Get answers from questions
A= 10b, so the original question is to ask you the greatest common divisor of 10b/b, and you can see that it is 10b, which is A, so choose A.
2.a, the internal angle between any triangle and 180.
3. B. If the distance is K, the speed of the truck is K/ 15, and the speed of the bus is K/ 10, and the ratio of the two is 3: 2.
4. C. The original area is the largest under the same circumference.
5.c, the remainder must be less than the divisor, so choose C.
6.b, because a point is determined, there are two opposite sides, so there are two heights. Choose B.
7. C. Under the same perimeter, the rectangular area is the smallest.
8. The number of B, A = 0.4× the number, so B: A =2.5.
9. B. Qualified rate = number of qualified pieces ÷ total pieces.
10.d, asking about the company, not the position.
1 1.a, etc. The volume of a cylinder is three times that of a cone.
12.a, x increases, and y also increases, so it is proportional.
13.b, division counts, do it yourself.
14.b, the more workers, the shorter the time, so it is inversely proportional.
15.d, because the rope length is not told, it cannot be calculated.
16. A. According to the meaning of the question, the first paragraph accounts for 4/7 of the total length, which is 3/4M, and the second paragraph is 7/28M, so the first paragraph is longer.
1, the natural number a divided by the natural number b, and the quotient is 10, then the greatest common divisor of a and b is (b).
a、a B、b C、 10
2. A triangle is divided into two triangles by drawing a line segment through one of its vertices, and the sum of the internal angles of a triangle is (A).
A, 180 B, 90 c, uncertain
3. It takes 10 hour for the bus to drive from A to B, and 15 hour for the truck. The speed ratio between the bus and the truck is (b).
a、2:3 B、3:2 C、2:5
4. When three iron wires with the length of 12 decimeter are enclosed in a rectangle, a square and a circle, the enclosed area (c) is the largest.
A, rectangle b, square c, circle
5. In the division formula m ÷ n = a ... b, (n≠0), the following formula is correct (c).
a、a>nB、n>a、C、n>b
6, parallelogram to the opposite side of a vertex can be made (b) high.
A, 1 B, 2 C, countless
7. Use three wires with the same length to form a circle, a square and a rectangle respectively, and (c) has the smallest area.
A, circle b, square c, rectangle
8. The ratio of number A to number B is 0.4, and the ratio of number B to number A is (b).
A.0.4 B.2.5 C. 2/5
9, processing a batch of parts, after inspection, 100 qualified, 25 unqualified, the qualified rate of this batch of parts is (b).
a、75% B、80% C、 100%
10, the third digit to the right of the decimal point is included in (d)
A, percentile b, thousandth c, 0.0 1 D, 0.00 1
1 1, and the specific volume (b) of an equal-bottom cylinder with the same height as the cone.
A, big B, twice as big C, small
12, if 4X=3Y, then x and Y( A)
A, proportional to B, inversely proportional to C, out of proportion
13,0.7 ÷ 0.3 If the quotient is 2, then the remainder is (b).
a、 1 B、0. 1 C、0.0 1 D、 10
14, manufacturing a batch of parts, if everyone's work efficiency is certain, then the number of workers and the time spent (b)
A. directly proportional; Inverse ratio; be disproportionate
15. Two ropes with the same length, one is cut by 3/7 meters, the other is cut by 3/7 meters, and (d) the root is cut longer.
A, the first root is long b, the second root is long c and the same length d, so it is impossible to judge.
16, a rope, cut into two sections, the first section is 3/7 meters long, the second section accounts for 3/7 of the total length, and the first section (a) is longer.
A, the first paragraph b, the second paragraph c, the same length d, can not be judged.
The stereoscopic graphics in the sixth grade of primary school are prone to errors (1), fill in the blanks.
1. A cuboid has () faces, () sides, () vertices, opposite side length () and opposite side ().
2. The transverse expansion of a cylinder is (), its length is cylinder () and its width is cylinder ().
3. A rectangle is 5cm long, 3cm wide and 2cm high. Its largest surface is () and its area is () square centimeters. The surface area of this cuboid is () square centimeters and the volume is () cubic centimeters.
