The sixth grade mathematics comprehensive training questions 1 1. Fill in the blanks.
1, if an increase of 3m is+3m, then-5m means (a decrease of 5m) and 0m means (neither an increase nor a decrease).
2. The flour yield of wheat is 85%, 3,000 kilograms of wheat can be ground into flour (2,550 kilograms), and 4,000 kilograms of wheat is needed to grind 3,400 kilograms of flour.
3. In proportion, (the product of two external terms) is equal to (the product of two internal terms), which is called (the basic property of proportion).
4. Use the numbers 5, 12, 4, 15 to form a proportion. (its1:5: 4 =15:12).
5. If 5a=3b, then a: b = (3: 5).
6. On the map with the scale of 1:4000000, the distance between the two places is 6 cm, and the actual distance is (240000) meters.
7. The school playground is180m long and 95m wide. It shall be drawn on the floor plan with the scale of 1: 1000, length (18) cm and width (9.5) cm.
8. The distance from A to B is 160km, and (0.4) cm should be drawn on the map of 1:40000000.
9. The radius of the cylinder bottom is 5 meters, the volume is 157 cubic meters, and the height is (2) meters.
40% of 10. 15 tons is (6 tons), and 15 tons is 50% more than 10 tons.
1 1. In a proportion, two internal terms are reciprocal, one external term is 4, and the other external term is (0.25 or 1/4).
12. The circumference of the cylinder bottom is 3 1.4 decimeter, and the height is 10 decimeter. Its lateral area is (3 14 square decimeter), its surface area is (47 1 square decimeter), and its volume is (785 cubic decimeter), which is equal to its bottom.
13. It is known that the relationship between a, b and c is a? B = C. If A is certain, then B and C are in (inverse) proportion; if C is certain, A and B are in (positive) proportion.
14, a kind of brine, is made by mixing salt and water at the ratio of 1: 100. Now, to prepare 8080 grams of this brine, 0.08 kilograms of salt is needed.
15, the two external terms of a proportion are 5 and 6 respectively, and their ratio is 3, that is, (5: 5/3 = 18: 6).
The statistical chart of 16 (dotted line) can not only show the quantity, but also clearly show the change of the quantity.
17 The iron wire with a certain length is divided into several sections on average, and the length of each section is inversely proportional to the number of sections.
Second, choose.
1, the side length and circumference of a square (1).
① Direct ratio ② Inverse ratio ③ Out of proportion.
2. The distance on the drawing is 2.4 cm, and the actual distance is1.2mm; The scale of this painting (2).
① 1:20 ②20: 1 ③20
3. Fixed unit price, total price and quantity (2)
① Direct ratio ② Inverse ratio ③ Out of proportion.
4. Known 0.4? 3.75=3? 0.5, which of the following proportional expressions cannot be established? (2)
a、0.4:3=0.5:3.75 B、3.75:0.5=0.4:3
c、3.75:3=0.5:0.4 D、0.5:0.4=3.75:3
5. Put 1g salt into 10g water, and the ratio of salt to brine is (2).
① 100: 10 1 ② 1: 10 1 ③ 1:99 ④ 1: 100
6. In proportion, the product of two external terms is certain, and the two internal terms become (2).
① Positive proportion ② Inverse proportion ③ Out of proportion ④ It is impossible to judge.
7. Xiao Wang's height and weight become (3).
① Positive proportion ② Inverse proportion ③ Out of proportion ④ It is impossible to judge.
8. The radius of small circle is 2 cm, the radius of large circle is 3 cm, and the ratio of small circle area to large circle area is (3).
①2:3 ②3:2 ③4:9 ④9:4
9. For a project, the ratio of completed projects to this project is 3:5, leaving (2) of this project.
①60% ②40% ③20% ④ 166.6%
10, a cylinder, if the height remains the same, the bottom area will be tripled and its volume will be enlarged (1).
3 times, 26 times, 39 times, 427 times.
Third, the judge.
