Class: _ _ _ _ _ _ Name: _ _ _ _ _ Score: _ _ _ _ _ _ _

I. Fill in the blanks (1 each blank, 30 * * *)

A cube is surrounded by __6__ faces, with _ _ 8 _ vertices and _ _ 12 _ _ edges. A cylinder is surrounded by ___2__ faces.

3. If 5℃ above zero is +5℃, then 3℃ below zero is _-3℃ _ _ _.

3. if a < 0, then a _ _ > _ 2a (fill in the blanks with, =).

4. In 74, radix is _ _ 74 _ _ _, index is __0__, in (-2) 3, radix is _ _-6 _ _ _, index is _ _ 0 _ _.

⒌(- 1)2000=_____-2000_____, (- 1)200 1=_____-200 1______,- 12002=___(- 1)2002__________。

6.A minus 70 15% can be expressed as _ _15% A-70 _ _ _ _ _ _.

If the side length of a cube is a, then the volume of the cube is _ _ _ _ a _ _ and the surface area is 6a _ _ _ _ _ _

⒏ The single digit of a two-digit number is A and the ten-digit number is B. Please use an algebraic expression to indicate that this two-digit number is _ _ _ _ _ _ _ _ _ _ _ _.

(9) The lengths of the three sides of a triangle are 2x, 4x and 5x respectively, and the circumference of this triangle is _ _ _ _ _ _ _ _ _.

⒑ In three consecutive even numbers, n is the smallest one, and the sum of these three numbers is _ _ _ _ _ _ _.

5. Please explain the meaning of the following algebraic expressions:

6P:_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

a2-B2:_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ .

25a+ 12b:_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ .

5] The price of a commodity is X yuan, so 1/2x can be interpreted as _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _.

12、( 1) 0.25 =_____′_____〃 (2) 1800〃=_____′_____

⒔ Fillet = _ _ _ _ _ Flat angle = _ _ _ _ Right angle = _ _ _ _ _ _ degrees.

Second, true or false questions (65438+ 0 points for each question, ***6 points)

1, rational numbers are divided into positive numbers and negative numbers. ( )

2. The absolute value of rational number must be greater than 0. ( )

3 、( 3x-2)=-3x-2()

4、8x+4= 12x()

5、3(x+8)=3x+24()

6、3x+3y=6xy()

Choice (2 points for each small question, *** 12 points)

1, if | a |a|=4, then a = ()

A, 4 B,-4 C, 4 or-4 D, neither.

2, the reciprocal of -3/8 is ()

a 、-3/8 B、8/3 C、8/3 D、3/8

3. subtract 3 from the number n and enlarge it by 5 times. The final result is ()

a、n-3×5 B、5(n-3) C、n-3+5n D、5n-3

4. In a class * * *, there is student A, of which 35% are boys, so the number of girls is ().

a、35%x B 、( 1-35%)x C、x/35% D、x/ 1-35%

5. Point out the shape symbol () of the geometric section in the drawing.

A.B. C. D。

Three. Calculation (3 points for each small question, *** 12 points)

1、( 1/3+ 1/4- 1/6)×24

2、0-23÷(-4)3- 1/8

3、(-2)3×0.5-(- 1.6)2/(-2)2

4, 23 ÷ [(-2) 3-(-4)] 1. It is known that equation 2a(x- 1)=(5-a)x+3b has countless solutions, so a = _ _ _ _, and b = _ _ _ _.

A: 2a(x- 1)=(5-a)x+3b。

2ax-2a=5x-ax+3b

3ax-5x=2a+3b

x(3a-5)=2a+3b

Equation 2a(x- 1)=(5-a)x+3b There are many solutions to x.

So no matter what value X takes, it always holds.

So this equation has nothing to do with X.

So 3a-5 = 0, 2a+3b = 0.

a=5/3，b= - 10/9

2. What is the sum of all possible four-digit numbers composed of natural number 1 ~ 9, and there are no duplicate numbers?

A: First of all, let's look at a * * *, and how many four digits there are.

There are nine possibilities in a thousand, eight possibilities in a hundred, seven possibilities in ten, and six possibilities in an individual.

A * * * has 3024 four digits.

Look at a seat first. Because every number has an equal status, so

One ninth, that is, 336 units are 1, 336 units are 2, 336 units are 3, ... 336 units are 9.

All these bits add up to 336× (1+2+...+9 )×1.

Look at ten more. Because every number has an equal status, so

One ninth, that is, 336 bits are 1, 336 bits are 2, 336 bits are 3, ... 336 bits are 9.

All these bits add up to 336× (1+2+...+9 )×10.

