Ged102

wave

any form of disturbance that carries energy as it moves.

subset

means that every element of A is also an element of B.

The area of a rectangle whose length is seven more than its width

(w+7)w

The quotient of the sum of two numbers by another number

(x+y)/z

The square of the sum of two numbers

(x+y)^2

This kind of pattern is unpredictable and it often contains fractals.

. Pattern of Visuals

What is the formula for fibonacci numbers

1/√5 [((1+√5)/2)^n-((1-√5)/2)^n]

Twelve more than a number.

12+x

What is the sum of Fib (1) up to Fib (10) ?

143

What is Fib (12) ?

144

What is Fib (1) * Fib (7) + Fib (12) - Fib (6) ?

149

Two ninths of a number is eleven.

2/9x=11

What if Fib (13) ?

233

Twice the square of a number

2x^2

Twice a number less eight is equal to one more than three times the number.

2x−8=3x+1 or 2x−8=1+3x

Three more than seven times a number is nine more than five times the number.

3+7x=9+5x

Twice of a number added by four

4+2x

The cube of a number less than five

5-x^3

What is Fib (8) + Fib (9) ?

55

What is the sum of Fib (10) + Fib(5)

60

What is Fib (20) ?

6765

Six times a number is fifty-four.

6x=54

.Eight minus a number.

8−x

588

A group of students were asked whether they are like basketball, softball, or both. If 456 likebasketball,384likesoftball,and252likeboth games,howmanystudentswerethere?

closed

A set is "_________" under operation if the operation assigns to every ordered pair of elements from the set an element of the set.

Math only - 5 filipino only - 30 history only - 15 did not like any of the 3 subjects - 6

A survey of 100 fourth year high school students revealed that 42 like mathematics, 62 like Filipino, 44 like History, 22 like both Math and History, 25 like both Math and Filipino, 17 like Filipino and History, and 10 like all the three subjects. How many like Math only? Filipino only? History only? How many did not like any of the three subjects?

All of the following statements are correct about Fibonacci except one: A. The logarithmic spiral growth of the Nautilus shell B. The total number of family members correspond to a Fibonacci number. C. Fibonacci numbers are the root of the discovery of the secret behind sunflower seeds. D. The numbers of petals of almost all flowers in the world correspond to the Fibonacci numbers.

B. The total number of family members correspond to a Fibonacci number.

Among the following, what is not a type of symmetry? A. Reflection C. Transformation B. Rotation D. Translation

C. Transformation

function

Determine if the following is a function or not a function. 2x+3y-1=0

not a function

Determine if the following is a function or not a function. x2+y2=1

not a function

Determine if the following is a function or not a function. y2=x+1

not a function

Determine if the following is a function or not a function. {(-1, -7), (1, 0), (2, -3), (0, -8), (0, 5), (-2, -1)}

function

Determine if the following is a function or not a function. {(0, -5), (1, -4), (2, -3), (3, -2), (4, -1), (5, 0)}

What type of sequence is 5, 8, 13, 21, 34, 55, ... ?

Fibonacci Sequence

To be able to determine if the above statement is a binary operation or not, we need to have a counter example. If a = 0 and b = 0, then ab does not exist, hence it is not an element of R If a = -4 and b = 1⁄2, then ab would be an element of a complex number C, so ab element R.

G element R defined by a * b = a^b

Let a, b element R+. If we take the sum of a + 17b element R+. Hence it is a binary operation

G element R+ definedbya*b=a+17b

Let a, b Z except -1, then a > -1 and b > -1 and a < -1 and b < -1. If a * b = a + b + ab, it follows that a * b = a + b + ab Z since in both case such as a and b > -1 and a and b < -1, the result would be Z, hence * is a binary operation.

G element Z \{-1} , defined * by a * b = a + b + ab for all set a, b element Z.

Let a element Z and b element Z. If we add a and b, then the sum a + b Z. Hence a * b = a + b is a binary operation.

G element Z define a * b = a + b (usual addition on Z

Let a, b element Z. Then the product of a and b, that is ab Z. Hence a * b = ab is a binary operation

G element Z define a * b = ab (usual multiplication on Z)

If a > b = a - b > 0 element Z+ If a < b = a - b < 0 element Z+ Therefore, * is NOT a binary operation

G element Z+,defined*by a*b=a-b for all set a,b element Z+.

If we let a=

G element Z, defined * by a * b = a2 - b2 for all set a, b element Z.

80,40,20,_,_? Type of Sequence:

Geometric 10, 5 r=1/2

2, 20, 200, 2000, _, _ ?Type of Sequence:

Geometric 20000, 200000 r=10

What kind of pattern is a series of shapes that are repeating?

Geometric Pattern

What type of sequence deals with common ratio?

