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Chapter 1 Flashcards

Math Foundations (82 cards)

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1
Q

What is math considered?

A

independent scientific discipline:
-analysis of geometric shapes & arithmetic of numbers
-analysis of certain conditions, characteristics and patterns

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2
Q

What are the two types of math?

A

-pure math
-applied math

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3
Q

What is pure math?

A

-focus on abstract, theoretical concepts
-they have no practical applications

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4
Q

What is applied math?

A

-application of math to solve practical problems e.g. in physics, medicine, and economics

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5
Q

What type of math is business math?

A

Applied math
Used in economics

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6
Q

What are the different subfields in business math

A

-functions theory
-differential calculus
-optimization
-financial math

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7
Q

How are numbers used in business math?

A

to quantify their economic quantities and relationships

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8
Q

Enumerate the sets of numbers

A

-real numbers
-natural numbers
-integers
-rational numbers
-irrational numbers

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9
Q

What is a natural number, what’s its symbol?

A

sign N:
all positive integers
from 1, 2, 3 - etc.
If you want to include 0, then N0

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10
Q

What is an integer, what’s its symbol?

A

sign Z:
numbers in the number line going left and right
-3, -2, 1, 0,, 1, 2,

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11
Q

What is a rational number, what’s is symbol?

A

sign Q:
Numbers that can be written as
fractions, both + and -

-2/3, -0.45, 1/2

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12
Q

What is a finite and infinite number in rational numbers?

A

a rational number with finite number of decimals: 2.4

a rational number with infinite number of decimals: 1/3 = 3.33333333333

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13
Q

What is a real number, what’s its symbol?

A

sign: R
all numbers in the number line

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14
Q

What is an irrational number

A

infinite number of decimal places that are not periodic

cannot be represented as a fraction

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15
Q

What is algebra?

A

symbolic arithmetic, using letters as placeholders for real numbers

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16
Q

What are the basic operation rules or laws in algebra ?

A

-commutative law of addition & multiplication
-associative law of addition and multiplication
-distributive law

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17
Q

What are summands

A

two numbers added together

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18
Q

what are factors

A

two real numbers

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19
Q

What is factoring?

A

rewriting a number or expression as a multiplication by using the gcf
e.g.
2(3+4) = 23 + 2*4

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20
Q

What happens if the denominator is zero?

A

not defined

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21
Q

What do you call a real number “a” multiplied “n” times?

A

nth power of a
a- base
n- exponent

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22
Q

What is a^0? e.g. 10^0?

A

1

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23
Q

What is a^1 e.g. 23^1

A

a e.g. 23

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24
Q

What numbers can only be used for logarithms?