4. Cut a cylindrical iron ventilation pipe with a diameter of 8 cm and a length of 2 m along the height to obtain a rectangle with a length of () m and a width of () m..
5. Use a square piece of paper with a side length of 6.28 cm to enclose the largest cylindrical paper tube. The height of this paper tube is () centimeters and the volume is () cubic centimeters.
6. The sum of the sides of a cube is 48 cm, its surface area is () square cm and its volume is () cubic cm.
7. The volume of the cone is 24 cubic centimeters, the bottom area is 8 square centimeters, and the height is () centimeters.
8. Put three cubes with side length of 1 decimeter into a cuboid. The surface area of this cuboid is () square decimeter and the volume is () cubic decimeter.
9. Cut a cubic wood with a side length of one meter into two small cuboids at will, and the surface area is () square meters more than the original.
10, cut a cube with a side length of 3 cm into the largest cylinder with a volume of () cubic cm.
1 1, cylindrical wood, the bottom diameter and height are 6 cm, its lateral area is () square cm, and its volume is () cubic cm. If processed into the largest cone, the volume of this cone is () cubic centimeters.
12, the height of a cylinder is 9.42 cm, the side is square, and the diameter of its bottom is () cm.
13, the side of a cylinder is a square with a side length of 3 1.4 cm, and the bottom area of this cylinder is () square cm.
In the sixth grade of primary school, the application and processing cost of a farm tool used to be in 80 yuan, but now it is in 64 yuan. How much is the cost reduced?
(80-64)/80=
The railway from city A to city B is 2 16 kilometers long. A train starts from a city and travels 96 kilometers in the first two hours. At this rate, how many hours will it take to get to B city?
2 16/(96/2)=
For a project, it takes 10 hour for Party A to do it alone and 15 hour for Party B to do it alone. How many hours does it take two people to finish half the project together?
1/2/( 1/ 10+ 1/ 15)=
A workshop produced *** 1280 copies of A, B and C, in which the ratio of A to B was 3: 2, and C was 80 more than A. How many copies did C produce?
( 1280-80)*3/(3+2+3)+80=
What do you ask about the wrong math problem (application problem) in the sixth grade of primary school?
With regard to the error-prone problem of plane graphics, it is necessary to clarify the error-prone places in the formula of sector perimeter.
Because sector = two radii+arc length
If the radius is r and the central angle of the sector is n, the perimeter of the sector is:
C=2R+nπR÷ 180
Sector area formula
In a circle with radius r, the sector area corresponding to the central angle of 360 is the circle area S = π r 2, and the sector area with central angle of n is:
S=nπR^2÷360
There is another area formula for the sector.
S= 1/2lR
Where l is the arc length and r is the radius.
Edit the arc length formula of this sector.
L=(n/ 180)*pi*r, l is the arc length, n is the central angle of the sector, pi is pi, and r is the radius of the sector.
Triangle area formula
Given that the base of a triangle is h, then S = Ah/2.
Given three sides A, B, C and half circumference P of a triangle, then S = √ [P (P-A) (P-B) (P-C)] (Helen's formula) (p=(a+b+c)/2).
And: (a+b+c)*(a+b-c)* 1/4.
Given the angle c between two sides a and b of a triangle, S = ABS Inc/2.
Let the three sides of a triangle be A, B and C respectively, and the radius of the inscribed circle be R.
Then the triangle area =(a+b+c)r/2.
Let the three sides of a triangle be A, B and C respectively, and the radius of the circumscribed circle be R.
Triangle area =abc/4r.
