A, multiple-choice questions (this question * *10 small questions, each small question 3 points, ***30 points)

1. The following statement:

(1) Algebraic expressions with unknowns are called equations;

② Only by replacing the unknown quantity in the equation with the solution of the equation can the equation represented by the equation be established;

③ When both sides of the equation are divided by the same number, the result is still an equation;

④x=- 1 is the solution of equation x+12-1= x+1.

The number of incorrect statements is ().

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

2. Given that the solution of equation 4x-3m=2 about x is x=m, then the value of m is ().

a . 2 B- 2 c . 2.7d-2.7

3. Given the equation |x|=2, the solution of the equation is ().

A.x=2 B.x=-2 C.x 1=2，x2=-2 D.x=4

4. The solution of equation 5x+2=7x+8 is ().

a . 2 B- 2 c . 3d-3

5. If solving equation 2x-3( 10-x)=5x-7(x+3), the error of the following solution is ().

a . 2x-30+3x = 5x-7x-2 1 b . 2x+3x-5x+7x =-2 1+30

C.7x=9 D.x=

6. If xa+2y3 and -3x3y2b- 1 are similar terms, then the values of A and B are () respectively.

A.a= 1，b=2

C.a=2，b= 1 D.a= 1，b= 1

7. When solving equation =2, after removing the denominator and brackets, the correct result is ().

a . 9x+ 1- 10x+ 1 = 1 b . 9x+3- 10x- 1 = 1

c . 9x+3- 10x- 1 = 12d . 9x+3- 10x+ 1 = 12

8. As shown in the figure, 50 grams of salt and 45 grams of salt are placed in two plates of the balance. To make the quality of salt in two plates equal, X grams of salt should be taken out of plate A and put into plate B, and the value of X is ().

A.2 B.2.5 C.3 D.3.5

9. Team A has 65,438+000 vehicles and Team B has 68 vehicles. To make two teams have the same number of cars, it is necessary to transfer X cars from Team A to Team B, from which the equation can be listed as ().

a . 100-x = 68 b . x+68 = 100

c . 100+x = 68-x d . 100-x = 68+x

10. A city will hold a dragon boat race on the Dragon Boat Festival. It is estimated that 330 people from 15 teams will participate. It is known that each team has a boat with equal number of people, each boat has 1 person to drum, 1 person to steer, and the rest row at the same time. Every ship has an X.

a . 15(x-2)= 330 b . 15x+2 = 330

c . 15(x+2)= 330d . 15x-2 = 330

Fill in the blanks (this topic is ***8 small questions, with 3 points for each small question and 24 points for * * *).

1 1. If (k- 1)x2+kx+8=0 is a linear equation about x, then k = _ _ _ _ _ _ _ _ _ _.

12. The solution of equation 5x=4x+9 is _ _ _ _ _ _ _.

13. The solution of the linear equation of one variable is -3. Please write this equation _ _ _ _ _ _ _ (only one).

14. Let, and represent three different objects and weigh them twice in the current balance, as shown in Figure 1 and Figure 2. Then their relationship with the masses of two objects is _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

15. Xiangtan has a long history. Because it is rich in Xianglian, it is known as? Liancheng? Li Hong bought eight lotus leaves, gave them to 50 yuan and found 38 yuan. Let the price of each lotus leaf be x yuan. According to the meaning of the question, the equation is _ _ _ _ _ _.

16. A store sells a batch of clothes at a price of 150 yuan. If you sell it at a 20% discount, you can still earn 20 yuan. If the cost price of this kind of clothes is X yuan per piece, then the' equation' satisfied by X is _ _ _ _ _ _ _.

17. The charging standard of a taxi is: the starting price is 6 yuan, that is, you have to pay 6 yuan fare if you drive less than 2 kilometers; 2.5 yuan will be charged for every increase of 1 km beyond 2km (if it is less than 1 km, it will be counted as 1 km). Vivi will take this taxi to pay the fare from A to B * * 26 yuan, and if Xin Wei's distance from A to B is X kilometers, then the value of X is _ _ _ _ _ _ _.

18. Someone goes downstream from A to B by boat, and then goes upstream to C. It takes 3 hours by boat. It is known that the speed of a ship in still water is 8 kilometers per hour, and the current speed is 2 kilometers per hour. If the distance between A and C is 2 kilometers, then the distance between A and B is _ _ _ _ _ _ _.

