Nigger

Question 1

A fundamental dscipline that plays a critical role in various aspects of life, science and technology

Answer 1

Importance of Mathematics

Question 2

Teaches logical reasoning, critical thinking, and ———.

Answer 2

Problem-Solving Skills

Question 3

Core concepts of mathematics

Answer 3

Numbers
Operations
Patterns and relationships

Question 4

The foundation of mathematics, including natural —–

Answer 4

Numbers

Question 5

Addition, subtraction, multiplication, division, etc

Answer 5

Operations

Question 6

Identifying and analyzing patterns to understand relationships between numbers and variables

Answer 6

Patters and relationships

Question 7

Science and engineering:

Example: Calculating the trajectory of a spacecraft using calculus and trigonometry

Application: Engineers use mathematics to design structure, analyze data, and create simulations.

Answer 7

Applications of mathematics

Question 8

• A mathematician
• Mathematics is our one and only strategy for understanding the complexity of nature

Answer 8

Ralph Abraham

Question 9

-Mathematics is the science of quantity
-Philosopher, and polymath

Answer 9

Aristotle

Question 10

-The science of indirect measures

Answer 10

Auguste Cosme

Question 11

-Mathematics is the language in which God has written in the universe

Answer 11

Galielo Galilei

Question 12

-Mathematics is the classification and study of all possible patterns and relationships

Answer 12

Walter Warwick Sawyer

Question 13

-Mathematics is a formal system of thought or recognizing, classifying, and exploiting patterns

Answer 13

Ian stewart

Question 14

Learning Mathematics stimulates —– development, enchancin memory, attention, and analytical abilities.

Answer 14

Cognitive Development

Question 15

Types of variable

Answer 15

Random variable
Discrete Variable
Continous Variable
Constant Variable
Parameter Variable
Independent Variable
Dependent Variable

Question 16

A variable that takes on different values based on the outcomes of a random process

Answer 16

Random Variable

Question 17

A variable that can take on a finite or countable numbers of values.

Answer 17

Discrete Variable

Question 18

A variable that can take on any value within a given range, often involving decimals

Answer 18

Continuous Variable

Question 19

A value that does not change within a given context or equation.

Answer 19

Constant Variable

Question 20

A variable that remains constant within a specific context but can change when the context changes.

Answer 20

Parameter Variable

Question 21

A variable that is manipulated or chosein in an equation or function

Answer 21

Independent variable

Question 22

A variable whose value depends on the independent variable

Answer 22

Dependent Variable

Question 23

Mathematics is not just about numbers; it is a way of thinking, a method of problem solving, and a tool for understanding the world.

Answer 23

Importance of mathematics

Question 24

Are symbols or letters used to represent numbers or other mathematical objects.

Answer 24

Variables.

Question 25

Definition of a variable:? Purpose Of variable:?

Answer 25

A variable is a symbol used to reprsent a number Variables enable generalazation in mathematics

Question 26

It provides of formal way to describe collection of objects and their relationships

Answer 26

Language of sets.

Question 27

A --- is a collection of distinct objects considered as a whole.

Answer 27

Set

Question 28

Sets are typically denoted by curly braces.

Answer 28

Notation

Question 29

A ------ is an individual object within a set.

Answer 29

Element

Question 30

Contains no elements.

Answer 30

Empty set

Question 31

Lists all elements of the set explicitly. For example B=(a,b,c)

Answer 31

Set Notation

Question 32

Types of Relation

Answer 32

Symmetric Relation Reflexive Relation Transitive Relation

Question 33

A relation 𝑅 R on a set 𝐴 A is called ------- if every element is related to itself. For every 𝑎 ∈ 𝐴 a∈A, ( 𝑎 , 𝑎 ) ∈ 𝑅 (a,a)∈R. Example: The relation "is equal to" on the set of real numbers, since every number is equal to itself.

