Mathematics Flashcards
1
Q
Define Whole Numbers
A
The numbers used in counting.
2
Q
Are negative numbers whole numbers?
A
No.
3
Q
Are fractions whole numbers?
A
No.
4
Q
Are decimals whole numbers?
A
No.
5
Q
Define Place Value
A
Depending on its place in the whole number, each digit of the number represents a number of units, tens, hundreds, thousands, and so on.
6
Q
What are the four fundamental operations performed on numbers?
A
Addition
Subtraction
Multiplication
Division
7
Q
What are the numbers that are added called?
A
Addends
8
Q
What is the answer obtained in addition?
A
Sum
9
Q
What is the number from which we subtract called?
A
Minuend
10
Q
What is the number being subtracted called?
A
Subtrahead
11
Q
What is the answer obtained in a subtraction?
A
Difference
12
Q
What is the number being multiplied called?
A
Multiplicand
13
Q
What is the number by which we multiply?
A
Multiplier
14
Q
What is the answer obtained in multiplication called?
A
Product
15
Q
What are factors?
A
Numbers being multiplied are factors of their product.
16
Q
What is the number being divided called?
A
Dividend
17
Q
What is the number by which we divide called?
A
Divisor
18
Q
What is the answer obtained in division?
A
Quotient
19
Q
What is the partial quotient?
A
The answer to a problem in division without the remainder.
20
Q
What is a total quotient?
A
The answer to a problem in division which includes the remainder.
(20/7 = 2 and 6/20)
21
Q
What is a proper fraction?
A
A fraction whose value is less than 1. In a proper fraction, the numerator is less than the denominator.
22
Q
What is an improper fraction?
A
A fraction whose value is equal to or greater than 1. In an improper fraction, the numerator is equal to or greater than the denominator.
23
Q
What are the terms of a fraction?
A
Its numerator and denominator.
24
Q
What are equivalent fractions?
A
Fractions that have the same value.
25
What is a mixed number?
A whole number plus a fraction.
26
How do you reduce a fraction to lowest terms?
Divide both numerator and denominator by the highest common factor.
27
What is a decimal?
A decimal or decimal fraction is a fraction whose denominator is 10, 100, 1000, or some other power of ten.
28
What is the rule for multiplying and dividing numbers by powers of ten?
Move the decimal point as many places as there are zeros in the power.
29
What is the difference between numerical and literal addends?
Numerical addends are numbers
| Literal addends are letters used to represent numbers being added.gTVbbb343::Xhm45 ,
30
What is the commutative law for addition?
Interchanging addends does not change their sum
31
What is a first degree equation in one unknown?
A first degree equation in one unknown is one that contains only one unknown and where the unknown has the exponent one.
32
What is a good rule for determining the order of inverse operations when balancing an equation?
Generally, undo addition and subtraction before undoing multiplication and division.
33
What is the rule of transposition in regards to equations?
To transpose a term from one side of the equation to the other, change its sign.
34
How are opposite terms different from one another?
Opposites are terms differing only in sign.
35
Define the Lowest Common Denominator (LCD)
The lowest common denominator of two or more fractions is the smallest number divisible by their denominators without a remainder.
36
How can a decimal be easily turned into a fraction?
A decimal may always be written as a fraction whose denomination is 10, 100 or a power of ten.
37
How can you clear decimals when solving an equation?
Clear of decimals by multiplying both sides of the equation by the denominator of the decimal having the greatest number of decimal places.
38
When is it not necessary to clear of decimals?
If the coefficient of the unknown is not a decimal, it may be better not to clear of decimals.
39
What qualifies an equation as a literal equation?
Literal equations contain two or more letters.
40
What are all formulas examples of?
Literal equations.
41
Which three undefined terms underlie the definitions of all geometric terms?
Point
Line
Plane
42
What are the basic characteristics of a plane?
A plane has length and width but no thickness.
43
What is the defining characteristic of a plane surface?
A plane surface is a surface such that a straight line connecting any two of its points lies entirely on it.
44
Two line segments having the same length are said to be _____.
Congruent
45
What is an equilateral polygon?
A polygon having congruent sides.
46
What is an equiangular polygon?
A polygon having congruent angles.
47
What is a regular polygon?
A polygon that is both equilateral and equiangular.
48
What is a chord?
A line joining any two points on the circumference of a circle.
49
What is a diameter?
A chord through the center of a circle.
50
What is a sector of a circle?
A part of the are of a circle bounded by an arc and two radii.
51
What is an equilateral triangle?
A triangle with 3 congruent sides and 3 equal angles of 60 degrees each.
52
What is an isosceles triangle?
A triangle that has at least 2 congruent sides and 2 congruent angles (called the base angles).
53
What is a scalene triangle?
A triangle that has no congruent sides.
54
What is a solid?
A solid is an enclosed portion of space bounded by plane and curved surfaces.
55
What is a polyhedron?
A polyhedron is a solid bound by plan surfaces only.
56
What is a prism?
A prism is a polyhedron two of whose faces are parallel polygons and whose remaining faces are parallelograms.
57
What is a rectangular solid?
A prism bound by 6 rectangles.
58
What is a pyramid?
A polyhedron whose base is a polygon and whose other faces meet at a point (its vertex).
59
What is a formula?
A formula is an equality expressing in mathematical symbols a numerical rule or relationship among quantities.
60
The area of a polygon or circle is the number of ____ _____ on its surface.
Square units
61
What is the formula for the area of a parallelogram?
A = BH
62
What is the formula for the area of a triangle?
A = BH/2
63
What is the formula for the area of a square?
A = S ^ 2
64
What is the formula for the area of a Trapezoid?
