Elgebra Math 10

Real number
Irrational numbers π , √��

Rational numbers Integers Whole
Natural

3 5 1 2 4 2 2 3

Rational Like:

Integers {…, -3, -2, -1, 0, 1, 2, 3…….} Whole {0, 1, 2, 3…} Natural {1, 2, 3…}

, , ,

Properties of real numbers 1234-

Reflexive property a=a Symmetric property a = b then b = a Transitive property a = b and b = c then a = c Principle of substitution if a = b then we can substitute b for a in any expirations

Commutative properties a+b=b+a , a.b=b.a Associative properties a+(b+c)=(a+b)+c=a+b+c a.(b.c)=(a.b).c=a.b.c Distributive properties a.(b+c)=a.b+a.c (a+b).c=a.c+b.c Identity Properties 0+a=a+0=a a.1=a.a=a additive inverse Properties a + (- a ) = - a +a = 0 Multiplicative inverse properties a. =
1 �� 1 ��

Multiplication by zero a.0=0

. �� = 1 if b ≠ 0

0 ��

Division properties =0
�� ��

= 1 if a ≠ 0
�� −�� −�� �� �� �� −�� −�� �� ��

Rules of signs a(-b ) = - (ab) Exponents ��n = a.a.a…….a , (-a)b = - (ab) , ( -a ) ( -b ) = ab , - ( -a ) = a , ��0 = 1 if a ≠ 0 , ��−n =
1 �� n

=

=-

,

=

n factors ,

,

if a ≠ 0
1

Laws of exponents

��n ��m = ��m+n , (��m )n = ��mn Square roots √��2 =|��|

(����)n = ��n �� n ,

�� �� �� ��

= ����−�� =

�� ��−��

���� �� ≠ 0

,

( )�� =
�� ��

�� �� ���� ,

���� �� ≠ 0

Geometry Review

�� 2 = ��2 + �� 2

Pythagorean Theorem

Geometry Formulas
1

Area = LW Perimeter = 2L + 2W

Area = 2bh

Circumference = 2πr = πd

Area = π�� 2

Volume = LWH Surface area= 2LW+ 2LH+2WH

Volume= π�� 2 ℎ =π�� 2 ℎ + 2πrℎ Surface area=

Volume= 3 ���� 3
4

Surface area=4π�� 2

Polynomials
Special Products Difference of two squares

( �� + �� )2 = �� 2 + 2���� + ��2 ( �� − �� )2 = �� 2 − 2���� + ��2

( x – a )( x + a ) = �� 2 − ��2

Squares of binomials or perfect squares

( �� + �� )3 = �� 3 + 3���� 3 + 3��2 �� + ��3 ( �� − �� )3 = �� 3 − 3���� 3 + 3��2 �� + ��3 Differences of two cubes (�� − ��)(�� 2 + ���� + ��2 ) = �� 3