Integrated Algebra 1

1

• Integrated Algebra 1
• Vocabulary

• 2008-2009

2

5 5 -5 5 -23 23 Absolute
value 61 61 -0.6 0.6 ½ ½

• y x 3
• Absolute value function
• y 4x 8- 9

3

• Addition counting principle
• If two events E1 and E2 can
• occur independently
• in exactly m ways and n ways
• respectively, then
• either of the two events
• can occur in (m n) ways.

2 6 8

• Adjacent angles
• 1 2
• 3 4
• 5 6
• 7 8

4

• Altitude of a triangle

• Angle bisector

5

• Area model
• for polynomial
• arithmetic (2x 3)(x 1) 2x2 5x 3

x x 1 1 1
x 1

• Asymptote

For this graph, the x and y axes are the
asymptotes
6

• Average rate of change
• For f(x) the average For f(x) x3 3x2 from
• rate of change is (-1,2) to (1,4), the average
  rate
• of change is

• Axis of
• symmetry

X 2
7

• Base angles of a trapezoid
• A B
• C D

• Base

8

• Best-fitting
• line

• Biased
• YES Asking Gwinnett County students to name the
  Georgia school system with the best sports teams.
• NO Asking random Georgia public school students
  which school system has the best sports teams.

9

• Biased question
• YES Would you rather have a juicy hamburger or
  the usual cheese sandwich?
• NO Do you like movies directed by Steven
  Spielberg?

• A if and only if B
• Biconditional statement
• Im breathing if and only if Im alive

10

• 3x2 5 2x2 4x 6
• Binomial
• 8x x3 9 x-3 5

• (x y)0 1
• (x y)1 x y
• (x y)2 x2 2xy y2
• (x y)3 x3 3x2y 3xy2 y3
• (x y)4 x4 4x3y 6x2y2 4xy3 y4
• (x y)5 x5 5x4y 10x3y2 10x2y3 5xy4
  y5

Binomial expansion
11

• Centroid

• Circumcenter

12

• Combination
• Given A, B, C, D
• Combinations
• 1. AB or BA 2. AC or CA 3. AD or DA
• 4. BC or CB 5. BD or DB 6. CD or DC

• Compound events
• Roll a 2 or an odd number Pick an ace and a
  spade

13

• Compound proposition
• FALSE 2 is an odd number AND 4 is a perfect
  square
• TRUE 2 is an odd number OR 4 is a perfect square

• Compound statements

14

• Conclusion
• conclusion

• Concurrent

15

• Conditional probability
• Event A is randomly selecting a club from a deck
  of cards
• Event B is randomly selecting a second club

• Conditional Statement
• hypothesis
  conclusion

16

• Congruent figures

• All odd numbers are prime
• Conjecture
• The product of any two odd integers is odd

17

• Contrapositive
• Statement
• Contrapositive

• Convenience sample
• A convenience sample chooses the individuals that
  are easiest to reach or sampling that is done
  easy. Convenience sampling does not represent the
  entire population so it is considered bias.

18

• Converse
• Statement
• Converse

• Coordinate proof
• Given Triangle A(1,1), B(4,4) and C(6,2)
• Prove Triangle ABC is a right triangle

19

• Corresponding parts
• A D
• F
• B C E

• Counterexample
• Conjecture All prime numbers are odd
• Counterexample 2 is a prime number that is not
  odd

20

• y x2 5 y 4x3
• Cubic function
• y -2x3 x2 9x y 3x4 7

• Deductive reasoning
• Deductive reasoning is when you move from things
  you know or assume to be true to conclusions that
  must follow from them. The most famous example of
  deduction is
• Socrates is a man.
• All men are mortal.
• Therefore, Socrates is mortal.
• The first two statements are premises, and the
  third statement is a conclusion. By the rules of
  deduction, if the first two statements are true,
  the conclusion must be true.

21

• 10a2b2 6m2n 8
• degree 4 degree
  3 degree 0
• Degree of a monomial
• xy 2x3y4 7d3
• degree 2 degree 7
  degree 3

• 9 2x2 2b2 10 b3
• degree 2
  degree 3
• Degree of a polynomial
• 4a 5a4 8a2 3m 4
• degree 4
  degree 1

22

• Dependent events
• Randomly drawing a card and then randomly drawing
  another card without replacing the first one

• Dependent
• variable

y2x-5
23

• Deviation from the mean
• 14, 17, 18, 19, 20, 24, 24, 30, 32 mean 22
• the deviation of 30 is 8
• the deviation of 17 is 5

• Diagonal

24

• Distance formula
• The distance between (-1,3) and (5,2) is

• Distance from a point to a line

P
m
25

• Domain

y2x-5

• End
• behavior

26

• Equidistant

Y
Z
X
Y is equidistant from X and Z

• Equivalent statements

27

• f(-x) f(x)
• Even function
• Examples
• f(x) x f(x) x2

• Excluded value

excluded value 3 excluded value 0
excluded value 3 -5
28

• E p1x1 p2x2 p3x3 pnxn
• Expected value
• Two thousand raffle tickets are sold for 1 each.
  The one prize awarded is worth 400. What is
  the expected value if you purchase one ticket?

