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Math 10 > Module 5: Numbers and Patterns > Flashcards

Module 5: Numbers and Patterns Flashcards

1
Q

Numbers

A

universally understood symbols that are often used to convey mathematical ideas

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2
Q

Positional Numeral System

A

The value of a numeral depends on its position

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3
Q

Earliest numerical system

A

Tally marks

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4
Q

Why did early civilizations opt to adapt a positional notation in their numerical systems?

A

A positional notation makes it easier to write or represent larger numbers.

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5
Q

Why were older positional notation systems that lacked a symbol for 0 difficult to use?

A

Lacking a 0 symbol makes it difficult to distinguish certain numbers from each other (example 63 and 603) and this leads to inconsisten and unreliable notation.

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6
Q

Where did the digits we commonly use today originate from?

A

North African Maghreb region of the Arab Empire (Hindu-Arabic numeral system)

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7
Q

Characteristics of the Egyptian numeral system (arnd. 3000 BC)

A

Base 10 hieroglyphics, additive, non-positional

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8
Q

Characteristics of the Babylonian numeral system (arnd. 3500 B.C.)

A

Sumerian numerals, cuneiform, sexagesimal system (Base 60) and decimal subsytem (Base 10), positional, left to right

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9
Q

What does acrophinic mean in the context of the early Greek numeral system?

A

the symbol for the numeral is the 1st letter of its name

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10
Q

Characteristics of the early Greek numeral system (arnd 1000 B.C.)

A

acrophonic, base 10, positional, additive

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11
Q

Characteristics of the Greek numeral system developed around 400 B.C.

A

alphabetic or ionic, contains 27 letters that stood for numbers, positional

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12
Q

Characterisitics of the early Roman numeral system (arnd. 900 B.C.)

A

Base 5, positional, additive and subtractive, left to right

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13
Q

Characteristics of the early Mayan numeral system (arnd 2000 B.C)

A

vigesimal system (base 20), quinary subsystem (base 5), positional, top to bottom

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14
Q

Characteristics of the early Chinese numeral system (1st form)

A

base 10, non positional, left to right

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15
Q

Characteristics of the early Chinese numeral system (2nd form)

A

base 10, positional, left to right, used counting boards

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16
Q

Inventor of the Abacus

A

Akkadians

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17
Q

Characteristics of the Baybayin numeral system (arnd. 2000 B.C)

A

Base 10

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18
Q

Who was the Indian mathematician that ‘invented’ 0 around 600 AD?

A

Brahmagupta

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19
Q

Characteristics of the Hindu-Arabic numeral system (arnd 6th to 7th century AD)

A

base 10, positional, left to right

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20
Q

Characteristics of the duodecimal numeral system

A

base 12 (dozenal), positional, left to right

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21
Q

Characteristics of the octal numeral system

A

base 8, positional, left to right

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22
Q

Characteristics of the binary numeral system

A

base 2, positional, left to right

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23
Q

Who promoted Hindu-Arabic numerals in Europe?

A

Leonardo of Pisa A.K.A Fibonacci

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24
Q

What was the title of Fibonacci’s book wherein he promoted Hindu-Arabic numerals in Europe?

A

Liber Abaci

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25
Q

What is the Arabic term for 0 according to Fibonacci’s Liber Abaci

A

zephirum

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26
Q

What are some factors of banned numbers?

A

political and religious controversies, symbolic representations, ideological threats and differences, etc.

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27
Q

The set of natural numbers is denoted by what symbol

A

N

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28
Q

The set of natural numbers, together with the number zero, forms the set of whole numbers which is denoted by what symbol

A

W

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29
Q

The set of natural numbers N, is also referred to as the set of __________, which is denoted by the symbol ____

A

positive integers; 𝐙+

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30
Q

The set of rational numbers is denoted by what symbol

A

Q

31
Q

The set of irrational numbers is denoted by what symbol

A

𝐐′

32
Q

The set of real numbers which is the union of the set of rational and irrational numbers is denoted by what symbol

A

R

33
Q

What are the four axioms that satisfy the real number system

A

closure, commutativity, associativity, distributivity of multiplication over addition, existence of the identity elements for addition and multiplication, and existence of inverse elements under addition and multiplication

34
Q

Closure axiom

A

For any pair of real numbers, a and b, their sum (a+b) and product (ab) are also real numbers

