The mid-term exam is coming soon. Can anyone tell me about the knowledge points of the compulsory subject 5 in mathematics, such as some commonly used theories or formulas (which are not in the book)

url=]Length unit conversion[/url]

1 kilometer = 1000 meters 1 meter = 10 decimeters

1 decimeter = 10 centimeters 1 Meter = 100 centimeters

1 centimeter = 10 millimeters

[url=]Area unit conversion[/url]

1 square kilometer = 100 hectares

p>

1 hectare = 10,000 square meters

1 square meter = 100 square decimeters

1 square decimeter = 100 square centimeters

1 square meter Centimeter = 100 square millimeters

[url=]Volume unit conversion[/url]

1 cubic meter = 1000 cubic decimeter

1 Cubic decimeter = 1000 cubic centimeters

1 cubic decimeter = 1 liter

1 cubic centimeter = 1 milliliter

1 cubic meter = 1000 liters

[url=] Weight unit conversion[/url]

1 ton=1000 kilograms

1 kilogram=1000 grams

1 kilogram=1 Kilogram

[url=]RMB unit conversion[/url]

1 yuan = 10 jiao

1 jiao = 10 cents

1 yuan = 100 cents

[url=]Time unit conversion[/url]

1 century = 100 years 1 year = 12 months

大月( 31 days) include: 1\3\5\7\8\10\December

Small months (30 days) include: 4\6\9\11 months

There are 28 days in February in ordinary years and 29 days in February in leap years

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

1 day = 24 hours and 1 hour = 60 minutes

1 minute = 60 seconds 1 hour = 3600 seconds

1. Length

(1) What is length

Length is a measure of one-dimensional space .

(2) Common units of length

* Kilometer (km) * Meter (m) * Decimeter (dm) * Centimeter (cm) * Millimeter (mm) * Micron (um) )

(3) Conversion between units

* 1 mm = 1000 microns * 1 cm = 10 mm * 1 decimeter = 10 cm * 1 meter = 1000 mm * 1 Kilometer = 1000 meters

2. Area

(1) What is area

Area is the size of the plane occupied by an object. The measurement of the surface area of ??a three-dimensional object is generally called surface area.

(2) Commonly used area units

* Square millimeters* Square centimeters* Square decimeters* Square meters* Square kilometers

(3) Area units Conversion

* 1 square centimeter = 100 square millimeters * 1 square decimeter = 100 square centimeters * 1 square meter = 100 square decimeters

* 1 metric meter = 10,000 square meters * 1 square kilometer = 100 hectares

3. Volume and volume

(1) What is volume and volume

Volume is the size of the space occupied by an object .

Volume, the volume that boxes, oil drums, warehouses, etc. can accommodate, is usually called their volume.

(2) Commonly used units

1 Volume unit

* Cubic meter* Cubic decimeter* Cubic centimeter

2 Volume unit* Liter * milliliter

(3) Unit conversion

1 volume unit

* 1 cubic meter = 1000 cubic decimeter; * 1 cubic decimeter = 1000 cubic meter Centimeter

2 volume unit

* 1 liter = 1000 ml; * 1 liter = 1 cubic meter; * 1 ml = 1 cubic centimeter

[url= ]4. Mass[/url]

(1) What is mass

Quality means how heavy an object is.

(2) Commonly used units

* Ton t * Kilogram kg * Gram g

(3) Common conversions

* One ton =1000 kilograms; * 1 kilogram = 1000 grams

[url=]5. Time[/url]

(1) What is time

means A period of time with a starting point and an end point

(2) Common units

Century, year, month, day, hour, minute, second

(3) Units Conversion

* 1 century = 100 years; * 1 year = 365 balance years; * One year = 366 days Leap year

* One, three, five, seven, eight, ten, Twelve is the big month and the big month has 31 days

* April, Saturday, September and November are the small months and the small month has 30 days

* February has 28 days in ordinary years There are 29 days in February in leap years

* 1 day = 24 hours * 1 hour = 60 minutes * 1 minute = 60 seconds

[url=]6. Currency[/url]

(1) What is money

Money is a special commodity that serves as the equivalent of all commodities. Money is a general representation of value and can purchase any other commodity.

