Check the article on the graphic knowledge points of the seventh grade mathematics life plane+February 65438, 2009+Wednesday 0611:131. Polygon: Generally speaking, a polygon is a closed figure surrounded by some end-to-end line segments.
We usually divide polygons into triangles, quadrilaterals and pentagons according to the number of sides ... 2.N-polygon: A closed figure surrounded by n end-to-end line segments is called an N-polygon (n is an integer greater than or equal to 3). 3. Polygon segmentation: Starting from a certain vertex of a polygon and connecting this vertex with other vertices respectively, the polygon can be divided into several triangles.
4. There are (n- 3) diagonal lines from a vertex of an n- polygon, and the N-polygon is divided into (n-2) triangles. N polygon * * * has n vertices, n edges and n(n-3)÷2 diagonals.
5. Circle: The figure formed by the rotation of a line segment around one end is called a circle. 6. The line segment between two points on a circle is called an arc, and the figure consisting of an arc and two radii passing through the end points of the arc is called a fan.
7. A circle can be divided into several sectors. 8. Two points on the circle (the line segment connecting the two points is not the diameter) divide the circle into two parts, one part is larger than the semicircle and the other part is smaller than the semicircle, so the two points on the circle are divided into two arcs, and each arc corresponds to a sector.
2. Primary school graphics knowledge points finishing
Check the article on the graphic knowledge points of the seventh grade mathematics life plane+February 65438, 2009+Wednesday 0611:131. Polygon: Generally speaking, a polygon is a closed figure surrounded by some end-to-end line segments.
We usually divide polygons into triangles, quadrilaterals and pentagons according to the number of sides ... 2.N-polygon: A closed figure surrounded by n end-to-end line segments is called an N-polygon (n is an integer greater than or equal to 3). 3. Polygon segmentation: Starting from a certain vertex of a polygon and connecting this vertex with other vertices respectively, the polygon can be divided into several triangles.
4. There are (n- 3) diagonal lines from a vertex of an n- polygon, and the N-polygon is divided into (n-2) triangles. N polygon * * * has n vertices, n edges and n(n-3)÷2 diagonals.
5. Circle: The figure formed by the rotation of a line segment around one end is called a circle. 6. The line segment between two points on a circle is called an arc, and the figure consisting of an arc and two radii passing through the end points of the arc is called a fan.
7. A circle can be divided into several sectors. 8. Two points on the circle (the line segment connecting the two points is not the diameter) divide the circle into two parts, one part is larger than the semicircle and the other part is smaller than the semicircle, so the two points on the circle are divided into two arcs, and each arc corresponds to a sector.
3. Knowledge of all geometric figures in primary schools.
(a) Space and graphics-the understanding and measurement of graphics
This part needs to be reviewed emphatically:
The understanding and characteristics of "five elements", "five angles", "seven shapes" and "four bodies" learned in primary schools;
(2) Knowledge about measuring and measuring units, perimeter and area of plane graphics, surface area and volume of three-dimensional graphics;
③ Relevant knowledge of the observed object.
(B) Space and graphics-positioning and transformation of graphics
This part needs to be reviewed emphatically:
① Axisymmetric graphics, translation and rotation are three basic geometric transformations;
② Several methods to determine the position. The focus of direction and position is the knowledge of direction angle (especially who is off by how many degrees) and distance, number pairs, circuit diagram and scale.
(3) Master the drawing operation and use the knowledge of proportion to calculate the area.
First, the plane graphics
(a) "five elements"-line segments, rays, straight lines, vertical lines and parallel lines.
A little bit can draw countless rays. A little bit can draw countless straight lines. You can only draw a straight line after two o'clock.
(2) "Pentagon"-acute angle, right angle, obtuse angle, right angle and rounded corner.
1, the definition of an angle: two rays are drawn from a point, and the figure formed is called an angle.
(1) This point is called the vertex of the angle, and these two rays are called the edges of the angle;
(2) The size of the angle is related to the size of both sides of the angle, and the size of the angle has nothing to do with the side length of the drawn angle;
③ The angle is expressed by "∞";
④ The unit of measuring angle is "degree", which is expressed by "degree".
2. Classification of angles
Acute angle: An angle less than 90 is called acute angle. Right angle: An angle equal to 90 is called a right angle.
Oblique angle: an angle greater than 90 and less than180 is called obtuse angle.
Flat angle: The two sides of an angle form a straight line, and the angle formed at this time is called a flat angle. Boxer 180.
Fillet: One side of the corner rotates once and coincides with the other side. Fillet 360.
