Fill in the blanks
1, 24 plus 8, () is the divisor of (), and () is the multiple of ().
2. In 1, 2, 3, 9, 24, 4 1 and 5 1, the odd number is (), the even number is (), the composite number is (), () is odd but not prime, and () is even but not.
3. The minimum multiple of a number is 12, and this number has () divisors.
All divisors of 4.2 1 are (), and all prime factors of 2 1 are ().
5. The prime factor of a composite number is all prime numbers within 10, and this composite number is ().
6.A = 2× 2× 5, B = 2× 3× 3, the greatest common divisor of A and B is (), and the least common multiple is ().
7.a and B are prime numbers, their greatest common divisor is (), and their least common multiple is ().
Within 8 and 20, the number that is both even and prime is (), and the number that is odd but not prime is ().
9. The prime factor of the decomposition of 17 1 is ().
Second, the judgment (tick "√" for the right and "×" for the wrong)
1, any natural number has two divisors. ( )
2. There is no common divisor between two prime numbers. ( )
3. All prime numbers are odd numbers. ( )
4. Natural numbers are either odd or even. ( )
5. Because 2 1? = 3, so 2 1 is a multiple and 7 is a divisor. ( )
6. Prime numbers can be odd or even. ( )
7. Because 60 = 3? So 3, 4 and 5 are all prime factors of 60. ( )
8, 8 is divisible by 0.4. ( )
9. 18 is both a divisor of 18 and a multiple of 18. ( )
Two numbers with common divisor 1 are called prime numbers. ( )
1 1. Because the common divisor of 8 and 13 is only 1, 8 and 13 are both prime numbers. ( )
12, the common divisor of all even numbers is 2. ( )
Third, choose (put the serial number of the correct answer in brackets)
1, the following groups of numbers, the first number can be divisible by the second number is ().
(1)0.2 and 0.24 (2)35 and 5 (3)5 and 25
2, the following groups, a group that must not be a prime number is ()
(1) prime numbers and composite numbers (2) odd numbers and even numbers
(3) Prime Numbers and Prime Numbers (4) Even Numbers and Even Numbers
3. The prime factor of decomposing 2 10 is ()
( 1)2 10=2×7×3×5× 1
(2)2 10=2×5×2 1 (3)2 10=3×5×2×7
4, the sum of two odd numbers ()
(1) is odd (2) is even (3) may be odd or even.
5. If both A and B are natural numbers, and a÷b=4, then the greatest common divisor of A and B is ().
( 1)4 2 a 3 b
6. A composite number has at least () divisors.
( 1) 1 (2)2 (3)3
7 and 6 are () of 36 and 48.
(1) divisor (2) common divisor (3) greatest common divisor
8, there are four numbers, 4, 5, 7, 8, which can form () groups of prime numbers.
( 1)3 (2)4 (3)5
9. The side length of a square is odd, and the circumference of this square must be ().
(1) prime number (2) odd number (3) even number
10, the number divisible by 3 in the following numbers is ()
( 1)84 (2)8.4 (3)0.6
1 1, the smallest number divisible by 2, 3 and 5 at the same time is ().
( 1) 100 (2) 120 (3)300
12, 8 and 5 are ()
(1) prime number (2) prime number (3) prime factor
13, it is known that A can be divisible by 23, so A is ().
(1)46 (2)23 (3) 1 or 23
14. If a is used to represent natural numbers, then even numbers can be expressed as ().
( 1)a+2(2)2a(3)a- 1(4)2a- 1
15, the smallest number divisible by 9, 12 and 15 is ().
( 1)3 (2)90 (3) 180
Ability and quality improvement
1, the greatest common divisor of numbers A and B is 3, the least common multiple is 30, the known number A is 6, and the number B is ().
2. When a number is divisible by 6, 7 and 8, it is 1, and the minimum number is ().
There are five numbers: 9, 7, 2, 1 and 0. The smallest four digits that can be divisible by 2, 3 and 5 at the same time is ().
4. A bus * * * starts from a bus stop. 1 Road runs every 5 minutes, Road 2 runs every 10 minutes, and Road 3 runs every 12 minutes. After these three cars leave at the same time, how long does it take to leave at the same time?
Infiltration, expansion and innovation
Students from classes 1 and 5 1 go to physical education class, with three rows less 1 person, four rows more than three people, five rows less 1 person, and six rows more than five people. What is the minimum number of people in physical education class?
