The most difficult math problem in senior one.

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

1. It is known that 4x2n-5+5=0 is a linear equation about x, then n = _ _ _ _ _ _

2. If x=- 1 is the solution of equation 2x-3a=7, then a = _ _ _ _ _

3. When x=______, the sum of algebraic expression x- 1 is opposite to each other.

4. It is known that the sum of x and 3 times of x is 6 less than 2 times of x, and the equation is _ _ _ _ _.

5. In the equation 4x+3y= 1, if y is expressed by the algebraic expression of x, then Y = _ _ _ _ _ _

6. When a commodity is sold at a 60% discount on the basis of the marked price in 300 yuan, the profit rate is 5%, and the marked price of the commodity is _ _ _ _ _ _ _.

7. Given that the sum of three consecutive even numbers is 60, these three numbers are _ _ _ _ _ _.

8. For a job, it takes 6 days for Party A to do it alone, 12 days for Party B to do it alone, and _ _ _ _ _ _ _ days for both parties to do it together.

Second, multiple choice questions. (3 points for each small question, * * * 30 points)

9. Equations 2m+x= 1 and 3x- 1=2x+ 1 have the same solution, then the value of m is ().

A.0 B. 1 C.-2 D

10. The solution of equation 3x =18 is ().

A. One solution is 6 b, and there are two solutions, both of which are 6.

C. No solution D. There are countless solutions

1 1. If the equation 2ax-3=5x+b has no solution, then a and b should satisfy ().

A.a，b≠3 B.a=，b=-3

C.a，b=-3 D.a=，b ≦- 3

12. The equation after converting the denominator of the equation into an integer is ().

13.800 meters on the runway, two people are practicing long-distance running. A runs 300 meters per minute, and B runs 260 meters per minute. They set out in the same place, at the same time and in the same direction, and met for the first time after t minutes, and t equals ().

A. 10 points B. 15 points C.20 points D.30 points.

14. A shopping mall found that the sales in the first quarter of this year increased by 10% in February and decreased by 10% in March, so the sales in March were higher than 1 month ().

A. increase10% B. decrease10% C. neither increase nor decrease D. decrease 1%.

15. in the trapezoid area formula S= (a+b)h, it is known that H = 6cm, A = 3cm and S = 24cm2, then B = () cm.

A. 1

16. It is known that there are 28 people in group A and 20 people in group B. Among the following deployment methods, the one that can make one group less than half of the other group is ().

A. transfer 12 people from group a to group b, and transfer 4 people from group b to group a.

C. transfer 12 people from group b to group a.

D transfer 12 people from group a to group b, or transfer 4 people from group b to group a.

17. The rules of football match are: win a game with 3 points, draw a game with 1 point, lose a game with 0 points, a team played 14 games and lost 5 games, and * * * got 19 points, so the team won () games.

a3 b . 4 c . 5d . 6

18. As shown in the figure, how many weights can be removed from the left plate in Figure A to keep the balance? ( )

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

Third, answer the question. (19, 20 questions 6 points, 2 1, 22 questions 7 points, 23 and 24 questions 10 points, ***46 points)

19. Solve the equation: -9.5.

20. Solve the equation: (x-1)-(3x+2) =-(x-1).

2 1. As shown in the figure, many information cards are neatly pasted on a display board. These cards are the same size, with three square spaces between them, which are marked with diagonal lines in the figure. It is known that the short side length of the card is10cm. If you want to fill in the blanks with three pictures, what size pictures should you match?

22. For three digits, the number on the hundredth digit is 1, and the number on the tenth digit is three times less than that on the tenth digit. 2. If the order of three digits is reversed, the sum of the obtained three digits and the original three digits is 1 17 1, so find these three digits.

It is understood that the train fare is determined by the method of "". It is known that the total mileage from Station A to Station H is1500km, and the reference price for the whole journey is 180 yuan. The following table shows the mileage from stations along the way to H station:

name of a station

From each station to H station

Mileage (m)15001130910 622 402 219 720

For example, to determine the train fare from Mile Mile to E station, the fare =87.36≈87 yuan.

(1) Find the train fare from station A to station F (the result is accurate to 1 yuan).

(2) Passenger Aunt Wang goes to her daughter's house by train. After getting on the train for two stops, she took the ticket and asked the flight attendant, "am I near the station?" When the flight attendant saw that Aunt Wang's ticket price was 66 yuan, she immediately said that the next stop was here. At which station does Aunt Wang get off?

24. The admission price of a park is as follows:

The number of ticket buyers is1~ 50,51~ 100, which exceeds100.

Fares 5 yuan 4.5 yuan 4 yuan

Class A and Class B 103 people from a school (among which Class A is more than Class B) came to visit the park. If the two classes buy tickets separately, they have to pay 486 yuan.

(1) How much can I save if two classes buy tickets together?

(2) How many students are there in each class? (Hint: This question should be discussed in different situations.)

