Total copies/number of copies = number of copies
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
Calculation formula of mathematical graphics in primary schools
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÷ height
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 = 2r
(2) area = radius × radius×∈
Cylinder 9
V: volume h: height s; Bottom area r: bottom radius c: bottom perimeter
(1) lateral 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 value
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 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
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
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
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 × (1-20%)
Universal unit conversion
Length unit conversion
1 km =1000m1m =1decimeter/decimeter =10cm1m =10cm/kloc-.
Area unit conversion
1 square kilometer = 100 hectare 1 hectare = 10000 square meter 1 square meter = 100 square decimeter.
1 dm2 = 100 cm2 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
1t = 1000kg 1kg = 1000g 1kg = 1kg。
Rmb unit conversion
1 yuan = 10 angle 1 angle = 10 point 1 yuan = 100 point.
Time unit conversion
1 century = 100 1 year =1February (3 1 day) Yes:1August (30 days) Yes: April and September.
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 hour = 60min 1 minute = 60s 1 hour = 3600s.
The first chapter is a rich graphic world.
1. Prisms include straight prisms and oblique prisms.
2. Graphics are composed of points, lines and surfaces.
3. Faces intersect to get lines, and lines intersect to get points.
4. Point to line, opposite the line, facing the body.
5. In a prism, the intersection of any two adjacent faces is called an edge, and the intersection of two adjacent sides is called a side. All sides of a prism are equal in length. The upper and lower bottom surfaces of the prism have the same shape, and the side surfaces are rectangular.
6. Cut a cuboid with a plane, and the section is called a section.
7. Call it front view, left view and top view.
8. A plane figure is a closed figure composed of some line segments that are not on the same straight line.
9. A graph consisting of an arc and two radii passing through the end of the arc is called a fan.
Chapter II Rational Numbers and Their Operations
1. rational number: integer positive number, 0, negative number; Irrational number: positive and negative fractions.
2. Numbers greater than 0 are called positive numbers, which are represented by the symbol+(pronounced as positive numbers).
3. A number less than 0 is called a negative number, which is represented by the symbol-(pronounced negative).
4.0 is neither positive nor negative.
5. Draw a horizontal straight line, take a point on the straight line to represent 0 (called the origin), choose a certain length as the unit length, and specify the right direction on the straight line as the positive direction to get the number axis.
6. Any rational number can be represented by a point on the number axis.
7. If two numbers are only different in sign, then we call one of them the inverse of the other number, which is also called the inverse of each other. The antonym of 0 is 0.
8. The number represented by two points on the number axis is always larger on the right than on the left.
9. Positive numbers are greater than 0, negative numbers are less than 0, and positive numbers are greater than negative numbers.
10. The distance between the point corresponding to a number and the origin on the number axis is called the absolute value of the number.
1 1. The absolute value of a positive number is itself; The absolute value of a negative number is its reciprocal; The absolute value of 0 is 0.
12. Comparing two negative numbers, the larger absolute value is smaller.
13. Add two numbers with the same symbol, take the same symbol, and add the absolute values; Two numbers with different signs are added, and the sum is 0 when the absolute values are equal; When the absolute values are not equal, take the sign of the number with larger absolute value and subtract the number with smaller absolute value from the number with larger absolute value; Add a number to 0 and you still get the number.
14. Subtracting a number is equal to adding the reciprocal of this number.
15. When two numbers are multiplied, the sign of the same symbol is negative, and the absolute value is multiplied. Multiply any number by 0, and the product is still 0.
16. Two rational numbers whose product is 1 are reciprocal.
17. Divide two rational numbers, the same sign is positive and the different sign is negative, and divide by the absolute value. Divide 0 by any number except 0 to get 0. 0 cannot be partitioned.
18. Dividing by a number is equal to multiplying the reciprocal of this number.
19. the operation of finding the product of n identity factors a is called power, the result of power is called power, a is called base, and n is called exponent.
20. Calculate the power first, then multiply and divide, and finally add and subtract; If there are brackets, count them first.
Chapter III Letter Representation of Numbers
1. The formula of numbers or letters connected by operation symbols is called algebraic expression, and a single number or letter is also an algebraic expression.
2. Items with the same letter and the same letter index are called similar items. Merging similar items into one item is called merging similar items.
3. When merging similar items, we add up the coefficients of similar items, and the indexes of letters and letters remain unchanged.
There is a "+"before the bracket. After removing the brackets and the "+"sign in front of them, the symbols of the items in the original brackets remain unchanged; There is a "-"before the brackets. After removing the brackets and the "-"sign in front of them, the symbols of the original brackets will change.
Chapter IV Plane Figures and Their Positional Relations
The 1. line segment has two endpoints; Extending a line segment infinitely in one direction forms a ray, which has an endpoint; A straight line is formed by an infinite extension of a line segment in two directions, and the straight line has no end points.
There is a straight line after two o'clock.
3. In the connection between two points, the line segment is the shortest. The length of the line segment between two points is called the distance between these two points.
4. An angle is a graph composed of two rays with a common endpoint, and the common endpoint of the two rays is the vertex of the angle.
5. An angle can also be regarded as a ray rotating around its endpoint.
6. A ray drawn from the vertex of an angle divides the angle into two equal angles. This ray is called the bisector of the angle.
7. We usually use "∨" to indicate parallelism. After passing a point outside the straight line, there is one and only one straight line parallel to this straight line; If both lines are parallel to the third line, then the two lines are parallel to each other; Two straight lines intersect and there is only one intersection.
8. We usually use ⊥. In the plane, there is one and only one straight line perpendicular to the known straight line; Of all the line segments connecting the outer point and the point on the line, the vertical line segment is the shortest.
9. If two straight lines intersect at right angles, they are perpendicular to each other.
10. The intersection of two vertical lines is called vertical foot.
Chapter 5 One-variable linear equation
1. In an equation, there is only one unknown x (element), and the exponent of the unknown is 1 (degree). Such an equation is called a one-dimensional linear equation.
2. Adding (or subtracting) the same algebraic expression on both sides of the equation at the same time, the result is still an equation.
3. Both sides of the equation are multiplied by the same number at the same time (or divided by the same number that is not 0), and the result is still an equation.
Chapter VI Data in Life
1. Use circles and sectors to represent the relationship between the whole and the parts, that is, use circles to represent the whole, each sector in the circle represents different parts of the whole, and the size of the sectors reflects the percentage of the parts in the whole. This kind of statistical chart is called departmental statistical chart.
2. In the sector statistical chart, the percentage of each part in the whole is equal to the ratio of the central angle of the sector corresponding to this part to 360.
3. The pie chart can clearly show the percentage of each part in the total.
Bar chart can clearly show the specific figures of each project.
5. The broken line statistical chart can clearly reflect the changes of things.
Chapter VII Possibility
1. In life, there are some things that we can be sure will happen in advance. These things are called inevitable events. Some things we can make sure in advance will not happen. These things are called impossible events. Inevitable events and impossible events are certain.
There are still many things that we can't be sure whether it will happen in advance. This kind of thing is called uncertain events. The possibility of an uncertain event depends on its size.