Xiaohong planted trees around the playground. At first, she planted a tree every 3 meters. After planting 9 trees, she found that there were not enough saplings, so she decided to replant and plant a tree every 4 meters instead. How many trees don't need to be pulled up when replanting at this time? Primary school mathematics graduation always reviews examination papers-four operations and elementary arithmetic
Basic knowledge of algebra
Fill in the blanks
Use letters to indicate the following quantities.
1. The library has X books and bought 240. There are () books in the library now.
2. Each book is RMB X, and Xiaoming bought 6 books, and the amount payable is RMB ().
The weight of apple is one kilogram, and the weight of pear is three times that of apple. Then, 3a stands for ().
4, A minus B, the difference is 8, A is A and B is ().
5. The circumference of a square with a side length of b cm is () cm and the area is () cm.
6. The train travels 78.5 kilometers per hour and () kilometers per hour.
7. Say the meaning of each formula.
(1) Students in Class One do a math problem A every day, denoted by 7a.
(2) Grade four students subscribe to China Youth Daily 120, which is x more than grade five, 120-x indicates. China Youth Daily costs one yuan each, 120a, (120-x) a) a.
(3) The side length of a square is one centimeter, denoted by 4a and denoted by a2.
(4) Teacher Zhang bought three volleyballs, each at X yuan, and paid the salesman 245 yuan, 245 -3x.
8、0.9∶0.6=9∶( )
9. If y=5x, then x and y are proportional to ().
10 1/2:3/4 The simplest integer ratio is ().
1 1, the number of A is five times that of B, and the ratio of A to B is ().
12, the ratio of a ratio is 3/4, its former term is 12, and its latter term is ().
13, if 7x=8y, then x∶y =()∴ ()
14 On the map with the scale of 1: 500000, the distance between Party A and Party B is 8 cm, and the actual distance between Party A and Party B is () km.
15 and 1/7: 0.04 The simplest integer ratio is ().
16, and the ratio of the radius of big circle to the radius of small circle is 3∶ 1, then the area of big circle is () times that of small circle.
Second, the judgment (tick "√" for the right and "×" for the wrong)
1 and 3+4x=23 are equations. ( )
2. Formulas containing unknowns are called equations. ( )
3、a2=2a .( )
4、c+c=2c .( )
5. What is the formula of 1 kg of tomato A? . ( )
6. The scale is certain, and the distance on the map is directly proportional to the actual distance. ( )
7.A is 5/7 of B, and the number A is directly proportional to the number B. ()
8. 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. ( )
9. If 4a=3b, then a: b = 3: 4. ( )
10, the circumference of a circle is fixed, and the diameter is inversely proportional to π. ( )
Third, multiple-choice questions (fill in the serial number of the correct answer in brackets)
1, in the following categories, () is an equation.
( 1)4x+5 (2)5？ = 15? 30+2x=80
2,4x+8 is misspelled as 4(x+8), and the result is better than the original ().
(1) greater than 4 (2) less than 4 (3) greater than 24 (4) less than 6.
3, x=25 is the solution of equation ().
( 1) 100- x=85
25+3x=90
4, 1.2 tons: 300 kilograms into the simplest integer ratio is ()
( 1) 1∶250 (2) 1200∶300
(3)4∶ 1 (4)4
5, put 5 grams of salt into 50 grams of water, the ratio of salt to water is ().
( 1) 1∶9 (2) 1∶8 (3) 1∶ 10
(4) 1∶ 1 1
6, the radius and area of the circle ().
(1) is directly proportional (2) is inversely proportional (3) is out of proportion.
7. On a map, the distance between A and B is 3cm, and the actual distance between A and B is 150km. The scale of this map is ()
( 1) 1∶50 (2) 1∶50000 (3) 1∶500000
8. On the map with the scale of 1: 100000, the distance between A and B is 3 cm. The actual distance between a and b is ().
(1) 300km (2) 30km (3) 3km (4) 0.3km.
Fourth, solve the proportion.
1、 1.25∶0.25=x∶ 1.6
2、3/4∶x=3∶ 12
5. List the equations and find their solutions.
1, 54 MINUS 4 times of a certain number equals 6, and find a certain number.
2. The sum of 3/5 plus 16 of a number is 28. Find this number.
Six, answer the application questions
1. The ratio of male to female teachers in an experimental primary school is 2: 5. There are 35 female teachers and how many male teachers are there?
2. Prepare a pesticide, in which the ratio of medicine to water is 1: 150.
① How many kilograms of medicine and water does it take to prepare 755 kilograms of this pesticide?
(2) There are 3 kilograms of medicine. How many kilograms can this pesticide be matched?
(3) If there is 525 kilograms of water, how many kilograms of medicine should be put in the preparation of this pesticide?
