Key points of mathematics knowledge in the second volume of grade five: unit 1: graphic transformation 1. Axisymmetric figure: a figure is folded in half along a straight line, and the figures on both sides can completely overlap, which is an axisymmetric figure. This straight line is called its axis of symmetry. 2. The characteristic of an axisymmetric figure: 1, and the distance from the symmetry point to the symmetry axis is equal; 2. The straight line connecting the corresponding points and the symmetry axis are perpendicular to each other. 3. Rotation: The phenomenon that a figure or an object moves around a point or an axis is called rotation. Unit 2: factors and multiples 1. Factors and multiples: In integer multiplication, if a× b = c, then A and B are factors of C, and C is multiples of A and B. 2. For convenience, when studying factors and multiples, we mean an integer (generally excluding 0). But 0 is also an integer. 3. The minimum factor of a number is 1, and the maximum factor is itself. The number of factors of a number is limited. The smallest multiple of a number is itself. There is no maximum multiple. The multiple of a number is infinite. 5. Every number has 0, 2, 4, 6 and 8. Numbers are multiples of 2. Every number has 0 and 5. Numbers are multiples of 5. A number, the sum of the numbers of each digit is a multiple of 3, and this number is a multiple of 3. 6. Among natural numbers, numbers that are multiples of 2 are called even numbers (numbers that are not multiples of 2 are called odd numbers). 7. The smallest odd number is 1 and the smallest even number is 0. The smallest prime number is 2. The smallest composite number is 4. 8. The law of parity in four arithmetic operations: odd+odd = even odd-odd = even odd × odd = even+even = even even even = even odd+even = odd odd odd = odd odd odd × even = even even odd = odd odd 9. A number, if only 60. If there are other factors besides 1 and itself, such a number is called a composite number. 10. 1 is neither prime nor composite. 1 1. Natural numbers can be divided into 1, prime numbers and composite numbers according to the number of factors. According to whether it is a multiple of 2, it is divided into odd and even numbers. 12. 100: 2, 3, 5, 7, 1 1, 13, 17,/kloc-0. Unit 3: Cubes and Cubes 1. Cubes are also called cubes. 2. Cubes are characterized by: ① Cubes have six faces; (2) Each face is rectangular (in special cases, two opposite faces are square); 3 the opposite side is exactly the same; ④ There are 12 edges; ⑤ The length of opposite sides is equal; ⑥ There are eight vertices. 3. The length of three sides intersecting at a vertex is called the length, width and height of a cuboid. A cube can be regarded as a cuboid with equal length, width and height. Cube is a special kind of cuboid. 5. Cubes are characterized by: ① Cubes have six faces; ② Every face is square; ③ All faces are exactly the same; ④ There are 12 edges; ⑤ All sides are equal in length; ⑥ There are eight vertices. 6. The sum of the sides of a cuboid = (length+width+height) × 4 7. Sum of sides of a cube = side length × 12 8. The sum of the areas of six faces of a cuboid is called the surface area of a cuboid. 9. Upper or lower area = length × width; Anterior region or posterior region = length × height; Area on the left or right = width× height. 10. The surface area of a cuboid = (length× width+length× height+width× height) ×2 1 1. Surface area of cube = side length 2×6 12. There are two opposite faces that are squares. The height is 14. The size of the space occupied by an object is called its volume. 15. The commonly used unit of volume is cubic centimeter, cubic decimeter and cubic meter, which can be written as cm3, dm3 and m3. They are 16. A cube with a side length of 1cm and a volume of1cm3; . A cube with a side length of 1dm and a volume of 1dm3; ; A cube with a side length of 1m and a volume of 1m3. 17. cuboid volume = length× width× height; Expressed in letters, it is V=abh 18. Volume of cube = side length 3; Expressed in letters, it is V=a3 19. Volume of cuboid (or cube) = bottom area × height = cross-sectional area × length 20. In engineering, 1 m3 is abbreviated as 1 m3. 2 1. 1 cuboid or cube, if all sides are expanded n times. The volume is expanded by n3 times. 22. A cuboid or cube with equal sides has the largest volume. 23. 1 m3 = 1000 cubic decimeter; 1 cubic decimeter = 1000 cubic centimeter. 24. The forward speed between every two adjacent length units is10; The propulsion rate between every two adjacent regional units is100; The propulsion rate between every two adjacent unit of volume is 1000. 25. The volume of objects that a container can hold is usually called their volume. Unit of volume is usually used to measure the volume. 26. The commonly used unit of volume is liter and milliliter, which can also be written as L and ml. 27. 1 liter, equivalent to 1 cubic decimeter. 