1-Symbols
-Symbols
[ ] Brackets
( ) Parentheses (commonly called brackets)
{} Braces
¯ Bar
' Prime
. Dot
= Equals sign
≠ Unequal sign
% Per Cent
-Arithmetic
+ 'plus' Addition
- 'minus' subtraction
± 'plus orminus'
×,* 'times' multiplication
÷, / division
<,≤,>,≥ Inequality:
a > b a greater than b
a ≥ b a greater than or equal to b
a< b a less than b
a ≤ b a less than or equal to b
≈ Approximate
√ Root
^ Power
-Set Theory
{ } Set
Member (bolang)
Non-member
Subset
Non-subset
Union
∩ Intersection
Ø Empty set 'Phi'
-Real
[ , ] closed interval
( , ) open interval
[ , ) or ( , ] Half-Open intervals
| | Absolute value
2- Definitions
Absolute Value:How far a number is from zero.
Example "6" is 6 away from zero, but "-6" is also 6 away from zero.
So, the absolute value of 6 is 6, and the absolute value of -6 is also 6.
Acute Angle:An angle less than 90° (90° is called a Right Angle)
Addition:Addition is finding the total, or sum, by combining two or more numbers.
Example: 5 + 11 + 3 = 19 is an addition
Additive Identity: Adding zero to a number leaves it unchanged:
a + 0 = 0 + a = a
Additive Inverse: The number you add to another number to get zero. The negative of a number.
Example: The additive inverse of -5 is 5, because -5 + 5 = 0. Also the additive inverse of 5 is -5.
Algebra: Algebra is the area of mathematics where letters (like x or y) or other symbols are used to represent unknown numbers.For example: in x - 5 = 2, x is unknown, but can be solved by adding 5 to both sides of the equal sign (=), like this:x - 5 = 2x - 5 + 5 = 2 + 5x + 0 = 7x = 7 (the answer)
Angle:The amount of turn between two straight lines that have a common end point (the vertex).
Anticlockwise:Moving in the opposite direction to the hands on a clock.
Also called Counterclockwise (US English).
Angles are usually measured anticlockwise.
Approximation:Not exact, but close enough to be used.
Example: if the bus ride takes 57 minutes, you could say "A one hour bus ride", that would be an approximation.
Arithmetic:The basic calculations we make in everyday life: addition, subtraction, multiplication and division.
It also includes fractions and percentages (related to division) and exponents (related to multiplication).
Clockwise:Moving in the direction of the hands on a clock.
The opposite direction is called Anticlockwise.
Taps and most screws and bolts are closed by turning clockwise.
Common Fraction:A fraction where both top and bottom are integers.
Example: 1/2 and 3/4 are both Common Fractions.
But 1.2/4 is NOT a Common Fraction.
(Note: sometimes "Common Fraction" is used to mean "not a Decimal Fraction", however Decimal Fraction also have integers at top and bottom, so are really also Common Fractions.)
Constant: A fixed value. In Algebra, a constant is a number on its own, or sometimes a letter such as a, b or c to stand for a fixed number. Example: in "x + 5 = 9", 5 and 9 are constantsIf it is not a constant it is called a variable.
Cosine:In a right angled triangle, it is the length of the adjacent side divided by the length of the hypotenuse.
The abbreviation is cos
Example: in a triangle with sides of 3, 4 and 5, the cosine of the angle where the sides of length 4 and 5 meet is 4/5
Decimal: Based on 10
Example: the numbers we use in everyday life are decimal numbers, because there are 10 of them (0,1,2,3,4,5,6,7,8 and 9).
Often "decimal number" is also used to mean a number that uses a decimal point followed by digits as a way of showing values less than one.
Example: 1.9 is a decimal number (one and nine tenths)
Decimal Fraction:A decimal fraction is a fraction where the denominator (the bottom number) is a power of ten (such as 10, 100, 1000, etc).
You can write decimal fractions with a decimal point (and no denominator).
This can make it a lot easier to do calculations like addition and multiplication on fractions.
