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Math Point Geometry Mode Numbers Conversion Table

Numbers

Prime Number (up to 1000)
A prime number can be divided, without a remainder, only by itself and by 1.

2	3	5	7	11	13	17	19	23	29
31	37	41	43	47	53	59	61	67	71
73	79	83	89	97	101	103	107	109	113
127	131	137	139	149	151	157	163	167	173
179	181	191	193	197	199	211	233	227	229
233	239	241	251	257	263	269	271	277	281
283	293	307	311	313	317	331	337	347	349
353	359	367	373	379	383	389	397	401	409
419	421	431	433	439	443	449	457	461	463
467	479	487	491	499	503	509	521	523	541
547	557	563	569	571	577	587	593	599	601
607	613	617	619	631	641	643	647	653	659
661	673	677	683	691	701	709	719	727	733
739	743	751	757	761	769	773	787	797	809
811	821	823	827	829	839	853	857	859	863
877	881	883	887	907	911	919	929	937	941
947	953	967	971	977	983	991	997

Arithmetic Operations on Functions

Sum	(f + g)(x) = f(x) + g(x)
Difference	(f - g)(x) = f(x) - g(x)
Product	(f × g)(x) = f(x) × g(x)
Quotient	(f/g)(x) = f(x)/g(x), if g(x) is not equal to 0.

Squares and Square Roots of Integers from 1 to 40

X	X²		X	X²
1	1	1	21	441	4.583
2	4	1.414	22	484	4.690
3	9	1.732	23	529	4.796
4	16	2	24	576	4.900
5	25	2.236	25	625	5
6	36	2.449	26	676	5.099
7	49	2.646	27	729	5.196
8	64	2.828	28	784	5.291
9	81	3	29	841	5.385
10	100	3.162	30	900	5.477
11	121	3.316	31	961	5.568
12	144	3.464	32	1024	5.657
13	169	3.606	33	1089	5.744
14	196	3.741	34	1156	5.831
15	225	3.873	35	1225	5.916
16	256	4	36	1296	6
17	289	4.123	37	1369	6/083
18	324	4.243	38	1444	6.164
19	361	4.259	39	1521	6.245
20	400	4.472	40	1600	6.325

Decimal, Binary and Hexadecimal Number Conversion

Decimal	Binary	Hexadecimal
0	0	0
1	1	1
2	10	2
3	11	3
4	100	4
5	101	5
6	110	6
7	111	7
8	1000	8
9	1001	9
10	1010	a
11	1011	b
12	1100	c
13	1101	d
14	1110	e
15	1111	f
16	10000	10
17	10001	11
18	10010	12
19	10011	13
20	10100	14

Negative Numbers Addition

Rule	Example
Positive Number + Positive = Positive Number	7 + 4 = 11 2 + 15 = 17
Negative Number + Negative Number = Negative Number	-4 + (-9) = -(4 + 9) = -13 -12 + (-43) = -(12 + 43) = -55
Positive + Negative OR Negative + Positive case 1: The positive number is larger: Answer = Positive case 2: The negative number is larger: Answer = Negative	case 1: 14 + (-5) = 14 - 5 = 9 case 2: -19 + 7 = -(19 - 7) = -12

Rules for Fractions

Addition (same denominators):	Addition (different denominators):
Subtraction (same denominators):	Subtraction (different denominators):
Multiplication:	Division:

Types of Numbers

Integers	{..., -3, -2, -1, 0, 1, 2, 3, ...}
Positive Integers	{1, 2, 3, 4, 5, ...}
Negative Integers	{-1, -2, -3, -4, -5, ...}
Odd Numbers	{1, 3, 5, 7, 9, 11, ...}
Even Numbers	{0, 2, 4, 6, 8, 10, ...}
Consecutive Integers	{n, n+1, n+2, ...}, n = integer
Consecutive Even Integers	{n, n+2, n+4, ...}, n = even integer
Consecutive Odd Integers	{n, n+2, n+4, ...}, n = odd integer
Prime Numbers	{2, 3, 5, 7, 11, 13, ...}

Names of Big Numbers (American System)

10¹	Ten
10²	Hundred
10³	Thousand
10⁶	Million
10⁹	Billion
10¹²	Trillion
10¹⁵	Quadrillion
10¹⁸	Quintillion
10²¹	Sextillion
10²⁴	Septillion
10²⁷	Octillion
10³⁰	Nonillion
10³³	Decillion
10³⁶	Undecillion
10³⁹	Duodecillion
10⁴²	Tredecillion
10⁴⁵	Quattuordecillion
10⁴⁸	Quindecillion
10⁵¹	Sexdecillion
10⁵⁴	Septendecillion
10⁵⁷	Octodecillion
10⁶⁰	Novemdecillion
10⁶³	Vigintillion

