All the math formulas in the seventh grade

Multiplication and factorization

a2-B2 =(a+b)(a-b)a3+B3 =(a+b)(a2-a b+B2)a3-B3 =(a-b)(a2+a b+B2)

Triangle inequality

| a+b |≤| a |+| b | | a-b |≤| a |+| b | | a |≤b & lt； = & gt-b≤a≤b

|a-b|≥|a|-|b| -|a|≤a≤|a|

Solution of quadratic equation in one variable

-b+√(B2-4ac)/2a-b-b+√(B2-4ac)/2a

Relationship between root and coefficient

X1+x2 =-b/ax1* x2 = c/a note: Vieta's 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.

formulas of trigonometric functions

Two-angle sum formula

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

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)

ctg(A+B)=(ctgActgB- 1)/(ctg B+ctgA)ctg(A-B)=(ctgActgB+ 1)/(ctg B-ctgA)

Double angle formula

tan2A = 2 tana/( 1-tan2A)ctg2A =(ctg2A- 1)/2c TGA

cos2a = cos2a-sin2a = 2 cos2a- 1 = 1-2 sin2a

half-angle formula

sin(A/2)=√(( 1-cosA)/2)sin(A/2)=-√(( 1-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))

ctg(A/2)=√(( 1+cosA)/(( 1-cosA))ctg(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

ctgA+ctgBsin(A+B)/Sina sinb-ctgA+ctgBsin(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..

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

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.

The arc length formula l=a*r a is the radian number r > of the central angle; 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

Oblique prism volume V=S'L Note: where s' is the straight cross-sectional area and l is the side length.

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

The 0 at the end of each stage is not read.

0 reading in front of each level.

The zeros in the middle of each level, no matter how many zeros there are, are read-only.

A cone is 1/3 cylinders.

A cylinder is three times as big as a cone.

The numerator is the same, and the smaller the denominator, the greater the score.

The denominator is the same, and the bigger the numerator, the smaller the score.

The numerator is above and the denominator is below.

encounter a problem

Meeting distance = speed and meeting time

Meeting time = meeting distance, speed and sum.

Speed Sum = Meeting Distance Meeting Time

Profit and discount problem

Profit = selling price-cost

Profit rate = profit cost 100% = (selling price cost-1) 100%.

Increase or decrease amount = percentage of principal increase or decrease

Interest = principal interest rate time

After-tax interest = principal interest rate time (1-20%)

Length unit conversion

1 km = 1 000m1m = 10 decimeter.

1 decimeter =10cm1m =10cm.

1 cm = 10/0mm

Area unit conversion

1 km2 = 100 hectare

1 ha = 1 10,000 m2

1 m2 = 100 square decimeter

1 square decimeter = 100 square centimeter

1 cm2 = 100 mm2

Volume (volume) unit conversion

1 m3 = 1000 cubic decimeter

1 cubic decimeter = 1000 cubic centimeter

1 cubic decimeter = 1 liter

1 cm3 = 1 ml

1 m3 = 1000 liter

Weight unit conversion

1 ton = 1000 kg

1 kg =1000g

1 kg = 1 kg

Rmb unit conversion

1 yuan = 10 angle.

1 angle = 10 point

1 yuan = 100 integral.

Time unit conversion

1 century = 100 1 year =65438+ February.

The big month (3 1 day) includes:1\ 3 \ 5 \ 7 \ 8 \10 \ 65438+February.

Abortion (30 days) includes: April \ June \ September \165438+1October.

February 28th in a normal year and February 29th in a leap year.

There are 365 days in a normal year and 366 days in a leap year.

1 day =24 hours 1 hour =60 minutes.

1 minute =60 seconds 1 hour =3600 seconds.

Number of copies × number of copies = total number of copies/number of copies = number of copies.

Speed × time = distance/speed = time

Distance/Time = Speed Unit Price × Quantity = Total Price

Total price/unit price = total quantity/quantity = unit price

Working efficiency × working time = total workload ÷ total workload ÷ working efficiency = working time ÷ total workload ÷ working time = working efficiency addend+addend = and

Sum- one addend = another addend minus-minus = difference.

Negative difference = negative difference+negative = negative.

Factor × factor = product ÷ One factor = another factor.

Dividend-Divider = Quotient Divider-Divider = Divider

Quotient × Divider = Divider

And folding problems.

(sum+difference) ÷ 2 = large number (sum-difference) ÷ 2 = decimal.

Sum ÷ (multiple- 1) = decimal × multiple = large number

Sum-Decimal = large number

Difference problem

Difference ÷ (multiple-1) = decimal× multiple = large number

Decimal+difference = large number

encounter a problem

Meeting distance = speed and x meeting time = meeting distance ÷ speed and

Speed Sum = Meeting Distance/Meeting Time

Profit and discount problem

Profit = selling price-cost profit rate = profit/cost × 100% = (selling price/cost-1) × 100%.

Discount = actual selling price ÷ original selling price × 100% (discount < 1) interest = principal× interest rate× time after tax interest = principal× interest rate× time × (1-20%)

Addition exchange rate: a+b = b+a.

Additive binding rate: a+b+c=a+(b+c)