Various formulas of junior high school mathematics application problems

Average problem formula (one number+another number) ÷2

The formula of the reverse driving problem is distance ÷ (large speed+small speed).

The formula of the problem of traveling in the same direction is the distance ÷ (large speed-small speed)

The formula of navigation problem is the same as above.

Formula of train crossing bridge (train length+bridge length) ÷ speed

Engineering problem formula 1÷ speed sum

Profit and loss problem formula (surplus+deficit) ÷ twice the difference.

Interest rate problem formula Total profit ÷ Cost×100% profit and loss (profit+loss) ÷ Difference between two distributions = number of shares participating in distribution.

(Big profit-small profit) ÷ Difference between two distributions = number of shares participating in distribution.

(big loss-small loss) ÷ The difference between two distributions = the number of shares participating in the distribution.

meet with

Meeting distance = speed × meeting time

Meeting time = meeting distance/speed and

Speed Sum = Meeting Distance/Meeting Time

catch up with

Catch-up distance = speed difference× catch-up time

Catch-up time = catch-up distance ÷ speed difference

Speed difference = catching distance ÷ catching time

Flowing water

Downstream velocity = still water velocity+current velocity

Countercurrent velocity = still water velocity-current velocity

Still water velocity = (downstream velocity+countercurrent velocity) ÷2

Water velocity = (downstream velocity-countercurrent velocity) ÷2

concentrate

Solute weight+solvent weight = solution weight.

The weight of solute/solution × 100% = concentration.

Solution weight × concentration = solute weight

Solute weight-concentration = solution weight.

Profits and discounts

Profit = selling price-cost

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

Up and down amount = principal × up and down percentage

Discount = actual selling price ÷ original selling price× 1 00% (discount <1)

Interest = principal × interest rate× time

After-tax interest = principal × interest rate × time × (1-20%) tree planting problem

1 The problem of planting trees on unclosed lines can be divided into the following three situations:

(1) If trees are planted at both ends of the non-closed line, then:

Number of plants = number of nodes+1 = total length-1.

Total length = plant spacing × (number of plants-1)

Plant spacing = total length ÷ (number of plants-1)

2 If you want to plant trees at one end of the unclosed line and not at the other end, then:

Number of plants = number of segments = total length ÷ plant spacing

Total length = plant spacing × number of plants

Plant spacing = total length/number of plants

(3) If no trees are planted at both ends of the non-closed line, then:

Number of plants = number of nodes-1 = total length-1.

Total length = plant spacing × (number of plants+1)

Plant spacing = total length ÷ (number of plants+1)

The quantitative relationship of planting trees on the closed line is as follows

Number of plants = number of segments = total length ÷ plant spacing

Total length = plant spacing × number of plants

Plant spacing = total length/number of plants 1 × number of plants = total number of plants.

Total copies/number of copies = number of copies

2 1 multiple × multiple = multiple

Multiply1Multiply = Multiply

Multiply/Multiply = 1 Multiply

3 Speed × Time = Distance

Distance/speed = time

Distance/time = speed

4 unit price × quantity = total price

Total price/unit price = quantity

Total price ÷ quantity = unit price

5 Work efficiency × working hours = total workload.

Total amount of work ÷ work efficiency = working hours

Total workload ÷ working time = working efficiency

6 addend+addend = sum

And-one addend = another addend

7 minuend-minuend = difference

Negative difference = negative

Difference+Minus = Minus

8 factor × factor = product

Product ÷ One factor = another factor

Dividend = quotient

Dividend = divisor

Quotient × Divider = Divider Sum and Difference Problem

(sum+difference) ÷ 2 = large number

(sum and difference) ÷ 2 = decimal

And folding problems.

Sum \ (multiple-1) = decimal

Decimal × multiple = large number

(or sum-decimal = large number)

Difference problem

Difference ÷ (multiple-1) = decimal

Decimal × multiple = large number

(or decimal+difference = large number) Is the area, perimeter, volume ... of a graph important? Halo, @ _ @|||| Factorization, trigonometric inequality, quadratic equation of one variable, sum and difference product, trigonometric function, sum formula of two angles, double angle and half angle, sine and cosine. . . . Do you want everything? In a coma . . . . Calculation formula of primary school mathematics graphics-Part I

1 square

Perimeter area side length

Perimeter = side length ×4

C=4a

Area = side length × side length

S=a×a

2 cubic meters

Volume a: edge length

Surface area = side length × side length ×6

S table =a×a×6

Volume = side length × side length × side length

V=a×a×a

3 rectangle

Perimeter area side length

Circumference = (length+width) ×2

C=2(a+b)

Area = length × width

S=ab

4 cuboid

V: volume s: area a: length b: width h: height.

