50 math questions with answers for the first grade of junior high school

1. Fill-in-the-blank questions (each question is 3 points, ***24 points)

1. (-1) 2002-(-1) 2003=_______________.

Answer: 2

2. It is known that a certain number is larger than it. If a certain number is x, then the equation can be written_______________.

Answer: x= x

3. As shown in Figure 1, points A, B, C, and D are on the straight line l. Then BC=_________-CD, AB ________ CD=AD; if AB=BC=CD, then AB= ________BD.

Figure 1

Answer: BD, BC,

4. If ∠α=41°32′, then its supplementary angle is____________ , its supplementary angle is __________.

Answer: 48°28′, 138°28′

5. As shown in Figure 2, find the following angles: ∠1=___________, ∠2=___________, ∠3=___________.

Figure 2

Answer: 62.5°, 25°, 130°

6. Two straight lines intersect, There are _____________ intersection points; when three straight lines intersect two by two, there are at most _____________ intersection points and at least _____________ intersection points.

Answer: And there are only one, three, and one

7.38°12′=_____________°, 67.5°=__________°___________′.

Answer: 38.2, 67, 30

8. If x2-3x=1 is about x For a linear equation of one variable, a=_______________.

Answer:

2. Multiple choice questions: (3 points for each question, ***24 points)

9. Among the following statements, the correct one is

A. |a| is not a negative number B. -a is a negative number

C. - (-a) must be a positive number D. is not an integer

Answer: A.

10. There are any three points on the plane. Draw a straight line through two of them. ***You can draw

A. A straight line B. Two straight lines C. Three straight lines D. One or three straight lines

Answer: D.

11. Among the following drawing statements, the correct one is

A .Draw ray OP=3 cm B. Connect two points A and B

C. Draw the midpoint of two points A and B D. Draw the distance between two points A and B

Answer: B.

12. Among the following figures that can be folded into a cube, there are

Figure 3

A.1 B.2 C. 3 D. 4

Answer: D.

13. The following figure is obtained by rotating the left figure around the straight line l.

4

Answer: D.

14. Figure 5 is a statistical chart of crops in a village, in which the proportion of rice is

Figure 5

A.40 B.72 C.48 D.52

Answer: C.

15. Which of the following statements is correct

①All All right angles are equal ② All supplementary angles are equal ③ The supplementary angles of equal angles are equal ④ Congruent angles are right angles. The correct ones are

A.①② B.①③ C.②③ D.③④

p>

Answer: B.

16. If |x- | (2y 1)2=0, then the value of x2 y2 is

A. B.

C.- D.-

Answer: B.

3. Answer the following questions

17. Calculation questions

(Each question is worth 3 points, ***12 points)

(1)(-)×(-1)÷(-1) (2)32÷(-2)3(-2) 3×(-)-22

(3)(-)÷(-)2÷(-6)2-(-)2

(4)1 ×〔3 ×(-)2-1]- [(-2)2-(4.5)÷3]

Answer: (1)-1 (2)-2 (3)- (4)-

18. Solving equations: (5 points for each question, ***10 points)

(1) [(x-)-8]= x 1

(2) - - =0

Answer: (1) x=- (2) x=-

19. (6 points) As shown in Figure 6, the AOB is known is a straight line, OC bisects ∠AOD, ∠BOD=50°, find the degree of ∠AOC.

Figure 6

Answer: 65°

20. ( 6 points) Three times the supplementary angle of an angle is 18° greater than the supplementary angle of the angle. Find the measure of the angle.

Answer: 36°

21. (6 points ) Make appropriate statistical charts to represent the data in the following table:

my country’s previous censuses after 1949

Year 1953 1964 1982 1990 2000

Population (100 million) 5.94 6.95 10.08 11.34 12.95

Answer: A bar chart can be made (omitted).

