1. A point on the center of the circle is called the center of the circle, which is represented by O. A line segment with one end on the center and the other end on the circle is called the radius, which is represented by R. A line segment with two ends on the circle and passing through the center of the circle is called the diameter, which is represented by D. 。

2. A circle has countless radii and diameters.

The center of the circle determines the position of the circle, and the radius determines the size of the circle.

Understanding of Circle (2)

Fold the circle in half, then fold it in half to find the center of the circle.

5. A circle is an axisymmetric figure, and a straight line with its diameter is the axis of symmetry. A circle has countless axes of symmetry.

6. The diameter of the same circle is twice as long as the radius, which can be expressed as d = 2r or r = d/2.

The circumference of a circle and the circumference of a semicircle:

7. The length of a circle is the circumference of a circle. The circumference of a semicircle is equal to half the circumference plus the diameter.

8. The quotient of the circumference divided by the diameter of the circle is a fixed number, called pi, which is usually taken as 3. 14 in calculation.

9.c = π d or c = π r.

10. 1π=3. 14 2π=6.28 3π=9.42 4π= 12.56 5π= 15.7 6π= 18.84 7π=2 1.98 8π=25. 12 9π=28.26 10π=3 1.4

Area of a circle

1 1. If S represents the area of a circle and R represents the radius of a circle, then S = π r 2s ring = π (r 2-r 2).

12. 1 1^2= 12 1 12^2= 144 13^2= 169 14^2= 196 15^2=225 / kloc-0/6^2=256 17^2=289 18^2=324 19^2=36 1 20^2=400

13. When the perimeters are equal, the area of the circle is the largest. When the areas are equal, the circumference of a circle is the smallest.

Application of percentage

The application of percentage (4)

14. Interest = principal times interest rate times time.

Understanding of ratio

15. The division of two numbers is also called the ratio of these two numbers. The latter term of the ratio cannot be 0. 16. The former term and the latter term of the ratio are multiplied or divided by the same number (except 0) at the same time. The constant ratio is called the basic property of the ratio.

Mathematics knowledge points in the sixth grade book (common to all primary schools and middle schools, which is more important)

Basic concept: Travel problem is to study the movement of objects, and it studies the relationship between the speed, time and travel of objects.

Basic formula: distance = speed × time; Distance ÷ time = speed; Distance/speed = time

Key question: determine the position in the journey.

Meeting problem: speed sum × meeting time = meeting distance (please write other formulas)

Pursuit problem: Pursuit time = distance difference ÷ speed difference (write other formulas)

Running water problem: downstream travel = (ship speed+water speed) × downstream time = (ship speed-water speed )× downstream time.

Downstream speed = ship speed+current speed = ship speed-current speed.

Still water velocity = (downstream velocity+upstream velocity) ÷2 Water velocity = (downstream velocity-upstream velocity) ÷2

Running water problem: the key is to determine the speed of the object, refer to the above formula.

Bridge crossing problem: the key is to determine the moving distance of the object, refer to the above formula.

Sum and difference problem formula

(sum+difference) ÷2= larger number; (sum and difference) ÷2= smaller number.

Sum-multiple problem formula

And present (multiple+1)= a multiple; A multiple x multiple = another number, or sum-a multiple = another number.

Formula of differential multiple problems

Difference ÷ (multiple-1)= smaller number; Smaller number × multiple = larger number, or smaller number+difference = larger number.

Average problem formula

Total quantity/total number of copies = average value.

General travel problem formula

Average speed × time = distance; Distance/time = average speed; Distance-average speed = time.

The formula of reverse travel problem can be divided into "encounter problem" (two people start from two places and walk in opposite directions) and "separation problem" (two people walk with their backs to each other). Both of these problems can be solved by the following formula:

(speed sum) × meeting (leaving) time = meeting (leaving) distance;

Meet (leave) distance ÷ (speed sum) = meet (leave) time;

Meet (leave) distance-meet (leave) time = speed and.

Formula of the problem of traveling in the same direction

Catch-up (pull-out) distance ÷ (speed difference) = catch-up (pull-out) time;

Catch up (pull away) the distance; Catch-up (pull-away) time = speed difference;

(speed difference) × catching (pulling) time = catching (pulling) distance.

