1. Math Exam Review Semester 2
By Kyle Skarr and Ryan McLaughlin

2. Solving First Power Equations in one Variable
Example problem 4x=24-2x
How to solve
4x=24-2x
+2x +2x
6x=24
/6 /6
X=4

3. Solving First Power Equations in one Variable continued
Equations containing fraction coefficients
Example equation
Least common denominator is 20

4. Solving First Power Equations in one Variable continued
Equations with variables in the denominators-
Example
Multiply by 2x because it is the least common denominator

5. Solving First Power Equations in one Variable continued
Special cases-
Example
All real
No solution

6. Properties Addition Property of Equality
If a=b then a+c = b+c and c+a = c+b

7. Properties Multiplication Property of Equality
If a,b,c are any real numbers and a=b then ca=cb and ac=bc

8. Properties Reflexive Property of Equality
If a is a real number then a=a

9. Properties
Symetric property of equality
a=b then b=a

10. Properties
Transitive property of equality
If a=b and b= c then a=c

11. Properties
Associative property of Addition
(a+b) + c = a + (b+c)

12. Properties
Associative property of multiplication
(ab)c = a(bc)

13. Properties
Commutative Property of Addition
a+b = b+a
ab=ba

14. Properties
Commutative property of multiplication

15. Properties
Distributive Property
a(b+c) = ab+ac

16. Properties
Prop. Of opposites or inverse property of addition
5+(-5)=0

17. Properties Property of reciprocals or inverses prop. Of multiplication
For every nonzero real number a, there is a unique 1/a

18. Properties Identity property of addition
There is a unique real number 0 such that for every real number a
a+0=a 0+a=0

19. Properties Identity property of multiplication
There is a unique real number 1 such that for every real number a,

20. Properties
Multiplicative property of zero

21. Properties Closure property of addition For all real numbers a and b:
a+b is a unique real number

22. Properties Closure property of Multiplication
For all real numbers a and b:
ab is a unique real number

23. Properties
Product of powers property

24. Properties
Power of a product property

25. Properties
Power of a power property

26. Properties
Quotient of powers property
Subtract the exponents

27. Properties
Power of a quotient property

28. Properties
Zero Power Property

29. Properties
Negative power property

30. Properties Zero product property
If (x+3)(x-2)=0, then (x+3)=0 or (x-2)=0

31. Properties
Product of roots property

32. Properties
Quotient of roots property

33. Properties
Root of a power property

34. Properties
Power of a root property

35. Solving first power inequalities in one Variable
Examples of a first power inequalities-
When something is equal to another number, then you use a dark circle, but when it isn’t equal to, you use a a non dark circle. 5 2

36. Solving first power inequalities in one Variable
Disjunction
A Disjunction uses the word or
Example- 1 3

37. Solving first power inequalities in one Variable
Conjunctions
conjunctions include and
Example- x<3 and x>1
Or 3>x>1 1 3

38. Linear equations in two variables
Slope of lines
Horizontal: 0
Vertical: Undefined
Linear: rise over run

39. Linear equations in two variables
Equations of lines
Slope intercept form- Y=mx+b
Standard form: ax+by=c
vertical X= a constant
Horizontal y=a constant

40. Linear equations in two variables
In order to graph a line you need
A point and slope
Or two point
Or an equation
Y intercept
slope
Y intercept

41. Linear equations in two variables
How to find intercepts
X intercept- look for a point on the graph where y equals zero
Y intercept- look for a point on the graph where x equals zero

42. Linear equations in two variables
How and when to use the point slope formula-
You use the point slope formula when you don’t know the y-intercept

43. Linear systems
Substitution Method-
Example-
Plug 15-x in for y

44. Linear systems Addition and Subtraction Method (Elimination) Example-
Since the y’s already cross each other out there is no need to use the least common denominator

45. Linear systems
You can use graphing but it only gives an estimate

46. Linear systems Check for understanding of terms-
Dependent system- Infinite set or all points (if same line is used twice)
Inconsistent system-Null set (if they are parallel)
Consistent system-One point (if they cross)