1. The total amount of money subscribed to the Primary School Learning Newspaper is directly proportional to the number of copies subscribed. (right)
2. Legends should be used to make composite bar charts. (right)
There are 55 students in the class, the ratio of male to female is 5:6, so there are 30 boys in this class. (wrong).
4. The lateral area of two cylinders is equal, and their bottom perimeters are equal. (error)
5. In the proportion, the product of two external terms is 10, one internal term is 5, and the other internal term is also 5. (error)
6. The circumference of a circle must be in direct proportion to its diameter. (right)
7. The circumference of a circle is proportional to its diameter. (error)
Fourth, calculation.
1.
0.3? 1.5=0.45 6.8? 17= 0.4 42? 60%= 70
38 +0.625=38.625 36? 0.6=60 7-0.35=6.65
1-25% = 0.75 12? 7= 12/7
2. Solution ratio.
( 1)、0.8:0.3=? :0.6(2)、40:? =2.5: 15
X= 1.6 X=240
(3)、5: 16=20:?
x=64
Verb (abbreviation of verb) formula calculation
1. The two internal terms are 2026 and 49 respectively, and the two external terms are x and 10 13 respectively.
Solution: x: 2026 = 49: 10 13.
X=98
2. Divide a number by 148 to get 37. What is 30% of this figure?
148? 37? Thirty percent
=4? 0.3
= 1.2
Six, application questions
1. A canal is 2 kilometers long. How many centimeters should I draw on the map with the scale of 1: 30000?
2 km = 200,000 cm
200000? 30000=20/3 (cm) or 6 2/3.
The sixth grade mathematics comprehensive training problem 2 1. Fill in the blanks for each question 1 point.
1, 4 12 tons = () tons () kilograms for 80 minutes = () hours.
2、()∶()=40()=80%=()? 40
3, () tons is 60 tons 13, and 40 meters is ()% of more than 30 meters.
4. There are 46 people in Class 5 (1) today, and 3 people are on leave due to illness. The attendance rate of students in Class Five (1) today is ().
The ratio of 5.0.8: 0.6 is (), and the simplest integer ratio is ().
6. The number of students in a class is between 50 and 60, and the ratio of male to female is 4: 5. There are boys () and girls () in this class
7. From City A to City B, it takes 7 hours by truck and 8 hours by bus. The simplest ratio between the speed of the truck and the speed of the bus is ().
8. Master Wang earns 3000 yuan a month. According to the new national tax law, the portion exceeding 1600 yuan is subject to 5% personal income tax. Master Wang's actual monthly salary is () yuan.
9. Xiaohong 15 hour driving 38 kilometers. She drives () kilometers per hour, and it takes () hours to drive 2 kilometers.
10. Make a circle with a rope 25. 12 meters long. The diameter of this circle is () and the area is ().
1 1. On a rectangular iron plate with a length of 12 decimeter and a width of 6 decimeters, at most () circular iron plates with a diameter of 2 decimeters can be intercepted.
12. Please fill in the appropriate graphic names circle, (), () and rectangle in the brackets according to the order of the number of graphic symmetry axes.
Second, judge 5 points
1, one eighth of 9 meters is as long as one ninth of 8 meters. ()
2. The areas of two circles with equal perimeters must also be equal. ? ()
3. 1 100 and 1% are both fractions with denominator of 100, and their meanings are exactly the same. ()
4.8 kg of salt is dissolved in 100 kg of water, and the salt content of brine is 8%. ? ()
5. The previous item of the ratio increased by 10%. To keep the proportion unchanged, the latter term should be multiplied by 1. 1. ? ()
Third, choose 5 points.
1, if b is a non-zero natural number, the largest calculation result in the following formula is ().
A.b？ 58B.b？ 58C.b？ 32D.32？ b
2. A bamboo pole is cut into two sections, the first section is 37m long, and the second section accounts for 37% of the total length.