Look at hundreds more. As can be seen from the above analysis, the sum of all hundreds is 336× (1+2+...+9 )×100.

Look at thousands more. As can be seen from the above analysis, the sum of all thousands is 336× (1+2+...+9 )×1000.

So the sum of all four digits is:

336×( 1+2+...+9)× 1+336×( 1+2+...+9)× 10+336×( 1+2+...+9)× 100+336×( 1+2+...+9)× 1000

=336×( 1+2+...+9)×( 1+ 10+ 100+ 1000)

=336×45× 1 1 1 1

= 16798320

A square table consists of a table top and four legs. 1 m3 of wood can be used to make 50 desktops or 300 legs. There are now 5 cubic meters of wood. How many pieces of wood can be used to make a desktop and how many legs can be used to make a square table?

The speed of the ship in still water is 1 hour 24 kilometers, and the current speed is 2 kilometers per hour. It takes six hours for the ship to go back and forth between A and B. How long does it take to sail downstream from A and from B to A respectively? What is the distance between A and B?

Warehouse A stores 200 tons of coal and warehouse B stores 70 tons. If warehouse A transports 15 tons and warehouse B transports 25 tons every day, how many days later will warehouse B store twice as much coal as warehouse A?

There are 27 workers in Workshop A and 0/9 workers in Workshop B, and now there are 20 new workers. In order to make the number of workers in workshop A twice that in workshop B, how should new workers be assigned to two workshops?

1, assuming that X square tables can be made, then

You need to make x desktops and 4x legs.

x *( 1/50)+4x *( 1/300)= 5

The solution is x= 150.

2. Solution: Let the distance between Party A and Party B be X kilometers.

According to the meaning of the question: x/(24+2)+x/(24-2)=6.

The solution is x=7 1.5.

rule ...........

Three questions

After x days of solution, the stored media is twice that of warehouse A.

Then 2*(200- 15x)=70+25x.

The solution is x=6.

Four questions

If x people are assigned to workshop a, 20-x people will be assigned to workshop B.

According to the meaning of the question, 27+x=2*( 19+20-x)

The solution is x= 17.

1. A two-digit number, where the ten digits are x and the digits are X- 1. What is the two-digit number obtained by exchanging ten digits with digits?

2. The little mother took Mi Yuan to the street to buy food. She spent half on meat and the remaining third on vegetables. So how much money does she have left?

Related answers:

The first question: 1 1X- 10

Question 2: M-m/2-m/2/3= 1/3M yuan.

As shown below, what is the fifth number in line 100?

1

2 3

4 5 6

7 8 9 10

1 1 12 13 14 15

16 17 ........

The answer is 4955.

From the outermost layer on the left of the graph,1247116, the number after it is always greater than the number before it.

The second ratio is 1 large 1 ... The third is 2 ... The fourth is 3 ... The fifth is 4 ... The sixth is 5. .......... is greater than the fifth, so we can set the nth number of the outermost layer on the left as x, Then x equals [1 plus 2 plus 3 plus < 100. The number of 1 is [1 plus 2 plus 3 plus ... plus < 100- 1 >], which is equal to 495/kloc.

So the fifth number in line 100 is 4955.

1. Calculate the value of1+3+5+7+…+1997+1999.

2. If the value of 2x+|4-5x|+| 1-3x|+4 is a constant, find the conditions that X should meet and the value of this constant.

Third, it is known that

1 2 3

- + - + - = 0 ①

x y z

1 6 5

- - - - - =0 ②

x y z

x y z

Try to find the value of-+-+-.

y z x

Fourth, arbitrarily add a "+"or "-"before each number in 1, 2, 3, …, 1998, so is the final result odd or even?

5. A school held a math contest in the first grade, and the number of participants was three times that of those who did not. If the number of students who do not participate is reduced by 6, then the ratio of the number of students who participate to the number of students who do not participate is

2. 1 Ask for the knowledge of participants and non-participants, and the number of junior one students.

Answer: A question:

Original formula = (1+1999) * [(1999-1)/2+

=2000* 1000 /2

= 1000000

Two questions:

If the value of 2x+|4-5x|+| 1-3x|+4 is constant, then

4-5X≥0， 1-3X≤0

So: 1/3≤X≤4/5.

Original formula =2X+4-5X+3X- 1+4=7.

Three questions:

Substitution: 1/X=6/Y+5/Z changed from ② to ①.

8/Y+8/Z=0

Therefore, if Y=-Z is substituted into 1/X=6/Y+5/Z, we get:

1/X= 1/Y

So: X=Y

X/Y+Y/Z+Z/X = 1- 1- 1 =- 1

Four questions:

In 1, 2, 3, …, 1998, * * has 999 odd numbers and 999 even numbers.