3. There are 150 books in kindergartens in Le Tong, 40% of which are allocated to large classes, and the rest are allocated to small classes and middle classes according to the ratio of 4: 5. How many books are there in the small class and the middle class?
4. Two workshops 150 people. If 50 people are transferred from the first workshop, the number of people in the first workshop is 2/3 of that in the second workshop. How many people are there in workshop 2?
Ability and quality improvement
1, the price of a set of desks and chairs is 105 yuan, of which the price of chairs is 5/7 of that of desks. What's the price of this chair? (Answer with different knowledge)
2. Maple Leaf Garment Factory received the task of producing a batch of shirts, and produced 600 pieces in the first five days, completing 40% of the task. According to this calculation, how many days will it take to complete this task? (Answer with different knowledge)
An airplane can use fuel for 6 hours. When the plane flies with the wind, the speed can reach 1500 km/h, and when it flies back against the wind, the speed can reach 1200 km/h. How many kilometers can this plane fly at most?
Infiltration, expansion and innovation
1. The school bought 8 soccer balls and 60 skipping ropes, which cost 274.2 yuan. The price of each football is more than the price of 32 skipping ropes. How much is each football, 0.7 yuan?
In the 2.60m race, when A crosses the finish line, it is ahead of B10m and C 20 meters. If B and C continue to rush to the finish line at the original speed, how many meters will B lead C when reaching the finish line?
There's another set
application problem
1, simple application problem, compound application problem
1. Which of the following formulas is correct? Please tick the formula.
(1) A highway maintenance team needs to build a road with a length of 2 100 meters. In the first five days, an average of 240 meters was repaired every day, and the remaining tasks were completed in three days. How many meters will be repaired on average every day?
①2 100-240×5÷3 ②(2400-240)÷3 ③(2 100-240×5)÷3
(2) A bookbinding team has to bind 2640 books, and 240 books have been bound in 3 hours. According to this calculation, how many hours will the remaining books be bound?
①(2640-240)÷240 ②2640÷(240÷3) ③(2640-240)÷(240÷3)
(3) A tractor team plowed 6.8 hectares of cotton fields for 4 days. According to this calculation, how many days will it take to plow 13.6 hectares of cotton field?
① 13.6÷(6.8÷4) ② 13.6÷(6.8÷4)+4
③( 13.6+6.8)÷(6.8÷4)
(4) A road construction team laid a section of railway, originally planned to lay 3.2km every day, which was completed in 15 days. In fact, 0.8 kilometers more than originally planned is paved every day. How many days has this railway been paved?
①3.2× 15÷0.8 ②3.2× 15÷(3.2-0.8) ③3.2× 15÷(3.2+0.8)
(5) A chemical plant uses 14 tons of raw materials every day after adopting new technology. In this way, the raw materials used for 7 days can now be used for 10 days. How many tons of raw materials does this factory save now than before?
① 14×7÷ 10- 14 ② 14× 10÷7- 14
③ 14- 14× 10÷7 ④ 14- 14×7÷ 10
2. Answer the following application questions.
(1) Changsheng Farm wants to harvest wheat 16.4 hectares, which has been harvested for 3 days, with a daily output of 1.8 hectares. If you harvest 2.2 hectares a day from the fourth day, how many days will it take to harvest the remaining wheat?
(2) The 120 tons of coal shipped from the canteen has been burned for 40 days, burning 1.2 tons every day, and the remaining 30 days will be burned out. How many tons are burned on average every day?
(3) A class has 150 science and technology books, and 50 story books are twice as few as science and technology books. How many story books are there?
(4) Five crushers can crush 37.5 tons of feed in 3 hours. According to this calculation, how many tons of feed can 12 identical pulverizers crush per hour?
(5) Bus A and Bus B start from two cities 600 kilometers apart. Car A travels 65 kilometers per hour, and car B travels 55 kilometers per hour. A few hours after departure, two cars met.
(6) Two warships A and B set out from two ports respectively. Ship A travels 42 kilometers per hour and ship B travels 38 kilometers per hour. The second ship leaves at 1 hour, and the first ship leaves. Four hours later, the two ships met. How many kilometers are the two ports apart?
(7) Zhang Mingjia used to use 28 tons of water every month. With the water-saving faucet, the water used in one year can now be used for two more months. How many tons of water are used every month now?
(8) There is a barrel of oil, 2/5 of which has been used, and there is 48kg left in the barrel. How much does this barrel of oil weigh?
(9) A garden factory planted 4,500 trees last year, and plans to plant 20% more trees this year than last year. How many trees do you plan to plant this year?
