Algebra II Rules - 1st Semester Flashcards
This flashcard deck was created using Flashcardlet's card creator (62 cards)
0
Q
- Number Sets
A
A. Counting B. Whole C. Integers D. Rational E. Irrational F. Real
1
Q
- Order of Operations
A
PEMDAS
2
Q
- Commutative of Addition
A
a+b=b+a
3
Q
- Commutative of Multiplication
A
ab=ba
4
Q
- Associative of Addition
A
(a+b)+c=a+(b+c)
5
Q
- Associative of Multiplication
A
(ab)c=a(bc)
6
Q
- Additive Identity
A
a+0=a
7
Q
- Multiplicative Identity
A
a*1=a
8
Q
- Additive Inverse
A
a+(-a)=0
9
Q
- Multiplicative Inverse
A
a*(1/a)=1
10
Q
- Distributive Property
A
a*(b+c)=ab+ac
11
Q
- Mr. Mostert’s Rule
A
You can only cancel whole factors.
12
Q
- Mr. Mostert’s Corollary
A
You can only square whole factors.
13
Q
- Reflexive
A
a=a
14
Q
- Symmetric
A
If a=b, then b=a
15
Q
- Transitive
A
If a=b and b=c, then a=c
16
Q
- Substitution
A
If a=b, then b can replace a in any mathematical expression or sentence.
17
Q
- Clearing Fractions Rule
A
Multiply all terms by the least common denominator.
18
Q
- Addition prop. Of equality
A
If a=b, then a+c=b+c
19
Q
- Subtraction prop. Of equality
A
If a=b, then a-c=b-c
20
Q
- Multiplication prop. Of equality
A
If a=b, then ac=bc
21
Q
- Division prop. Of equality
A
If a=b, then a/c=b/c
22
Q
- Steps for Solving Inequalities
A
- Find Boundary Points
2. Find Solution Intervals
23
Q
- Definition of Absolute Value:
A
|a|=
a, if a >=0
-a, if a<0
24
25. Requirements for a Complete Graph
A. X intercepts
B. y intercepts
C. Scales, endpoints, arrows
25
26. Slope Formula
M=y,2 - y,1/x,2 - x,1
26
27. Slope-intercept form of a line:
Y=mx+b
27
28. Point-slope form of a line:
Y-y,1=m(x-x,1)
28
29. Standard form of a line:
Ax+By=C
29
30. Two intercept form of a line:
x/a + y/b = 1
30
31. Vertical line:
x=a
31
32. Horizontal line:
Y=b
32
33. Slopes of parallel lines:
Same slopes
33
34. Slopes of perpendicular lines:
Opposite reciprocal slopes.
34
34. Direct variation:
y=kx
35
36. Cross product:
If a/b = c/d, then ad=cb.
36
37. Methods for solving equations
1. Graphing
2. substitution
3. elimination
37
38.Definition of a function
For every x, there is exactly one y
38
39. Domain
Set of all first (input) values
39
40. Range
Set of all second (output) numbers
40
41. Vertical line test
F(x) is a function IFF any vertical line intersects f(x) at no more than one point.
41
42. Def. value of a function
F(x)=y
42
43. Definition of composite functions
(F•g)(x)=f(g(x))
43
44. Steps for finding the inverse of a function
1. Switch x and y
| 2. Solve for y
44
45. Horizontal line test
F-1(x) is a function IFF any horizontal line intersects f(x) at no more than one point.
45
46. Test for inverses
F(g(x))=g(f(x))=x
46
Bonus: addition fraction rule:
a/b+c/d=(ad/+bc)/bd
47
47. Horizontal shift
F(x-h)
48
47.
| 2. Horizontal shrink/stretch
F(bx)
49
47.
| 3. Horizontal flip
F(-x)
50
47.
| 4. Vertical shift
F(x)+k
51
47.
| 5. Vertical stretch/shrink
A*f(x)
52
47.
| 6. Vertical flip
-f(x)
53
48. Standard form of a quadratic equation
Ax^2+bc+c=0
54
49. Solving x^2=a for x:
X=+/square root a
55
50.
| 1. Product property
✔Ab=✔a*✔b if a >/= 0, b>/=0
56
50.
| 2. Quotient property
✔A/b=✔a/✔b if a >/=0, b>0
57
51. Simplest radical form
1. No perfect square factors in radicand
2. No fractions in radicand
3. No radicals in denominator
58
52. Pythagorean Thm.
a^2+b^2=c^2
59
53. Zero Product Property
If ab=0, then a=0 or b=0
60
54. Factoring the difference of squares:
a^2-b^2=(a-b)(a+b)
61
55. Factoring perfect square trinomials
1. a^2+2ab+b^2=(a+b)^2
| 2. a^2-2ab+b^2=(a-b)^2