Examples:
43/100 is a decimal fraction and it can be shown as 0.43
51/1000 is a decimal fraction and it can be shown as 0.051
Decimal Number System:The number system we use every day, based on 10 digits (0,1,2,3,4,5,6,7,8,9).
Position is important, with the first position being units, then next on the left being tens, then hundreds and so on.
Decimal Point:A point or dot used to separate the whole number part from the fractional part of a number.
Example: in the number 36.9 the dot separates the 36 (the whole number part from the 9 (the fractional part, which really means 9/10)
Degree (Angles):A measure for angles. There are 360 degrees in a full rotation.
The symbol for degrees is °
Example: 90 degrees (90°) is a right angle.
Denominator:The bottom number in a fraction.
Shows how many equal parts the item is divided into.
Digit: A symbol used to make numerals.
0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 are the ten digits we use in everyday numbers.
Example: the numeral 153 is made up of 3 digits ("1", "5" and "3").
Element: A member of a set.
Examples:
Pants are an element of this set of clothes.
The number 2 is an element of the set {1,2,3}
Equal:Exactly the same amount or value
Examples:
3 + 4 is equal to 7
1 Dollar is equal to 100 Cents
The symbol is =
Equation:An equation says that two things are the same, using mathematical symbols.
An equal sign (=) is used
Example: 7+2 = 10-1
Equation of a Straight Line:An equation that defines a straight line.
Even Number:Any integer that can be divided exactly by 2.
The last digit will be 0, 2, 4, 6 or 8
Example: -24, 0, 6 and 38 are all even numbers
If it is not an even number, it is called an odd number.
Example: -3, 1, 7 and 35 are all odd numbers
Exponent:The exponent of a number shows you how many times the number is to be used in a multiplication.
It is written as a small number to the right and above the base number.
Example: 82 = 8 × 8 = 64
(Another name for exponent is index or power)
Greatest Common Factor:The highest number that divides exactly into two or more numbers.
If you find all the factors of two or more numbers, and you find some factors are the same ("common"), then the largest of those common factors is the Greatest Common Factor.
Abbreviated "GCF". Also called "Highest Common Factor"
Example: the GCF of 12 and 30 is 6, because 1, 2, 3 and 6 are factors of both 12 and 30, and 6 is the greatest.
Horizontal:Going side-to-side, like the horizon.
Parallel to the horizon.
(Up-down is called vertical)
Identity: An equation that is true no matter what values are chosen.
Example: a/2 = a × 0.5 is true no matter what value is chosen for "a"
Infinite:Without an end. Not finite.
Example: There are infinite whole numbers (0,1,2,3,4, … )
Integer:A number with no fractional part.
Includes the counting numbers {1,2,3,…}, zero {0}, and the negative of the counting numbers {-1, -2, -3, …}
You can write them down like this: {…, -3, -2, -1, 0, 1, 2, 3, …}
Examples of integers: -16, -3, 0, 1, 198
Intersection: Where lines cross over (have some common point).
Irrational Number: A number that cannot be written as a simple fraction - the decimal goes on forever without repeating.
Example: Pi is an irrational number
Least Common Denominator:The smallest number that can be used for all denominators (the bottom number) of 2 or more fractions.
Example: the Least Common Denominator of 1/2 and 2/3 is 6, because they can be written as 3/6 and 4/6.
(Also called Lowest Common Denominator)
Least Common Multiple:The smallest number that is a multiple of two or more numbers.
Example: the Least Common Multiple of 3 and 5 is 15, because 15 is a multiple of 3 and also a multiple of 5. Other common multiples include 30 and 45, etc, but they are not the smallest (least).
(Also called Lowest Common Multiple)
Line:A long thin mark made by a pen, pencil, etc.
In geometry a line:
* is straight (no curves),
* has no thickness, and
* extends in both directions without end (infinitely).
If it does have ends it would be called a "Line Segment".
Linear Equation: An equation that makes a straight line when it is graphed.
Often written in the form: y = mx+b
Mixed Fraction: A mixed fraction is a whole number and a fraction combined into one "mixed" number.