Roman Numerals

One	I
Two	II
Three	III
Four	IV
Five	V
Six	VI
Seven	VII
Eight	VIII
Nine	IX
Ten	X
Eleven	XI
Twelve	XII
Thirteen	XIII
Fourteen	XIV
Fifteen	XV
Sixteen	XVI
Seventeen	XVII
Eighteen	XVIII
Nineteen	XIX
Twenty	XX
Thirty	XXX
Forty	XL
Fifty	L
Sixty	LX
Seventy	LXX
Eighty	LXXX
Ninety	XC
One hundred	C
Five hundred	D
One thousand	M

Absolute Value

| -x | = x

| xy | = | x | × | y |

| x |² = x²

| x | = a, then x = -a or x = a

| x | < a, then -a < x < a

| x | > a, then x < -a or x > a

Basic Identities

Closure Axiom of Addition
Sum (or difference) of 2 real numbers equals a real number.

Additive Identity
a + 0 = a
e.g. 5 + 0 = 5 and 0 + 5 = 5

Additive Inverse
a + (-a) = 0
e.g. 3 + (-3) = 0

Associative of Addition
(a + b) + c = a + (b + c)
e.g. (2 + 3) + 5 = 2 + (3 + 5)

Commutative of Addition
a + b = b + a
e.g. 3 + 4 = 4 + 3

Definition of Subtraction
a - b = a + (-b)
e.g. 4 - 6 = 4 + (-6)

Closure Axiom of Multiplication
Product (or quotient if denominator is not equal to 0) of 2 real numbers equal to a real number.

Multiplicative Identity
a × 1 = a
e.g. 6 × (1) = 6 and 1× (6) = 6

Multiplicative Inverse
a × (1/a) = 1 (a is not equal to 0)
e.g. 6 × (1/6) = 1

Multiplication Times Zero
a × 0 = 0
e.g. 7 × 0 = 0

Associative of Multiplication
(a × b) × c = a ×(b × c)
e.g. (2 × 3) × 6 = 2 × (3 × 6)

Commutative of Multiplication
a × b = b × a
e.g. 4 × 6 = 6 × 4

Distributive Law
a (b + c) = ab + ac
e.g. 2 (3 + x) = 2(3) + 2(x)

Definition of Division
a/b = a(1/b)
e.g. 3/5 = 3(1/5)

Exponents and Powers

X⁰ = 1, X is not equal to 0.

X¹ = X

X^(-a) = 1/X^a

X^aX^b = X^a+b

(XY)^a = X^aY^a

(X^a)^b = X^ab

X^a/X^b = X^(a-b), X is not equal to 0.

(X/Y)^a = X^a/Y^a, X and Y are not equal to 0.

(X/Y)^a = X^a/Y^a

X^1/b =

,the bth root of X

X^a/b =

, the bth root of X raised to the a

Logarithm

log_b(1) = 0

log_bb = 1

log_b (x × y) = log_b(x) + log_b(y)

log_b(x/y) = log_b(x) - log_by

log_b(xⁿ) = n log_b(x)

Factorials
The factorial of a number is the product of all the whole numbers, except zero, that are less than or equal to that number.

1!	1 = 1
2!	2 × 1 = 2
3!	3 × 2 × 1 = 6
4!	4 × 3 × 2 × 1 = 24
5!	5 × 4 × 3 × 2 × 1 = 120
6!	6 × 5 × 4 × 3 × 2 × 1 = 720
7!	7 × 6 × 5 × 4 × 3 × 2 × 1 = 5,040
8!	8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 40,320
9!	9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 362,880
10!	10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 3,628,800
11!	11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 39,916,800
12!	12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 479,001,600

Consecutive Integers

Term	Example	Variable Using
Consecutive Integers	4, 5, 6, 7	x, x+1, x+2, x+3
Consecutive Even Integers	2, 4, 6, 8	x, x+2, x+4, x+6
Consecutive Odd Integers	3, 5, 7, 9	x, x+2, x+4, x+6

Example:
If the sume of the first and third consecutive integers is increased by 8, the result is 5 less than
triple the second integer. Find the integers.

Solution:
Let first integer = x,
second integer = x + 1,
third integer = x +2,
x + (x+2) + 8 = 3(x+1) - 5

Polynomial Vocabulary

Vocabulary	Definition	Example
Polynomial	Expression containing a finite sum of terms.	6x x²+ 5x = 1
Monomial	Polynomial with 1 term.	7 2x
Binomial	Polynomial with 2 terms.	x² - 9 3x + 1
Trinomial	Polynomial with 3 terms.	x² + 2x + 1 4x² + 6x - 3

Math Point Geometry Mode Numbers Conversion Table