = 13
2x-3 = 13 or 2x-3 = -13
2x-3 = 13 or 2x-3 = -13
|2x-3| = 13
Distance formula
√(x1-x2)^2 + (y1-y2)^2
√(x1-x2)^2 + (y1-y2)^2
Distance formula
Midpoint formula
(x1+x2/2,y1+y2/2)
(x1+x2/2,y1+y2/2)
Midpoint formula
Circle standard equation
(x-h)^2 + (y-k)^2 = r^2 with center (h,k)
(x-h)^2 + (y-k)^2 = r^2 with center (h,k)
Circle standard equation
If (x1,y1) and (x2,y2) are the points on a line, then its slope is
m = y2-y1/x2-x1
m = y2-y1/x2-x1
If (x1,y1) and (x2,y2) are the points on a line slope
Point-slope formula
y-y1 = m(x-x1)
y-y1 = m(x-x1)
Point-slope formula
Negative reciprocal slopes formula
m1•m2=-1
m1•m2=-1
Negative reciprocal slopes