Example: 1½ (one and a half) is a mixed fraction
(Also called a Mixed Number)
Multiplication:The basic idea of multiplication is repeated addition.
For example: 5 × 3 = 5 + 5 + 5 = 15
But as well as multiplying by whole numbers, you can also multiply by fractions or decimals.
For example 5 × 3½ = 5 + 5 + 5 + (half of 5) = 17.5
Multiplicative Identity: Multiplying a number by 1 leaves it unchanged:
a × 1 = 1 × a = a
Natural Number:The whole numbers from 1 upwards: 1, 2, 3, and so on ...
Or from 0 upwards in some fields of mathematics: 0, 1, 2, 3 and so on ...
No negative numbers and no fractions.
Negative:Less than zero.
(Positive means more than zero. Zero is neither negative nor positive.)
A negative number is written with a minus sign in front
Example: -5 is negative five.
Sometimes abbreviated "-ve"
Notation:A system of symbols used to represent special things.
Example: In mathematical notation "∞" means "infinity".
Number:A number is a count or measurement.
They are really an idea in our minds. We write or talk about numbers using numerals such as "5" or "five". We could also hold up 5 fingers, or tap the table 5 times. These are all different ways of referring to the same number.
There are also different types of numbers, such as whole numbers (1,2,3) decimals (1.48, 50.5), fractions (1/2, 3/8), and more.
Number Line:A line with numbers placed in their correct position.
Useful for addition and subtraction, and for showing relations between numbers.
Numerator: The top number in a fraction.
Shows how many parts we have.
Obtuse Angle: An obtuse angle is one which is more than 90° but less than 180°
In other words, it is between a right angle and a straight angle.
Odd Number:Any integer that can not be divided exactly by 2.
The last digit will be 1, 3, 5, 7 or 9
Example: -3, 1, 7 and 35 are all odd numbers
If it is not an odd number, it is called an even number.
Example: -24, 0, 6 and 38 are all even numbers
Parallel:Always the same distance apart and never touching.
Parallel Lines: Lines that are always the same distance apart and will never meet.
Parameter:A value that is already "built in" to a function.
Example: if a function that works out the height of a tree is h(year) = 20 × year, then "year" is a variable and "20" is a parameter.
Parameters can be changed so that the function can be used for other things.
Example: A different tree might have a growth rate of 30 cm per year, and its function would be h(year) = 30 × year
We could even make it more general by writing
h(age; rate) = rate × age
and in this case a semicolon (;) is used to separate the variable(s) from the parameters(s)
Percent: Percent means parts per 100
The symbol is %
Example: 25% means 25 per 100
Perpendicular:At right angles (90°) to
Perpendicular Lines:Lines that meet at right angles (90°)
Plot:To draw on a graph or map.
Polynomial:A polynomial is an expression made with constants, variables and exponents, which are combined using addition, subtraction and multiplication, ... but not division.
The exponents can only be 0,1,2,3,… etc
It cannot have an infinite number of terms.
Positive:Greater than zero.
(Negative means less than zero. Zero is neither negative nor positive.)
Example: 5 is positive five.
Sometimes abbreviated "+ve"
Proper Fraction:A proper fraction is a fraction where the numerator (the top number) is less than the denominator (the bottom number).
Example: 1/4 (one quarter) and 5/6 (five sixths) are proper fractions.
Radical:An expression that has a square root, cube root, etc.
The symbol is √
Rational Number:Any number that can be made by dividing one integer by another. The word comes from "ratio".
Examples:
1/2 is a rational number (1 divided by 2, or the ratio of 1 to 2)
0.75 is a rational number (3/4)
1 is a rational number (1/1)
2 is a rational number (2/1)
2.12 is a rational number (212/100)
-6.6 is a rational number (-66/10)
Real Number: The type of number we normally use, such as 1, 15.82, -0.1, 3/4, etc…
Positive or negative, large or small, whole numbers or decimal numbers are all Real Numbers.
They are called "Real Numbers" because they are not Imaginary Numbers.
