Unit 1: Graphic Transformation

1. Axisymmetric graph: a graph is folded in half along a straight line, and the graphs on both sides can completely overlap. This graph is an axisymmetric graph. This straight line is called its axis of symmetry.

2. The characteristics of axisymmetric graphs are: 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 Multiplies

1. factors and multiples: in integer multiplication, if a× b = c, then a and b are factors of c, and c is a multiple of a and b. ..

For convenience, when studying factors and multiples, we refer to integers (generally excluding 0). But 0 is also an integer.

The smallest factor of a number is 1, and the largest factor is itself. The number of factors of a number is limited.

The minimum multiple of a number is itself, and there is no maximum multiple. The multiple of a number is infinite.

5. Numbers 0, 2, 4, 6 and 8 are all multiples of 2. Numbers with 0 and 5 are multiples of 5. A number, the sum of the numbers on 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 (0 is also even numbers), and 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 and the smallest composite number is 4.

8.

Parity law in four operations;

Odd+odd = even odd-odd = even odd × odd = odd.

Even+even = even-even = even × even = even.

Odd+even = odd odd-even = odd odd × even = even

Parity = odd number

9. If a number has only 1 and its own two factors, it is called a prime number (or prime number); 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 can be divided into odd and even numbers.

A table of prime numbers within 12. 100: 2, 3, 5, 7, 1 1, 13, 17, 19, 23, 29, 365438+.

Unit 3: Cuboid and Cube

1. Cubes are also called cubes.

2. The characteristics of cuboids are: ① Cuboids 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 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. Cubes are special cuboids.

5. The characteristics of a cube are as follows: ① A cube has 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 cube sides = 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; Left or right area = 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. The surface area of a cuboid with two opposite faces is square = area of square face ×2+ area of rectangular face ×4.

13. Side area of cuboid = perimeter of bottom × height.

14. The size of the space occupied by an object is called the volume of the object.

15. The commonly used unit of volume is cubic centimeter, cubic decimeter and cubic meter, which can be written as cm3, dm3 and m3 respectively.

16. A cube with length 1cm and volume 1 cm3; 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; Represented by letters is V=abh.

18. Volume of cube = side length 3; Represented by letters is V=a3.

19. cuboid (or cube) volume = 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 side lengths are expanded n times, then the sum of side lengths is also expanded n times, the surface area is expanded n2 times and the volume is expanded 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 propulsion rate 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 generally used to measure volume.

26. To measure the volume of liquid, the commonly used unit of volume is liters and milliliters, which can also be written as L and ml.

27. 1 l is equivalent to 1 cubic decimeter, and 1 ml is equivalent to 1 cubic centimeter, 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 smaller than the volume.

29. The volume of an object submerged in water = the volume of water now-the original volume of water = the length of the container × the width of the container × the rising height of the water surface.

30. How to measure the volume of irregular objects? First, put a proper 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: Meaning and Properties of Fractions

1. The whole of an object or several objects can be represented by the 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 7 parts on average and take 3 of them.

3.5/8m is divided into 8 copies according to the meaning of the score, and 5 copies are taken. According to the relationship between fraction and division, it means: divide 5m into 8 parts and take 1 part.

4. Divide the unit "1" into several parts on average, and the number representing one part is called fractional 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 quotient in division.

6. Divide a whole into several parts on average, work out how much each part costs, and then divide it. Total copies/copies = copies.

7. Find the score of another quantity from one quantity and divide it. One quantity ÷ another quantity = fraction (multiple).

8. Fractions with numerator less than denominator are called true fractions. The true score is less than 1.

9. Fractions with numerator greater than denominator or numerator equal to denominator are called false fractions. False score is greater than or equal to 1.

10. Band score includes integer part and fractional part, and the fractional part should be true score. Band score is greater than 1.

1 1. The way to change a false fraction into a fraction 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 turn a band fraction into a false fraction is to multiply the product of integer parts by the denominator, and add the original molecule as the numerator, and the denominator remains unchanged.

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 the fraction are multiplied or divided by the same number at the same time (except 0), and the size of the fraction remains unchanged. This is called the basic nature of fractions.

14. The common factor of several numbers is called the common factor of these numbers, and the greatest common factor is called their greatest common factor. 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. To find the greatest common factor or the smallest common multiple, you can decompose the prime factor by enumeration or short division.

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.

18. The result of division calculation can be expressed in fractions, which is more convenient. If the calculation result can be simplified, it should be simplified to the simplest score.

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. number A× number B = their greatest common factor× their least common multiple.

22. There are several special cases where both numbers are prime numbers: 1, 1 and any number are prime numbers; 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 that is equal to it, but with smaller numerator and denominator, is called divisor. Changing several fractions with different denominators into fractions with the same mother equal to the original fraction is called the total score.

24. Fractions are converted into decimals by dividing the numerator by the denominator; The method of fractional component number is to write fractions with denominators of 10 and 100 ... First, separate them.

25. If the denominator of the simplest fraction contains no other prime factors except 2 and 5, then the fraction can be reduced to a finite decimal.

26. The greatest common factor of two numbers is equal to the product of prime factors shared by two numbers; The least common multiple of two numbers is equal to the prime factor shared by 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 data comes from the Internet. I hope it helps you.