22. (12 points) A passenger train is 200 m long and a freight train is 280 m long. They are traveling in opposite directions on parallel tracks. It takes 18 s from the time the two cars meet at the front to the time the two cars separate at the rear. It is known that the speed ratio of the passenger car and the truck is 5:3. How many meters per second do the two cars travel?

Solution: Suppose the speed of the passenger car is 5x, then the speed of the truck is 3x. According to the meaning of the question, we get

18 (5x 3x) = 200 280.

The solution is x=, That is, the speed of the passenger car is m/s. The speed of the truck is 10 m/s.

Reference: /question/42971029.html?si=9

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[Master's student]

54980516 [Master's student] 2009-1-12 09:35:04 PM 222.64.119.* Report

Can I bring the answer? Final test paper for the first semester of seventh grade

(Time: 100 minutes, full score: 100 points)

1. Fill-in-the-blank questions (3 points for each question, ***24 points)

1. (-1) 2002 - (-1) 2003 =_______________.

Answer: 2

2. It is known that a certain number is greater than it, If a certain number is Above. Then BC=________-CD, AB ________ CD=AD; if AB=BC=CD, then AB=________BD.

Figure 1

Answer: BD, BC,

4. If ∠α=41°32′, then its supplementary angle is ____________, and its supplementary angle is __________.

Answer: 48°28′, 138° 28′

5. As shown in Figure 2, find the following angles: ∠1=___________, ∠2=___________, ∠3=___________.

Figure 2

Answer: 62.5°, 25°, 130°

6. When two straight lines intersect, there are _____________ intersections

points; when three straight lines intersect two by two, there are at most _____________ intersection points and at least _____________ intersection points.

Answer: And there are only one, three, and one

7.38°12′ =___________°, 67.5°=__________°___________′.

Answer: 38.2, 67, 30

8. If x2-3x=1 is a linear equation of one variable with respect to x, then a=_______________.

Answer:

2. Multiple choice questions: (3 points for each question, ***24 points)

9. Among the following statements , the correct one is

A.｜a｜is not a negative number B.-a is a negative number

C.-(-a) must be a positive number D. is not an integer

Answer: A.

10. There are any three points on the plane. Draw a straight line through two of the points. ***You can draw

A. One straight line B. Two straight lines C .Three straight lines D. One or three straight lines

Answer: D.

11. Among the following drawing statements, the correct one is

A. Drawing rays OP= 3 cm B. Connect two points A and B

C. Draw the midpoint of two points A and B D. Draw the distance between two points A and B

Answer: B .

12. Among the following figures that can be folded into cubes:

Figure 3

A.1 B.2 C.3 D.4

Answer: D.

13. The following figure is obtained by rotating the left figure around the straight line l.

Figure 4

Answer: D.

14. Figure 5 is a statistical chart of crops in a village, in which the proportion of rice is

Figure 5

A. 40 B.72 C.48 D.52

Answer: C.

15. Which of the following statements is correct

①All right angles are equal② All supplementary angles are equal ③ The supplementary angles of equal angles are equal ④ Congruent angles are right angles. The correct one is

A.①② B.①③ C.②③ D.③④

Answer: B.

16. If |x- | (2y 1)2=0, then the value of x2 y2 is

A. B.

C.- D. -

Answer: B.

3. Answer the following questions

17. Calculation questions (each question is 3 points, ***12 points )

(1)(-)×(-1)÷(-1) (2)32÷(-2)3 (-2)3×(-)-22

(3)(-)÷(-)2÷(-6)2-(-)2

(4)1×〔3×(-)2-1〕-〔(- 2) 2-(4.5)÷3〕

Answer: (1)-1 (2)-2 (3)- (4)-

18. Solve the equation: ( Each question is worth 5 points, ***10 points)

(1) [(x-)-8]= x 1

(2) - - =0

Answer: (1) x=- (2) x=-

19. (6 points) As shown in Figure 6, it is known that AOB is a straight line, OC bisects ∠AOD, ∠BOD=50 °, find the degree of ∠AOC.