1 ml is equivalent to 1 cm3, so 1 l = 1000 ml. 28. The calculation method of cuboid or cube container volume is the same as that of volume, but the length, width and height should be measured from the inside of the container, so the volume of the container is less than the volume. 29. The volume of an object immersed in water = First, put an appropriate amount of water in the measuring cup, and write down the scale corresponding to the water surface, then immerse the object in the water, and then write down the new scale corresponding to the water surface. The difference between the two scales is the volume of this irregular object. Unit 4: The meaning and nature of the fraction 1 An object or a whole composed of several objects can be represented by a natural number 1. We usually call it the unit "1". 2. Divide the unit "1" into several parts on average, and the number representing such a part or parts is called a fraction. For example, 3/7 is to divide the unit "1" into seven parts and take three of them. 3.5/8m means according to the meaning of the score, which means: Representation: divide 5m into 8 parts, and take 1 part. 4. Divide the unit "1" into several parts, and the number representing one part is called decimal unit. 5. The relationship between fraction and division is that the numerator of fraction is equivalent to the dividend in division, the fractional line of fraction is equivalent to the divisor in division, and the denominator of fraction is equivalent to the divisor in division. The decimal value of a fraction is equivalent to the quotient in division. 6. Divide a whole into several parts, calculate how much each part is, and divide by division. Total number ÷ number of parts = number of parts. 7. Find out how much one quantity is part of another. By division, one quantity ÷ another quantity = a fraction (several times). 8. A fraction whose numerator is smaller than the denominator is called a true fraction. Fractions with numerator greater than denominator or numerator equal to denominator are called false fractions. False score is greater than 1 or equal to 1. 10. The fractional part should be a true fraction. The fractional part is greater than 1. 1 1. The method to convert a false fraction into a decimal part is to divide the numerator by the denominator, the quotient is the integer part, the remainder is the numerator, and the denominator remains unchanged. The way to convert the decimal part into a false fraction is to multiply the product of denominator by the integer part and add the original molecule as the numerator. The denominator remains the same. 12. Integer can be regarded as a false fraction whose denominator is 1. For example, 5 can be regarded as 5/ 1. 13. The numerator and denominator of a fraction are multiplied or divided by the same number (except 0) at the same time, and the size of the fraction remains unchanged. This is called the basic nature of fractions. 5438+04. The greatest common divisor is called their greatest common divisor. The minimum common factor must be 1. 15. The common multiple of several numbers is called the common multiple of these numbers, and the smallest common multiple is called their smallest common multiple. There is no greatest common multiple. 16. Enumeration can be used to find the greatest common factor or the least common multiple. You can also use short division to decompose prime factors. 17. Two numbers whose common factor is only 1 are called prime numbers. A fraction whose numerator and denominator are prime numbers is called simplest fraction. Simplest fraction is not necessarily a true score. The result of division can be expressed in fractions, which is more convenient. If the calculation result can be simplified, it can be simplified to the simplest fraction. 19. If two numbers are multiples, their greatest common factor is small and their smallest common multiple is large. 20. If two numbers are coprime, their greatest common factor is 1 and their least common multiple is their product. 2 1. quantity A× quantity B = their maximum value. 2. Two adjacent natural numbers must be prime numbers; 3. Two adjacent odd numbers must be prime numbers; 4. Two different prime numbers must be prime numbers; 5. The sum of a prime number and a multiple of it must be a prime number. 23. Changing a fraction into a fraction equal to it, but with smaller numerator and denominator, is called divisor. Changing several fractions with different denominators into fractions with the same denominator and equal to the original fraction is called general fraction. 24. The way to turn a fraction into a decimal is to divide the numerator by the denominator; The decimal method of component number is to write the fractions with denominators of 10 and 100. The least common multiple of two numbers is equal to the common prime factor of two numbers × their unique prime factor. 27. The common factor of two numbers is the factor of the greatest common factor of these two numbers; The common multiple of two numbers is the multiple of the least common multiple of these two numbers. This information comes from the Internet. I hope it helps you.