A. the first paragraph is B. the second paragraph is C. the same length is D. it cannot be determined.
3. The forest farm planted 20,000 saplings last year and randomly selected 2,000 saplings at the end of the year, with a mortality rate of 2%. You predict that the survival rate of these saplings planted in the forest farm is (). A.20%B.80%C.2%D.98%
4, a farm, raising 1800 ducks, raising 35 more chickens than ducks, how many more chickens than ducks? The correct formula is ()
A. 18000？ 35B. 1800+ 18000？ 35C. 1800- 18000？ 35D. 1800？ 35
5. To cut a circular paper with an area of 28.26 square centimeters, at least one paper with an area of () square centimeters (? Take 3. 14).
A.28.26B. 18C.36D.28
Four, the calculation problem (***35 points)
1, the number is written directly.
67? 2=35? 25=3-37=2+2%= 16-56? 15=
78? 7 10=6? 23=43? 75%=78? 5? 87= 12? 88+88? 12=
2. Solve the equation
X+27X= 1 14X？ 18= 18? 2340%X+ 14=7 12
3. How to calculate the following questions as simply as possible?
72? 58+32? 85 1-58? 2528+3 10(23-4 15? 56)? 202 145? [(35- 12)? 2]
4, column comprehensive formula or equation calculation
1, 20% of a number is 150, what is 35 of this number? 2. 58 of a number is smaller than 6 of 40. What's this number?
Verb (abbreviation for verb) picture
Draw the following points in the picture on the right and connect them in turn:
A(2，0)、B(4， 1)、C( 1，5)、D(4，6)、E(5，4)。
VI. Application Problems (***3 1 min)
1, column calculation (8 points):
Wangzhuang Coal Mine produced 2.8 million tons of coal last year, an increase of 280,000 tons this year. What percentage has the output increased?
(2) The original story book of 70 yuan is now sold at 10% off the original price. What's the current price?
③ Repairing a batch of books, 80 books have been repaired, accounting for 25% of the unrecovered books. How many books are there in this batch?
(4) Xiaohua's father deposited 6000 yuan in the bank for two years at an annual interest rate of 3.70%. How much interest can he actually get when it expires? (Free of interest tax)
2. Answer the following questions completely (***23 points, including 3 points for the fifth question and 4 points for each other question):
1, Hong Guang Soap Factory 10 10 has produced 75,000 boxes of soap in October, and 25 boxes have not yet been produced. How many boxes of soap are planned to be produced in June+10, 5438?
2. The road team plans to build a road with a length of 1500m. 25% of the total length is repaired in the first week, and 13 of the total length is repaired in the second week. How many meters is the first week less than the second week?
3. It is known that the side length of a cuboid is 84cm and the ratio of length to width to height is 3: 2: 1. What is the volume of this cuboid?
The sixth grade mathematics comprehensive training problem 3 1. Fill in the blanks. (22 points)
The length of a number is 5 in hundreds of millions, 5 in tens of thousands, 5 in the highest place, and all other numbers are 0. This number is written as (), and the mantissa after omitting tens of thousands is ().
2, 2 hours 15 minutes = () 4.2 tons = () kg.
3. The number of basketball is 125% of that of football, and basketball is ()% more than football.
4、6? 15=()45 =( )% =24? () = _ _ _ _ _ _ (fill in decimal places).
5. The volume of the cone is 76 cubic centimeters, and the bottom area is 19 square centimeters. The height of this cone is () cm.
6. Turn 2 18: 1 23 into the simplest integer. The ratio is () and the ratio is ().
7. In a right triangle, the ratio of two acute angles is 3: 2, which are () degrees and () degrees respectively.
8. Four numbers can be selected from the factor of 12 to form a ratio. Please write two different proportions: ().
9. The ratio of Party A to Party B is 5: 4, with Party A having ()% more people than Party B and Party B having ()% less people than Party A. ..
10, which is three times more than a, is calculated as () by a formula containing letters. When a=2.4, the value of this formula is ().
1 1, throw 100 coins face up, 48 times, then the possibility of throwing 10 1 coins face up is ().
12. Cut a 2-meter-long straight cylindrical wood horizontally by 2 decimeters. Compared with the original, the surface area of the remaining cylindrical wood is reduced by 12.56 square decimeter. The original cylindrical wood had a bottom area of () square decimeter and a volume of () cubic decimeter.