Third, answer the question (this is entitled ***5 small questions, ***46 points)

19.(20 points) Solve the following equation:

( 1)(40+x)？ 80%=40? 92%;

(2) = 1;

(3) ;

(4)

20.(6 points) A group of students went to a power station site for social practice activities. Boys wear white helmets and girls wear red helmets. They sat together during the break and found an interesting phenomenon. Every boy sees as many white helmets as red helmets, while every girl sees twice as many white helmets as red helmets.

Question: Based on this information, please guess how many students there are in this group.

2 1.(6 points) Xiaoming went to the stationery store to buy 2B pencils, and the owner said, If you buy more, I will give you a 20% discount. Xiao Ming calculated. If you buy 50 pencils, it will be cheaper than the original price, 6 yuan. What is the original price of each pencil?

22.(6 points) When the ship sails between two wharves, it sails downstream for 4 hours and upstream for 5 hours, and the current speed is 2 kilometers per hour. Find the speed of the ship in still water.

23.(8 points) If the car travels at a speed of 45 kilometers per hour from A to B, it will arrive half an hour later than originally planned; If you drive at a speed of 50 kilometers per hour, you can arrive half an hour earlier than originally planned. Find the distance between a and b and the original planned time.

Reference answer

1 answer: b dial: 1344 error.

2 answer: micro-push: this question mainly examines the definition and solution of the solution of a linear equation. According to the definition of the solution of the equation, it is known that 4m-3m=2 and the solution is m=2, so A is chosen.

3 answer: c-dial: from |x|=2, x=? 2. so, choose C.

4 Answer: D inching: shifting term, 5x-7x=8-2, merging similar terms, -2x=6, coefficient 1, x=-3, so D is selected.

5 answer: D.

6 answer: a nudge: according to the meaning of the question, a+2=3, 2b- 1=3, while a= 1, b =2. Therefore, a was chosen.

7 answer: c

8 answer: b

9 answer: d

10 answer: c

1 1 Answer: 1 -8 Cuo: From the definition of a linear equation, we get k- 1=0, k? 0.？ K= 1。 The original equation becomes x+8=0 and the solution is x=-8.

12 answer: x=9. Dialing: Equation 5x=4x+9 Subtract 4x from both sides to get 5 x-4x=9, so x=9.

13 answer: x+2=- 1 or equal (the answer is not unique).

14 answer: 3 =2 2 =

15 answer: 50-8x=38 Cuo: the equivalence of this question is: 50 yuan-the price of 8 lotus flowers =38 yuan.

16 answer: 150 80%-x=20: according to? Price tag? 80%- cost price = profit? , the countable equation is 150? 80%-x=20。

17 answer: 10 nudge: According to the meaning of the question, Xin Wei's riding distance is more than 2km, and 6 yuan is charged for the first 2km, and 2.5 (x-2) yuan is charged for the last (x-2) km, so 6+2.5 (x-2) = 26, and x = 6544.

18 answer: 10 km or 12.5 km. Because the position of C is not clear, it should be discussed in two situations: C is between A and B, and C is upstream of A. If the distance between A and B is X km, it is =3 or =3, and x = 60 according to the meaning of the question.

19 solution: (1) Cut off 80% of both sides and get 40+x=46.

So x=6.

(2) Divide by the denominator to get 2(2x+ 1)-(x- 1)=6.

Without brackets, 4x+2-x+ 1=6.

Shift term, 4x-x=6-2- 1.

If you combine similar projects, you get 3x=3.

The coefficient is 1 and x= 1.

(3) From the basic nature of the score,

That is,15x-3 = 4x-3-10x-42.

Moving items and merging similar items get 2 1x=-42.

The coefficient is 1 and x=-2.

(4) first remove the brackets to get xx-6 = x+1+0.

If the term is shifted, x- x= 1+ +6.

Combining similar projects, we get -x=7,

The coefficient is 1 and x=-7.

20 solution: suppose there are x boys, then there are (x- 1) girls. According to the meaning of the question, x=2(x- 1- 1).

X=4，x- 1=3。

4+3=7 (person).

There are seven students in this group.

2 1 solution: let the original price of each pencil be x yuan, then according to the meaning of the question, 50x( 1-0.8)=6, and the solution is x=0.6.

A: The original price of each pencil is 0.6 yuan.

Solution: Assume that the speed of the ship in still water is x km/h, which is 4(x+2)=5(x-2) according to the meaning of the question.

The solution is x= 18.

A: The speed of the ship in still water is18km/h. 。

Solution: Let the distance between A and B be x kilometers.

Solve this equation and get x=450.

So =9.5 (hours).

A: The distance between A and B is 450 kilometers, and the original planned time is 9.5 hours.