Figure 6

Answer: 65°

20. (6 points) 3 times the ratio of the supplementary angle of an angle The supplementary angle of this angle is 18° greater. Find the measure of this angle.

Answer: 36°

21. (6 points) Make an appropriate statistical chart to represent the data in the following table:

my country’s previous censuses after 1949

Year 1953 1964 1982 1990 20

00

Population (100 million) 5.94 6.95 10.08 11.34 12.95

Answer: A bar graph can be made (omitted).

22. (12 points) One column A passenger car is 200 m long, and a freight train is 280 m long. They are running in opposite directions on parallel tracks. It takes 18 seconds from the time when the fronts of the two cars meet to when the two rear cars separate. It is known that the speed ratio of the passenger car to the freight car is 5:3. Question: How many meters do each travel per second?

Solution: Assume the speed of the passenger car is 5x, then the speed of the truck is 3x. According to the meaning of the question, we get

18 (5x 3x) = 200 280.

The solution is x= , that is, the speed of the passenger car is m/s. The speed of the truck is 10 m/s.

Reference: /question/42971029.html?si=9

]Seventh grade final mathematics review questions

(Full score is 100 points, 90 minutes to complete the paper)

1. Multiple choice questions: (Each question is 3 points, ***24 points)

1. In , , - , , 3.14, 2 , - , 0, , 1.262662666..., the number of irrational numbers is ( )

A .3 B. 4 C. 5 D. 6

2. If alt; 0, in the plane rectangular coordinate system, translate the point (a, -3) to the left and upward respectively. 4 units, the position of the corresponding point that can be obtained is ( )

A. The first quadrant B. The second quadrant C. The third quadrant D. The fourth quadrant

3. There are 4 wooden bars, the lengths of which are 4cm, 7cm, 9cm and 11cm respectively. Choose three of them to form a triangle. The selection method is ( )

A. 1 type B. 2 types C. 3 types D. 4 types

4. The solution of the linear inequality group is ( )

A. xgt; -3 B.xlt; 2 C.2lt; xlt; 3 D. -3lt; xlt; 2

5. Among the following propositions, the number of correct propositions is ( )

①. In the same plane, two line segments that do not intersect are called parallel lines ②. Two straight lines that do not intersect are called parallel lines

③. Through a point, there is and is only one straight line that is parallel to the known straight line ④. Two straight lines perpendicular to the same straight line are parallel

A.0; B.1 C.2 D.3

6. If each interior angle of a polygon are equal to 144?, then the sum of its interior angles is ( )

A. 1260? B. 1440? C. 1620? D. 1800?

7. A car is driving on a straight road. After turning twice, it is still moving parallel to the original direction

. Then the angle of the two turns is ( )

A. The first turn to the right is 60 degrees, the second turn to the left is 120 degrees;

B. The first turn to the left is 120 degrees, the second turn to the right is 120 degrees;

C. Turn right for 60 degrees for the first time and 60 degrees for the second time;

D. The first turn to the left is 60?, and the second turn to the left is 120?.

8. As shown in Figure 1, straight lines a and b are intercepted by straight lines c and d. Under the following conditions, a‖ cannot be determined b is ( )

A.∠1=∠2

B. ∠5=∠7 C. ∠4=∠6 D. a⊥d, d⊥b

7. Assume "●", "▲" and "■" represent three different objects. Now Weighed twice with a balance, the situation is as shown in Figure 2, then the three objects ●, ▲, and ■ are arranged in order from large to small in mass ( )

A. ■●▲ B. ■▲● C. ▲●■ D. ▲■●

10. An intelligence test has 20 multiple-choice questions. The scoring standard is: 5 points for each correct question, and 2 points deducted for each incorrect question. No points will be awarded or points will be deducted for not answering the questions. Xiao Ming has left two questions unanswered. If he answers at least a few questions correctly, the total score will not be less than 60 points. Then the at least number of questions Xiao Ming answered correctly is ( )

A.7 questions B.8 questions C.9 questions D.10 questions

2. Fill in the blanks: (3 points for each question, ***24 points)

11 .Calculation - (-3) - - = .

