Volume and surface area
Area of triangle = base × height ÷2. The formula S= a×h÷2.
Area of square = side length × side length formula S= a2
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.
The surface area of a cuboid = (length× width+length× height+width× height )× 2 Formula: S=(a×b+a×c+b×c)×2.
Surface area of cube = side length × side length ×6 Formula: S=6a2.
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 = a3.
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
arithmetic
1, additive commutative law: Two numbers are added to exchange the position of addend, and the sum is unchanged.
2. Additive associative law: A+B = B+A.
3. Multiplicative commutative law: a× b = b× a.
4. Multiplicative associative law: a × b × c = a ×(b × c)
5. Multiplicative distribution law: a× b+a× c = a× b+c.
6. The nature of division: a ÷ b ÷ c = a ÷(b × c)
7. 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. O is divided by any number that is not O. Simple multiplication: the multiplicand and the end of the multiplier are multiplied by O. You can multiply 1 before o first, and zero does not participate in the operation, and add a few zeros at the end of the product.
8. Division with remainder: dividend = quotient × divisor+remainder
Equations, Algebras and Equality
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.
Equation: An equation with an unknown number is called an equation.
One-dimensional linear equation: An equation with an unknown number of degree 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.
Algebra: Algebra means replacing numbers with letters.
Algebraic expression: Expressions expressed by letters are called algebraic expressions. For example 3x = AB+C.
mark
Fraction: divide the unit "1" into several parts on average, and the number representing such a part or points is called a fraction.
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.
Addition and subtraction of fractions: add and subtract fractions with the same denominator, only add and subtract numerators, and the denominator remains the same. Fractions of different denominators are added and subtracted, first divided, then added and subtracted.
Fraction multiplied by integer, numerator is the product of fractional and integer multiplication, denominator remains unchanged.
Fractions are multiplied by fractions, the product of numerator multiplication is numerator, and the product of denominator multiplication is denominator.
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 concept of reciprocal: 1 If the product of two numbers is 1, we call one of them the reciprocal of the other. These two numbers are reciprocal. The reciprocal of 1 is 1, and 0 has no reciprocal.
A fraction divided by an integer (except 0) is equal to this fraction multiplied by the reciprocal of this integer.
The basic properties of a fraction: the numerator and denominator of a fraction are multiplied or divided by the same number (except 0), and the size of the fraction.
The law of division of fractions: dividing by a number (except 0) is equal to multiplying the reciprocal of this number.
True fraction: The fraction with numerator less than denominator is called true fraction.
False fraction: Fractions with numerator greater than denominator or numerator equal to denominator are called false fractions. False score is greater than or equal to 1.
With a score: write a false score as an integer, and a true score is called with a score.
The basic nature of the fraction: the numerator and denominator of the fraction are multiplied or divided by the same number (except 0) at the same time, and the size of the fraction remains unchanged.
Calculation formula of quantitative relationship
Unit price × quantity = total price 2, single output × quantity = total output
Speed × time = distance 4, work efficiency × time = total workload.
Appendix+Appendix = and one addend = and+another addend.
Negative-negative = differential negative = negative-differential negative = negative+difference.
Factor × factor = product One factor = product ÷ another factor.
Frequency divider/frequency divider = frequency divider = frequency divider/frequency divider = quotient × frequency divider
Length unit:
1 km = 1 km 1 km = 1000 m
1 m = 10 decimeter 1 decimeter =10 cm1cm =10 mm.
Area unit:
1 km2 = 1 00ha1hectare =10000m2
1 m2 = 100 square decimeter 1 square decimeter = 100 square centimeter 1 square centimeter = 100 square millimeter
1 mu = 666.666 square meters.
volume unit
1 m3 = 1000 cubic decimeter
1 cm3 = 1000 cm3
1 liter = 1 cubic decimeter = 1000 ml 1 ml = 1 cubic centimeter.
Unit right
1 ton = 1 000kg1kg = 1 000g = 1 kg =1kg.
compare
What is the ratio? When two numbers are divided, it is called the ratio of two numbers. For example, the first and second terms of the ratio of 2÷5 or 3:6 or 1/3 are multiplied or divided by the same number at the same time (except 0), and the ratio remains unchanged.
What is proportion? Two formulas with equal ratios are called proportions. For example, 3: 6 = 9: 18
The basic property of proportion: in proportion, the product of two external terms is equal to the product of two internal terms.
Solution ratio: the unknown term in the proportion is called solution ratio. Such as 3: χ = 9: 18.
Proportion: two related quantities, one of which changes and the other changes. If the ratio (i.e. quotient k) corresponding to these two quantities is constant, these two quantities are called proportional quantities, and the relationship between them is called proportional relationship. For example: y/x=k( k must be) or kx = y.
Inverse proportion: two related quantities, one of which changes and the other changes accordingly. If the product of the corresponding two numbers in these two quantities is certain, these two quantities are called inverse proportional quantities, and their relationship is called inverse proportional relationship. For example: x×y = k( k must be) or k/x = y.
per cent
Percentage: a number that indicates that one number is a percentage of another number, which is called percentage. Percentages are also called percentages or percentages.
To convert decimals into percentages, just move the decimal point two places to the right and add hundreds of semicolons at the end. In fact, to convert a decimal into a percentage, just multiply this decimal by 100%. To convert percentages to decimals, simply remove the percent sign and move the decimal point two places to the left.