47. Factoring Methods GCF- always look for the GCF first
Difference of Squares- used for binomials
Sum or Difference of cubes- used for binomials
PST- For trinomials
Reverse of FOIL- Trinomials
Grouping- Grouping

48. Factoring
GCF
Example-

49. Factoring
Difference of Squares

50. Factoring
Sum or difference of cubes

51. Factoring
Perfect Square Trinomial

52. Factoring
Reverse Foil-
Trial and error

53. Factoring
Grouping-
Example-

54. Rational expressions
Simplify by factor and cancel-

55. Rational Expressions Addition and Subtraction of rational expressions
Addition-use LCM to cancel out the variable

56. Rational Expressions Subtraction of rational expressions
Use LCM to cancel out the variables-
Example-

57. Rational Expressions
Multiplication and division of rational expressions
Example-

58. Quadratic equations in one variable
Solve by factoring
Example

59. Quadratic equations in one variable
Solve by taking the square root of each side
Example-

60. Quadratic equations in one variable
Solve by completing the square
Example-
Take half of x and square it

61. Quadratic equations in one variable
Quadratic formula
Example
Quadratic Equation

62. Quadratic equations in one variable
What does the discriminant tell you?
Discriminant is the value of

63. Functions What does f(x) mean?
F(x)= name of independent variable or argument
Usually equal to “Y”
Not all relations are functions (those that are undefined)
Ex.

64. Functions range and domain of a function Domain- set of all x values
Range- set of all y values
Ex. Ex.(2)

65. Functions
Ordered pairs
Ex. (1,1) (5,5)
Slope equals

66. Functions Quadratic functions How to graph a parabola
If A>0 then it opens up
If A<0 then it opens down
Vertex- is equal to a –b/2a to find x
Plug into f(x) to find y
Axis of symmetry- vertical through the vertex so x= -b/2a

67. Functions How to graph a parabola cont. Y int. let x=0 or f (0)
X int. let y=0 or f (x) (0)
Factor and find solutions

68. Simplifying expressions with exponents
A.) Product of powers

69. Simplifying expressions with exponents
B.) quotient of powers

70. Simplifying expressions with exponents
C.) Power of a Power

71. Simplifying expressions with exponents
D.) Power of a Product

72. Simplifying expressions with exponents
E.) Power of a Quotient

73. Simplifying expressions with radicals
A.) Root of a Power
B.) Power of a Root

74. Simplifying expressions with radicals
C.) Rationalizing the Denominator
Use the multiplication identity property

75. Word Problems Example 1-
A baseball game has 1200 people attending. Adult tickets are 5 dollars an student tickets are two dollars. The total amount of money made a tickets was 3660 dollars. The visiting team is entitled to half of the adult tickets sales. How much money does the visiting team get?

76. Word Problems Example 2-
Al left MUHS at 10:30 AM walking 4 mi/hr. Bob left MUHS at noon running to catch up with Al. If Bob overtakes Al at 1:30 PM how fast was he running.
Step 1- label variables
Step 2- write an equation
rate
time
distance Al
Bob
3 hrs
12 mi
Equal distance
Step 3- solve for the variable
Step 4
Bob’s rate-

77. Word Problems Example 3-
A serving of beef has 320 more calories than a serving of chicken. The calories in 3 servings of beef is equal to the calories in seven servings of chicken. Find the number of calories in a serving of each meat.

78. Word Problems Example 4-
The length of a rectangle is 3 cm less then twice the width. The perimeter is 34 cm more then the width. Find the length and width of the rectangle?
2w-3 w w
2w-3
8cm
13 cm

79. Line of Best fit or Regression line
You use to the line of best fit to estimate what the average is for the data
Your TI-84 calculator can determine the line of best fit for you

80. Line of Best fit or Regression line
What is the best fit line here?
Draw a line on the graph if you want.