Ability and quality improvement
1. The cargo ship Yellow River sailed 85 kilometers from Port A to Port B, which is just 5/7 of the waterway between Port A and Port B. How far is this cargo ship from Port B?
2. The paving team paved a road, 2.5 kilometers per day, and completed 5/8 of the total length in 7 days. How many kilometers is this road?
Infiltration, expansion and innovation
1 and grade 5 participated in the math competition, and girls 12, equivalent to 2/3 of the number of boys. As a result, the number of winners accounted for 70% of the participants. How many winners are there?
Aunt Li wants to buy two bags of rice (35.4 yuan each),1meat from 4.8 yuan, vegetables from 6.7 yuan and1fish from 2.8 yuan. Aunt Li brought 100. Is that enough?
Appreciation of intelligent interesting problems
Xiaohong and Xiao Qiang set out from home at the same time and walked in the opposite direction. Xiaohong walks 52 meters per minute and Xiao Qiang walks 70 meters per minute. They meet on the way. If Xiaohong leaves four minutes early and the speed remains the same, and Xiao Qiang walks 90 meters every minute, then the two will still meet at point A. How many meters away is Xiaohong from Xiao Qiang's home?
2. Solve application problems with equations and use proportional knowledge.
1, find the equal relationship between the following quantities.
(1) There are seven more boys than girls in one class.
(2) The number of basketball is four times that of football.
(3) Pear trees 15 are three times more than apple trees.
(4) It costs more to buy three pens than five ballpoint pens 1.5 yuan.
(5) Two iron wires with the same length, one in a square and the other in a circle.
2, column equation to solve the following application problems.
The price of radio this year is 25% lower than last year. This year, the price of each radio is 36 yuan. How much did it cost last year?
(2) Distance between the two places 120km. Two people, A and B, start from two places by bike at the same time. A car runs every hour 14km. Four hours later, I met car B. What is the speed of car B?
(3) There are 800 exhibits in the school painting and calligraphy exhibition. Among them, the ratio of art exhibits to calligraphy exhibits is 5: 3. How many pieces are there in each of the two exhibits?
(4) The actual distance between A and B is 120km. What is the distance between the two cities on the map with the scale of 1: 4000000?
(5) On the map of China with the scale of 1: 4000000, the distance from Beijing to Shaoshan is 35cm. What is the actual distance from Beijing to Shaoshan?
(6) A loom can weave 24 meters in 4 hours. According to this calculation, how many hours does it take to weave 54 meters? (Use proportional solution)
(7) Wang Gang walks 60 meters from home to school. He can walk to school 15 minutes. If you walk 75 meters per minute, how many minutes can you walk to school? (Use proportional solution)
(8) There are two barrels of oil, and the weight of barrel A is 1.2 times that of barrel B. If 5 kg of oil is poured into barrel B, the two barrels of oil are equally heavy. How many kilograms are there in two barrels of oil?
Ability and quality improvement
1. The road repair was originally planned 15 days. In fact, 300 meters are built every day. The result was completed three days in advance. How many meters was originally planned to be built every day?
2. A car has 102 liters of oil in its fuel tank, and it consumes 8 liters of oil when running 56 kilometers. According to this calculation, how many kilometers can the remaining oil travel?
Someone walked 22.4 kilometers in 4 hours. At this rate, if you walk for another three hours, how many kilometers can a * * * walk? (Use proportional solution)
4. There are 150 books in kindergartens in Le Tong, 40% of which are allocated to large classes, and the rest are allocated to small classes and middle classes according to the ratio of 4: 5. How many books are there in the small class and the middle class?
6. The price of a set of desks and chairs is 105 yuan, of which the price of chairs is 5/7 of that of desks. What's the price of this chair? (Answer with different knowledge)
7. Maple Leaf Garment Factory received the task of producing a batch of shirts, and produced 600 pieces in the first five days, completing 40% of the task. According to this calculation, how many days will it take to complete this task? (Answer with different knowledge)
Infiltration, expansion and innovation
1. In a workshop, the original zinc and copper were * * * 84kg. Now, if zinc and copper are to be cast into an alloy according to the ratio of 1∶2, it is necessary to add 12kg of copper. How many kilograms of copper?
2. For a cuboid model, the sum of all sides is 72 decimeters, and the ratio of length to width to height is 4∶3∶2. What is the volume of this cuboid model?
Appreciation of intelligent interesting problems
Xiaoming read a book and read part of it in the morning. At this time, the ratio of read pages to unread pages is 1: 9. Read six more pages in the afternoon than in the morning. At this point, the ratio of read pages to unread pages becomes 1: 3. How many pages are there in this book?