12. A piece of triangular paper ABC, ∠A=55?, ∠B=65?, now fold one corner of the paper,

Let point C fall in ΔABC, as shown in Figure 3. If ∠1=30?, then ∠2= . A

13. If y= 2, then 3x the square root of 4y-1 Yes.

14. Given a pair of values, please write a system of linear equations of two variables,

so that the pair of values ??satisfies the solution of this system of equations.

15． As shown in Figure 4, in ΔABC, AB=2.5cm, BC=4cm, then the ratio of AD to CE of ΔABC is .

16. Can some arbitrary quadrilaterals of the same shape and size be inlaid into a flat pattern? (Fill in “can” or “can’t”), the reason is: .

17. As shown in Figure 5, translate the right-angled trapezoid ABCD along the AD direction to the trapezoid EFGH,

HG=24m, MG=8m, MC=6m, then the area of ??the shaded part is.

18. Observe the following equations, =2, =3,

=4. Please write an equation containing n (ngt; the natural number of 2) to express the generalized formula of the above rules: .

3. Answer questions: (Questions 19, 20, 21, 22, and 23 are worth 6 points each, questions 24 and 25 are worth 8 points each, ***46 points)

19. Solve the system of equations x-2=2(y-1), 2(x-2) y=1=5

21. A shopping mall purchases 50 pieces of two commodities, A and B. The purchase price of commodity A is 35 yuan per piece, and the profit margin is 20. The purchase price of commodity B is 20 yuan each, and the profit margin is 15. The profit margin is 278. Yuan, how many pieces of each commodity A and B purchased? twenty two. As shown in Figure 6, the quadrilateral ABCD is in the plane Cartesian coordinate system. A (2, 2)

(1) Write the coordinates of B, C, and D respectively.

(2) Find the area of ??quadrilateral ABCD. (Keep two significant figures) 23. As shown in Figure 7, in ΔABC, ∠A=40?, ∠ABC=110?, CE bisects ∠ACB, CD⊥AB is in D, and DF⊥CE.

Find the degree of ∠CDF?

24. A certain company organized soldiers into 8 groups during a mission. If the number of people assigned to each group is 1 more than the scheduled number, then the total number of soldiers will exceed 100; if the number of people assigned to each group is more than 100, If the number of scheduled soldiers is 1 less, then the total number of soldiers will be less than 90. Please reserve the number of soldiers assigned to each group. 25. In order to protect the environment, a company decided to purchase 10 sewage treatment equipment. There are currently two types of equipment, A and B. , the price of each unit, the monthly sewage treatment volume and the annual consumption fee are as follows:

According to the budget, the company's funds for purchasing equipment shall not exceed 1.05 million yuan.

(1) Please design several purchase options for the company;

(2) If the company produces 2040 tons of sewage per month, which one should be chosen in order to save money?

(3) Under the conditions of question (2), if the service life of each piece of equipment is 10 years, and the sewage treatment fee for the sewage plant is 10 yuan per ton, please calculate, How many thousands of yuan will the company save in 10 years compared with treating sewage by itself versus treating it in a sewage plant? (Note: The cost of sewage treatment by enterprises includes the funds for purchasing equipment and consumption expenses)

Example 1 A certain school spent 600 yuan on buying basketballs and volleyballs. The basketballs were 45 yuan each and the volleyballs were 30 yuan each. Yuan, it is known that 10 basketballs were bought, how many volleyballs were bought?

Analyzing the equality relationship of this question is: total price of basketball + total price of volleyball = 600 yuan

Solution: Suppose you bought a volleyball. According to the meaning of the question, we get (subtract 450 from both sides at the same time )

(Divide both sides by 30 at the same time)

Answer: I bought 5 volleyballs.