Given three sides A, B and C of a triangle, then S = √ {1/4 [C2A2-((C2+A2-B2)/2) 2]} ("Tridiagonal quadrature" in the Southern Song Dynasty).
| a b 1 |
S△= 1/2 * | c d 1 |
| e f 1 |
| a b 1 |
| c d 1 | is a third-order determinant, and this triangle ABC is in the plane rectangular coordinate system A(a, b), B(c, d), C(e, f), where ABC.
| e f 1 |
It is best to choose from the upper right corner in counterclockwise order, because the results obtained in this way are generally positive. If you don't follow this rule, you may get a negative value, but it doesn't matter, just take the absolute value and it won't affect the size of the triangle area!
Circular area formula
Let the radius of a circle be r and the area be s.
Then the area S= π*r*r π stands for π.
The area of a circle is equal to pi times circle radius times circle radius.
Bow area formula
Let the arc opposite to the bow AB be the arc AB, then:
When the arc AB is minor, then S-bow = S-sector-S △ AOB (A and B are the endpoints of the arc and O is the center of the circle).
When arc AB is a semicircle, then S bow = S sector = 1/2S circle = 1/2× π r 2.
When arc AB is the optimal arc, then S-bow = S-sector+S △ AOB (A and B are the endpoints of the arc, and O is the center of the circle).
The calculation formula is as follows:
S=nπR^2÷360-ah÷2
S=πR^2/2
S=nπR^2÷360+ah÷2
Rhombic area formula
Diamond area = half of diagonal product, that is, S=(a×b)÷2.
The area of a diamond can also be equal to the base times the height.
Parabolic arcuate area formula
Parabolic chord length formula and its application
In this paper, a formula is introduced, which can simply and accurately calculate the chord length of a parabola cut straight line, and can also be used to judge the positional relationship between a straight line and a parabola and solve some problems related to chord length. This method is simple and clear, and can be used for reference.
The parabolic arch area formula is equal to 3/4 of the inscribed triangle with the secant as the base and the tangent point parallel to the base as the vertex, namely:
Parabolic arch area = s+1/4 * s+116 * s+1/64 * s+... = 4/3 * s.
Theorem The length of the chord AB cut by the straight line y=kx+b(k≠0) by the parabola y2=2Px is
∣AB∣= ①
It is proved that x= y=kx+b is substituted into Y2-+= 0 of y2=2Px.
∴ y 1+y2=，y 1y2=。
∣y 1-y2∣==2，
∴∣AB∣=∣y 1-y2|=
When the straight line y=kx+b(k≠0) is out of focus, b =-, if it is substituted into ①, ∣AB∣=P( 1+k2),
So the following inference is drawn:
It is inferred that the straight line y = kx-(k ≠ 0) of 1 over-focus is the chord of the parabola y2=2Px.
The length of AB is
∣AB∣=P( 1+k2) ②
In (1), it is easy to draw the following inference:
Inference 2 The straight line l: y=kx+b(k≠0) and the parabola C:y2=2Px are known.
I) when p > 2bk, l and c intersect at two points (intersection points);
Ii) When P=2bk, L and C intersect at a point (tangency);
Ⅲ) When p < 2bk, L and C have no intersection (phase separation).
It takes longer than B to answer the wrong questions (true or false questions) 1.× A in sixth grade mathematics, and the speed of A must be lower than B.
2.× 180 is a right angle, not an obtuse angle.
3.× should be separable, not separable.
The leap year is 366 days.
5.√ Cylinder volume = bottom area × height and bottom area ×3, then the left side of the equation is also ×3.
6. X is converted into 4/5, and the denominator is 5, which can be converted into a finite decimal.
7.× 3 is divisible by 3, but not by 9.
8.A√ a÷c=b, so b is the divisor of a.
When B× b= 1, a=c, and c is not a divisor of b.
C√ is obtained from A, which is a multiple of B, so A is the least common multiple of A and B. ..
D√ is obtained from A, which is a multiple of B. Similarly, A is a multiple of C, so A is a common multiple of B and C. ..
9.x can be an acute angle or a right angle.
10.√ The product of internal terms is equal to the product of external terms. If the inner term is reciprocal, the product is 1 and the product of the outer term is also 1, so the outer term is reciprocal.