(2) Commonly used units

* Yuan* Jiao* Cent

(3) Unit conversion

* 1 Yuan = 10 Jiao * 1 angle = 10 points

The formula for calculating the perimeter, area and volume of geometric shapes in elementary school

1. Perimeter of a rectangle = (length and width) × 2C = (a b) × 2

2. Perimeter of square = side length × 4C = 4a

3. Area of ??rectangle = length × width S = ab

4. Area of ??square =Side length×Side length S=a.a=a

5. Area of ??triangle = base×height÷2S=ah÷2

6. Area of ??parallelogram=base×height S=ah

7. Area of ??trapezoid = (upper and lower base) × height ÷ 2S = (a + b) h ÷ 2

8. Diameter = radius × 2d = 2r radius = Diameter÷2r=d÷2

9. Circumference of a circle = pi × diameter = pi × radius × 2c = πd = 2πr

10. Area of ??a circle = pi × radius × Radius

Definition theorem formula of a collection of commonly used formulas in primary school mathematics

The area of ??a triangle = base × height ÷ 2. Formula S=a×h÷2

The area of ??a square = side length×side length Formula S=a×a

The area of ??a rectangle = length×width Formula S=a×b

The area of ??the parallelogram = base × height formula S = a × h

The area of ??the trapezoid = (upper and lower base) × height ÷ 2 formula S = (a b) h ÷ 2

Sum of interior angles: The sum of interior angles of a triangle = 180 degrees.

The volume of the cuboid = length × width × height formula: V = abh

The volume of the cuboid (or cube) = base area × height formula: V = abh

Volume of the cube = Edge length × Edge length × Edge length Formula: V = aaa

Circumference of the circle = Diameter × π Formula: L = πd = 2πr

Circle Area = Radius × Radius × π Formula: S = πr2

The surface (side) area of ??the cylinder: The surface (side) area of ??the cylinder is equal to the perimeter of the base multiplied by the height. Formula: S=ch=πdh=2πrh

Surface area of ??a cylinder: The surface area of ??a cylinder is equal to the circumference of the base multiplied by the height plus the area of ??the circles at both ends. Formula: S=ch 2s=ch 2πr2

The volume of a cylinder: The volume of a cylinder is equal to the base area times the height. Formula: V=Sh

The volume of the cone = 1/3 base × area height. Formula: V=1/3Sh

Rules for adding and subtracting fractions: To add and subtract fractions with the same denominator, only add and subtract the numerators, leaving the denominator unchanged. To add and subtract fractions with different denominators, first add and subtract the common denominators.

The rule of multiplication of fractions: use the product of the numerators as the numerator and the product of the denominators as the denominator.

Rule of division for fractions: dividing by a number is equal to multiplying by the reciprocal of that number.

Arithmetic aspects

1. Commutative law of addition: When two numbers are added, the positions of the addends are exchanged, and the sum remains unchanged.

2. The associative law of addition: To add three numbers, add the first two numbers first, or add the last two numbers first, and then add them to the third number. The sum remains unchanged. .

3. Commutative law of multiplication: When two numbers are multiplied, the positions of the factors are exchanged, and the product remains unchanged.

4. The associative law of multiplication: To multiply three numbers, first multiply the first two numbers, or first multiply the last two numbers, and then multiply them by the third number. Their product constant.

5. Distributive law of multiplication: If the sum of two numbers is multiplied by the same number, you can multiply the two addends by the number respectively, and then add the two products, the result remains unchanged.

For example: (2 4) × 5 = 2 × 5 4 × 5

6. Properties of division: In division, the dividend and divisor expand (or shrink) the same at the same time Multiples, the quotient remains unchanged. O divided by any number that is not O is O.

Simple multiplication: For multiplications with O at the end of the multiplicand and multiplier, you can multiply the ones before the O first. Zeros do not participate in the operation. Several zeros are dropped and added to the end of the product.

