1. Axisymmetric:
Axisymmetric figure: a figure has one or more axes of symmetry;
Axisymmetric figure: There are two figures with only one axis of symmetry.
2. The essence of an axisymmetric figure: the distance between the corresponding point and the axis of symmetry is equal. The connecting line of the corresponding point intersects the symmetry axis vertically.
3. Drawing method: find the key points, determine the symmetrical points of the key points, and then connect them.
4. Four elements of rotation: fixed point, moving point, direction and angle.
5. The essence of rotation: after rotation, the shape and size of the figure have not changed, but the position has changed.
Factors and multiples of the second unit
1. Integer a × b=c (a≠0, b≠0, A, B and C are integers), then A and B are called factors of C, and C is called multiples of A and B..
The minimum factor of a number is 1, the maximum factor is itself, and the number of factors of a number is limited.
The smallest multiple of a number is itself. There is no maximum multiple, and the multiple of a number is infinite.
Factors and multiples are interdependent.
Characteristics of multiples of 2.2, 3 and 5.
Multiply of 2: Numbers with 0, 2, 4, 6 and 8 are multiples of 2.
Multiply of 5: Every number has 0 and 5. Numbers are multiples of 5.
Multiply of 3: The sum of the numbers on each bit is a multiple of 3, and this number is a multiple of 3.
In natural numbers, numbers that are multiples of 2 are called even numbers. Numbers that are not multiples of 2 are called odd numbers. 0 is also an even number. Even numbers are even numbers and odd numbers are singular. )
4. A number with a bit of 0 is a multiple of 2 and also a multiple of 5. Several numbers that are multiples of 2 and 5 at the same time must be 0.
5. It is a multiple of 2, 3 and 5 at the same time. The minimum two digits are 30 and the maximum two digits are 90; The smallest three digits are 120 and the largest three digits are 990.
6. Odd and even numbers: odd+odd = even × even = even-even = even-odd = odd-odd = odd.
Odd × even = even odd-odd = even even+even = even odd+even = odd.
7. Prime number: If a number has only two factors: 1 and itself, it is called a prime number.
Composite number: A number is called a composite number if it has other factors besides 1 and itself.
8. Quality table within100: 2.3.5.7.1.13.17.19.23.29.35438+0.37+
Unit 3 Cuboid and Cube
1. Understanding of a cuboid: A cuboid is a three-dimensional figure surrounded by six rectangles (in special cases, two opposite faces are squares).
2. Features of a cuboid: it has 6 faces, 8 vertices and 12 sides, with the opposite faces having the same area and the opposite sides having the same length.
3. Understanding of Cubes: Cubes are three-dimensional figures surrounded by six identical squares.
4. Features of a cube: It has 6 faces, 8 vertices and 12 sides, and each face is a square with equal area. Each side is equal in length. The length, width and height of a cube are all equal, which is collectively called the edge length.
5. Relationship between cuboid and cube: Cube is a special cuboid.
6. Formula for the sum of side lengths: the sum of side lengths of a cuboid = (length+height+width) ×4.
Length = sum of side lengths ÷4- width-height-width = sum of side lengths ÷4- length-height = sum of side lengths ÷4- length-width
7. Sum of cube sides = side length × 12 side length = sum of side lengths ÷ 12
8. Surface area of cuboid and cube: The total area of six faces of cuboid and cube is called its surface area.
9. Calculation formula of surface area:
The surface area of a cuboid = (length× width+length× height+width× height )× 2 (AB+AC+BC )× 2.
Surface area of cube = side length × side length× 66a?
Cube = bottom area ×6 bottom area = surface area ÷6
10. The space occupied by an object is called its volume. Commonly used unit of volume: cubic centimeter (cm? ), cubic decimeter (dm? ) and cubic centimeters (m? )
1 1. Volume formula:
Cuboid volume (volume) = length × width × height v = abha = V÷ b÷ h b = V÷ a÷ h h = V÷ a÷ b a ÷ b.
Cube volume) = side length × side length × side length V=a?
Volume of cuboid or cube = bottom area × height v = sh h = v ÷ s s = v ÷ h
12. 1 m？ = 1000 dm？ 1dm？ ; = 1000 cm？ 1 m？ = 1000000 cm？
13. The volume of the object that a container can hold is called the volume of the container. Commonly used unit of volume is liter (L) and milliliter (ml).
14. 1L= 1 dm？ 1L = 1000ml 1ml = 1cm？
15. The surface area is multiplied by the square of the side length multiple, and the volume is multiplied by the cube of the side length multiple.
Unit 4 Significance and Properties of Fractions
1. Divide the unit "1" into several parts on average, and the number representing such a part or parts is called a fraction.
2. Divide the unit "1" into several parts on average, and the numbers representing such parts are called decimal units. A score consists of several fractional units.
3. Scoring rate: divide the unit "1" into several shares on average, and find the scores of other quantities in the total shares.
Single quantity: total quantity ÷ quantity = single quantity (expressed by fraction) (denominator of single quantity and fraction is average total number of shares).
4. Relationship between score and divisor: dividend ÷ divisor = dividend/divisor A ÷ B = A/B (b ≠ 0)
5. Unit conversion: When changing the name of a low-level unit to the name of a high-level unit, if the number on the low-level unit is not divisible by the advancing rate, the quotient can be expressed by a fraction. (Result discount points)
6. Comparison of scores: two numbers with the same denominator, and the number with the larger numerator is larger. Two numbers with the same numerator, the number with the smaller denominator is larger.
7. Fractions with numerator less than denominator are called true fractions. Features: True score is less than 1.
Fractions with numerator greater than or equal to denominator are called false fractions. Features: false score