23. The following are advertisements from three companies:

Company A: Recruiting 1 person with an annual salary of 30,000 yuan. After one year, the salary will be increased by 2,000 yuan per year

Company B: Recruiting 1 person, with a half-year salary of RMB 10,000, which will increase by 20% every six months after half a year.

Company C: Recruiting 1 person, with a monthly salary of 2,000 yuan, and a monthly salary increase of 100 yuan after one year.

If you apply for the job, which company do you plan to choose? (The contract period is 2 years)

A: 3 3.2=62,000

B: 1 1.2 1.2*1.2 1.2*1.2*1.2=1 1.2 1.44 1.728=53,680

C: 0.2*24 0.01 0.02 0.03 0.04…0.12=4.8 0.78=55,800

A has the highest salary, go to A

24.1. Collective tickets for a certain scenic spot The charging standard is: within 20 people (including 20 people). 25 yuan per person. If there are more than 20 people, the excess is 10 yuan per person. A certain class of 51 students visited the scenic spot. How much does it cost to purchase tickets?

20*25 (51-20)*10=810 (yuan)

25.2. A company sells a certain product and there are two options for paying the salesman a monthly salary. :

Option 1: A basic salary of 600 yuan regardless of the amount of sales, and an additional sales fee of 2 yuan for each product sold;

Option 2: No basic salary, and an additional sales fee of 2 yuan for each product sold. product, a sales fee of 5 yuan is paid;

If Xiao Ming sells 300 products a month, which salary plan should he choose to be more cost-effective? Why?

Option one: 600 2×300=1,200 (yuan)

Option two: 300×5=1,500 (yuan)

So option two is cost-effective.

26. A store sold two pieces of clothing at a price of 60 yuan each at a certain time. One of them made a profit of 25 and the other lost 25. The total profit from selling these two pieces of clothing was Is it still a loss, or is it neither profit nor loss?

Suppose the original price of one of the clothes is X nothing and the other is Y yuan, then

X (1 25) = 60, we get >Y (1-25) = 60, we get Y = 80

The overall situation is selling price - original price, 40 80-60*2=0

So it is not profitable or not Loss

27. A store first increased the original selling price of a certain model of color TV by RMB 40, and then wrote "Big deal, 20% off" in the advertisement. After complaints from customers, the law enforcement department determined that it was illegal. A fine of 2,700 yuan per unit will be imposed if it is 10 times the income. Ask for the selling price of each color TV?

Illegal income of 270 yuan

Original selling price x

1.4x*0.8-x=270

x=2250

Original price: 2,250 yuan

28. One passenger in the ordinary cabin of the aircraft can carry up to 20 kilograms of luggage for free, and a luggage ticket will be charged for each kilogram in excess of 1.5 of the flight fare. A passenger brought 35 kilograms of baggage on board and paid 1,323 yuan for the ticket and baggage fee. What is the passenger's ticket price?

Suppose the air ticket price is Scored 82 points, scored 96 points in the second test, and scored at least the number of points in the third test. In order to make the average score of the three tests not less than 90 points?

The average score is no less than 90 points, and the total score is no less than 3*90=270 points.

So the third test requires at least 270-82-96=92 points.

30. A set off from A in a certain city on a bicycle. 2 hours later, B walked on the same road for 3 hours. After 3 hours, they were 16km apart. At this time, B continued to chase, and A rested at the same place for 11/ Returning from the original place after 3 hours, and after another 1 hour, A and B are separated from each other at point C. "How far is point C from a certain city A?

Suppose A's speed is X km/s and B's speed is Y km/s.

