# Algebra

Home > Preview

The flashcards below were created by user atcannon on FreezingBlue Flashcards.

1. Natural numbers
• Includes numbers we use for counting:
• 1,2,3,4,5,6,7,8,9,...
2. Whole numbers
• Includes natural numbers together with 0:
• 0,1,2,3,4,5,6,7,8,9,...
3. Integers
• includes natural numbers, 0, and the negatives of the natural numbers:
• -5,-4,-3,-2,-1,0,1,2,3,4,5,...
4. Prime numbers
• Are natural number greater than 1 that are divisible by 1 and themselves:
• 2,3,5,7,11,13,17,19,23
5. Composite numbers
• Are natural numbers greater than 1 that are not prime:
• 4,6,8,9,10,12,14,15,16,18,20,21
6. Even integers
• Are integers that are exactly divisible by 2:
• -8,-6,-4,-2,0,2,4,6,8,...
7. Odd integers
• Are integers that are not exactly divisible by 2:
• -9,-7,-5-3-1,1,3,5,7,9,...
8. Rational numbers
• a a is an integer and b is a nonzero integer
• b
9. Irrational numbers
x x is a nonterminating, nonrepeating decimal
10. Real numbers
x x is a terminating decimal, a repeating decimal, or a nontermination nonrepeating decimal
11. Interval notation
• (-5,8]
• parenthesis indicates that endpoints are not included, brackets indicates that the endpoints are included
12. Compound Inequalities
Expressions that involve more than one inequality and involves the word (or,and) so it can be written in interval notation with the union symbol (U, upside down for and)
13. Absolute value
is the distance on a number line between 0 and the point with the coordinate.
14. Sum
Result when two numbers are added
15. Difference
Result when one number is subtracted from another number
16. Product
Result when two numbers are multiplied
17. Quotient
• Result when two numbers are divided
• Division by 0 is undefined
18. Mean
The Sum of the values divided by the number of values
19. Median
• The middle value
• if odd, choose the middle
• if even, find the mean of the middle two values
20. Mode
Value that occurs mors often
21. Perimeter
• Distance around a figure
• Square P=4s
• Rectangle P=2l+2w
• Triangle P= a+b+c
• Trapezoid P=a+b+c+d
22. Circumfrence
• Distance around a circle
• C=pie * D
• (pie is approximately)
23. Communitive Property
• a+b = b+a
• ab = ba
24. Associative Property
(a+b) + c= a + (b+c)
25. Distributive Property
a(b+c) = ab + ac
26. The product Rule of exponents
xm xn = xm+n
27. Power Rules of Exponents
• (xm)n = xm*n
• (xy)n = xn*yn
• (x/y)n= xn/yn
28. Zero exponents
x0=1
29. Negative Exponents
• x-n = 1/xn
• and
• 1/x-n = xn
30. Quotient Rule
xm/xn = xm-n
31. Fractions to Negative Powers
(x/y)-n = (y/x)n = yn/xn
32. Equation
A statement indicating that two quantities are equal
33. Conditonal equations
Equations have exactly one solution
34. Identiy
Equation that is satisfied by every number for which both sides of the the equation are defined. All real numbers
Equation that has no solution
36. Right angle
angle whose measure is 90 degree
37. Straight angle
Angle whose measure is 180 degree
38. Acute anle
Angle whose measure is greater than 0 degree but less than 90
39. Complementary angles
the sum of two angles equals 90 degrees
40. Supplementary anles
the sum of two angles equals 180 degrees
41. Coordinate System
• x-axis-horizontal line
• y-axis-vertical line
• origin-point where axis cross
• coordinate plane-two axis form this
• quadrants-coordinate plane divide into four regions
• x-coordinate-point on x axis
• y-coordinate-point on y axis
• ordered pair-when the order of the coordinate is important
42. Linear equation
general form
• When the graph of an equation is a line
• Ax + By = C
• A,B,C are constants
• x,y are variables
43. Y-intercept
Point of a line where the line intersects the y-axis
44. X-intercept
Point of a line where the line intersects the x-axis
45. Horizonatal and Vertical lines
• the graph of x=a is a vertical line with x-intercept at (a,0)
• the graph of y=b is a horizoneal line with y intercept at (0,b)
46. Midpoint
the middle point of a line with ends at P(x1,y1) and Q(x2,y2) calculated:

