Mathematics

VOCABULARY MATHEMATICS

UNIT 1 : SETS

1 well-defined (adj.) แจ่มแจ้ง, อย่างชัดเจน The term “well defined” means that the collection is described in such a way that we can determine whether any given object belongs to that collection.

2 roster form (n.) เซตแบบแจกแจง

3 set builder form (n.) เซตแบบบอก เงื่อนไข In the roster form, all elements of the set are listed, the elements being separated by a comma (“,”) and are enclosed within braces (“{ }”). For example : the set representing scores of three students can be a set of three numbers, one of which is repeated as S = {80, 90, 70}.

In the set builder form, all the elements of the set are often characterized by a common property. For example : in the set {a, e, i, o, u} all the elements possess a common property - each of them is a vowel in the English alphabet, and no other alphabet possesses this property. Denoting this set by V, we write V = {x | x is a vowel in the English alphabet}.

4 empty set (n.) เซตว่าง The set that has no members or elements is called an “empty set”. For example : the set of integers between 1 and 2 is an empty set because there are no integers in this range.

5 universal set (n.) เอกภพสัมพัทธ์ Define a set that contains all the sets under consideration as subsets. It is denoted by U, and the set U is called

“The Universal Set”.

6 finite set (n.) เซตจ�ากัด A Finite set is a set that has a finite number of members.

7 infinite set (n.) เซตอนันต์ An infinite set is a set that has an infinite or uncountable number of members.

8 equal sets (n.) เซตที่เท่ากัน Two sets A and B are said to be equal if they have exactly the same elements and we write A = B to represent “A is equal to B”.

9 equivalent sets (n.) เซตที่เทียบเท่ากัน Two finite sets A and B are said to be equivalent if they have the same number of elements.

10 subset (n.) เซตย่อย A set “A” is a subset of set “B”, if each element of set “A” is also an element of set “B”.

11 power sets (n.) เซตก�าลัง Power set is a collection of all possible subsets of a given set.

12 Venn diagram (n.) แผนภาพของ เวนน์ The universal set U is represented by a rectangle. Other sets are represented by circles. If A and B are arbitrary sets, then we can use a Venn diagram to represent the relationship between A and B.

13 union of sets (n.) ส่วนรวมของเซต The union of two sets A and B is the set C, which consists of all the elements that are either in A or in B (including those which are in both).

14 intersection of sets (n.) ส่วนร่วมของเซต The intersection between sets A and B is the set of all elements that belong to both sets.

15 complement of a set (n.) ส่วนเติมเต็มของ

เซต

16 difference of sets (n.) ผลต่างของเซต The complement of A with respect to U is the set of all elements of U that are not the elements of A.

The difference between sets A and B,

in this order, is the set of elements that belong to A but not to B.

UNIT 2 : EXPONENTS

17 base (n.) ฐาน The ‘exponent’ stands for ‘‘how many times the number or variable is being multiplied by itself”. The number that is being multiplied is called ‘base’.

18 exponents (n.) เลขยกก�าลัง Exponents are used as a shorthand representation for multiplications.

19 radical (n.) กรณฑ์

20 denominator (n.) จ�านวนส่วนของ เลขเศษส่วน

21 simplify (n.) ท�าให้ง่ายขึ้น The symbol n x is called a radical, n is called the index and x is called the radicand.

To rationalize the denominator, we multiply the numerator and denominator by a suitable factor that will rationalize the denominator that is, will leave the denominator free of radicals.

Simplify each of the following, expressing the answers with positive indices.

22 power (n.) เลขยกก�าลัง

23 not defined (n.) ให้ค�านิยาม

24 rational exponents (n.) เลขยกก�าลังที่เป็น จ�านวนตรรกยะ

25 properties of radicals (n.) สมบัติของกรณฑ์ The exponent is called the “power” which the number is ‘raised to’, like 53 is expressed as 5 raised to the 3rd power.

For n = 0 and a ≠ 0, a0 = 1 but 00 is not defined.

An expression with rational numbers as exponents or power.

Properties of Radicals for a positive integer n greater than 1, where x and y are positive real numbers: 1. ( n x )n = x 2. n x n = |x | 3. n x ⋅ n y = n xy

4.

n x

n y x

n y

26 square root (n.) กรณฑ์ที่สอง “3 is a square root of 9” because 32 = 9

27 cube root (n.) กรณฑ์ที่สาม “2 is a cube root of 8” because 23 = 8

28 surd (n.) ตัวเลขที่ไม่

สามารถถอด กรณฑ์ได้ Roots of numbers that cannot be completely determined are called surds.

UNIT 3 : RELATION AND FUNCTION

29 ordered pair (n.) คู่อันดับ The points on the graph sheet (x, y) where x is regarded as the first element and y as the second element, thus (x, y) ≠ (y, x).

30 cartesian product (n.) ผลคูณคาร์ทีเชียน Given two sets A and B, we can take an ordered pair (a, b) where element “a” is taken from A and b from B. The set of all such possible ordered pairs denoted as A × B is called the Cartesian Product.