A = H/2 * (B + B')
65
What is the formula for the area of a Circle?
A = pi * r2 or A = (pi * d ^ 2)/4
66
The volume of a solid is the number of ____ ____ it contains.
Cube units
67
What is the formula for the volume of a rectangular solid?
L * W * H
68
What is the formula for the volume of a prism?
V = BH where B is the area of the base
69
What is the formula for the volume of a cylinder?
V = BH or V = pi * r ^ 2 * H where B is the area of the base
70
What is the formula for the volume of a cube?
V = e ^ 3 where e is the measure of one side of a face
71
What is the formula for the volume of a pyramid?
V = 1/3BH where B is the area of the base
72
What is the formula for the volume of a cone?
V = BH or V = 1/3 pi * r ^ 2 * H
73
What is the formula for the volume of a sphere?
V = 4/3 * pi * r ^ 3
74
What is the subject of a formula?
The letter that has been isolated and expressed in terms of the other letters.
75
What does it mean to transform a formula?
Transforming a formula is the process of changing the subject.
76
The x coordinate of a point, its _______, is its distance from the y axis.
Abscissa
77
The y coordinate of a point, its _______, is its distance from the x axis.
Ordinate
78
In stating the coordinates of a point, the x coordinate _______ the y coordinate, just as x ________ y in the alphabet.
preceeds
79
A linear equation is an equation whose _____.
graph is a straight line.
80
The ______ is where the line crosses an axis.
intercept
81
An equation of the first degree in two unknowns is one in which, after it has been simplified, _______.
contains only two unknowns, each of them in a separate term and having the exponent 1.
82
Is 2xy = 7 an equation of the first degree in two unknowns?
No because x and y are not in separate terms.
83
The graph of a first degree equation in one or two unknowns is a _______.
straight line
84
The graph of a first degree equation in only one unknown is _______.
The x axis, the y axis, or a line parallel to one of the axes.
85
If a point is on the graph of an equation, its coordinates ____ the equation.
satisfy
86
The ________ of two linear equations is the one and only one pair of values that satisfies both equations.
common solution
87
When are equations consistent?
If one and only one pair of values satisfies both equations.
88
When are equations inconsistent?
When no pair of values satisfies both equations (the lines are parallel)
89
When are equations dependent?
When any pair of values that satisfy one also satisfy the other.
90
How can the value of m be found in a linear equation with the form y = mx + b when looking at a table of coordinates?
By using the ratio of the y difference to the corresponding x difference, that is:
m = y difference/x difference = difference of two y values/corresponding difference of two x values
91
Think of M as the _____ of x in y = mx + b.
multiplier
92
What is the formula for determining midpoints of a line segment?
Xm = 1/2 * (x1 + x2) and Ym = 1/2 * (y1 + y2) where x1 and y1 are the coordinates of one end of the segment and x2 and y2 are the coordinates of the other end of the line segment
93
__________ are numbers that distinguish between above and below 0 numbers.
Signed numbers
94
Since signed numbers involve direction, they are also called _______.
Directed numbers
95
Descartes combined a horizontal and vertical number line to make a graph in _____.
1637
96
A _____ is the answer obtained by applying the exponent.
Power
97
What is a term?
A number or product of numbers.
98
Each of the numbers being multiplied is a ____ of the term.
factor
99
An _____ consists of one or more terms.
Expression
100
A _____ is an expression of one term.
Monomial
101
A ______ is an expression of two or more terms.
polynomial
102
A _____ is an expression of two terms
binomial
103
A _____ is an expression of three terms.
trinomial
104
How do you multiply the powers of the same base?
Keep the base and add the exponents.
105
How do you find the power of a power of a base?
Keep the base and multiply the exponents.
106
What is the commutative law of multiplication?
Changing the order of the factors does not change their product.
107
What is the distributive law of multiplying polynomials by a monomial?
To multiply a polynomial by a monomial, multiply each term of the polynomial by the monomial.
108
When you are dividing powers that have the same base, what do you do if the exponent of the numerator is larger than the exponent of the denominator?
Keep the base and subtract the smaller exponent from the larger.
109
When you are dividing powers that have the same base, what do you do if the exponent of the denominator is larger than the exponent of the numerator?
Make the numerator of the quotient 1 and, to obtain its denominator, keep the base and subtract the smaller exponent from the larger.
110
How do you divide a polynomial by a polynomial?
Set up as a form of long division in which the polynomials are arranged in descending order, and leave space for missing terms. Divide the first term of the divisor into the first term of the dividend and then multiply and subtract and bring down, just like in normal long division.
111
What are the first five digits of the golden ratio?
1.6181
112
What is the formula for the golden ratio?
(1 + square root of 5)/2
113
What equation does the golden ratio satisfy?
the square of the golden ratio = the golden ratio + 1
114
What are like terms or similar terms?
Terms having the same literal factors, each with the same base and same exponent.
115
What is an equality?
A mathematical statement that two expressions are equal.
116
What is the left hand side of an equality called?
the left member
117
What is an equation?
A conditional equality in which the unknown or unknowns may have only a particular value or values.
118
What is an identity?
An identity is an equality in which a letter or letters may have any values. An identity is an unconditional equality.
e.g. y + x = x + y or 2x + 5x = 7x
119
A solution to an equation is also called a ____ of the equation.
root
120
Inverse operations are two operations such that if one is involved with the unknown in the equation, then the other is ____.
Used to solve the equation.
| Addition and subtraction are the inverse of each other.
121
What is the rule of equality for all operations?
The same operation, using equal numbers, may be performed on both sides of an equation, except by 0.