When a fraction is converted into a percentage, the fraction is generally converted into a decimal (three decimal places are generally reserved when it is not used up), and then the decimal is converted into a percentage. In fact, to turn a fraction into a percentage, you must first turn the fraction into a decimal and then multiply it by 100%.
Divide the percentage into components, and rewrite the percentage into components first, so that the quotation that can be lowered can be made into the simplest score.
We should learn to decompose fractions into components and fractions into decimals.
Multiples and divisors
Maximum common divisor: The common divisor of several numbers is called the common divisor of these numbers. There is a finite common factor. The largest one is called the greatest common divisor of these numbers.
Least common multiple: The common multiple of several numbers is called the common multiple of these numbers. There are infinite common multiples. The smallest one is called the least common multiple of these numbers.
Prime number: the common divisor has only 1 two numbers, which is called prime number. Two adjacent numbers must be prime numbers. Two consecutive odd numbers must be coprime. 1 and any number coprime.
Comprehensive score: the difference between scores of different denominators is changed into the same denominator score equal to the original score, which is called comprehensive score. (Common divisor is the least common multiple)
Decrement: divide the numerator and denominator of a fraction by the common divisor at the same time, and the fraction value remains unchanged. This process is called dropping points.
Simplest fraction: The numerator and denominator are fractions of prime numbers, which are called simplest fraction. At the end of the score calculation, the score must be converted into the simplest score.
Prime number (prime number): If a number only has 1 and its two divisors, it is called a prime number (or prime number).
Composite number: a number. If there are other divisors besides 1 and itself, such numbers are called composite numbers. 1 is neither prime nor composite.
Prime factor: If a prime number is a factor of a certain number, then this prime number is the prime factor of this number.
Prime factor decomposition: A composite number is represented by the complementary way of prime factors, which is called prime factor decomposition.
Multiple characteristics:
Characteristics of multiples of 2: You are 0, 2, 4, 6, 8.
Characteristics of multiples of 3 (or 9): The sum of the numbers on each digit is multiples of 3 (or 9).
Characteristics of multiples of 5: You are 0, 5.
Characteristics of multiples of 4 (or 25): The last two digits are multiples of 4 (or 25).
Characteristics of multiples of 8 (or 125): the last three digits are multiples of 8 (or 125).
Characteristics of multiples of 7 (1 1 or 13): the difference (big-small) between the last three digits and other digits is a multiple of 7 (1 1 3).
Characteristics of multiples of 17 (or 59): the difference (big-small) between the last three digits and the rest digits is a multiple of 17 (or 59).
Characteristics of multiples of 19 (or 53): the difference (big-small) between the last three digits and other seven digits is a multiple of 19 (or 53).
Characteristics of multiples of 23 (or 29): The difference (big-small) between the last four digits and the other five digits is multiples of 23 (or 29).
Of the two numbers in the multiple relation, the greatest common divisor is smaller and the smallest common multiple is larger.
The coprime relation between two numbers, the greatest common divisor is 1, and the least common multiple is the product.
When two numbers are divided by their greatest common divisor, the quotient is coprime.
The product of two numbers and the least common multiple is equal to the product of these two numbers.
The common divisor of two numbers must be the greatest common divisor of these two numbers.
1 is neither prime nor composite.
A prime number greater than 3 divided by 6 must get 1 or 5.
Odd and even numbers
Even numbers: Numbers are numbers of 0, 2, 4, 6 and 8.
Odd number: The number is not 0, 2, 4, 6 or 8.
Even even = even Qiqi = Qiqi.
Even numbers add up to even numbers, and odd numbers add up to odd numbers.
Even × even = even × odd = odd × even = even.
The sum of two adjacent natural numbers is odd, and the product of adjacent natural numbers is even.
If one number in the multiplication is even, then the product must be even.
Odd ≠ even number
separable
If c | a, c | b, then c | (a b)
If, then b | a, c | a
If b | a, c | a and (b, c)= 1, then BC | a.
If c | b, b | a, then c | a
decimal
Natural number: an integer used to represent the number of objects, called natural number. 0 is also a natural number.
Pure Decimal: Decimal in units of 0.
With Decimal: Decimal with more than 0 digits.
Cyclic decimal: a decimal, starting from a certain bit of the decimal part, and one or several numbers are repeated in turn. Such decimals are called cyclic decimals. Like 3. 14 14 14.
Acyclic decimal: a decimal, starting from the decimal part, without one number or several numbers appearing repeatedly. Such a decimal is called acyclic decimal. Like 3. 14 1592654.
Infinite cycle decimal: a decimal, from the decimal part to the infinite digits, and one or several numbers are repeated in turn. Such decimals are called infinite cyclic decimals. For example, 3. 14 14 14 ...
Infinite acyclic decimal: a decimal, from decimal part to infinite digits, is called infinite acyclic decimal without one number or several numbers appearing repeatedly. Such as 3. 14 1592654. ...
profit
Interest = principal × interest rate × time (time is usually in years or months, which should correspond to the unit of interest rate).
Interest rate: The ratio of interest to principal is called interest rate. The ratio of interest to principal for one year is called annual interest rate. The ratio of interest to principal in January is called monthly interest rate.