7. What is an equation? The formula in which the value on the left side of the equal sign is equal to the value on the right side of the equal sign is called an equation.

Basic properties of equations: If both sides of the equation are multiplied (or divided) by the same number at the same time, the equation still holds.

8. What is an equation? Answer: An equation containing unknown numbers is called an equation.

10. Fraction: Divide the unit "1" evenly into several parts, and the number that represents such a part or several points is called a fraction.

11. Rules for adding and subtracting fractions: When adding and subtracting fractions with the same denominator, only add and subtract the numerators, leaving the denominator unchanged. To add and subtract fractions with different denominators, first add and subtract the common denominators.

12. Comparison of fractions: Compared with fractions with the same denominator, the one with the larger numerator is larger and the one with the smaller numerator is smaller. When comparing fractions with different denominators, first make the common denominator and then compare; if the numerators are the same, the one with the larger denominator will be smaller.

13. When multiplying a fraction by an integer, use the product of the numerator of the fraction and the integer as the numerator, and the denominator remains unchanged.

14. To multiply a fraction by a fraction, use the product of the numerators as the numerator, and the product of the denominators as the denominator.

15. Dividing a fraction by an integer (except 0) is equal to the fraction multiplied by the reciprocal of the integer.

16. Proper fraction: The fraction whose numerator is smaller than the denominator is called a proper fraction.

17. Improper fractions: A fraction whose numerator is greater than the denominator or whose numerator and denominator are equal is called an improper fraction. An improper fraction is greater than or equal to 1.

18. Mixed numbers: Writing improper fractions in the form of integers and proper fractions is called mixed numbers.

19. The basic properties of fractions: If the numerator and denominator of a fraction are multiplied or divided by the same number at the same time (except 0), the size of the fraction remains unchanged.

20. Dividing a number by a fraction is equal to multiplying the number by the reciprocal of the fraction.

21. Dividing number A by number B (except 0) is equal to the reciprocal of number A times number B.

1. Unit price × quantity = total price 2. Unit output × quantity = total output

3. Speed ??× time = distance 4. Work efficiency × time = total amount of work

5. Addend Addend = sum and one addend = sum + another addend

Minuend - Minuend = Difference Minuend = Minuend - Difference Minuend = Subtraction Number + difference

Factor × factor = product one factor = product ÷ another factor

Divisor ÷ divisor = quotient divisor = dividend ÷ quotient dividend = quotient × divisor

Division with remainder: dividend = quotient Change. Example: 90÷5÷6＝90÷(5×6)

6. 1 kilometer = 1 kilometer 1 kilometer = 1000 meters

1 meter = 10 decimeters 1 Decimeter = 10 centimeters 1 centimeter = 10 millimeters

1 square meter = 100 square decimeters 1 square decimeter = 100 square centimeters

1 square centimeter = 100 square millimeters

1 cubic meter = 1000 cubic decimeters 1 cubic decimeter = 1000 cubic centimeters

1 cubic centimeter = 1000 cubic millimeters

1 ton = 1000 kilograms 1 kilogram = 1000 Gram = 1 kilogram = 1 catty

1 hectare = 10,000 square meters. 1 mu = 666.666 square meters.

1 liter = 1 cubic decimeter = 1000 milliliters 1 milliliter = 1 cubic centimeter

7. What is ratio: The division of two numbers is called the ratio of the two numbers. For example: 2÷5 or 3:6 or 1/3

The front and back terms of the ratio are multiplied or divided by the same number (except 0) at the same time, and the ratio remains unchanged.

8. What is proportion: The formula that expresses the equality of two ratios is called proportion. For example, 3:6=9:18

9. Basic properties of proportion: In proportion, the product of two external terms is equal to the product of two internal terms.