• Exterior angles of a polygon

29

• Extraneous
• solution

BUT, only 2 is a solution to the original
problem. SO, -3 is an extraneous solution.

• Factor by grouping
• X3 3x2 5x 15
• (X3 3x2) (5x 15)
• x2(x 3) 5(x 3)
• (x 3)(x2 5)

30

• Factor completely
• x3 x
• not factored completely factored
  completely
• x(x2 1) x(x2 1)
• x(x 1)(x -1 )

• Family of functions

Linear functions f(x) mx b
Radical functions y vx
Quadratic functions y ax2 bx c
31

• Flow proof

• d rt I Prt
• Formula
• A bh C ?r2 E mc2

32

• Function
• y 3x 5
• y x2

• f(x) mx b y 2x2 3x 5
• Function notation
• y mx b f(x) 2x2 3x - 5

33

• Hypotenuse

• Hypothesis
• hypothesis

34

• If-then form
• If it is Sunday, then there is no school.

• Implication

35

• Incenter

• Independent events

36

• Independent
• variable

y2x-5

• Indirect proof
• Steps in an Indirect Proof
• Assume that the opposite of what you are trying
  to prove is true.
• From this assumption, see what conclusions can be
  drawn. These conclusions must be based upon the
  assumption and the use of valid statements.
• Search for a conclusion that you know is false
  because it contradicts given or known
  information.  Oftentimes you will be
  contradicting a piece of GIVEN information.
• Since your assumption leads to a false
  conclusion, the assumption must be false.
• If the assumption (which is the opposite of what
  you are trying to prove) is false, then you will
  know that what you are trying to prove must be
  true.

37

• Inductive reasoning
• Inductive reasoning is when you move from a set
  of examples to a theory that you think explains
  all the examples, as well as examples that will
  appear in the future. The simplest kind of
  induction looks like this
• The sun came up this morning.
• The sun came up the day before that.
• The sun came up the day before that. . .
• Therefore, the sun comes up every day, and will
  come up tomorrow too.

• Input

y2x-5
38

• Interior angles of a polygon

• Interquartile range
• 18, 23, 28, 29, 36, 42
• Lower quartile Upper quartile
• Interquartile range 36 23 13

39

• Inverse
• Statement
• Inverse

• Isosceles
• trapezoid

40

• Kite

• -7x3 x2 8 4y2 6y4 y3 9
• Leading coefficient
• 5x 8 3a 2a2 7 9x

41

• Least common denominator of rational expressions
• 1. Factor the denominators 2. Find the LCD

Find the LCD

• Leg of a right triangle

Hypotenuse
Leg
Leg
42

• Legs

• Linear extrapolation
• "Extrapolation" is the term you should use when
  you have to calculate a value before or beyond
  the given values ("extra" is Latin for outside).

43

• Linear interpolation
• "Interpolation" means that you have to calculate
  a value between two given values ("inter" is
  Latin for between).

• Linear pair

44

• Logically equivalent
• Two propositions whose truth tables have the same
  last column are called logically equivalent. To
  test whether or not two propositions are
  logically equivalent we make a truth table for
  each of them and compare their last columns. If
  they are identical then the two propositions are
  logically equivalent, otherwise they are not.

• Lower quartile
• 18, 23, 28, 29, 36, 42
• Lower quartile

45

• Maximum
• value

• Mean
• 12, 14, 17, 27 3, 4, 7
• 1214172770 34714
• 70 4 17.5 14 3 4.6

46

• Mean absolute deviation
• Data Set 2, 2, 4, 8, 14 Mean (224814)/5
  6
• Mean absolute deviation 2-6 2-6 4-6
  8-6 14-6
• 
  6
• 4 4 2 2 8 20 3.3
• 6 6

• Measure of
• dispersion

variance
range
standard deviation
47

• Median
• 12, 14, 17, 27 3, 4, 7
• 141731
• 31 2 15.5 4

• Median of a triangle

48

• Midpoint
• A M B

• Midpoint
• formula
• The midpoint of a line segment
• with endpoints (-1,-2) (3,-4) is

49

• Midsegment of a trapezoid

• Midsegment of
• a triangle

50

• Minimum
• value

• 1,3,4,4,5,7
• Mode
• 23,23,24,24,24,25,26

51

• 10a2b2 6m2n 8
• Monomial
• xy 2x3y4 7d3

• Multiplication counting principle
• 6 shirts x 2 pants
  12 outfits

52

• Mutually exclusive events
• Rolling a 3 and rolling
• an even number are
• mutually exclusive

• 5! 5 4 3 2 1 120
• n factorial (n!)
• 0! 1 3! 3 2 1 6

53

• Negation
• Statement Math is FUN!! ?
• Negation Math is not fun.