Formula of train crossing bridge problem

(bridge length+conductor) ÷ speed = crossing time;

(Bridge length+conductor) ÷ Crossing time = speed;

Speed × crossing time = sum of bridge and vehicle length.

Navigation problem formula

(1) general formula:

Still water speed (ship speed)+current speed (water speed) = downstream speed;

Ship speed-water speed = water flow speed;

(downstream speed+upstream speed) ÷2= ship speed; (downstream speed-upstream speed) ÷2= water flow speed.

(2) Formula for two ships sailing in opposite directions:

Downstream speed of ship A+downstream speed of ship B = still water speed of ship A+still water speed of ship B.

(3) Formula for two ships sailing in the same direction:

Hydrostatic speed of rear (front) ship-Hydrostatic speed of front (rear) ship = the speed of narrowing (expanding) the distance between two ships.

(Find out the speed of narrowing or widening the distance between the two ships, and then solve it according to the relevant formula above).

For reference only:

Engineering problem formula

(1) general formula:

Efficiency × working hours = total workload; Total workload ÷ working time = working efficiency; Total amount of work ÷ efficiency = working hours.

(2) Assuming that the total workload is "1", the formula for solving engineering problems is:

1÷ working time = the fraction of the total amount of work completed in unit time;

1What is the score that can be completed per unit time = working time.

(Note: If the hypothetical method is used to solve the engineering problem, you can arbitrarily assume that the total workload is 2, 3, 4, 5 ... Especially if the total workload is the least common multiple of several working hours, the fractional engineering problem can be transformed into a relatively simple integer engineering problem, and the calculation will become simpler. )

Formula of profit and loss problem

(1) A surplus (surplus) and a deficit (deficit), the formula can be used:

(surplus+deficit) ÷ (the difference between two distributions per person) = number of people.

For example, "children divide peaches, each person 10, 9 less, and 8 more 7s per person." Q: How many children and peaches are there? "

Solution (7+9)÷( 10-8)= 16÷2

=8 (a) ........................................................................................................................................................................

10×8-9=80-9=7 1 (pieces)

Or 8×8+7=64+7=7 1 (pieces) (omitted)

(2) Both times are surplus (surplus), and the formula can be used:

(large surplus-small surplus) ÷ (the difference between two distributions per person) = number of people.

For example, "soldiers carry bullets for marching training, each carrying 45 rounds and more than 680 rounds; If each person brings 50 rounds, then 200 rounds more. Q: How many soldiers are there? How many bullets are there? "

Solution (680-200)÷(50-45)=480÷5

=96 (person)

45×96+680=5000 (hair)

Or 50×96+200=5000 (hair) (omitted)

(3) If twice is not enough (loss), the formula can be used:

(big loss-small loss) ÷ (the difference between two distributions per person) = number of people.

For example, "send a batch of books to students, each with 10 copies, with a difference of 90 copies;" If each person sends 8 copies, there are still 8 copies left. How many students and books are there? "

Solution (90-8)÷( 10-8)=82÷2.

=4 1 (person)

10×4 1-90=320 (this) (omitted)

(4) If one time is not enough (deficit) and the other time is just used up, you can use the formula:

Loss = number of people.

(Example omitted)

(5) One time there is surplus, and the other time it is just used up. This formula can be used to:

Surplus (the difference between two distributions per person) = number of people.

(Example omitted)

Formula of chicken and rabbit problem

(1) Given the total number of heads and feet, find the number of chickens and rabbits:

(total number of feet-number of feet per chicken × total number of heads) ÷ (number of feet per rabbit-number of feet per chicken) = number of rabbits;

Total number of rabbits = number of chickens.

Or (number of feet per rabbit × total head-total feet) ÷ (number of feet per rabbit-number of feet per chicken) = number of chickens;

Total number of chickens = rabbits.

For example, "Thirty-six chickens and rabbits, enough 100. How many chickens and rabbits are there? "

Solution1(100-2× 36) ÷ (4-2) =14 (only)

36-