(x1+x2/2 , y1=y2/2)
47. Slope of the line
Constant rate of change of line passing through points (x1,y1) and (x2,y2) calculated:

• m= Change in y/Change in x
• m= y2-y1/ x2-x1
• m+ rise/run
48. Slopes of Horizontal and Vertical lines
• all horizontal lines (lines with equations of the form y=b) have a slope of O
• all vertical lines (lines with equations of the form x=a) have no defined slope
49. Slope of parallel lines
• Nonvertical parallel lines have the same slope, and lines having the same slope are parallel
• Since vertical lines are parallel, lines with no defined slop are parallel
50. Negative reciprocals
Two real numbers a and b if ab=-1
51. Slopes of perpendicular lines
If two nonvertical lines are perpendicular, their slopes are negative reciprocals.
52. Point slope form
• the point slope equation of a line passing through P(x1,y1) and with the slope M is:
• y-y1=m(x-x1)
53. Slope-Intercept Form
• The slope-intercept equation of a line with slope m and y-intercept (0,b) is:
• y=mx+b
54. Slope and Y-intercept from the general form
• Ax+By=C
• slope = - a/b
• y-inetercept = (0, c/b)
55. Relations
Sets of ordered pairs
56. Domain of the relation
the set of all the first components in the relation
57. Range of the relation
The set of all the second components in the relation
58. Function
Is any set of ordered pairs (a relation) in which each first component determines exactly one second component
59. Vertical line test
Determines whether the graph of an equation represents a function. If every vertical line that intersects a graph does so exactly once, the graph represents a function.
60. Function Notation
The notation y= f(x) denotes that the variable is a function of x.
61. y is a Function of x
An equation, table, or graph in x and y in which each value of x (the input) determines exactly one value of y (the output) is a function of x.
62. Graph of a function
the graph of the ordered pairs (x,f(x)) that define the function
63. Linear function
• a function defined by an equation that can be written in the form:
• f(x)=mx+b
• or
• y=mx+b
64. Squaring function
• f(x)=x^2 (or y=x^2)
• parabola
65. Cubing function
f(x)=x^3 (or y=x^3)
66. Absolute value function
• f(x)=lxl (or y=lxl)
• V shaped graph
67. Horizontal Translations
• If f is a fuction and k is a positive number, then:
• the graphe of f(x-k) is identical to the graph of f(x), except that it is translated k units to the right
• The graph of f(x+k) is identical to the graph of f(x), except that it is translated k units to the left.
68. Vertical translations
• If f is a function f and k is a positive number, then:
• The graph of f(x)+k is identical to the graph of f(x), except that it is translated k units upward
• The graph of f(x)-k is identical to the graph f(x), except that it is translated k units downward
69. Reflection of a Graph
The graph of y=-f(x) is the graph of f(x) reflected about the x-axis
70. Solving the system
The process of finding the ordered pair that satisfies both equations in the system
71. Consistent system
When the system has a solution
72. Inconsistent system
When the system has no solution, the solution set is 0 (put line thru the zero)
73. Dependent system
When the system has infinately many solutions, 2 equations give the same line.
74. Substitution method
• 1. solve one equation for one of its variables
• 2. substitute the result from Step 1 into the other equation and solve
• 3. find the value of the other variable by substittuting the value from step 2 into one of the original equations.
• 4. State the solution
• 1. write both equations in general form
• 2. if necessary, multiply the terms of one or both equations to cake the coefficients on one of the variables differ only in sign
• 3. Add the equation and solve.
• 4. substitute the value in step 3 into either of the original equations and solve
• 5. state the solution
76. Solving a system of three linear equations in three variables
• 1. pick any two equations and elimate a variable
• 2. pick a different pair and elinate the same variable
• 3. solve the resulting pair of two equations in two variables
• 4. find the value of the third variable, substitute the values from step three into one of the original equations with three variables and solve the equation

### Card Set Information

 Author: atcannon ID: 133165 Filename: Algebra Updated: 2012-02-08 12:11:17 Tags: Intermediate Algebra Folders: Description: Test Chapters 1-3 Show Answers:

Home > Flashcards > Print Preview