• f(-x) -f(x)
• Odd function
• Examples
• f(x) x f(x) x3

54

• Orthocenter

• Output

y2x-5
55

• Overlapping events
• Rolling a 3 and rolling an odd
• number are overlapping events

• Parabola

56
Parallel Yes Yes No Yes

• Parallelogram

57

• Parent linear
• function

f(x) x

• Parent quadratic
  function

y x2
58

• Parent square root function

• Pascals triangle

59

• 4 22 49 72 81 92
• Perfect square
• x26x9 (x3)2 x2-10x25 (x-5)2

• Permutation
• Given A, B, C
• Permutations
• 1. ABC 2. ACB 3. BAC
• 4.BCA 5. CAB 6. CBA

60

• Perpendicular
• Yes No Yes

• Perpendicular
• bisector

61

• Perpendicular lines
• Yes No Yes

• Point of concurrency

62

• 9 2x2 2b2 10 b3
• Polynomial
• 4a 5a4 8a2 3m 4

• Population
• Population Sample

63

• Postulate
• A postulate is an assumption, that is, a
  proposition or statement, that is assumed to be
  true without any proof. Postulates are the
  fundamental propositions used to prove other
  statements known as theorems.

• Proof
• A proof is a logical argument demonstrating that
  a specific statement, proposition, or
  mathematical formula is true.

64

• Propositional form
• Statements that include the words and, or, not,
  if-then, and if-and-only-if.

• 4x2 3x 6 0 x2 12 8x
• Quadratic equation
• ax2 bx c 0 x2 x 20

65

• Quadratic functions
• f(x) ax2 bx c
• f(x) -2x2 x - 1
• f(x) x2 3x 2

• Quadrilateral

66

• Quartile
• 18, 23, 28, 29, 36, 42
• Lower quartile Upper quartile

• Radical conjugates

67

• Radical equation
• A "radical" equation is an equation in which the
  variable is hiding inside a radical symbol (in
  the radicand).
• is a radical equation is NOT a radical equation

• Radical
• expression

68

• Radical function

• Radicand

69

• Random sample
• In statistical terms a random sample is a set of
  items that have been drawn from a population in
  such a way that each time an item was selected,
  every item in the population had an equal
  opportunity to appear in the sample.

Range
y2x-5
70

• Rate of change

• Rational
• equation

71

• Rational
• expression

• Rational
• function

72

• Rationalizing
• the
• denominator

• Rectangle

73

• Reflection
• If y f(x), then
• y f(-x) is its reflection
• about the y-axis,
• y -f(x) is its reflection
• about the x-axis.
• 
  Original reflected over x-axis
  reflected over y-axis

• Representative sample
• A random sample that accurately reflects the
  characteristics of a population.

74

• Rhombus

• Roots
• Solve (x - 3)(x 6) 0 Solve 6x2
  12x 0
• x - 3 0 or x 6 0 6x(x 2)
  0
• x 3 or x -6 6x 0
  or x 2 0
• roots x 0 or x
  -2

75

• Self-selected sample
• A type of convenience sample comprising research
  participants or subjects who have volunteered to
  participate.

• (x1, x2, x3,) (a, ar, ar2, ar3,)
• Sequence
• (0, 1, 1, 2, 3, 5,) (4, 6, 8, 10)

76

• Simplest form of a radical expression

• Simplest form of a rational expression

77

• Slope
• y mx b

Slope-intercept form y mx b slope
y-intercept
78

• Square

• Square root

79

• Square root function

• Statement
• A fact or assertion offered as evidence that
  something is true .

80

• Stratified random sample
• A random sample of a population in which the
  population is first divided into distinct
  subpopulations, or strata, and random samples are
  then taken separately from each stratum.

• Survey
• A collection of information about members of a
  population.

81

• Systematic sample
• In a systematic sample every nth item is included
  in the sample.

• Terms
• 3x2 4x 7 6y 2b
• term term term term term

82

• Theorem
• A theorem is a statement that can be demonstrated
  to be true by accepted mathematical operations
  and arguments.

• Transformation

rotation
reflection
dilation
translation
83

• Transversal

• Trapezoid

84

• 3y3 2y 16 5a4 8a2 4a
• Trinomial
• 18c6 14c4 11c 2x2 5x 1

• Truth value
• The truth value of a statement is T or 1 if it is
  true.
• The truth value of a statement is F or 0 if it is
  false.

85

• Two-column proof

• Upper quartile
• 18, 23, 28, 29, 36, 42
• Upper quartile

86

• 3x4 12 2m-7
• Variable
• 8y9 28 2a-4b6c

• Vertex

87

• h -16t2 vt s
• Vertical motion model
• Example To catch a frisbee, a dog leaps into
  the air with an initial velocity of 14 feet per
  second. Write a model for the height of the dog
  above the ground.
• h -16t2 14t because v 14 and s 0

• Vertical
• shift

2 -1
88

• Vertical
• shrink
• When y a f(x), multiply the y values of f(x)
  by a.  Leave the x values alone.  This is a
  vertical shrink (if a lt 1).

yf(x) y ½f(x)

• Vertical
• stretch
• When y a f(x), multiply the y values of f(x)
  by a.  Leave the x values alone.  This is a
  vertical stretch (if a gt 1).

yf(x) y2f(x)
89

• Volume model
• for polynomial
• arithmetic

x 2
x 2
x 4
(x 4)(x 2)(x 2) X3 8x2 20x 16

• x-intercept

90

• y-intercept

• Zero of
• a function