10. Solving the proportion: Finding the unknown items in the proportion is called solving the proportion. Such as 3: χ = 9: 18

11. Direct proportion: two related quantities. If one quantity changes, the other quantity will also change. If the corresponding quantity of the two quantities If the ratio (that is, the quotient k) is constant, these two quantities are called directly proportional quantities, and their relationship is called a directly proportional relationship. For example: y/x=k (k is certain) or kx=y

12. Inverse proportion: two related quantities, if one quantity changes, the other quantity will also change. If these two quantities The product of two corresponding numbers in a quantity is constant. These two quantities are called inversely proportional quantities, and their relationship is called an inversely proportional relationship. For example: x × y = k (k is certain) or k / x = y

Percent: A number that expresses how many percent a number is of another number is called a percentage. Percentage is also called percentage or percentage.

13. To convert a decimal into a percentage, just move the decimal point two places to the right and add a percent sign at the end. In fact, to convert a decimal into a percentage, just multiply the decimal by 100.

To convert a percentage to a decimal, just remove the percent sign and move the decimal point two places to the left.

14. To convert a fraction into a percentage, usually first convert the fraction into a decimal (when division cannot be completed, usually keep three decimal places), and then convert the decimal into a percentage. In fact, to convert a fraction into a percentage, you first need to convert the fraction into a decimal and then multiply it by 100.

To convert a percentage into a fraction, first rewrite the percentage into a fraction, and then reduce the ratio that can be reduced to the simplest fraction.

15. Learn how to convert decimals into fractions and fractions into decimals.

16. Greatest common divisor: Several numbers can be divisible by the same number at once. This number is called the greatest common divisor of these numbers. (Or the common divisor of several numbers is called the common divisor of these numbers. The largest one is called the greatest common divisor.)

17. Coprime numbers: two numbers whose common divisor is only 1 , called a relatively prime number.

18. Least common multiple: The common multiple of several numbers is called the common multiple of these numbers, and the smallest one is called the least common multiple of these numbers.

19. Common fraction: converting fractions with different denominators into fractions with the same denominator that are equal to the original fraction is called a common fraction. (Use the least common multiple for common fractions)

20. Reduction: Turning a fraction into a fraction that is equal to it but with smaller numerator and denominator is called a reduction. (Use the greatest common divisor to reduce)

21. Simplest fraction: A fraction whose numerator and denominator are relatively prime numbers is called the simplest fraction.

At the end of the fraction calculation, the number must be converted into the simplest fraction.

Numbers whose units digits are 0, 2, 4, 6, and 8 are all divisible by 2, that is, they can be reduced by 2

. Any number whose units digit is 0 or 5 can be divisible by 5, that is, it can be reduced by 5. Pay attention when making an appointment.

22. Even numbers and odd numbers: Numbers that can be divided by 2 are called even numbers. Numbers that are not divisible by 2 are called odd numbers.

23. Prime number (prime number): If a number has only two divisors, 1 and itself, such a number is called a prime number (or prime number).

24. Composite number: If a number has other divisors besides 1 and itself, such a number is called a composite number. 1 is neither a prime number nor a composite number.

28. Interest = principal × interest rate × time (time is generally in years or months, which should correspond to the unit of interest rate)

29. Interest rate: interest and principal The ratio is called the interest rate. The ratio of one year's interest to the principal is called the annual interest rate. The ratio of one month's interest to the principal is called the monthly interest rate.

30. Natural numbers: Integers used to represent the number of objects are called natural numbers. 0 is also a natural number.

31. Repeating decimal: A decimal, starting from a certain digit of the decimal part, one number or several numbers appear repeatedly in sequence. Such a decimal is called a recurring decimal. Such as 3. 141414...

32. Non-recurring decimals: A decimal, starting from the decimal part, does not have a number or several numbers that repeatedly appear in sequence. Such a decimal is called a non-repeating decimal.

For example, 3. 141592654

33. Infinite non-recurring decimals: A decimal, from the decimal part to an infinite number of digits, no number or several numbers are repeated in sequence. Such decimals are called infinite non-repeating decimals. Such as 3. 141592654...