1 1.× should be the volume of milk.
12.× x = (k- 1) y, if k is certain, then (k- 1) is also certain, so x and y are proportional.
13.√ Four are defined on the basis of conditional quadrilateral.
14.× As long as the values of the bottom area× height of the two are equal.
15.× It can be 2:333 or something.
16.× It's all one kilogram, the same weight.
17.√ 1% is so defined.
18.× See Article 14.
19.×
20. The sum of the internal angles of any quadrilateral is 360.
2 1.× cube is also a kind of cuboid, not just two opposite faces.
22.× Two rectangles with equal perimeters, the smaller the difference between the two sides, the larger the area of the rectangle.
23.× If it is only within the range of a cuboid, as long as the height is not 1 decimeter, the bottom area is not 1 decimeter.
24. According to the question, if the side length of a cube is 1 decimeter, the volume must be 1 square decimeter.
25. Make sure that the total amount of × is inversely proportional.
26.√ The previous increase of the ratio 10% means that the previous period is multiplied by 1. 1, and the previous and subsequent items of the ratio are multiplied by 1. 1 at the same time, and the ratio remains unchanged.
27.× should be 5 ÷105 =1/21,which is about 4.76%.
28. If the scale is large and the denominator is small, the actual distance is also small.
29.√ If both perimeters are A, then the area of the square is A? /16, the area of the circle is a? /4π, so the area ratio of square to circle should be π: 4.
30. I don't know what a fractional unit is.
3 1 .×7/8 & lt； 1 & lt； 8/7。
32.x should be in the same plane.
33.× 99÷99= 1= 100%。
34. Find 1 worker 5 hours to process 1 part, and control a quantity.
35.× Add two zeros to the end of a decimal, and this number remains unchanged.
Collection of application questions, error-prone questionS And puzzles for the sixth grade of primary school 2007-05- 13 12:36 Collection of application questions, error-prone questions and puzzles for the sixth grade of primary school The first one: Set the distance as s a per hour x.
Equal according to time
1 divided by 30+3S divided by 60 = 2S divided by x+3s divided by 2X.
Simplified to 48 S=6X 5S.
Divide both sides by 1 of s at the same time, and finally X=40.
The next one won't
Urgent! Mathematics in the sixth grade of primary school is prone to mistakes. A stick is stuck in the ground, and there is something 4m that can hold a dog. The dog's activity is 4π instead of12.56 m.
I wrote 12.56 wrong before.
Error-prone equation of sixth grade in primary school, easy to calculate 1. From city A to city B, it takes 6 hours for car A and 4 hours for car B. Now, car A and car B start from city A and city B respectively and drive relatively at the same time. When they met, car A traveled 96 kilometers. How far is the distance between cities A and B?
2. For a project, Party A and Party B cooperate to complete 1/6 of the project every hour. If Party A is asked to do it for 4 hours first, Party B will do it for 3 hours. Two fifths of all the projects are still unfinished. How many hours does it take Party A to complete all the projects alone?
3. For Xiaoqing's birthday, light two red and yellow candles of equal length. Red candles can burn for 5 hours and yellow candles can burn for 4 hours. At 8 o'clock in the evening, two candles are lit at the same time, and at a certain moment, two candles are extinguished at the same time. At this time, the remaining part of the red candle is twice that of the yellow candle. What time does the candle go out?
The store bought a batch of volleyball at the price of 6 yuan, with the retail price of 8 yuan. With 10 left, 200 yuan asked how many volleyballs are there?
5. The pipeline team laid 2620 meters of natural gas pipelines, with an average of 80 meters laid every day in the first four days. The rest are required to be paved12m more every day than before. How many days will it take to complete the laying?
6. This year, the father is nine times as old as his son. Nine years later, the father and son will be 60 years old. How old are the father and son this year?
1. A certain unit of the People's Liberation Army has to March 502 kilometers every day and start hiking for 60 kilometers. After walking for 3 days, the remaining distance is 20.5 kilometers per day. How many days will it take to finish it?