Because B is chasing A During the 3 hours, A is also moving forward, so there is an equation 5x-3y=16

A rests for 11/3 hours. This is the time that A walks less than B. The distance they walked is 16KM

So there is an equation (1 11/3) y x=16

Solving the system of equations we can get

y=192/79(km)

x=368/79

Because A has moved forward for a total of 5 hours and returned for one hour, the distance between point C and point A should be 4 times X

It should be 1472/79, approximately is 18.633 KM

That is, point C is about 18.633km away from point A

32. A certain unit ordered x white shirts and y floral shirts in the store. The price was one and a half times the price of the floral shirt. After buying the shirt, I found that the number of pieces of white shirts and floral shirts was exactly the same as the number of pieces I originally wanted to buy. After checking, I found that the order was filled in incorrectly, and it was expressed as a fraction. The ratio of the original amount of money required to the actual amount paid.

Suppose the price of a single white shirt is z, then the amount of money spent is 2z.

The imagined amount of money is. : xz＋2yz (Note: the cost of x white shirts and y floral shirts)

The actual amount of money is: 2xz＋yz (Note: the cost of x floral shirts and y white shirts)

To find the ratio, the result we are looking for is: (x 2y)/(2x y)

33. There are 199 teachers and students in the first grade of a school who want to rent a car to travel. If they rent it, they can take 45. For a Class A station wagon with 32 passengers, the rental fee is 400 yuan per vehicle; if you rent a Class B station wagon that can accommodate 32 passengers, the rental fee is 300 yuan per vehicle.

If I rent two cars at the same time, what is the minimum cost for renting two cars each? What is the minimum fee?

199=45*3 32*2

400*3 300*2=1800yuan

34. The starting price of a taxi in a certain city is 10 yuan ( That is, you need to pay a fare of 10 yuan within 5 kilometers). After reaching or exceeding 5 kilometers, 1.2 will be added for each kilometer traveled (less than 1 kilometer will be counted as 1 kilometer

). Now a person takes a bus from point A to point B and pays a fare of 17.2 yuan. What is the approximate distance from point A to point B?

Explanation:

Because it exceeds 10 yuan, it exceeds 5 kilometers.

Suppose the distance is x kilometers

(x-5)*1.2 10=17.2

The solution is: x=11

Answer:...

35. The distance between two places is 300KM. A ship sails between the two places. If it takes 15H with the current and 20H with the current, find the speed format of the ship sailing in still water and against the water. How many?

First understand; the speed along the current = the speed of the boat and the speed of the water; the speed against the current = the speed of the boat - the speed of the water

Then the speed along the current * 15 is equal to the distance between the two places of 300km, and the speed against the current * 20 It is also equal to 300km

Solution: Suppose the ship speed is x kilometers/hour and the water speed is y kilometers/hour.

15(x y)=300

20(x-y)=300

The solution is x=17.5 y=2.5

Then the speed of the ship in still water is 17.5km/h, and the speed against the water is (17.5-2.5) =15km/hour

36. There are 10 coins of 1 jiao, 5 jiao and 1 yuan each. Take 15 coins out of them, with a maximum value of 7 yuan. 1 jiao, 5 jiao and 1 yuan coins each. How many coins should be taken?

In fact, 7 yuan is an integer:

If there is no 1 jiao, there will not be 15 coins.

2 If there is 1 jiao, , then the number of 1-corner can only be 5 or 10 or 0:

① If there are 5 pieces of 1-corner, then the number of 5-corner should be an odd number, and the number of 5-corner can only be 9. 7, 5 coins. Analyze that 9 coins will not work, 7 coins will be just right, and 5 coins will not work either. Then you can get a result: 5 coins for 1 jiao, 7 coins for 5 jiao, and 3 coins for 1 yuan.

② If there are 10 pieces of 1-corner pieces, then the number of 5-corner pieces should be an even number. The 5-corner pieces can only be 4, 2, 0 pieces (***15 pieces). Analyze that 0 pieces will not work, and 2 pieces will not work. No, 4 pieces still won’t work.

③ If there is no 1 jiao, then the minimum combination of 5 jiao and 1 yuan ***15 should be 10 5 jiao and 5 1 yuan, ***10 yuan, no.

The final result is: 3 pieces for 1 yuan, 7 pieces for 50 cents, and 5 pieces for 1 dime.