34. What is algebra? Algebra is to use letters to replace numbers.

35. What is an algebraic expression? An expression represented by letters is called an algebraic expression.

For example: 3x =ab c

1. Graphic formula

1. Perimeter of rectangle = (length and width) × 2 C=(a b) × 2

2. Perimeter of the square = side length × 4 C = 4a

3. Area of ??the rectangle = length × width S=ab

4. Area of ??the square = side length × Side length S=a.a= a

5. Area of ??triangle = base×height÷2 S=ah÷2

6. Area of ??parallelogram=base×height S=ah

7. Area of ??trapezoid = (upper and lower base) × height ÷ 2 S = (a + b) h ÷ 2

8. Diameter = radius × 2 d = 2r radius = diameter ÷2 r= d÷2

9. Circumference of a circle = pi × diameter = pi × radius × 2 c=πd =2πr

10. Area of ??a circle = pi × Radius Height V =abh

13. Surface area of ??cube = edge length × edge length × 6 S = 6a

14. Volume of cube = edge length × edge length × edge length V= a.a.a= a

15. The side area of ??the cylinder = the circumference of the base circle × height S = ch

16. The surface area of ??the cylinder = the area of ??the upper and lower bases and the side area

S=2πr 2πrh=2π(d÷2) 2π(d÷2)h=2π(C÷2÷π) Ch

17. Volume of cylinder = base area × height V = Sh

V=πr h=π(d÷2) h=π(C÷2÷π) h

18. Volume of cone = base area × height ÷3

V=Sh÷3=πr h÷3=π(d÷2) h÷3=π(C÷2÷π) h÷3

19. Cuboid (cube, Cylinder)

2. Algorithm formula

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 = how many multiples how many multiples ÷ 1 multiple = how many multiples ÷ multiples = 1 multiple

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 time = total amount of work total amount of work Amount ÷ work efficiency = total amount of working time ÷ working time = work efficiency

6. Addend + addend = sum and sum - one addend = another addend

7 , Minuend - Minuend = Difference Minuend - Difference = Minuend Difference + Minuend = Minuend

8. Factor × Factor = Product ÷ One factor = Another factor

9. Divisor ÷ Divisor = Quotient Divisor ÷ Quotient = Divisor Quotient × Divisor = Divisor

Commonly used stroke formulas for encounter problems

Two moving objects move toward each other or When moving backwards on a circular track, they will inevitably meet face to face as time goes by. This type of problem is called an encounter problem. Its characteristic is that two moving objects travel the entire distance simultaneously.

The itinerary problem in primary school mathematics textbooks generally refers to the encounter problem.

Meeting problems can be divided into three types based on quantitative relationships: finding the distance, finding the encounter time, and finding the speed.

Their basic relationship is as follows:

Total distance = (speed A and speed B) × meeting time

Meeting time = total distance ÷ (speed A and speed B) speed)

Another speed = the speed of A and B and - a known speed

Commonly used stroke formulas for boating problems on flowing water

Downward and countercurrent The above problem is usually called the flow problem. The flow problem is a journey problem and can still be solved by using the relationship between speed, time and distance. When answering, pay attention to the meaning of various speeds and the relationship between them.

When a boat travels in still water, the distance traveled per unit time is called the rowing speed or the paddling force; the speed of the boat traveling with the current is called the downstream speed; the speed of the boat traveling against the current is called the countercurrent speed; when the boat is placed in the middle current, When traveling along the current without relying on power, the distance traveled per unit time is called the water flow speed. The relationship between various speeds is as follows:

(1) Rowing speed, water speed = downstream speed

(2) Rowing speed - water speed = countercurrent speed

(3) (Flower flow speed and countercurrent flow speed) ÷2 = rowing speed

(4) (Flower flow speed - countercurrent speed) ÷2 = water flow speed

Flowing water problem The quantitative relationship is still the relationship between speed, time and distance. That is: speed × time = distance; distance ÷ speed = time; distance ÷ time = speed. However, the river is flowing, so there is a difference between downstream and countercurrent. When calculating, it is very necessary to clarify the relationship between various speeds.

I wish you success in the exam