Answer:

I. 1.3

2.-3 (fine-tuning: substitute x=- 1 into equation 2x-3a=7, and get -2-3a=7, and get a=-3).

3. (cuddle: solve the equation x- 1=- to get x=)

4.x+3x=2x-6 5.y= - x

6.525 (hint: if the set price is X yuan, it will be 5%, and X will be 525 yuan).

7. 18,20,22

8.4[ Note: If it takes X days to complete, then x(+)= 1, and the solution is x=4]

Two. 9.d

10.b (hug: classified discussion:

When x≥0, 3x= 18, ∴x=6.

When x

Therefore, this question should choose b)

1 1.d (hint: from 2ax-3=5x+b, we get (2a-5)x=b+3. To make the equation unsolvable, we must make 2a-5=0, a=, b+3≠0, b ≠-.

12.b (inching; In the process of deformation, the numerator and denominator of the fraction are simultaneously expanded or reduced by the same multiple by using the properties of the fraction, and the decimal equation is transformed into an integer equation.

13.c (hint: when A and B meet again, A runs 800 meters more than B. The equation is 260t+800=300t, and the solution is t=20).

14.D

15.B (inching: according to the formula S= (a+b)h, b =-3 = 5cm)

16.D 17。 C

18.a (nudge: Attribute 2 according to equation)

Three. 19. solution: the original equation is transformed into

200(2-3 years) -4.5= -9.5

∴400-600y-4.5= 1- 100y-9.5

500y=404

∴y=

20. solution: remove the denominator and get.

15(x- 1)-8(3x+2)= 2-30(x- 1)

∴2 1x=63

∴x=3

2 1. solution: let the length of the card be x cm. According to the meaning of the picture and the meaning of the question, you can get

5x=3(x+ 10), and the solution is x= 15.

Therefore, the side length of a square picture should be 15- 10=5 (cm).

Answer: You need a square picture with a side length of 5 cm.

22. Solution: Let the number in the tenth place be X, then the number in the single digit is 3x-2, and the number in the hundredth place is x+ 1, so

100(x+ 1)+ 10x+(3x-2)+ 100(3x-2)+ 10x+(x+ 1)= 1 17 1

The solution is x=3.

A: The original three-digit number was 437.

23. Solution: (1) can be obtained from known =0. 12.

The actual mileage from Station A to Station H is1500-219 =1281(km).

So the train fare from Station A to Station F is 0.12×1281=153.72 ≈154 (yuan).

(2) Assuming that Aunt Wang's actual mileage is X kilometers, according to the meaning of the question, it is =66.

X=550。 According to the table, the distance from Station D to Station G is 550 kilometers, so Aunt Wang gets off at Station D or Station G. 。

24. Solution: (1) ∵103 > 100

∴ The total fare for each ticket in 4 yuan is 103×4=4 12 (RMB).

Can save 486-4 12=74 yuan.

(2) ∵ Class A and Class B *** 103, and the number of students in Class A is greater than that in Class B.

There are more than 50 people in Class A, but there are two situations in Class B:

① If there are less than 50 people in Class B and X people in Class B, then there are (103-x) people in Class A..

5x+4.5( 103-x)=486

X=45, ∴ 103-45=58 (person)

There are 58 students in Class A and 45 students in Class B. 。

② If there are more than 50 people in Class B and X people in Class B, then there are (103-x) people in Class A..

According to the meaning of the question, you must

4.5x+4.5( 103-x)=486

This equation does not hold, and this situation does not exist.

Therefore, there are 58 students in Class A and 45 students in Class B. 。

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3.2 Solve the linear equation of one variable (1)

-Merge similar items and shift items.

Classification training of knowledge points

Merge and move items of knowledge point 1

1. Is it correct to solve the deformation of the following one-dimensional linear equation? If not, point out where the mistake is and correct it.

(1) From 3x-8=2, 3x = 2-8 is obtained; (2) From 3x=x-6, 3x-x=6 is obtained.

2. In the following variant:

① divide the equation =2 by the denominator to get x-12 =10;

② Divide by both sides of the equation x= to get x =1;

③ Shift the term of equation 6x-4=x+4 to get 7x = 0；;

④ Equation 2- Multiply both sides by 6 to get 12-x-5=3(x+3).

The number of error deformations is ().

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

3. If the values of formulas 5x-7 and 4x+9 are equal, the value of x is equal to ().

4. Combine the following formulas and write the results on the horizontal line.

( 1)x-2x+4x = _ _ _ _ _ _ _ _ _ _ _ _ _； (2)5y+3y-4y = _ _ _ _ _ _ _ _ _；

(3)4y-2.5y-3.5y = _ _ _ _ _ _ _ _ _ _ _ _ _。

5. Solve the following equation.

( 1)6x=3x-7 (2)5=7+2x

(3)y- = y-2 (4)7y+6=4y-3

6. Find the value of x according to the following conditions:

The difference between (1)25 and x is -8. (2) The sum of x and 8 is 2.