37. There were (5A-4) passengers on a bus. When it arrived at the station, (9-2A) passengers got off the bus. How many passengers were there on the bus?

5a-4≥ 9-2a —— ①

9-2a>0 —— ②

From ①, we get a≥13/7

From ②, we get a<9/ 2

Both (5a-4) and (9-2a) should be positive integers, so a must be an integer.

The integer solution that satisfies 13/7≤a<9/2 is a1=2; a2=3; a3=4, so there are 6, 11 or 16 passengers in the car.

38. The school organizes students to go to a rural social practice 31 kilometers away from the school. They go for 3 hours in the morning and 4 hours in the afternoon. The average speed in the afternoon is 1 kilometer slower than that in the morning. Find the upper and lower speed. What is the average speed in the afternoon?

Suppose the speed in the morning is >Solution: A plastic empty water bottle was lost. When he traveled 50 meters to point B, he found that the water bottle was lost and immediately returned to look for it. He found it at point C. The swimming speed of this person was 1.5 times the speed of the water flow. How many meters did he swim from the time when he lost the water bottle to when he found it?

Suppose the kettle's floating distance is 1.5v+v=2.5v meters/second. According to the meaning of the question (kettle floating time = this person’s swimming time), we get 50/0.5v (50 x)/2.5v=x/v.

Solving this equation, we get x=200.

So from losing to finding the kettle, we swam 50×2+200=300 meters.

40. There are three types of stationery: A, B, and C. If you buy 2 pieces of A, 1 piece of B, and 3 pieces of C, it will cost 23 yuan; if you buy 1 piece of A, 4 pieces of B, and 3 pieces of C 5 pieces of *** cost 36 yuan. How much does it cost to buy 1 piece of A, 2 pieces of B, and 3 pieces of C?

Explanation: Suppose the purchase of A costs x yuan, B costs y yuan, and C costs z yuan, then

2x y 3z=23

x 4y 5z= 36

The simultaneous solution is

y z=7

x z=8

Now we require x 2y 3z=x z 2(y z) =8 7*2=22 yuan

So it costs 22 yuan to buy 1 piece of A, 2 pieces of B, and 3 pieces of C.

41. A and B cost 400 Practice running on a 1-meter circular track. If they run in the same direction, they will meet every 3 minutes and 2 seconds. If they run opposite, they will meet every 40 seconds. What is the speed of A and B?

The speeds of A and B are x and y respectively

(x y)*40=400

(x-y)*182=400

42. A centipede with 40 legs and a dragon with 3 heads are in a cage. *** has 26 heads and 298 legs. A centipede with 40 legs has only one head. How many legs does a dragon with 3 heads have?

Three unknowns, two equations.

Suppose the dragon has a legs, x centipedes, and y dragons.

The equation 40x ay=298 (1)

x 3y=26 (2)

It can be seen from Equation 1 that the possible solutions of x are 7, 6, 5, 4, 3, 2, 1, 0

There are 2 more formulas to get x=5, y=7 or x=2, y=8 (only y=7 and y=8 divisible)

Substituting into equation 1, we get a=14

43. A batch of parts has a maximum of 840 pieces. If A works for 4 days first and B joins the cooperation, then It takes 8 days to complete. If B does it for 4 days first and A joins in the cooperation, then it will take 9 days to complete. How many pieces can each of them do each day?

Suppose A makes x machine parts every day, and B makes y machine parts every day. According to the meaning of the question, we get

(4 8)x 8y=840

9x (4 9)y=840

Solution

x=50

y=30

Answer: A Two people, B and B, make 50 and 30 machine parts respectively every day.

44. Xiao Ming plays a game with his classmates. It is stipulated that from a certain point, walk forward 20 meters, turn left 30 degrees, walk forward 20 meters, and then turn left 30 degrees until returning to a certain point. How many meters did Xiao Ming*** walk?

Solution: The final result is actually a regular 12-sided polygon.

360/30=12.

Result: 20*12=240 meters.

