▲ law of multiplication:

Multiplicative commutative law: a×b = b×a

The law of multiplicative association: a×b×c = a×(b×c)

Multiplication and distribution law: a×c+b×c=c×(a+b)

a×c - b×c=c×(a - b)

▲ nature of division: a÷b÷c = a÷(b×c)

▲ Subtraction property: A–B-C = A-(B+C)

▲ Law of solving equations:

◇ Addendum+Addendum = sum;

Appendix = sum-another addend.

◇ Subtraction–Subtraction = difference;

Subtraction = difference+subtraction;

Subtraction = minuend-difference.

Factor × factor = product;

Factor = product ÷ another factor.

Divider divisor = quotient;

Dividend = quotient × divisor;

Divider = dividend quotient.

◆ Travel problems:

Distance = speed × time;

Time = distance/speed;

Speed = distance/time.

◆ Meeting questions:

Meeting distance = (speed A+ speed B) × meeting time;

Meeting time = meeting distance ÷ (speed A+ speed b);

A speed = meeting distance ÷ meeting time -B speed;

B speed = meeting distance ÷ meeting time -A speed.

◆ Engineering problems:

Total amount of work = working efficiency × working hours;

Working hours = total amount of work ÷ working efficiency;

Work efficiency = total workload ÷ working hours;

Total amount of work = planned work efficiency × planned work time;

Total amount of work = actual working efficiency × actual working time;

Actual working hours = total amount of work ÷ actual working efficiency;

Actual working efficiency = total workload ÷ actual working time;

◆ buying and selling problems:

Total amount = unit price × quantity;

Quantity = total amount ÷ unit price;

Unit price = total amount ÷ quantity.

Grade?Six

(1)S=nR2-nr2 or S=n(R2-r2)

(2)(a-b) divided by b* 100% or (b-a) divided by b* 100%.

(3) The number of attendees divided by the total number.

(4)b*( 1+C%) or b*( 1-C%)

(5) Interest = principal * interest rate * time, interest tax = principal * interest rate * time *( 1-5%)

(6)a divided by (1+C%) or A divided by (1-C%)

Grade?Seven

Table of Common Mathematical Formulas: Formula Expressions

Square difference a2-b2=(a+b)(a-b)

The square of sum and difference (a+b) 2 = A2+B2+2ab (a-b) 2 = A2+B2-2ab.

Cubes of sum and difference A3+B3 = (a+b) (A2-AB+B2) A3-B3 = (A-B) (A2+AB+B2)

Trigonometric inequality | A+B |≤| A |+B||||| A-B|≤| A |+B || A |≤ B < = > -b≤a≤b

|a-b|≥|a|-|b| -|a|≤a≤|a|

The solution of the unary quadratic equation-b+√ (B2-4ac)/2a-b-b+√ (B2-4ac)/2a

The relationship between root and coefficient x1+x2 =-b/ax1* x2 = c/a Note: Vieta theorem.

Discriminant b2-4a=0 Note: The equation has two equal real roots.

B2-4ac >0 Note: The equation has real roots.

B2-4ac & lt； 0 Note: The equation has multiple yokes.

Table of Common Mathematical Formulas: formulas of trigonometric functions

Two-angle summation formula sin (a+b) = sinacosb+cosasinbsin (a-b) = sinacosb-sinbcosa.

cos(A+B)= cosa cosb-Sina sinb cos(A-B)= cosa cosb+Sina sinb

tan(A+B)=(tanA+tanB)/( 1-tanA tanB)tan(A-B)=(tanA-tanB)/( 1+tanA tanB)

cot(A+B)=(cotA cotB- 1)/(cot B+cotA)cot(A-B)=(cotA cotB+ 1)/(cot B-cotA)

Double angle formula sin2a = 2sina cos atan2a = 2tana/(1-tan2a)

cos2a = cos2a-sin2a = 2 cos2a- 1 = 1-2 sin2a cot2A =(cot2A- 1)/2 cota

Half-angle formula sin (a/2) = √ ((kloc-0/-COSA)/2) sin (a/2) =-√ ((kloc-0/-COSA)/2).

cos(A/2)=√(( 1+cosA)/2)cos(A/2)=-√(( 1+cosA)/2)

tan(A/2)=√(( 1-cosA)/(( 1+cosA))tan(A/2)=-√(( 1-cosA)/(( 1+cosA))

cot(A/2)=√(( 1+cosA)/(( 1-cosA))cot(A/2)=-√(( 1+cosA)/(( 1-cosA))

Sum-difference product 2sina cosb = sin (a+b)+sin (a-b) 2cosasinb = sin (a+b)-sin (a-b)

2 cosa cosb = cos(A+B)-sin(A-B)-2 sinasinb = cos(A+B)-cos(A-B)

sinA+sinB = 2 sin((A+B)/2)cos((A-B)/2 cosA+cosB = 2 cos((A+B)/2)sin((A-B)/2)

tanA+tanB = sin(A+B)/cosa cosb tanA-tanB = sin(A-B)/cosa cosb

cotA+cot bsin(A+B)/Sina sinb-cotA+cot bsin(A+B)/Sina sinb

The sum of the first n terms in some sequences is1+2+3+4+5+6+7+8+9+…+n = n (n+1)/21+3+5+7+9+/kloc-0.

2+4+6+8+ 10+ 12+ 14+…+(2n)= n(n+ 1) 12+22+32+42+52+62+72+82+…+N2 = n(n+ 1)(2n+ 1)/6

13+23+33+43+53+63+…n3 = N2(n+ 1)2/4 1 * 2+2 * 3+3 * 4+4 * 5+5 * 6+6 * 7+…+n(n+ 1)= n(n+ 1)(n+2)/3

Sine theorem a/sinA=b/sinB=c/sinC=2R Note: where r represents the radius of the circumscribed circle of a triangle.

Cosine Theorem b2=a2+c2-2accosB Note: Angle B is the included angle between side A and side C..

Table of common mathematical formulas: analytic geometric formulas

The standard equation of a circle (x-a)2+(y-b)2=r2 Note: (A, B) is the center coordinate.

General equation of circle x2+y2+Dx+Ey+F=0 Note: D2+E2-4f > 0

Parabolic standard equation y2=2px y2=-2px x2=2py x2=-2py

Commonly used mathematical formula table: geometric figure formula

Lateral area of a straight prism S=c*h lateral area of an oblique prism s = c' * h.

Lateral area of a regular pyramid S= 1/2c*h' lateral area of a regular prism S= 1/2(c+c')h'

The lateral area of the frustum of a cone S = 1/2(c+c')l = pi(R+R)l The surface area of the ball S=4pi*r2.

Lateral area of cylinder S=c*h=2pi*h lateral area of cone s =1/2 * c * l = pi * r * l.

Arc length formula l=a*r (a is the radian number of central angle r >; 0) sector area formula s= 1/2*l*r

Conical volume formula V= 1/3*S*H Conical volume formula V= 1/3*pi*r2h

Cylinder volume formula V=s*h cylinder V=pi*r2h

Oblique prism volume V=S'L (S' is the straight cross-sectional area and l is the side length) Note: pi = 3.14159265358979. ...