Answer 33

Reflexive Relation

Question 34

A relation 𝑅 R on a set 𝐴 A is called ------ if whenever ( 𝑎 , 𝑏 ) ∈ 𝑅 (a,b)∈R, then ( 𝑏 , 𝑎 ) ∈ 𝑅 (b,a)∈R for all 𝑎 , 𝑏 ∈ 𝐴 a,b∈A. Example: The relation "is married to" on a set of people is symmetric because if person A is married to person B, then person B is also married to person A.

Answer 34

Symmetric Relation

Question 35

A relation 𝑅 R on a set 𝐴 A is ----- if whenever ( 𝑎 , 𝑏 ) ∈ 𝑅 (a,b)∈R and ( 𝑏 , 𝑐 ) ∈ 𝑅 (b,c)∈R, then ( 𝑎 , 𝑐 ) ∈ 𝑅 (a,c)∈R for all 𝑎 , 𝑏 , 𝑐 ∈ 𝐴 a,b,c∈A. Example: The relation "is less than" (<) on the set of real numbers is transitive because if 𝑎 < 𝑏 a

Answer 35

Transitive Relation

Question 36

This relation is a? X= -2, -1, 0, 4, 5 Y= 0, -2, 3, -1, -3

Answer 36

This relation is a Function

Question 37

(-2,1), (-2,3), (0,-3), (1,4), (3,1) Determine the domain/range

Answer 37

Domain/x= -2, 0, 1, 3 Range/y = 1, 3, -3, 4,

Question 37

This relation is ? x= -3, -1, 0, 5, 5 y= 7, 5, -2, 9, 3

Answer 37

This relation is a Not Function Because there are repititions or duplicates of x values with different y values.

Question 38

Is the set of all x or input values. We may describe it as the colleciton of the FIRST values in the ordered pairs

Answer 38

Domain

Question 39

The set of all y Output values. we may describe it as the part of the collection of the second values in the ordered Pairs

Answer 39

Range

Question 40

OBJECTS THAT WE USE IN MATH?

Answer 40

Numbers Variables Operations Sets Relations Functions

Question 41

Properties of Real numbers

Answer 41

Closure Commutative Associative Distributive Identity + x Inverse + x

Question 42

Definition: Given real numbers a and b (a, bE R), then 、1 a + b is a real number (a + b E R). Therefore, the set of reals is CLOSED with respect to addition. ab is a real number (ab E R). Therefore, tho set of reals is CLOSED with respect to multiplication.

Answer 42

Closure Property

Question 43

Changing the order of the numbers in addition os multiplication will not change the result.

Answer 43

Commutative Property

Question 44

States: a+b = b+a Ex: 2 + 3 = 3 + 2

Answer 44

Commutative Property of addition

Question 45

States: a+(b+c) = (a+b)+c 3+(4+5)=(3+4)+5

Answer 45

Associative Property of addition

Question 45

states: ab = ba *Ex. 4 x 5 = 5 x 4

Answer 45

Commutative property of multiplication

Question 46

Changing the GROUPING of the numbers in addition or multiplication will not change the result.

Answer 46

Associative Property

Question 47

States: (ab)c= a(bc) (2x3) x 4 = 2x (3x4)

Answer 47

Associative Property of multiplication

Question 48

Multiplication Distributes over Addition a(b+c) = Ab+ac 3(2+5) = 3x2 + 3x5

Answer 48

Distributive Property

Question 49

There exists a unique number 0. In other words adding zero to a number does not change its value a+0 = a and 0+a =a

Answer 49

Additive identity property

Question 49

For each real number there exist a real number such as -a their sum is zero IN other words opposites add to zero 0 a + (-a) = 0

Answer 49

Additive Inverse Property

Question 50

There exists a unique number 1 such that the number 1 preserves identities under multiplication In other words multiplying a number by 1 does not change the value of the number a x 1 = a and 1 x a = a

Answer 50

Multiplicative Identity Property

Question 51

For each number there exist a unique real number 1/a such that ther product is 1. a x 1/a = 1

Answer 51

Multiplicative Inverse Property