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Math Study Sheet for Algebra
 

1.              What is the most important sentence in Algebra?

            Whatever you do to one side of an equation, you MUST also do to the other.

2.                List the Order of Operations.

       i)   Inner Inclusions

      ii)  Outer Inclusions

      iii)  Powers and Roots

     iv)  Multiplication and Division

      v)         Addition and Subtraction

3.                What property allows us to eliminate inclusions?

                  Distributive

4.                What property allows us to move addends and factors?

                  Commutative

5.                For addition and subtraction of signed numbers:

When the signs are the     same    , you take the      sum     .

When the signs are   different  , you take the   difference  .

The answer will have the same sign as the    larger    number.

  6.                For multiplication and division of signed numbers:

An odd number of negatives will produce a negative  answer.

An even number of negatives will produce a positive  answer.

Addition

7.                    Addend

            +         Addend

   -------------------------------

                           Sum

Subtraction

8.                  Minuend

            -    Subtrahend

  -________________

                  Difference

Multiplication

9.                      Factor

            ·           Factor

   __________________

                       Product

Division

10.               Dividend

            ÷        Divisor

   __________________

                     Quotient  

11.  What is another word for opposite?

            Inverse

12.  What are the Area and Perimeter of a Circle?

            A=πr2              P=2πr

13.  What are the Area and Perimeter of a Square?

            A=S2                P=4S

14.  What are the Area and Perimeter of a Rectangle?

            A=lw               P=2l+2w

15.  What are the Area and Perimeter of a Triangle?

            A=½bh            P=S1+S2+S3

16.  What is a 3-sided polygon called?

            Triangle

17.  What is a 4-sided polygon called?

            Quadrilateral

18.  What is a 5-sided polygon called?

            Pentagon

19.  What is a 6-sided polygon called?

            Hexagon

20.  What is a 7-sided polygon called?

            Heptagon

21.  What is an 8-sided polygon called?

            Octagon

22.  What is a 9-sided polygon called?

            Nonagon

23.  What is a 10-sided polygon called?

            Decagon

24.  What is an 11-sided polygon called?

            Undecagon

25.  What is a 12-sided polygon called?

            Dodecagon

26.  What is a 13-sided polygon called?

            13gon   (14gon, 15gon, 16gon,...)

27.  What does equilateral mean?

            Equal Sides

28.  What does equiangular mean?

            Equal Angles

29.  What does regular mean?

            Equilateral and Equiangular

30.  What is a scalene triangle?

            No equal sides

31.  What is an isosceles triangle?

            Two equal sides

32.  What is an equilateral triangle?

            Three equal sides

33.  What is an obtuse triangle?

            One obtuse angle

34.  What is an acute triangle?

            All acute angles

35.  What is a right triangle?

            One right angle

36.  How many degrees are in a triangle?

            180º

37.  What is an acute angle?

            Less that 90º

38.  What is a right angle?

            Equal to 90º

39.  What is an obtuse angle?

            Greater than 90º and Less than 180º

40.  What is a straight angle?

            Equal to 180º

41.  What is a reflex angle?

            Greater than 180º

42.  What is a point?

            Defines a location with no width, height, or length

43.  What is a line?

            Infinite length with no width or height

44.  What is a ray?

            Part of a line with a definite start point but no end point

45.  What is a line segment?

            Part of a line with a definite start point and end point

46.  What is an angle?

            Two rays with a common endpoint

47.  What is a plane?

            Infinite in two dimensions with zero third dimension

48.  What are intersecting lines?

            Two lines with one common point

49.  What are perpendicular lines?

Intersecting lines that form right angles

50.  What are parallel lines?

            Lines in a plane that do not intersect

51.  What is a circle?

            All points in a plane a given distance from center

52.  What is a radius?

            Line segment from center to circle

53.  What is a chord?

            Line segment from one point on circle to another point on circle

54.  What is a diameter?

            Chord through center

55.  What is a tangent?

            Line with exactly one point on circle

56.  What is an equilateral quadrilateral?

            Rhombus

57.  What is an equiangular quadrilateral?

            Rectangle

58.  What is an equiangular, equilateral, quadrilateral?

            Square

59.  What is a trapezoid?

            Quadrilateral with exactly two parallel sides

60.  What is a parallelogram?

            Quadrilateral with two pairs of parallel sides

61.  What is ‘is’ in Algebra?

            Equals (=)

62.  What is ‘of’ in Algebra?

            Times (X)

63.  What is ‘percent’ in Algebra?

            Divided by 100

64.  What are the two parts of a term?

            Coefficient and Variable

65.  What is the numerical portion of a term called?

            Coefficient

66.  What is the non-numerical portion of a term called?

            Variable

67.  When may terms be added or subtracted?

            When they are like

68.  When are terms considered ‘like’?

            When they have the same variable part

69.  Give an example of the distributive property using a, b, and c.

            a(b+c)=ab+ac

70.  Give an example of the commutative property using a, b, and c.

            a+b+c=c+b+a or abc=cba

71.  What is the identity number for addition?

            0  (Ex   DUCK + 0 = DUCK)

72.  What is the identity number for subtraction?

            0  (Ex   DUCK − 0 = DUCK)

73.  What is the identity number for multiplication?

            1  (Ex   DUCK • 1 = DUCK)

74.  What is the identity number for division?

            1   (Ex  DUCK ÷ 1 = DUCK)

75.  What is another word for the perimeter of a circle?

            Circumference

76.  What is another word for average?

            Mean

77.  What is anything raised to the zero power?

            One

78.  What is anything raised to the first power?

            Itself

79.  What is a ratio?

            Fraction

80.  What is a proportion?

            An equality of ratios

81.  What do you always do to a proportion to solve it?

            Cross Multiply

82.  Does p equal 3.14?

            NO!

83.  What is √    called?

            Radical Sign

84.  Natural numbers are also called what?

            Counting Numbers

85.  What are the natural numbers?

            {1,2,3,…}

86.  What are the whole numbers?

            {0,1,2,…}

87.  What are integers?

            {…,-3,-2,-1,0,1,2,3,…}

88.  What are rational numbers?

            Numbers that may be represented as a ratio of integers

89.  What are irrational numbers?

            Numbers that may not be represented as a ratio of integers

90.  What are the four symbols of inclusion?

            {Brackets},|Absolute Value|,[Braces],(Parentheses)

91.  What is Loewy’s first Law?

            Units must be included in the answer if they are given in the problem.

92.  What is Loewy’s second Law?

            All answers must be reduced.

93.  What is Loewy’s third Law?

            You must show all work.

94.  What is Loewy’s fourth Law?

            Never substitute an approximation for pi (π).

95.  What is Loewy’s fifth Law?

            All assignments must be received complete and on time.

96.  What is Loewy’s sixth Law?

            Improper fractions are acceptable answers (see law 2).

97.  What is Loewy’s seventh Law?

            Mixed numbers are acceptable answers (see law 2).

98.  What is Loewy’s eighth Law?

            Mercy and Grace are directly proportional to personal motivation and effort.

99.  What is Loewy’s ninth Law?

            Unless otherwise instructed, any legitimate methods of solving are acceptable.

100.  What is Loewy’s tenth Law?

            Wailing and Gnashing of teeth are strictly prohibited (in class).