Geometric area: the most difficult knowledge point of mathematics in the sixth grade graduation exam
Basic idea:
In the calculation of some areas, if the formula cannot be used directly, it is generally necessary to cut, translate, rotate, fold, decompose, deform and superimpose the graphics to make the irregular graphics into regular graphics for calculation; In addition, we need to master and remember some conventional regional rules.
Common methods:
1. Connection auxiliary line method
2. Use two triangles with equal bases and equal heights, with equal areas.
3. Bold assumptions (some points are set at any point in the topic, and you can set any point in a special position when solving problems).
4. Use special laws
(1) isosceles right triangle, it is known that any side can find the area. (The square of hypotenuse divided by 4 equals the area of isosceles right triangle)
(2) After trapezoid diagonal connection, the waist areas are equal.
③ The area of the circle accounts for 78.5% of the circumscribed circle.
Sixth grade mathematics knowledge points
1. What is the circumference of the graph?
The sum of all the edges of a figure is the perimeter of the figure.
2. What is the area?
The size of the surface of an object or the plane figure surrounded by it is called their area.
3, the relationship between the parts of addition:
One addend = and-the other addend.
4, the relationship between the parts of subtraction:
Minus = Minus-Difference Minus = Minus+Difference
5, the relationship between the parts of multiplication:
One factor = product ÷ another factor
6, the relationship between the parts:
Divider = divider, quotient dividend = quotient × divisor
7. Angle
(1) What is an angle?
A figure composed of two rays drawn from a point is called an angle.
(2) What is the vertex of an angle?
The endpoint of an angle is called a vertex.
(3) What is the edge of a corner?
The rays that form an angle are called the edges of the angle.
(4) What is a right angle?
An angle of 90 degrees is a right angle.
(5) What is a right angle?
The two sides of an angle are on a straight line, and such an angle is called a right angle.
(6) What is an acute angle?
An angle less than 90 is an acute angle.
(7) What is an obtuse angle?
An angle greater than 90 and less than180 is an obtuse angle.
(8) What is a fillet?
The angle formed by a ray rotating around its endpoint is called a fillet, and the fillet is equal to 360.
Knowledge points of sixth grade mathematics unit: statistical chart.
(1) Meaning: A graph that represents the quantitative relationship between related quantities with the area of dotted line is called a statistical graph.
(2) Classification
1, bar chart
Use a unit length to represent a quantity, draw straight lines with different lengths according to the quantity, and then arrange these straight lines in a certain order.
Advantages: It is easy to see the quantity of each.
Note: When drawing a bar chart, the width of the bars must be the same.
Take the unit length to express the quantity, depending on the specific situation;
The straight lines representing different items in the composite bar chart should be distinguished by different lines or colors, and the legend should be displayed below the drawing date.
General steps to make a bar chart:
(1) Draw two vertical rays according to the drawing size.
(2) On the horizontal ray, reasonably distribute the position of the strip and determine the width and interval of the straight line.
(3) On the deep line perpendicular to the horizontal ray, according to the specific situation of the data size, determine how much the unit length represents.
(4) Draw straight lines with different lengths according to the data size, and indicate the number.
2, broken line statistics
Use a unit length to represent a quantity, draw points according to the quantity, and then connect the points in turn with line segments.
Advantages: it can not only represent quantity, but also clearly represent the change of quantity.
Note: When the horizontal axis of the broken line statistical chart represents different years, months and other times, the distance between different times should be determined according to the interval of years or months.
General steps of making broken-line statistical chart:
(1) Draw two vertical rays according to the drawing size.
(2) On the horizontal ray, the positions of broken lines are appropriately distributed, and the width and interval of straight lines are determined.
(3) On the deep line perpendicular to the horizontal ray, according to the specific situation of the data size, determine how much the unit length represents.
(4) Draw all points according to the data size, and then connect them with line segments in turn, and indicate the quantity.
3, fan map
Use the area of the whole circle to represent the total, and use the sector area to represent the percentage of each part in the total.
Advantages: It clearly shows the relationship between each part and the whole.
General steps of making industry statistical chart:
(1) Calculate the percentage of each part in the total first.
(2) Calculate the degree of the fan-shaped central angle representing the number of each part.
(3) Draw a circle with an appropriate radius, and draw all sectors in the circle according to the central angle calculated above.
(4) In each sector, indicate the number name and percentage of each part, and distinguish each sector with different colors or stripes.
Knowledge points of sixth grade mathematics volume: cylinder and cone
1. Know cylinders and cones and master their basic characteristics. Know the bottom, sides and height of a cylinder. Know the bottom and height of the cone.
2. Explore and master the calculation method of lateral area and surface area of cylinder, as well as the calculation formula of cylinder and cone volume, and use the formula to calculate the volume to solve simple practical problems.
3. By observing, designing and making cylinder and cone models, we can understand the relationship between plane graphics and three-dimensional graphics and develop students' spatial concept.
4. The two circular surfaces of a cylinder are called the bottom surface, the surrounding surfaces are called the side surfaces, the bottom surface is a plane, and the side surfaces are curved surfaces.
5. The side of the cylinder is rectangular after being unfolded along the height, the length of the rectangle is equal to the circumference of the bottom of the cylinder, and the width of the rectangle is equal to the height of the cylinder. When the perimeter and height of the bottom are equal, the edge height is square after expansion.
6. The surface area of a cylinder = lateral area of the cylinder+bottom area ×2, that is, S table =S side +S bottom ×2 or 2πr×h+2×π.
7. lateral area of cylinder = perimeter of bottom × height, that is, S-side =Ch or 2πr×.
8. The volume of the cylinder = the bottom area of the cylinder × the height, that is, V=sh or πr2×.
Step-by-step method: More materials are actually used than the calculated results. Therefore, when you want to keep numbers, the omitted digits are 4 or less, and you must go forward 1. This approximate method is called step-by-step method.
9. A cone has only one bottom surface, and the bottom surface is a circle. The side of a cone is a curved surface.
10. The distance from the apex of the cone to the center of the bottom is the height of the cone. The cone has only one height. (Measuring the height of the cone: firstly, lay the bottom of the cone flat, place a flat plate horizontally above the apex of the cone, and measure the distance between the flat plate and the bottom vertically. )
1 1. Expand the side of the cone to get a sector.
12. The volume of a cone is equal to one third of the volume of a cylinder with the same height as its bottom surface, that is, V-cone = 1/3Sh or πR2×h \
13. Common cylindrical cone solving problems:
(1) Road surface area (transverse area) of the roller;
(2) The length of the road surface pressed by the roller (find the perimeter of the bottom surface);
(3) Tin bucket (side area and bottom area);
(4) Chef's hat (side area and bottom area); Ventilation pipe (side area).
Summary of key knowledge points in the first volume of sixth grade mathematics;
★ Sort out and summarize the knowledge points of the first volume of mathematics in the sixth grade.
★ Summary of knowledge points in the first volume of sixth grade mathematics
★ Review the knowledge points in the first volume of sixth grade mathematics.
★ Summary of percentage knowledge points in the first volume of sixth grade mathematics
★ Summary of mathematical knowledge points in the first volume of the sixth grade
★ Summary of the knowledge points reviewed at the end of the sixth grade mathematics.
★ Summary of knowledge points in the first volume of the sixth grade mathematics textbook.
★ Review materials of knowledge points in the first volume of sixth grade mathematics.
★ Summary of sixth grade mathematics knowledge points in People's Education Edition
★ The first volume of sixth grade mathematics knowledge points
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