45. 200 students in the first grade of a school took the midterm exam. The average score of the passing students in mathematics was 87 points, and the average score of the failing students was 43 points. The average score of the first grade students was 87 points. The score is 76 points. How many people passed and failed the exam?

Suppose the number of people who passed the exam is x and the number of people who failed is y.

x y=200

87x 43y=200*76

x=150

y=50

46. An engineering team It is necessary to recruit 150 workers of two types, A and B. The monthly wages of workers A and B are 600 yuan and 1,000 yuan respectively. It is now required that the wages of workers of type B should not be less than twice that of workers of type A. When asking how many workers A and B can recruit, the wages are least?

Suppose X people of type A, Y people of type B, the amount of money is S

2X is greater than or equal to Y

X Y=150

3X=150

X=50

The least money is when 2X=Y

600X 1000Y=S

600X 1000 (2X) =S

Substitute X=50

600*50 1000* (2*50)

=30000 100000

=130000 Yuan

Answer: A has 50 people and B has 100 people. The salary is at least 130,000 yuan.

Use the quadratic function of Chapter 3 to do something ``````

47. A shopping mall plans to allocate 90,000 yuan to purchase 50 TV sets from the manufacturer. It is known that the The factory prices of three different models of TV sets produced by the manufacturer are 1,500 yuan each for type A, 2,100 yuan each for type B, and 2,500 yuan each for type C.

(1) If the mall purchases two of them at the same time There are ***50 TV sets of different models, costing 90,000 yuan. Please study the purchase plan.

(2) If the mall sells a TV A and earns a profit of 150 yuan, B a profit of 200 yuan, and a TV C earns a profit of 150 yuan. 250 yuan, in the plan in (1), what is the highest profit?

Solution: Assume X station of type A, station Y of type B, and station Z of type C.

Option 1: Buy A and B

X Y=50

1500X 2100Y=90000

X=25 Y=25

Option 2: Buy A and C

X Z=50

1500X 2500Z=90000

X=35 Z=15

Option 3: Buy B and C

Z Y=50

2500Z 2100Y=90000

Y=-37.5 Z=87.5 (dropped)

So there are 2 options

Option one: 25*150 25*200=8750

Option two: 35*150 15*250=9000

Option two is more profitable

48. The cross-lake section of Hangzhou East Road, known as the city’s scenic line, is 1,857 meters long. Its various greening indicators are shown in the table below. Analyze the table below and answer the following questions:

Number of main tree species

Camphora 336

Willow 188

Palm 258

Osmanthus 50

Total 832

It is known that the total length of Hangzhou East Road is 4744 meters. If the distance between the rows of trees (the horizontal distance between two trees) remains unchanged, please estimate the number of camphor and palm trees planted along the entire line (keep the result as an integer)

The distance between trees is 2.23m, the trees along the entire line are 4744/2.23 1=2128, the camphor ratio is 336/832, the entire line is 2128*336/832=859 palms=659

49. Someone He used a certain amount of RMB to buy a one-year bond with an annual interest rate of 10. After maturity, he took out half of the principal for shopping, and the remaining half and the interest earned purchased the one-year bond (interest unchanged), after maturity, he will receive principal and interest plus 1,320 yuan. How much did this person spend to buy this bond?

1,200 yuan

Suppose he spent x to start buying the bond Yuan, according to the equation of the question, we get:

x·10·0.5+x+(x·10·0.5) (x·10·0.5)·10=1320

Solve to get x ＝1200

50. There are 20 questions in the mathematics competition *** for first-year students in a certain school. Each correct answer is worth 5 points, and each wrong answer or no answer is deducted 1 point. The result is 70 How many questions do you need to answer correctly?

Solution:

20×5=100 (points)

100-70=30 points

30÷(5+1)=5 questions

20-5=15 questions

Answer: To get 70 points, you must answer 15 questions correctly and 5 questions wrong~

Finally, I’ll give you a question ^_^