3. Draw and measure angles
If we are allowed to draw an angle at will, we can use a ruler. To draw an angle of a specified degree, you must draw it with a protractor.
(1) Draw a ray first, so that the center of the protractor coincides with the endpoint of the ray, and the zero scale line coincides with the ray;
(2) Point a little on the angular scale line drawn by the protractor;
(3) Take the endpoint of the ray as the endpoint and draw another ray through the point just drawn.
(3) Seven shapes-triangle, rectangle, square, parallelogram, trapezoid, circle and sector.
4. Primary school mathematical graphics and measurement knowledge points
(1) rectangle 1. Features: All six faces are rectangular (sometimes two opposite faces are square). The areas of the opposite sides are equal, and the lengths of the four opposite sides of 12 are equal. There are eight vertices. The lengths of three sides intersecting at a vertex are called length, width and height respectively. An edge where two faces intersect is called an edge. The point where three sides intersect is called an edge. You can only see three faces at most. The total area of six faces of a cuboid or cube is called its surface area. 2. The formula s=2(ab+ah+bh) V=sh V=abh (II) cube 1. Features: All six faces are squares, the area of six faces is equal to 12 sides, and all sides are equal to 8 vertices. v=a？ (3) Cylinder 1, the upper and lower surfaces of the cylinder are called the bottom surface. A cylinder has a surface called a side. The distance between the two bottom surfaces of a cylinder is called the height. The actual materials used are more than the calculated results. Therefore, when this number is to be retained, the omitted positions are 4 or less. We must advance to 1. This approximate method is called one-step method. 2. calculation formula s side =ch s table =s side +s bottom *2 v=sh/3 (4) understand that the bottom of a cone is a circle and the edge of a cone is a surface. The distance from the apex of the cone to the center of the bottom is the height of the cone. To measure the height of the cone, put the bottom of the cone first. Measure the distance between the flat plate and the bottom surface vertically. Enlarge the side of the cone to get a sector. 2 the formula v= sh/3 (5) ball 1. Knowing that the surface of a ball is a curved surface is called a sphere. A ball is similar to a circle and also has a center, which is represented by O. The line segment from the center to any point on the spherical surface is called the radius of the ball, which is represented by R. Each radius is equal. The line segment passing through the center of the sphere and having both ends on the sphere is called the diameter of the sphere, which is represented by d, each diameter is equal, and the length of the diameter is equal to twice the radius, that is, d=2r. 2 calculation formula d=2r.
5. Five little knowledge of primary school mathematics
Commonly used quantitative relationships are 1, number of shares * number of shares = total number of shares ÷ number of shares = number of times of 2,65438 per share +0 * multiple = multiple of 65438+multiple of 0 = multiple of 65438+multiple of 0 = multiple of 65438+multiple of 0 = 3. Quantity = total price ÷ total price ÷ unit price = total price ÷ quantity = unit price 5, working efficiency * working time = total work ÷ working efficiency = working time ÷ total work = working efficiency 6, addend+addend = sum- one addend = another addend 7, minuend-minuend = difference. Divider ÷ Divider = quotient dividend ÷ quotient = divisor quotient * Divider = divider calculation formula for primary school mathematical figures 1, square (c: perimeter s: area a: side length) perimeter = side length *4 C=4a area = side length * side length S=a*a 2, cube (3). Width S=ab 4, cuboid (v: volume s: area a: length b: width h: height) (1) height V=abh 5, triangle (s: area a: bottom h: height) area = bottom * height ÷2 s=ah÷2 triangle height = area. Height ÷2 s=(a+b)* h÷28, circle (s: area c: perimeter л d= diameter r= radius) (1) perimeter = diameter *л=2*л* radius c = л. Height =ch(2лr or лd) (2) surface area = lateral area+bottom area *2 (3) volume = bottom area * height (4) volume = lateral area ÷2* radius 10, cone (v: volume h: height s: bottom area r). The formula of sum difference problem: (sum+difference) ÷2= large number (sum-difference) ÷2= decimal 13, and the problem of multiple: sum ÷ (multiple-1)= decimal * multiple = large number (or sum-decimal = large number). Meet time = meet distance ÷ speed and; Speed sum = meeting distance ÷ meeting time 16, concentration problem Solute weight+solvent weight = solution weight * 100%= concentration solution weight * concentration = solute weight ÷ concentration = solution weight 17, profit and discount problem. Profit rate = profit/cost * 100%= (selling price/cost-1)* 100% fluctuation amount = principal * fluctuation percentage; Interest = principal * interest rate * time; After-tax interest = principal * interest rate * time * (1-20%) common unit conversion length unit conversion 1 km =1000m1m =1decimeter1decimeter =/kloc. = 100 ha 1 ha = 10000 m2 1 m2 = 100 cm2 1 cm2 = 1 00 mm2. Kloc-0/ kg = 1 kg RMB unit conversion: 1 yuan = 10 angle 1 0 minute 1 yuan = 100 minute time unit conversion:. \3\5\7\8\ 10\ 12 Abortion (30 days) is: 4\6\9\ 1 1 February 28th in a flat year, February 29th in a leap year, and June 30th in a flat year. Leap year 366 days 1 day =24 hours 1 hour =60 minutes 1 minute =60 seconds 1 hour = 3,600 seconds Basic concepts Chapter I Calculation of Numbers and Numbers A concept (I) Integer 1 Meaning: sum of natural numbers.