31 relation (n.) ความสัมพันธ์

32 domain (n.) โดเมน A correspondence between the elements of the two sets. Example : {(1, 2), (1, 3), (2, 3)}, defines a relation that the x elements are less than the y elements.

The Domain (D) is the set of all the first component of ordered pairs in a relation as well as in a function.

33 range (n.) เรนจ์

34 function (n.) ฟังก์ชัน

35 inverse of relation (n.) อินเวอร์สของ ความสัมพันธ์ The range (R) is the set of all the second component of the ordered pairs.

A function is a set of ordered pairs with the property such that no two ordered pairs have the same first component and different second component.

Inverse relation is a relation that gives opposite or inverse of a relation.

36 inverse function (n.) ฟังก์ชันอินเวอร์สห รือฟังก์ชันผกผัน The inverse mapping may be written as h-1 (3) = 8. We call h-1 as the inverse function h.

37 linear function (n.) ฟังก์ชันเชิงเส้น A function f is a linear function if f(x) = mx + b where m and b are real numbers and m ≠ 0.

38 quadratic function (n.) ฟังก์ชันก�าลังสอง A function f is a quadratic function if f(x) = ax2 + bx + c where a, b, c are real numbers and a ≠ 0.

39

40

41 Piecewisedefined function (n.)

absolute value function (n.)

exponential function (n.) ฟังก์ชันค่าสัมบูรณ์ A function f is an absolute value function if f(x) = a |x – h| + k where a, h, k are real numbers and a ≠ 0.

ฟังก์ชันเอกซ์ โพเนนเชียล A function f is an exponential function if f(x) = ax-h + k where a, h, k are real numbers and a > 0 but a ≠ 1.

ฟังก์ชันพีซไวส์ A function f is a piecewise-defined function if f is defined by different formulas for different parts of its domain.

42 step function (n.) ฟังก์ชันขั้นบันได A function is a step function if f is a piecewise-defined function where each part of its domain is divided into more than 2 parts and is defined by different constant functions.

43 turning point (n.) จุดวกกลับ

44 constant function (n.) ฟังก์ชันคงตัว

45 slope (n.) ความชัน

46 x-intercept (n.) ระยะตัดแกน x

47 y-intercept (n.) ระยะตัดแกน y

48 vertex (n.) จุดยอด

49 parabola (n.) พาราโบลา

50 axis of the parabola (n.) แกนสมมาตร

51 asymptote (n.) เส้นก�ากับ The lowest or highest point on the parabola, whichever exists is called the “vertex” or the “turning point”.

A function of the form f(x) = b is called a constant function and it is not a linear function.

For example, f(x) = -3x - 2. The slope is -3.

For example, g(x) = -3x - 6. The x-intercept is 0 = -3x - 6, x = - 2.

For example, f(x) = 2x + 1. The y-intercept is f (0) = 2(0) + 1 = 1.

The vertex (turning point) of the parabola f(x)= ax2 + bx + c is (h, f(h)) and h = b 2a. A “parabola” is the graph of a quadratic function.

A line that passes through the turning point of a parabola that is parallel to the vertical axis denoted by x = h.

In the equation f(x) = ax-h + k, the horizontal asymptote is the line y = k.

UNIT 4 : PROBABILITY

52 probability (n.) ความน่าจะเป็น When dealing with experiments that are random and well-defined, probability describes the statistical number of outcomes divided by the number of all outcomes.

53 tree diagram (n.) แผนภาพต้นไม้ A tree diagram is a tool that we use in general mathematics, probability, and statistics that allows us to calculate the number of possible outcomes of an event.

54 random experiment (n.)

55 sample space (n.) การทดลองสุ่ม

เซตของผลลัพธ์ ทั้งหมดที่อาจเกิด ขึ้นได้ Before rolling a die you do not know the result, this is an example of a

random experiment.

The concept of a sample space is fundamental to probability theory, it is the set of all possibilities of some uncertain process.

56 event (n.) เหตุการณ์

57 simple event (n.) เหตุการณ์ที่มี สมาชิกเพียงตัว เดียว

58 compound event (n.) เหตุการณ์ที่มี สมาชิกมากกว่า 1 ตัว

59 equally likely event (n.) เหตุการณ์ที่มีโอกาส เกิดขึ้นเท่าๆ กัน In probability theory, an event is a set of outcomes of an experiment to which a probability is assigned.

Simple event is the event where one experiment happens at a time and it will be having a single outcome.

Compound event in math involves finding the probability of more than one event occurring at the same time.

Each number on a die is equally likely event to occur when the die is tossed.

60 mutually exclusive events (n.) เหตุการณ์ที่เป็น อิสระต่อกัน

61 incompatible events (n.) เหตุการณ์ที่ไม่เกิด ร่วมกัน Mutually exclusive events are two events that cannot take place at the same time.

With incompatible events, it is

impossible for both events to happen at the same time, since it is not possible for a single question to be both true and false.

62 toss (n.) การทอย

63 unbiased (adj.) เที่ยงตรง Most people assume the toss of a coin is always a 50/50 probability.

Unbiased coin means that the probability of heads is the same as the probability of tails, each being ½.