No matter the addition or subtraction between two even numbers, the result is even, so only the relationship between odd numbers is considered.

Because the result of addition and subtraction between any two odd numbers is even,

So, in the final analysis, it's all addition and subtraction between odd and even numbers.

So, the final result is very strange.

Five questions:

Suppose the number of people who didn't participate in the competition is X, then the number of people who participated in the competition is 3X, and the total number of students in the whole school is 4X.

If the grade is reduced by 6 students, the total number is 4X-6.

If the number of non-participants increases by 6, the number of non-participants is X+6.

The number of participants is 4X-6-(X+6)=3X- 12.

The ratio of participants to non-participants is 2: 1.

So: 3X- 12=2*(X+6)

Solution: X=24 (people), the number of participants 3X=72, and the total number of students in the whole school 4X=96.

Negative one-half one-third

Negative quarter, negative fifth, negative sixth.

One seventh, one eighth, one ninth and one tenth. . . . . .

What is the seventh number in line 2007 in this group?

The line number of 1 is 1.

There are two numbers in the second line.

There are three numbers in the third line.

....

So there are n numbers in row n,

1 to line 2006, total:

1+2+3+...+2006 = 2006 * 2007/2 = 20 1302 1.

20 1302 1+7=20 13028

The score of the seventh line in 2007 is 1/20 13028.

It is also found that the odd positions of each row are negative.

So the seventh line in 2007 is:-1/20 13028.

1. It is known that the equation 2a(x- 1)=(5-a)x+3b about x has countless solutions, so a = _ _ _ _ _ _ _ _ _

A: 2a(x- 1)=(5-a)x+3b。

2ax-2a=5x-ax+3b

3ax-5x=2a+3b

x(3a-5)=2a+3b

Equation 2a(x- 1)=(5-a)x+3b There are many solutions to x.

So no matter what value X takes, it always holds.

So this equation has nothing to do with X.

So 3a-5 = 0, 2a+3b = 0.

a=5/3，b= - 10/9

2. What is the sum of all possible four-digit numbers composed of natural number 1 ~ 9, and there are no duplicate numbers?

A: First of all, let's look at a * * *, and how many four digits there are.

There are nine possibilities in a thousand, eight possibilities in a hundred, seven possibilities in ten, and six possibilities in an individual.

A * * * has 3024 four digits.

Look at a seat first. Because every number has an equal status, so

One ninth, that is, 336 units are 1, 336 units are 2, 336 units are 3, ... 336 units are 9.

All these bits add up to 336× (1+2+...+9 )×1.

Look at ten more. Because every number has an equal status, so

One ninth, that is, 336 bits are 1, 336 bits are 2, 336 bits are 3, ... 336 bits are 9.

All these bits add up to 336× (1+2+...+9 )×10.

Look at hundreds more. As can be seen from the above analysis, the sum of all hundreds is 336× (1+2+...+9 )×100.

Look at thousands more. As can be seen from the above analysis, the sum of all thousands is 336× (1+2+...+9 )×1000.

So the sum of all four digits is:

336×( 1+2+...+9)× 1+336×( 1+2+...+9)× 10+336×( 1+2+...+9)× 100+336×( 1+2+...+9)× 1000

=336×( 1+2+...+9)×( 1+ 10+ 100+ 1000)

=336×45× 1 1 1 1

= 16798320

Number of known columns: 1, 6, 1 1, 16. .......

Q:

What is the number 17?

The sum of the top 20?

Please answer with the formula given.

Question 2:

There is a column number: 2.4.6.8... 192.

Q:

Their sum?

Please decide which position in the series is 48. (Equation can be listed)

3. There is an integer, 70, 1 10 and 160 divided by which the sum of the three remainders is 50, so what is this integer?

4. Let M and N be natural numbers, remember that PM is the sum of all digits of natural number M and PN is the sum of all digits of natural number N. Also remember that M*N is the remainder of m divided by n, given that M+N=4084, what is the value of (PM+PN)*9?

5. As shown in the figure, it is known that CD=5, DE=7, EF= 15 and FG=6. The straight line AB divides the figure into two parts, the area of the left part is 38, and the area of the right part is 65. What is the area of triangle ADG?

6. A natural number can be expressed as the sum of 9 consecutive natural numbers, 10 consecutive natural numbers and 1 1 consecutive natural numbers. What is the minimum natural number that satisfies the above conditions?

7. It is known that the pure alcohol content of alcohol A is 72%, the pure alcohol content of alcohol B is 58%, and the pure alcohol content after mixing the two alcohols is 62%. If the amount of each alcohol is more than the original 15 liter, and the pure alcohol content after mixing is 63.25%, how many liters of methanol will be taken for the first time?

