于木公主的小小世界

A. Rules for the operations of directed number

Addition and subtraction
a+(+b)=a-(-b)=a+b
a+(- b)=a-(+b)=a-b

Multiplicatio

(+a)×(+b)=(-a)×(-b)=+(a×b)
(+a)×(-b) =(-a)×(+b)=-(a×b)

Division
(+a)÷(+b)=(-a)÷(-b)=+(a÷b
(+a)÷(-b) =(-a)÷(+b)=-(a×b)

B. Percentage

Percentage increase
Increase = new value - original value
Percentage increase = ( increase ÷ original value ) × 100%
Increase = original value × percentage increase
New value = original value × ( 1 + percentage increase )

Percentage decrease
Decrease = original value - new value
Percentage decrease = decrease ÷ original value × 100%
Decrease = original value × percentage decrease
New value = original value x (1 - percentage decrease)

Percentage change = (new value - original value) ÷ original value x 100%

Profit
Profit = selling price - cost price
Profit per cent = ( profit ÷ cost price ) x 100%
Profit = cost price x profit per cent
Selling price = cost price x (1 + profit per cent)

Loss
Loss = cost price - selling price
Loss per cent = ( loss ÷ cost price ) x 100%
Loss = cost price x loss per cent
Selling price = cost price ×( 1 - loss per cent )

Discount
Discount = marked price - selling price
Discount per cent = ( discount ÷ marked price ) x 100%
Discount = marked price × discount per cent
Selling price = marked price x ( 1 - discount per cent )

C. Conditions for congruent triangles
SSS
SAS
ASA
AAS
RHS

D. Conditions for similar triangles
AAA
3 sides prop.
ratio of sides, inc. angle

E. Angles related to intersecting lines
adj. angles on st. line
angles at a point
vert. opp. angles

F. Angles related to parallel lines
corr. angles, AB//CD
alt. angles, AB//CD
int. angles, AB//CD

G. Three conditions for parallel lines
corr. angles equal
alt. angles equal
int. angles equal