2 natural numbers: when we count objects, 1, 2, 3 ... the numbers used to represent the number of objects are called natural numbers. There is no object, which is represented by 0.
0 is also a natural number. Counting units one (one), ten, one hundred, one thousand, ten thousand, one hundred thousand, one million, ten million, one hundred million ... are all counting units.
The propulsion rate between every two adjacent counting units is 10. This counting method is called decimal counting method.
4 digits: Counting units are arranged in a certain order, and their positions are called digits. The divisible integer A of the number 5 is divisible by the integer B (b ≠ 0), and the divisible quotient is an integer with no remainder, so we say that A can be divisible by B, or that B can be divisible by A. ..
If the number A is divisible by the number B (b ≠ 0), then A is called a multiple of B, and B is called a divisor of A (or a factor of A). Multiplication and divisor are interdependent.
Because 35 is divisible by 7, 35 is a multiple of 7, and 7 is a divisor of 35. The divisor of a number is finite, in which the smallest divisor is 1 and the largest divisor is itself.
For example, the divisor of 10 is 1, 2,5, 10, where the smallest divisor is 1 0 and the largest divisor is 10. The number of multiples of a number is infinite, and the smallest multiple is itself.
The multiple of 3 is: 3, 6, 9, 12 ... The minimum multiple is 3, but there is no maximum multiple. Numbers in units of 0, 2, 4, 6 and 8 can be divisible by 2, for example, 202, 480 and 304 can be divisible by 2.
Numbers in units of 0 or 5 can be divisible by 5, for example, 5,30,405 can be divisible by 5.
The sum of the numbers in each bit of a number can be divisible by 3, so this number can be divisible by 3. For example, 12,108,204 can all be divisible by 3.
The sum of each digit of a number can be divisible by 9, and so can this number. A number divisible by 3 may not be divisible by 9, but a number divisible by 9 must be divisible by 3.
The last two digits of a number can be divisible by 4 (or 25), and this number can also be divisible by 4 (or 25). For example,16,404 and 1256 can all be divisible by 4, and 50,325,500 and 1675 can all be divisible by 25.
The last three digits of a number can be divisible by 8 (or 125).
6. Review the knowledge points of the People's Education Edition of primary school graphics and geometry (complete solution of the textbook)
(a) the understanding of graphics and measurement 1. A unit of length is used to measure the length of an object.
Commonly used length units are: kilometers, meters, decimeters, centimeters and millimeters. 2. Length unit: 1 km =1000m1m =1decimeter1decimeter =10cm1cm =
Public area units: square kilometers, hectares, square meters, square decimeters and square centimeters. Four, the calculation of land area, usually in hectares.
The square with a side length of 100 meters covers an area of 1 hectare. Five, measuring a large area of land, usually in square kilometers.
Square land with side length 1000 m, area 1 km2. 6. Area unit: (1 00)1km2 =100 hectares1hectare =10000m21m2 =100m2 = 65438.
Commonly used unit of volume are: cubic meter, cubic decimeter (liter) and cubic centimeter (milliliter). Unit of volume: (1000) 1 m3 = 1000 m3 = 1000 cm3 = 1 l = 1000 ml, understanding of plane figure, perimeter and area. Extending one end of the line segment indefinitely can get a ray; Extend both ends of a line indefinitely and you can get a straight line.
Line segments and rays are both parts of a straight line. A line segment has two endpoints and its length is limited. A ray has only one endpoint, a straight line has no endpoint, and both rays and straight lines are infinitely long.
Second, two rays from a point form an angle. The size of the angle is related to the size of both sides, and has nothing to do with the length of the sides.
The unit of measurement of angle size is (). Third, the classification of angles: angles less than 90 degrees are acute angles; An angle equal to 90 degrees is a right angle; An angle greater than 90 degrees and less than 180 degrees is an obtuse angle; The angle equal to 180 degrees is a flat angle; An angle equal to 360 degrees is a fillet.