A

Real and positive numbers

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25
What numbers can be used for natural logarithms
Natural numbers
26
What symbol is used as a summation sign
Sigma sign or the greek E
27
What is are the numbers below the summation sign
lower summation limit or running index all natural numbers
28
What do you call above the summation sign
upper summation limit it should be greater than or equal 2
29
What kinds of numbers are on the side of the summation sign
Real numbers
30
What symbol is used to denote multiplication
PI
31
What are parameters?
symbols (letters) that can stand for any given number e.g.: a, b or c So c can equal 8 or 10
32
What are constants?
Symbols that have a single fixed numerical value e.g.: pi-symbol or e
33
What are variables?
unspecified numbers but can be defined through application, they can change e.g. x, y or z y can change depending on function of x
34
What is a domain?
range of numbers that indicate the values of a variable symbol: D
35
What is a term or expression?
A combo of numbers, parameters, constants, variables linked together by mathematical operations x+y (a+b)^2
36
What is an equation?
if left side is equal to right- true statement or satisfied equation Otherwise, false
37
What is a linear equation?
equation with 1 variable with 2 parameters e.g. ax+b a cannot equal 0
38
What is a nonlinear equation and give examples
equations that cannot be transformed to linear equations So anything that is not ax+b e.g.: quadratic equations and cubic equations
39
What are inequalities
the relations of parameters are stated e.g. smaller, larger, equal to
40
What does this symbol <=> mean ?
transformation has not changed the value of equation, because operation was performed on both sides
41
What is this symbol II called?
penultimate line
42
What does a quadratic equation consist of
Consists of 1 variable and 3 parameters ax^2+bx+c b, c or both can be zero
43
A solution in the quadratic formula can only exist if:
b^2-4ac is greater than or equal 0
44
What is the rule of transitivity?
If a
45
What is a set?
A group of elements symbol: S e.g. set of natural numbers: N={1,2,3,4....}
46
What does ... mean in a set?
Ellipsis elements are not complete
47
What is the symbol ∈ mean?
Element those elements belong to a set
48
What is the meaning of this symbol ⊂?
It is a subset That all elements of A are also found in B
49
What is a subset?
if a certain set also belongs to another set e.g. Natural numbers is a subset of integers: N ⊂ Z
50
What does this symbol mean ∪?
Union displays all elements that belong to set A and B, you don’t have to repeat similar numbers e.g.: If A={1,2,3) and B={2,3,4,5} then, A ∪ B = {1,2,3,4,5}
51
What does this symbol mean ∩?
Intersection shows all elements that the 2 sets have in common (like a bridge) e.g. If A ={1,2,3} & B={3,4,5} then A ∩ xB = {3}
52
What dies this symbol mean \?
Difference shows elements that belongs to a set but not the other. You look at what is inclusive of the first letter e.g. If A={1,2,3,} & B={3,4,5} A \ B= {1,2}
53
What does percentage mean?
out of 100
54
What does percentage sign mean
that a number is divided by 100
55
What is the percentage formula
W=G*p%
56
What is the opposite of parameter?
Constant Because parameter is selectable and constant is fixed
57
When do you use percentage calculations in the business?
For price reductions, salary increases, value added tax
58
What are elements
Single objects within a set
59
When does the direction of an inequality change?
When you multiply by a negative number
60
What is equivalence transformation?
The process of determining the value of a variable in an equality
61
What determines if an equation is true or false?
The numerical value of the variable
62
What is the most efficient way of testing if equations are true or false?
Through isolation of variables and transformations
63
What is the solution to a linear equation for variable x?
x= — b/a
64
How do you know of there is a solution to a quadratic equation using the quadratic formula?
If b^2 -4ac> 0
65
When do quadratic equations also exist, aside from normal ax^2 +bx+c?
When b = 0 When c = 0 When b and c = 0
66
What is the 1st binomial formula?
(a+b)^2 = a^2+2ab+b^2
67
What is the second binomial formula?
(a-b)^2= a^2 -2ab+ b^2
68
What is the third binomial formula?
(a+b) (a-b) = a^2 -b^2
69
What are placeholders?
alphabetical letters that stand in for numbers
70
What is the meaning of laws of arithmetic
basic calculation rules for algebra
71
What are examples of the laws of arithmetic? 10
Commutative Associative Distributive Fraction Power Roots Logarithms Binomial formulas Product and sum notations Sequence of operations
72
What are parentheses used for?
To indicate which calculation should be performed first
73
What is expanding?
Each summand is multiplied then added together
74
What is a reciprocal?
The interchange of the numerator and denominator
75
What is an exponent
A number set in superscript
76
What is a root exponent?
n or the number on the outer left side of the root
77
What is a radicand?
“a” or the number inside the root
78
How do you read this loga b?
Log b to the base a
79
When is natural logarithm used?
to describe some natural processes e.g. radioactive decay
80
What is the rule for logarithm of a product?
loga (b*c) = loga (b) + loga (c)
81
What is the rule for logarithm of a quotient?
loga (b/c) = loga (b) - loga (c)
82
What business practices are crucial for a company’s success? 2
Quantifying and systematizing

Business Math (8 decks)

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