35
Q

Commutativity axiom

A

For any pair of real numbers, their sum and product give the same result even if the elements combined are swapped

36
Q

Associativity Axiom

A

a + ( b + c ) = ( a + b ) + c and a ⋅ ( b ⋅ c ) = ( a ⋅ b ) ⋅ c

37
Q

Distributivity of Multiplication over Addition axiom

A

a ⋅ ( b + c ) = ( a ⋅ b ) + (a ⋅ c) and ( b + c ) ⋅ a = ( b ⋅ a ) + (c ⋅ a)

38
Q

Existence of the Identity Elements for Addition and Multiplication axiom

A

a+0 = 0+a = a and a(1) = 1(a) = a

39
Q

Existence of Inverse Elements under Addition and Multiplication axiom

A

a + (-a) = (-a + a) = 0 and a(a^-1) = a^-1(a) = a, provided that a is not equal to 0

40
Q

True or False: PEMDAS is an axiom, therefore operations must be done left to right.

A

FALSE

41
Q

What is an imaginary number?

A

a real number multiple of i, where i = √−1

42
Q

What is a complex numebr?

A

a combination of a real number and an imaginary number of the form z= a +bi where a,b are real numbers and i = √−1

43
Q

What is a prime number?

A

a natural number whose factors are one and itself

44
Q

What is a composite number?

A

a natural number that has other factors in addition to one and itself

45
Q

TRUE OR FALSE: One (1) is a prime number.

A

FALSE; it it neither prime nor composite

46
Q

How is a modular set of n elements (subset of whole numbers) represented?

A

𝑍𝑛 = {0,1,2,3,… , 𝑛 − 1}

47
Q

What is the formula for the additive inverse in modular sets?

A

a + b ≡ 0 (mod n)

48
Q

What is the formula for the multiplicative inverse in modular sets?

A

ab ≡ 1(mod n)

49
Q

What is cryptography?

A

The study of encoding and decoding messages

50
Q

What is the numebr pattern shown: 1,3,5,7,9,11,…

A

positive odd numbers

51
Q

What is the number pattern shown: 2,7,12,17,22,…

A

arithmetic progression

52
Q

What number pattern is shown: 1, 10, 100, 1000, 10000, …

A

powers of 10

53
Q

What number pattern is shown: 2, 6, 18, 54, 162

A

geometric progression

54
Q

What number pattern is shown: 1,4,9,16,25

A

perfect squares

55
Q

What number pattern is shown: 1,8,27,64,125,…

A

perfect cubes

56
Q

What number pattern is shown: 1,3,6,19,15,21

A

triangular numbers

57
Q

What are patterns used for?

A

retention and prediction

58
Q

Who invented Pascal’s Triangle?

A

Blaise Pascal

59
Q

Fibonacci series

A

1,1,2,3,5,8,13,21,32,55,89,144,233,…

60
Q

What is the golden ratio?

A

a+b/a = a/b = 1.618

61
Q

an intristic property of a mathmatical object which causes it to remain invariant under certain classes of transformations

A

Symmetry

62
Q

What are the different kinds of symmetry?

A

reflectional, rotational, translational, glide

63
Q

What is the angle of rotation

A

the smallest angle that would preserve the figure when the figure is rotated

64
Q

What is the order of rotation?

A

the number of positions that preserves the figure when it is repeatedly rotated until it reaches one revolution (360/angle of rotation)

65
Q

What is a frieze pattern?

A

a strip with a symmetric pattern, repetitive in one direction

66
Q

How many possible Frieze patterns can be created out of a design that is of one color

A

7

67
Q

What frieze pettern displays only translational symmetry?

A

HOP

68
Q

What frieze pettern displays only translational and glide symmetries

A

STEP

69
Q

What frieze pettern displays only translational and vertical reflection symmetries?

A

SIDLE

70
Q

What frieze pettern displays only translational and rotational by a half turn symmetries?

A

SPINNING HOP

71
Q

What frieze pettern displays only translational, glide, and rotational by a half turn symmetries?

A

SPINNING SLIDE

72
Q

What frieze pettern displays only translational and horizontal reflection symmetries?

A

JUMP

73
Q

What frieze pettern displays transational, horizontal and vertical reflections, and rotational symmetries?

A

SPINNING JUMP

Math 10 (4 decks)

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