Beijing normal university printing plate sixth grade first volume mathematics examination questions one.
I. Fill in the blanks (28 points)
1. The survey team erected a 3-meter-long bamboo pole on the ground and measured its shadow length as 1.2 meters. At the same time, the shadow length of a flagpole on campus is 4.8 meters, and the actual height of the flagpole is () meters.
2. If 3 =5 (? 0, ? 0), then: = (): ().
3. Choose 4 factors from 36 factors to form a proportion: ().
4. The diameter and height of the bottom of the cone is 6 cm, and its volume is () cubic cm, and the volume of a cylinder with the same bottom and the same height is () cubic cm.
5. 1.5︰( )= =0.6=( )? 10=( )%= () fold。
6. When the total price is fixed, the unit price is directly proportional to the quantity (). When the scale is fixed, the distance on the map is proportional to the actual distance.
7. If the number of A equals the number of B, the ratio of A to B is (): ().
8. Three piles of chess pieces, each with 50 pieces. There are as many sunspots in Bai Zi in the first pile as in the second pile, and half of the third pile is Bai Zi. This pile of chess pieces has () spots.
9. The front wheel width of the roller is 2m, and the diameter is1m.. The front wheel is rolled once, and the road pressing area is () m2.
10. The radius of the bottom of the cylinder is 2 decimeters and the height is 6 centimeters. The surface area of this cylinder is () square decimeter and the volume is () cubic decimeter.
1 1. The bottom area ratio of cylinder and cone is 2 1, and the volume ratio is 3.2. If the height of the cylinder is 3 cm, then the height of the cone is () cm.
12. The following is a statistical diagram of the operation of a train.
(1) The speed of this bullet train is100km per hour. The distance traveled by this bullet train is proportional to the time.
(2) At this speed, the distance from Guangzhou to Wuhan is about 1000 km, and it takes several hours to drive.
14. The scale of the map is, and rewriting this scale into a digital scale is ().
15. A conical measuring cup with a height of 24 cm is filled with water. If water is poured into a cylindrical measuring cup with the same bottom area, the water surface is () cm high.
16. Cubes, cylinders and cones have equal base areas and equal heights. If the volume of a cylinder is 1000 cubic centimeter, then the volume of a cone is about cubic centimeter; The side length of a cube is centimeters, and the bottom area of a cylinder is square centimeters.
17. There are 26 sets of chess and checkers in the school, just enough for students to carry out activities at the same time. Two people play chess and six people checkers. There are () pairs in chess and () pairs in checkers.
Second, choose the correct answer and score □ (16)
1. The small square enlarges a square with a side length of 3 cm according to the ratio of 2: 1. What is the enlarged area of this square?
6 cm □ 18 cm2 □ 36 cm2 □
2. The colored part in the picture on the right is represented by a fraction, and the correct one is ().
3. Cut a cylindrical piece of wood into a cone as big as possible. The cone weighs 8 kilograms, so the original piece of wood weighs ().
8 kg □ 24 kg □ 16 kg □
Lin Min is reading a story book. What is the relationship between the number of pages he has read and the number of pages he has not read?
In direct proportion □ in inverse proportion □ out of proportion □
5. In a square field with a side length of 10 meter, there are two paths, vertical and horizontal. As shown in the figure, the road width is 1m,
The rest of the land is planted with grass. How many square meters is the area of the grass planting part?
80 □ 8 1 □ 82 □
6. A miniature part, which is 4 mm long and 8 cm long on the drawing. The scale of this picture is ().
1︰20 □ 1︰2 □ 2︰ 1□ 20︰ 1 □
7. There are three numbers: A, B, C, B is a number and C is a number. The relationship between numbers a, b and c is ().
A > B > C□C > B > A□B > C > A□
8. The ratio of the circumference of the cone to the bottom of the cylinder is 1￠2, the height of the cone is six times that of the cylinder, and the volume of the cylinder is a cone ().
2 times □□□□□□□
Three, solve the equation (9 points)
︰ = ︰ +50% = 30 =
Four, solve practical problems (28 points)
1. A cement road has been repaired, and it is still 720 meters away from the finish line. How long is this cement road? (4 points)
2. Pave the same piece of land with square bricks. If you use a square brick with a side length of 0.3 meters, you need 720 pieces; If you use a square brick with a side length of 0.4 meters, how many pieces do you need? (4 points)
3. A cone-shaped sand pile with a bottom radius of 1m and a height of 7.5m How long, 5m long and 2cm thick can a road surface be paved with this sand pile? (4 points)
On the map with the scale of 1: 100000, the distance between the two places is12cm. What is the actual distance between the two places? (4 points)
5. Forty-six people in the class went boating and took 12 boat, including 5 people in the big boat and 3 people in the small boat. Q: How many big boats and small boats are there? (4 points)
There are 3000 chickens in the chicken farm, and the number of cocks is the number of hens. How many cocks are there? (4 points)
7. Cut a cylinder with a height of 1 m into many equal sectors at the bottom, and then assemble it into an approximate cuboid. It is known that the surface area of the assembled cuboid is 40 square decimeters higher than that of the original cylinder. What is the volume of the original cylinder? (4 points)
Beijing normal university printing plate sixth grade first volume mathematics examination questions two
I. Calculation (22 points)
1. Write the number directly. (10)
+ = 8? 3.9? 0. 125= - = ? 24=
14-7.4= 13? (2+7 13 ) = 0.375? = 5.6-3.27= 0.75? 15=
2. Solve the equation (12 points)
= 1.6:? = :
? - ? = : =? :0. 1
Two. Fill in the blanks (65438+ 0 points for each blank, ***20 points)