(1) Surface area (L× W+L× H+W× H) ×2

S=2(ab+ah+bh)

(2) Volume = length × width × height

V=abh

5 triangle

S area a bottom h height

Area = bottom × height ÷2

s=ah÷2

Height of triangle = area ×2÷ base.

Triangle base = area ×2÷ Calculation formula of primary school mathematics figure-the following figure

6 parallelogram

S area a bottom h height

Area = bottom × height

S = ah

7 trapezoid

Height of upper bottom b and lower bottom h in s area a

Area = (upper bottom+lower bottom) × height ÷2

s=(a+b)× h÷2

8 laps

Area c perimeter d= diameter r= radius

(1) circumference = diameter ×∏=2×∏× radius

C=∏d=2∏r

(2) area = radius × radius×∈

Cylinder 9

V: volume h: height s; Bottom area r: bottom radius c: bottom perimeter

(1) Transverse area = bottom circumference × height.

(2) Surface area = lateral area+bottom area ×2

(3) Volume = bottom area × height

(4) Volume = lateral area ÷2× radius.

10 cone

V: volume h: height s; Bottom area r: bottom radius

Volume = bottom area × height ÷3

Total number ÷ total number of copies = average multiplication and factorization

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

a3+b3=(a+b)(a2-ab+b2)

a3-b3=(a-b)(a2+ab+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| formulas of trigonometric functions-Two-Corner Sum Formula

sin(A+B)=sinAcosB+cosAsinB

sin(A-B)=sinAcosB-sinBcosA

cos(A+B)=cosAcosB-sinAsinB

cos(A-B)=cosAcosB+sinAsinB

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)/(ctgb-ctga) formulas of trigonometric functions-double angle formula.

tan2A=2tanA/( 1-tan2A)

ctg2A=(ctg2A- 1)/2ctga

Cos2a = cos2a-sin2a = 2cos2a-1=1-2sin2a trigonometric function formula-half angle formula.

sin^2(α/2)=( 1-cosα)/2

cos^2(α/2)=( 1+cosα)/2

tan^2(α/2)=( 1-cosα)/( 1+cosα)

Tan (α/2) = sinα/(1+cosα) = (1-cosα)/sinα formulas of trigonometric functions-sum differential product formula.

sinα+sinβ= 2 sin[(α+β)/2]cos[(α-β)/2]

sinα-sinβ= 2cos[(α+β)/2]sin[(α-β)/2]

cosα+cosβ= 2cos[(α+β)/2]cos[(α-β)/2]

Cos α-cos β =-2 sin [(α+β)/2] sin [(α-β)/2] trigonometric function formula-product sum and difference formula.

sinαcosβ=( 1/2)[sin(α+β)+sin(α-β)]

cosαsinβ=( 1/2)[sin(α+β)-sin(α-β)]

cosαcosβ=( 1/2)[cos(α+β)+cos(α-β)]

Sinα sinβ =-(1/2) [cos (α+β)-cos (α-β)] The formula of trigonometric function-the double angle formula, has not found the mathematical symbol before, so it is not clear enough. Please modify it.

Formulas of trigonometric functions-double angle formula

sin(2α)=2sinα cosα

cos(2α)=cos^2(α)-sin^2(α)=2cos^2(α)- 1= 1-2sin^2(α)

Tan (2 α) = 2 tan α/[1-tan 2 (α)] formulas of trigonometric functions-universal formula

sinα=2tan(α/2)/[ 1+tan^2(α/2)]

cosα=[ 1-tan^2(α/2)]/[ 1+tan^2(α/2)]

Tan α = 2tan (α/2)/[1-tan 2 (α/2)] Quadruple angle, quintuple angle. . . . . The ten-angle formula has never been learned and will not be learned. . . . sine law

a/sinA=b/sinB=c/sinC=2R

Note: where r represents the radius of the circumscribed circle of the triangle.

cosine theorem

B2 = a2+C2-2 acco b

Note: Angle B is a standard equation containing a circle between side A and side C..

(x-a)2+(y-b)2=r2

Note: (a, b) is the central coordinate.

Circular general equation

x2+y2+Dx+Ey+F=0

Note: D2+E2-4f > 0 unary quadratic equation

Ax 2+bx+c = 0 (a, b and c are real numbers a≠0).

X 2+2x+ 1 = 0 arc length formula