Second, the judgment (7 points)
1, the radius of the cone bottom is expanded by 3 times, the height is unchanged, and the volume is also expanded by 3 times.
2. In proportion, if the product of two internal terms is 1, then the two numbers that make up the out-of-proportion terms must be reciprocal. ( )
3. There are 10 cards with the number 1 10 written on them. Pick any one, and the probability of encountering an even number is 1/5. ( )
4. If 4a=3b, then a: b = 4: 3. ( )
5. It took Party A 10 minutes and Party B 12 minutes to walk from school to the cinema. The simplest integer ratio of the distance traveled by A and B per minute is 5: 6. ( )
6. Two adjacent nonzero natural numbers must be prime numbers. ( )
7. Of the 90 parts produced, 10 is rejected, and the qualified rate is 90%. ( )
Third, choose. (7 points)
1, 47 girls in a class equals 23 boys, so the number of boys () the number of girls.
A. less than B. greater than C. equal to
2. The price of a product before the price reduction was 150 yuan, and the price after the price reduction was 120 yuan, which decreased by ().
A.20% B. 25% C. 80% D. 75% ]
3, the following three sentences, the correct is ()
A. If a commodity is sold at a 20% discount, it will only make a profit of 20% without discount.
The largest angle in a triangle is not less than 60 degrees.
C. Fractions whose denominators are divisible by 2 and 5 must be reduced to finite decimals.
Two 2-meter-long iron wires, the first cut off its 34 meters, and the second cut off its 34 meters. The rest ().
A, the length is equal to b, the first length is c, and the second length is C.
5. Use three equal-length ropes to form a rectangle, a square and a circle respectively, and the largest area is ().
A, rectangle b, square c, circle
6, in the following items, the two quantities are inversely proportional to ().
A, the perimeter and side length of a square b, a certain distance, time and speed.
C, 4x=5y D, radius and area of a circle.
7. On the map with the scale of 1: 2000000, the distance from city A to city B is 2 cm, and the actual distance from city A to city B is ().
A.0.4 km B. 4 km C. 40 km D. 400 km
Four, calculation (26 points)
1, write directly. (8 points)
199+49= 10-0.0 1= 5+ 1.4+ 1.6= 2.5? 40=
23 ? 9 10 = 24? 67 = 14 + 13 = 13 ? 2? 13 =
2. Calculation of parting (12)
84 1-3248? 16 17.68? 5.2+3.7? 1.5
38 ? [( 12 ? 13 )? 23 ] 5 1 1 ? 79 +79 ? 6 1 1
3, column calculation (6 points)
What is the quotient of the product of (1)0.6 and 2.25 minus the difference between 3.2 and l.85?
(2) 34 of a number is 1.5 which is more than 25% of 30, so find this number.
Verb (abbreviation of verb) completes the following questions as required. (8 points)
Operate as required and fill in the blanks. (Each square is a small square with a side length of 1 cm)
The area of (1) trapezoid is () square centimeters.
(2) Draw a parallelogram with the same area as the trapezoid.
(3) Draw an enlarged diagram of parallelogram according to the ratio of 2: 1.
(4) The ratio of the enlarged area to the original area is ()
Six, solve the problem (30 points)
1, the distance between a and b is 360 kilometers. A car drove 49 miles from A to B.. How many kilometers is it from a at this time?
2. On March 1 day, 2008, my uncle deposited 2000 yuan in the bank, with a fixed term of three years and an annual interest rate of 5.22%. When due, I should pay 5% interest income tax. How much can uncle get back when withdrawing money?
3. The master and the apprentice processed 80 parts, and the number of parts processed by the apprentice was 35 of that of the master. How many parts do master and apprentice process respectively?
The taper tools used by builders are made of steel. Its bottom circumference is 12.56 cm and its height is 6 cm. If steel weighs 7.8 grams per cubic centimeter, how many kilograms does this tool weigh?
5. Repairing a road will be completed in 0/2 days for Team A and 0/5 days for Team B.. How many days does it take for two teams to repair together?