The circumference of a rectangle = (length+width) ×2 C=(a+b)×2.
Circumference of a square = side length ×4 C=4a
Area of rectangle = length× width S=ab
Area of a square = side length × side length s = a.a = a.
Area of triangle = base × height ÷2 S=ah÷2.
Area of parallelogram = base × height S=ah
Trapezoidal area = (upper bottom+lower bottom) × height ÷ 2s = (a+b) h ÷ 2.
Diameter = radius ×2 d=2r Radius = diameter ÷2 r= d÷2.
Circumference = π× diameter = π× radius× 2c = π d = 2π r
Area of circle = π× radius× radius
Area of triangle = base × height ÷2. The formula S= a×h÷2.
Square area = side length × side length formula S= a×a
Area of rectangle = length× width Formula S= a×b
Area of parallelogram = base× height Formula S= a×h
Trapezoidal area = (upper bottom+lower bottom) × height ÷2 Formula S=(a+b)h÷2
Sum of internal angles: sum of internal angles of triangle = 180 degrees.
Cuboid volume = length× width× height formula: V=abh
Volume of cuboid (or cube) = bottom area × height formula: V=abh.
Volume of cube = side length × side length × side length formula: V=aaa.
Circumference = diameter × π formula: L = π d = 2π r
Area of circle = radius × radius× π formula: s = π R2.
Surface (side) area of cylinder: The surface (side) area of cylinder is equal to the perimeter of bottom multiplied by height. Formula: s = ch = π DH = 2π RH.
Surface area of cylinder: the surface area of cylinder is equal to the perimeter of the bottom multiplied by the height plus the area of the circles at both ends. Formula: S=ch+2s=ch+2πr2.
Volume of cylinder: the volume of cylinder is equal to the bottom area multiplied by the height. Formula: V=Sh
Volume of cone = 1/3 bottom× product height. Formula: V= 1/3Sh
Law of fractional addition and subtraction: Fractions with the same denominator are added and subtracted, only the numerator is added and subtracted, and the denominator remains unchanged. Fractions of different denominators are added and subtracted, first divided, then added and subtracted.
The multiplication of fractions is: use the product of molecules as numerator and the product of denominator as denominator.
The law of division of fractions: dividing by a number is equal to multiplying the reciprocal of this number.
Second, the unit conversion
(1)1km =1km =1000m1m =10 decimeter1decimeter =10 cm/kloc.
(2) 1 m2 = 100 square decimeter 1 square decimeter = 100 square centimeter 1 square centimeter = 100 square millimeter.
(3) 1 m3 = 1000 cubic decimeter 1 cubic decimeter = 1000 cubic centimeter 1 cubic centimeter = 1000 cubic millimeter.
(4)1t =1000 kg1kg =1000 mg =1kg = 2 kg.
(5) 1 hectare = 1 ten thousand square meters 1 mu = 666.666 square meters.
(6) 1 liter = 1 cubic decimeter = 1000 ml 1 ml = 1 cubic centimeter.
(7) 1 yuan = 10 angle 1 angle = 10 point 1 yuan = 100 point.
(8) 1 century = 100 1 year =1February (3 1 day):1\ 3 \ 5 \ 7 \ 8 \/kloc-
February 28th in a normal year and February 29th in a leap year: 365 days in a normal year and 366 days in a leap year: 1 =24 hours: 1 =60 minutes.
1 minute =60 seconds 1 hour =3600 seconds.
Third, the calculation formula of quantitative relationship
1, number of copies × number of copies = total number of copies/number of copies = total number of copies/number of copies = number of copies.
2. 1 multiple× multiple = multiple1multiple = multiple/multiple = 1 multiple
3. Speed × time = distance/speed = time/distance/time = speed
4. Unit price × quantity = total price ÷ unit price = total quantity ÷ quantity = unit price
5. Work efficiency × working hours = total workload ÷ work efficiency = working hours ÷ total workload ÷ working hours = work efficiency.
6. Appendix+Appendix = sum, and-one addend = another addend.
7. Minus-Minus = Minus-Minus = Minus+Minus = Minus
8. Factor × factor = product ÷ one factor = another factor.
9. Dividend = quotient dividend = divisor quotient × divisor = dividend
Fourth, arithmetic.
1. additive commutative law: Two numbers are added to exchange the position of addend, and the sum is unchanged.