Reciprocal:To get the reciprocal of a number, just divide 1 by the number
Example: the reciprocal of 2 is 1/2 (half)
Every number has a reciprocal except 0 (1/0 is undefined)
It is shown as 1/x, or x-1
If you multiply a number by its reciprocal you get 1
Example: 3 times 1/3 equals 1
Also called the "Multiplicative Inverse"
Reflex Angle:A Reflex Angle is one which is more than 180° but less than 360°
Remainder:The amount left over after division (as happens if one number can't be divided exactly by the other)
Example: 19 cannot be divided exactly by 5. The closest you can get without going over is 3 x 5 = 15, which is 4 less than 19.
So the answer of 19 ÷ 5 is 3 with a remainder of 4.
Right Angle:A right angle is an angle which is equal to 90°, one quarter of a full revolution.
Root: Where a function equals zero.
In this example, -2 and 2 are the roots of the function x2 - 4
But sometimes "root" is used as a quick way of saying "square root"
Rounding:Rounding means reducing the digits in a number while trying to keep it's value similar.
The result is less accurate, but easier to use.
This is the common method
* Decide which is the last digit to keep
* Increase it by 1 if the next digit is 5 or more (this is called rounding up)
* Leave it the same if the next digit is less than 5 (this is called rounding down)
Example: 243 rounded to the nearest ten is 240 (because 3 is less than 5)
Scientific Notation: Where a number is written in two parts:
First: just the digits (with the decimal point placed after the first digit),
Followed by: ×10 to a power that would put the decimal point back where it should be.
Set:A collection of "things" (objects or numbers, etc).
Each member is called an element of the set.
There should only be one of each member (all members are unique).
Example: {1,2,3,4} is the set of counting numbers less than 5
Sign:Used with a name means a symbol used instead of words, such as the "Stop" sign shown.
Example: "%" is the percent sign.
Used on its own means negative or positive.
Example: what sign is the number? Is it negative?
Sine:In a right angled triangle, it is the length of the opposite side divided by the length of the hypotenuse.
The abbreviation is sin
Example: in a triangle with sides of 3, 4 and 5, the sine of the angle where the sides of length 4 and 5 meet is 3/5
Slope:How steep a straight line is.
Square Root:The square root of a number is that special value that, when multiplied by itself, gives the number.
Example: 4 × 4 = 16, so the square root of 16 is 4.
The symbol is √
Example: √36 = 6 (because 6 x 6 = 36)
Straight Angle:A straight angle changes the direction to point the opposite way. It looks like a straight line.
It measures 180° (half a revolution, or two right angles)
Straight Line: A line that does not curve.
In geometry a line is always straight (no curves).
Subtraction:Taking one number away from another.
If you have 5 apples and you subtract 2, you will be left with 3.
The symbol of subtraction is -
Example: 5 - 2 = 3
Sum:The result of adding two or more numbers.
Example: 9 is the sum of 2, 4 and 3, because 2 + 4 + 3 = 9.
Unequal:Not equal
The symbol is ≠
Example: 7 ≠ 5 (7 is not equal to 5)
Value:Money how much something is worth.
Mathematics the result or 'output' of a calculation.
Example: 3 × 4 gives the value of 12.
Variable:A symbol for a number we don't know yet. It is usually a letter like x or y.
Example: in x + 2 = 6, x is the variable
If it is not a variable it is called a Constant
Vertical Angles:Vertical Angles are the angles opposite each other when two lines cross.
Imperial: fluid ounce, cubic inch, cubic foot, pints, gallons, bushels
Whole Number: The numbers {0, 1, 2, 3, …} etc.
There is no fractional or decimal part. And no negatives.
Example: 5, 49 and 980 are all whole numbers.
X:The letter "x" is often used in algebra to mean a value that is not yet known. It is called an "unknown" or a "variable".
But it doesn't have to be "x", it could be "y", "z" or any letter or symbol.
X Axis: The line on a graph that runs horizontally (left-right) through zero.
It is used as a reference line so you can measure from it.
