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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