8. In the following formula, different Chinese characters represent different numbers, and the same Chinese characters represent the same numbers. So what are the three digits represented by "Happy New Year"?

9. There are two shopping centers. When the profit of the first mall decreases by 15% and the profit of the second mall increases by 18%, the profits of the two malls are the same. Then, how many times is the profit of the first shopping mall more than that of the second shopping mall?

10, take three from nine numbers 1~9, and these three numbers can form six different three digits. If the sum of six three digits is 3330, what is the largest of these six three digits?

1 1. There are five teams, A, B, C, D and E, and every two teams will play one game. When the game is about to end, the statistics are as follows:

Team name wins, draws, negative numbers, goals scored and goals conceded.

A piece of 2 1 0 4 1

B 1 2 0 4 2

C 1 1 1 2 3

D 1 0 3 5 5

E 0 2 1 1 5

It is known that A and E and B and C are tied, and the scores are all 1: 1. What's the score between b and d?

12, a bus and a van set off from A and B at the same time and walked in opposite directions. The bus speed is 32 kilometers per hour, and the van speed is 40 kilometers per hour. When the two cars reached the second place and the first place respectively, they immediately returned to the starting point. When returning, the bus speed increased by 8 kilometers per hour and the van speed decreased by 5 kilometers per hour. Given that the two encounters are 70 kilometers apart, how many hours before the bus, does the van return to the starting point?

A (1) and B (2) are walking in the escalator of a shopping mall. 1 from the floor of 1 to the second floor, and 2 from the second floor to the floor of 1. 1 Stand on the elevator and go up two steps every second (note: the elevator is also moving). It takes 50 seconds to walk to the second floor.

Take three of the nine numbers 1~9, and these three numbers can form six different three-digit numbers. If the sum of six three digits is 3330, what is the largest of these six three digits?

The question comes first and the answer comes last.

2. Let a, b and c be real numbers, and | a |+a = 0, | ab | = ab, | c |-c = 0, and find the value of the algebraic expression | b |-| a+b |-c-b |+| a-c |.

3. If m < 0, n > 0, | m |

4. Let (3x-1) 7 = A7X7+A6X6+…+A1X+A0, and try to find the value of A0+A2+A4+A6.

5. Known equation

If there is a solution, find the value of k.

6. Solve equation 2 | x+ 1 |+x-3 | = 6.

7. Solving equations

8. Solve the inequality || x+3 |-x- 1 || > 2.

9. Compare the following two figures:

10.x, y and z are nonnegative real numbers and satisfy:

x+3y+2z=3，3x+3y+z=4，

Find the maximum and minimum values of u = 3x-2y+4z.

1 1. Find the quotient and remainder of x4-2x3+x2+2x- 1 divided by x2+x+ 1.

12. As shown in figure 1-88, Zhu Xiao lives in village A and grandma lives in village B. On Sunday, Zhu Xiao went to visit her grandmother. She first cut a bundle of grass on the north slope, and then cut a bundle of firewood on the south slope to send it to her grandmother. Excuse me, which route should Zhu Xiao take for the shortest journey?

13. As shown in figure 1-89, AOB is a straight line, OC and OE are bisectors of ∠AOD and ∠DOB, respectively, and ∠ COD = 55. Find the complementary angle of ∠DOE.

14. As shown in figure 1-90, the bisected line ∠ABC, ∠ CBF = ∠ CFB = 55, ∠ EDF = 70. Verification: BC ∠ AE.

15. As shown in figure 1-9 1. In △ABC, EF⊥AB, CD⊥AB, ∠ CDG = ∠ BEF. Verification: ∠ AGD = ∠ ACB.

16. As shown in figure 1-92. In △ABC, ∠B=∠C, BD⊥AC is in D.

17. As shown in figure 1-93. In △ABC, e is the midpoint of AC, d is on BC, BD∶DC= 1∶2, and AD and BE intersect at F. Find the ratio of the area of △BDF to the area of quadrilateral FDCE.

18. As shown in figure 1-94, two opposite sides of quadrilateral ABCD extend and intersect at K and L, and diagonal AC‖KL and BD extension lines intersect at F. Verification: KF = FL.

19. Can the sum of the number obtained by arbitrarily changing the order of a three-digit number and the original number be 999? Explain why.

20. There is a piece of paper with 8 rows and 8 columns, in which 32 squares are randomly painted black and the remaining 32 squares are painted white. Next, the color grid paper is operated, and each operation changes the color of each square in any horizontal or vertical column at the same time. Can you finally get a grid paper with only one black square?