X Coordinate:The horizontal value in a pair of coordinates. How far along the point is.
Always written first in an ordered pair of coordinates (x,y), such as (12,5).
Also called "Abscissa"
Y Axis: The line on a graph that runs vertically (up-down) through zero.
It is used as a reference line so you can measure from it.
Y Coordinate:The vertical value in a pair of coordinates. How far up or down the point is.
Always written second in an ordered pair of coordinates (x,y) such as (12,5).
Also called "Ordinate"
Y Intercept: Where a straight line crosses the Y axis of a graph.
Zero:The whole number between -1 and 1, with the symbol 0
Shows that there is no amount.
Example: 6 - 6 = 0 (the difference between six and six is zero)
Useful as a "place-holder" so that you can write a numeral properly.
Example: 502 (five hundred and two) could be mistaken for 52 (fifty two) without the zero in the tens place.
3- Definitions
A:
Absolute Value:قيمة مطلقة
Acute Angle:زاوية حادة
Addition:عملية الجمع
Additive Identity:المحايد الجمعي
Adjacent: مجاور
Algebraic operation:عملية جبرية
Angle:زاوية
Anticlockwise:عكس اتجاه عقارب الساعة
Approximation:تقريبي
Arithmetical:علم الحساب
Arrange: يرتب
Ascending:تصاعدي
Associative: تجميعي
Assume: يفترض
Average: متوسط
Axiom: مسلمة
Axis: محور
B:
Base:أساس
Belong:ينتمي
Binomial:حدانية
C:
Calculate:احسب
Cartesian:إحداثيات كارتيزية
Celsius:مئوية
Center:مركز
Change:تغير
Chord: وتر
Circle:دائرة
Clockwise: اتجاة حركة عقارب الساعة
Closed:مغلق
Closure: انغلاق
Coefficient: معامل
Column: عمود
Common Fraction:
Commutative:تبادل
Complement:متمم
Complex number: عدد مركب
Constant:ثابت
Conversion:تحويل
Cosine:جيب تمام الزاوية
Critical angle:زاوية حرجة
Cube:مكعب
Cube root: جذر تكعيبي
Curve:منحنى
D:
Decimal:عشري
Decrease:تناقص
Decrement:تناقص
Decuple:يضرب في عشرة
Defined:يعرف
Definite:معرف
Degree (Angles):درجة
Denominator:المقام
Descending:تنازلي
Diagonal:قطر
Diameter: قطر
Difference:فرق
Digit:رقم
Dimension:بعد
Direction:اتجاة
Discriminate:المميز
Divided by:مقسوم علي
Divided:المقسوم
Divisible:قابل للقسمة
Division long:القسمة المطولة
Domain:مجال
Dot product: حاصل ضرب
Double: مضاعف
E:
Element:عنصر
Elimination:حذف
Empty Set:مجموعة خالية
Equal: يساوي
Equation:معادلة
Equation of a Straight Line:معادلة الخط المستقيم
Equivalent:مكافئ
Error:خطاء
Estimate:يقدر
Even Number: عدد زوجي
Exponent: أس
Expression: تعبير
F:
Factor:عامل
Factorization theorem:نظرية التحليل إلى عوامل
Finite:منتهي
Formula:صيغة
Fourth root:الجذر الرابع
Fraction:كسر
Function:دالة
Fundamental:أساس
G:
General:عام
Geometry:هندسة
Greater than:أكبر من
Greatest Common Factor:العامل المشترك الأكبر
H:
Half:نصف
Horizontal:أفقي
Hypothesis:فرضية
I:
Identity: محايد
Image:صورة
Imaginary: تخيلي
Increase:زيادة
Infinite: غير منتهي
Integer: الأعداد الصحيحة
Intersection:تقاطع
Irrational Number:غير قياسي /غير نسبي
L:
Law:قانون
Least:اصغر
Least Common Denominator:المقام المشترك الاصغر
Least Common factor: العامل المشترك الاصغر
Least Common Multiple: المضاعف المشترك الاصغر
Left:يسار