The rice in bag a weighs 68kg. After pouring 15kg from bag A into bag B, bag A is 5kg heavier than bag B ... How many kilograms of raw rice is there in bag B?
A steel mill produces 830 tons of steel every day for the first 3 days and 850 tons every day for the next 5 days. How many tons of steel is produced on average every day?
The motorcyclist traveled 60 kilometers at the speed of 20 kilometers per hour, and came back 30 kilometers per hour. What is the average speed of going back and forth?
5. Workers in the first workshop of a machine tool factory use 18 lathe to produce 720 machine parts in two hours. How many machine parts do 20 such lathes produce in three hours?
6. You can make120kg tofu with 30kg soybeans. According to this calculation, how many kilograms of soybeans do you need to make 600 kilograms of tofu?
An express train and an ordinary bus leave from two cities at the same time. The speed of express train is 90 kilometers per hour, and that of ordinary bus is 48 kilometers per hour. Two and a half hours later, two trains met on the road. How many kilometers is the railway between city A and city B?
8. The distance between the two places is 28 kilometers, and two cars, A and B, travel in the same direction from both places at the same time. A car travels 25 kilometers per hour, and B car travels 32 kilometers per hour. Car A is in the front and car B is in the back. How many hours will car B catch up with car A?
9. Cut a rectangular piece of paper with a length of 90 cm and a width of 20 cm into several square pieces of paper with the same size. It is required that the side length of the square is the largest, so as not to waste paper. How many squares can you cut?
10. In order to green the highway, the Bureau of Landscape Architecture planted a tree every 4 meters on both sides of a section of highway, and planted 74 trees at a time. Now it plans to plant a tree every 6 meters. So, how many trees will not be transplanted?
1 1, Party A has 14.8 yuan and Party B has 15.2 yuan. They want to buy a football together. The price of a football is twice their money. How much is a football? How much are they short of?
12. A machine plows 15 hectares in 3 hours. According to this calculation, how many hours does it take for five machines to plow 75 hectares?
13. There are 14 boxes of duck eggs in the store. Sold 250 kilograms, leaving 4 boxes of 20 kilograms. How many kilograms are there in each box of duck eggs?
14. bright primary school donated books to mountain students, with 240 books in grade four, twice as many as in grade five, and more books in grade six than in grade five 120. How many books did he donate per grade on average?
15. The grain store delivered 20 bags of rice and 20 bags of flour, each of which was 90kg of rice and 25kg of flour. How many kilograms more rice is brought in than flour? (Answer in two ways)
16. Two ropes * * * are 48.4m long. After cutting 6.4 meters from the first rope, the second rope is 6 meters more than the remaining two of the first rope. How long are the two ropes?
17. Students in Grade 4 and Grade 5 collect tree species, and the students in Grade 4 collect tree species 18.6 kg, and the students in Grade 4 collect 2.5 kg less than those in Grade 5. How many kilograms of tree species were collected in the second grade?
18. a workshop used to use 2450 kilowatts of electricity every month? At that time, after carrying out the saving activities, the electricity consumption of the original year can now be increased by two months. How many kilowatts does this workshop save electricity on average every month? What time?
19. The students took part in tree planting activities. 96 students in Grade 4 * * *, each of whom planted 3 trees. There are 87 people in the fifth grade, each of whom planted 4 trees. How many more trees were planted in the fifth grade than in the fourth grade?
20. Six students in the first group scored 86, 79, 98, 100, 89 and 94 respectively in the math test. What is their average score?
2 1. The car travels for 3 hours 135km, and the plane is 28 times faster than the car and flies 60km less. How many kilometers does this plane fly per hour?
A clothing factory produced 850 suits in five days. According to this calculation, how many suits are produced a month? (30 days a month)
23. The store delivered 8 baskets of apples, 12 baskets of pears, 38 kg of apples and 42 kg of pears in each basket. How many kilograms of fruit did this shop ship?