7. If equation 3x+4=0 and equation 3x+4k=8 are the same solution, then k = _ _ _ _ _ _

8. If the equations about y 3y+4=4a and y-5=a have the same solution, the value of a is _ _ _ _ _.

Knowledge point 2: Solving practical problems by using one-dimensional linear equation analysis

9. The gross weight of a barrel of salad oil is 8kg. After half of the oil was taken out of the barrel, the gross weight was 4.5 kilograms. How many kilograms of oil was there in the barrel?

10. As shown in the figure, the two plates of the balance contain 50 grams and 45 grams of salt respectively. How much salt should be taken from plate A and put into plate B in order to make the quality of salt in the two plates equal?

1 1. Xiaoming starts from home at 7: 50 every morning and goes to 1000m school. His walking speed is 80 meters/minute every day. One day, five minutes after Xiao Ming left home, his father chased Xiao Ming at the speed of 180m/min, and caught up on the way.

(1) How long did it take Dad to catch up with Xiaoming?

(2) How far is it from school when catching up with Xiao Ming?

Comprehensive application improvement

12. It is known that y 1=2x+8 and Y2 = 6-2x.

(1) When x is taken, y 1=y2? (2) At what value of X, y 1 is 5 less than y2?

13. It is known that the root of equation x=-2 is 2 larger than that of equation 5x-2a=0. Find the solution of equation X-15=0.

Openness, exploration and innovation

14. Write an application problem to meet the following requirements:

The meaning of (1) applies to linear equations with one variable;

(2) The compiled application questions are complete and clear, and conform to real life.

Actual combat of the real questions in the senior high school entrance examination

15. (Jiangxi) As shown in Figure 3-2, a schematic diagram of the tourist route of scenic spot A, where B, C and D are scenic spots and E is the intersection of two roads. The data in the figure is the distance between two corresponding points (unit: km). A student starts from A, walks at a speed of 2 kilometers per hour, and stays at each scenic spot for 0.5 hours.

(1) When he returned to A along the A-D-C-E-A route, it took * * * 3 hours to find the length of CE.

(2) If this student intends to start from A and return to A after seeing three scenic spots in the shortest time with the same walking speed and staying time at each scenic spot, please design a walking route for him and explain the reasons for this design (regardless of other factors).

Answer:

1.( 1) The question is wrong. If -8 moves from the left to the right of the equal sign, the sign should be changed to 3x = 2+8.

(2) The question is wrong. -6 is not shifted to the right of the equal sign, so the sign should not be changed, and it should be changed to 3x-x =-6.

2.b [nudge: equation x=, two sides divided by the same to get x =]

3.b [Hint: From the meaning of the question, the equation 5x-7=4x+9 can be listed, and the solution is x= 16].

4.( 1)3x (2)4y (3)-2y

5.( 1) 6x = 3x-7, shift term, 6x-3x=-7, merge, 3x=-7, coefficient to 1, x=-.

(2)5=7+2x, that is, 7+2x=5. After shifting and merging, 2x=-2 and x =- 1.

(3)y- = y-2, shift term, y- y=-2+, merge, y=-, coefficient 1, y =-3.

(4)7y+6=4y-3, shifting terms to get 7y-4y=-3-6, merging similar terms to get 3y=-9,

The coefficient is 1 and y =-3.

6.( 1) According to the meaning of the question, we can get the equation: 25-x =-8; If we move the term, we get 25+8 = x；; If we merge, we get x = 33.

(2) According to the meaning of the question, we can get the equation: x+8=2, shift the term and get x=2-8, merge and get x=-6.

The coefficient is 1, and x =- 10.

7.k=3 [light shift: solve equation 3x+4=0 to get x=-, substitute 3x+4k=8 to get -4+4k=8 to get k = 3].

8. 19 [Direction: ∫3y+4 = 4a, y-5=a is the same solution equation, ∴y= =5+a, and the solution is a= 19].

9. Solution: Suppose there is X kilograms of oil in the barrel, and the gross weight of salad oil after removing half of the oil is (8-0.5x) kilograms. According to the known conditions, the gross weight of the remaining salad oil is 4.5kg. Because the gross weight of the remaining salad oil is constant, it can be listed as equation 8-0.5x = 4.5.

Solve this equation and get x = 7.

Answer: There are 7 kilograms of oil in the barrel.

[Hug: There are other arrangements]

10. Solution: Assuming that X grams of salt is taken out from plate A, the table can be listed as follows:

Disk a disk b

Raw salt (g) 50 45

Existing salt (g) 50 x 45+x

Suppose you want to take x grams of salt out of plate A and put it in plate B, then according to the meaning of the question, 50-x = 45+x.

Solve this equation and get x=2.5, which is in line with the meaning of the question.

Answer: Take 2.5 grams of salt from plate A and put it in plate B. 。

1 1. solution: (1) suppose dad used x points when he caught up with Xiaoming.

180x=80x+80×5，