3. If it is stipulated that going east is positive, then walking 500m west is marked as (); +350m means ().
4. A map with 12cm representing the actual 30km, and the scale of this map is ().
5. Distribute 720 books to the sixth and fifth grades according to the ratio of 5: 4, and get () books in the fifth grade.
6. Expand the side of the cylinder to get a rectangle whose length is equivalent to the length of the cylinder ().
7. According to 4.5? 2=9? 1, write a ratio with the largest ratio: ().
8. in a? In B=C (neither is 0), when b is constant, A and C are proportional to (), and when c is constant, A and B are proportional to ().
9. In a proportional formula, the ratio of two ratios is, and the two internal terms of this ratio are two adjacent prime numbers within 10 respectively. This proportional formula is ().
10. 12, 15 and these four numbers make up a ratio of ().
1 1. Every time the height of a certain area increases 100m, the temperature drops by 0.6℃, and the temperatures measured by Xiaoming and Xiaohong at the foot of the mountain and the top of the mountain are 6℃ and? 1.2℃, the mountain is () meters high.
12. The lateral expansion of the cylinder is a square with a side length of 9.42dm, the diameter of the bottom surface of the cylinder is () dm, and the height of the cylinder is () dm.
13. The volume of the cylinder is 80m3, the bottom area is 16m2, and the height is () m. ..
14. Take a walk. It takes Party A 4 hours and Party B 3 hours. The walking speed ratio between Party A and Party B is ().
15. If the number of A is 20% less than the number of B, the ratio of A to B is (), and B is ()% more than A. ..
16. A cylinder with a bottom radius of 2dm, a height of 6dm, a surface area of () and a volume of ().
Third, the judge. (5 points)
17. Cubes, cubes and cones with equal base areas and heights must have equal volumes. ( )
18. When the former term of the ratio is fixed, the latter term of the ratio is inversely proportional to the ratio. ( )
19. The sum of the volumes of three cones is exactly equal to the volume of a cylinder. ( )
20. Enlarge a part to 5 times its original size and draw it on the drawing. The scale of this drawing is 1:5. ( )
2 1. Because 5 2, it is -5 -2. ( )
Fourth, choose. (10)
22. What's on some biscuit packages? Net content: 100? 3g？ , indicating that the quality of this bag of biscuits is ().
a . 97g b . 103g c . 97 ~ 103g
23. The radius and height of the bottom surface of a cylinder are expanded by three times, and its volume is expanded by a multiple of ().
A.6 B.9 C.27
24.Sum some, addend and another addend ().
A. directly proportional; Inverse ratio; be disproportionate
25. The scale is 1: 500000, which means that the distance of 1cm on the map is equivalent to the actual distance ().
A.50m B.50km C.5km
26. Cut a piece of wood into the largest cylinder, and the side length of this cube is equivalent to that of the cylinder ().
A. Bottom radius or height B. Height or bottom diameter C. Bottom circumference
Verb (abbreviation for verb) operation. (4+8= 12 points)
27. Enlarge the graph in the grid by 3: 1, and then reduce it by 1:2. What is the graph? Draw a picture.
28. The following is a simple schematic diagram of his neighborhood drawn by Kong Ming:
(1) The actual distance from Kongming's home to the school is 1.2km, which is 3cm on the map, so the scale of this sketch is ().
(2) The distance from Kongming's home to the fitness center on the map is 6cm, and the actual distance is () km.
(3) The cinema is 800 meters due north of Kongmingjia. Please draw it on the picture.
(4) Please ask a math question and answer it according to the picture above.
Sixth, application. (6 points for the last question, 5 points for the other party, ***3 1 point)
29. Xiaoxiao's father received a manuscript fee of 3,000 yuan, of which 800 yuan was tax-free, and the rest was subject to personal income tax at the rate of 20%. How much personal income tax should I pay for this manuscript?
30.20kg wheat grindable 17kg flour. According to this calculation, how many tons of wheat is needed to grind 5. 1t flour? (Solve in two ways)
3 1. The front wheel of the road roller is cylindrical, with a wheel width of 2.5m and a diameter of 1 .2m. When the road roller is working, the front wheel is rolled 20 times per minute, and the road surface area that has been pressed1hour is square meters.
32. If you use a square brick with a side length of 6dm, you need 80 pieces. If you use a square brick with a side length of 8dm, how many pieces do you need? (Use proportional solution)
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