Four, two straight lines intersecting at right angles are perpendicular to each other; Two straight lines that do not intersect in the same plane are parallel to each other. 5. A triangle is a figure surrounded by three line segments.
Each line segment constituting a triangle is called an edge of the triangle, and the intersection of every two line segments is called the vertex of the triangle. 6. Triangle can be divided into acute triangle, right triangle and obtuse triangle according to angle.
According to different sides, it can be divided into equilateral triangle, isosceles triangle and arbitrary triangle. 7. The sum of the internal angles of a triangle is equal to 180 degrees.
8. In a triangle, the sum of any two sides is greater than the third side. Nine, in a triangle, there is at most one right angle or at most one obtuse angle.
X. A quadrilateral is a figure surrounded by four sides. Common special quadrangles are parallelogram, rectangle, square and trapezoid.
Xi。 A circle is a curved figure. The distance from any point on the circle to the center of the circle is equal, and this distance is the length of the radius of the circle.
The line segment passing through the center of the circle with both ends in the circle is called the diameter of the circle. Twelve, there are some graphics, folded in half along a straight line, and the graphics on both sides of the straight line can completely overlap. This graph is an axisymmetric graph.
This straight line is called the axis of symmetry. Thirteen, the sum of all the edges of a figure is the perimeter of the figure.
Fourteen, the size of the surface of the object or the closed plane figure is called their area. Fifteen. Derivation of the formula for calculating the area of a plane figure: 1 derivation process of the area formula of a parallelogram ① A parallelogram can be transformed into a rectangle through shearing and translation.
② The length of rectangle is equal to the base of parallelogram, the width of rectangle is equal to the height of parallelogram, and the area of rectangle is equal to the area of parallelogram. ③ Because rectangular area = length * width, parallelogram area = bottom * height.
Namely: S=ah. 2 derivation process of triangle area formula ① Two identical triangles can be combined into a parallelogram.
② The base of parallelogram is equal to the base of triangle, the height of parallelogram is higher than that of triangle, and the area of triangle is equal to half of the area of parallelogram with the same height as its base; (3) Because the area of parallelogram is equal to the base * height, the area of triangle is equal to the base * height ÷2. Namely: S=ah÷2.
3 Derivation process of trapezoid area formula ① Two identical trapezoids can be combined into a parallelogram ② The base of the parallelogram is equal to the sum of the upper and lower base of the trapezoid, the height of the parallelogram is higher than the height of the trapezoid, and the area of the trapezoid is equal to half of the area of the parallelogram ③ Because the area of the parallelogram = bottom * height, the area of the trapezoid = (upper bottom+lower bottom) * height ÷2. Namely: S=(a+b)h÷2.
Draw a picture to illustrate the derivation process of the formula of circle area ① Divide the circle into several equal parts and make it into an approximate rectangle after cutting. ② The length of a rectangle is equivalent to half of the circumference, and the width is equivalent to the radius of the circle.
③ Because: rectangular area = length * width, so: circular area =πr*r=πr2. Namely: S=πr2 XVI. The formula for calculating the perimeter and area of plane graphics: rectangle perimeter = (length+width) * 2 rectangle area = length * width square perimeter = side length * 4 square area = side length * side length parallelogram area = bottom * height triangle area = bottom * height ÷ 2 three-dimensional graphics cognition, perimeter, area 1, cuboid and cube.
Cubes are special cuboids. Second, the characteristics of the cylinder: one side, two bottom surfaces, and countless heights.
Third, the characteristics of the cone: a side, a bottom, a vertex and a height. 4. Surface area: The sum of all the areas of a three-dimensional figure is called the surface area of this three-dimensional figure.
Verb (abbreviation of verb) Volume: The size of the space occupied by an object is called the volume of the object. The volume that a container can hold other objects is called the volume of the container.
6. Three relationships between a cylinder and a cone: ① Equal base and equal height: volume 1︰3 ② Equal base and equal volume: height 1︰3 ③ Equal height: base area 1︰3 7. Cylinders and cones with equal bottoms and equal heights: ① The volume of a cone is 1/3 of that of a cylinder; ② The volume of a cylinder is three times that of a cone; ③ 8. Cylinders and cones with equal bottoms and equal heights: cone 1, difference 2, columns 3 and 4.
9. Formula derivation of three-dimensional figure: 1 What figure is obtained after the side of the cylinder is unfolded? What is the relationship between each part of this figure and the cylinder? (Deduction process of cylindrical lateral area formula).