Geometric sequence

Arithmetic sequence

It is a sequence of numbers that follows a definite pattern If common difference is observed

(f+g)(x) = f(x) + g(x)= (2x + 1) + (3x + 2) = 2x + 3x + 1 + 2 = 5x + 3

Iff(x)=2x+1andg(x)=3x+2,whatis(f+g)(x)? Solution:

(g f)(x) = g(f(x)) = g(2x + 1) = 3(2x + 1) + 2 = 6x + 3 + 2 = 6x + 5

Iff(x)=2x+1andg(x)=3x+2,whatis(gºf)(x)

Roster or Tabular Method

It is done by listing or tabulating the elements of the set.

Rule or Set-builder Method

It is done by stating or describing the common characteristics of the elements of the set

What is said to be the most basic pattern in nature?

Pattern of Rhythm

FALSE

TRUE OR FALSE A set with two elements has 2 subsets.

FALSE

TRUE OR FALSE Counting number is an example of a finite set.

FALSE

TRUE OR FALSE Empty set is also called a unit set.

FALSE

TRUE OR FALSE Equivalent set is also an equal set.

FALSE

TRUE OR FALSE {Ø}isanemptyset.

Patterns of Flow.

The flow of liquids provides an inexhaustible supply of nature's patterns.

Fibonacci Sequence

This specific sequence was named after an Italian mathematician Leonardo Pisano Bigollo (1170 - 1250). He discovered the sequence while he was studying rabbits

(f • g)(x) = f(x) • g(x)= (2x + 1)(3x + 2) =6x2 +7x+2

What is (f • g)(x) if f(x) = 2x + 1 and g(x) = 3x + 2?

2

What is (𝑓/g)(𝑥) if f(x) = 2a + 6b and g(x) = a + 3b?

Patterns of Texture

a quality of a certain object that we sense through touch. It exists as a literal surface that we can feel, see, and imagine.

pattern

a structure, form, or design that is regular, consistent, or recurring

Rotations

also known as rotational symmetry, captures symmetries when it still looks the same after some rotation (of less than one full turn).

Cardinal Number; n

are numbers that used to measure the number of elements in a given set. It is just similar in counting the total number of element in a set.

Wind waves

are surface waves that create the chaotic patterns of the sea

1,4,7,10,_,_?

arithmetic 13, 16 d=3

56, 46, 36, 26, _, _?Type of Sequence:

arithmetic 16,6 d=-10

bilateral symmetry

can be divided into two identical halves

What are the next two terms of the sequence, 8, 17, 26, 35?

d=9 44,53

Equal set

equal number of cardinality and the element/s are identical. There is a 1 -1 correspondence.

Spirals

exist on the scale of the cosmos to the minuscule forms of microscopic animals on earth.

Translations

exists in patterns that we see in nature and in man-made objects

.1,1,2,3,5,8,_, _?Type of Sequence:

fibonacci 13,21

Reflection symmetry

mirror symmetry, captures symmetries when the left half of a pattern is the same as the right half.

Symmetries

if a figure can be folded or divided into two with two halves which are the same

Disjoint Sets

if and only if they are mutually exclusive or if they don't have common element/s.

Joint Sets

if and only if they have common element/s.

Equivalent set

if and only if they have the exact number of element. There is a 1 - 1 correspondence

Patterns of Movement

in the human walk, the feet strike the ground in a regular rhythm: the left-right-left-right-left rhythm. When a horse, a four-legged creature walks, there is more of a complex but equally rhythmic pattern. This prevalence of pattern in locomotion extends to the scuttling of insects, the flights of birds, the pulsations of jellyfish, and also the wave-like movements of fish, worms, and snakes.

Geometric Patterns

is a kind of pattern which consists of a series of shapes that are typically repeated

Unit Set

is a set that contains only one element.

Infinite set

is a set that elements in a given set has no end or not countable.

Empty set or Null set;

is a set that has no element.

Finite set

is a set that the elements in a given set is countable.

Patterns of Rhythm

is conceivably the most basic pattern in nature

Universal set

is the set of all elements under discussion.

Geometric sequence.

look for the common ratio

golden rectangle

of squares whose sizes, surprisingly is also behaving similar to the Fibonacci sequence.

mechanical waves

propagate through a medium ---- air or water, making it oscillate as waves pass by

Sequence

refers to an ordered list of numbers called terms, that may have repeated values.

Spots and Stripes

resent in different organisms are results of a reaction-diffusion system

An unknown quantity less fourteen.

x−14

Harmonic Sequence

the reciprocal of the terms behaved in a manner like arithmetic sequence

A number increased by five

x+5

A number less by three

x-3

The sum of the squares of two numbers

x^2+y^2

The difference of a square of two numbers

x^2-y^2