2. Law of addition and association: When three numbers are added, the first two numbers are added first, or the last two numbers are added first, and then they are the same as the first number.
Three numbers add up, and the sum remains the same.
3. Multiplication and exchange law: when two numbers are multiplied, the position of the exchange factor remains unchanged.
4. Multiplication and association law: When three numbers are multiplied, the first two numbers are multiplied, or the second two numbers are multiplied first, and then the third number is multiplied, and the product remains unchanged.
5. Multiplication and distribution law: When two numbers are multiplied by the same number, you can multiply the two addends by this number respectively, and then add the two products, and the result remains unchanged. Such as: (2+4) × 5 = 2× 5+4× 5.
6. Nature of division: In division, the dividend and divisor are expanded (or reduced) by the same multiple at the same time, and the quotient remains unchanged. Divide 0 by any number other than 0 to get 0.
7. Equation: An equation in which the value on the left of the equal sign equals the value on the right of the equal sign is called an equation. Basic properties of the equation: When both sides of the equation are multiplied (or divided) by the same number at the same time, the equation is still valid.
8. Equations: Equations with unknowns are called equations.
9. One-dimensional linear equation: An equation with an unknown number of 1 is called a one-dimensional linear equation.
Example method and calculation of learning linear equation of one variable. That is, an example is given to illustrate that the formula is replaced by χ and calculated.
10. Score: divide the unit "1" into several parts on average, and the number representing such a part or points is called a score.
1 1. Addition and subtraction of fractions: add and subtract fractions with denominator, only add and subtract numerators, and the denominator remains unchanged. Fractions of different denominators are added and subtracted, first divided, then added and subtracted.
12. Comparison of fraction size: Compared with the fraction of denominator, the numerator is large and the numerator is small. Compare the scores of different denominators, divide them first and then compare them; If the numerator is the same, the denominator is big and small.
13. Fractions are multiplied by integers, and the product of the multiplication of fractions and integers is a numerator, and the denominator remains unchanged.
14. Fractions are multiplied by fractions, the product of numerator multiplication is numerator, and the product of denominator multiplication is denominator.
15. Fraction divided by integer (except 0) equals fraction multiplied by the reciprocal of the integer.
16. True fraction: The fraction with numerator less than denominator is called true fraction.
17. False fraction: the fraction with numerator greater than denominator or numerator equal to denominator is called false fraction. False score is greater than or equal to 1.
18. With score: write the false score as an integer, and the true score is called with score.
19. The basic nature of the fraction: the numerator and denominator of the fraction are multiplied or divided by the same number at the same time (except 0), and the size of the fraction remains unchanged.
20. A number divided by a fraction is equal to the number multiplied by the reciprocal of the fraction.
2 1.A divided by b (except 0) equals the reciprocal of a multiplied by b.
Verb (abbreviation of verb) special problems
Formula of 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)
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 unclosed 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 trees are planted at one end of the non-closed line, but 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
The question of 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.
encounter a problem
Meeting distance = speed × meeting time
Meeting time = meeting distance/speed and
Speed Sum = Meeting Distance/Meeting Time
Catch up with the problem
Catch-up distance = speed difference× catch-up time
Catch-up time = catch-up distance ÷ speed difference
Speed difference = catching distance ÷ catching time
Tap water problem
(1) general formula:
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
(2) Formula for two ships sailing in opposite directions:
Downstream speed of ship A+downstream speed of ship B = still water speed of ship A+still water speed of ship B.
(3) Formula for two ships sailing in the same direction:
Hydrostatic speed of rear (front) ship-Hydrostatic speed of front (rear) ship = the speed of narrowing (expanding) the distance between two ships.
Concentration problem
Solute weight+solvent weight = solution weight.
The weight of solute/solution × 100% = concentration.
Solution weight × concentration = solute weight
Solute weight-concentration = solution weight.
Profit and discount problem
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 × (1-5%)
Engineering problems
(1) general formula:
Work efficiency × working hours = total workload.
Total workload ÷ working time = working efficiency
Total amount of work ÷ work efficiency = working hours
(2) Assuming that the total workload is "1", the formula for solving engineering problems is:
1÷ working time = a fraction of the total workload completed in unit time?
1What is the score that can be completed per unit time = working time.
Are you satisfied with the above answers?