2) -6 times +3

3)3-4[ 1-3(2-x)] is greater than or equal to 59 (x is less than or equal to -3)

4)6( 1-3 1x) is greater than or equal to 2+51(10-15x) (x is greater than or equal to -2).

5) 7x > 3x-8 of 6-13 (x > -3)

6)4x- 10 & lt； 15x-(8x-2)(x & gt； -4)

7)x-2-2/2-x >； 3x-2(x & gt； 2)

8) x-6 2-x-3 4x-3 is greater than or equal to 0 (x is less than or equal to 4)

9)3 x-2 x- 1

10)2(5-3x)>3(4x+2)

1 1) 1-2 1x >； 2

12)7x-2(x-3)& lt； 16

13)3(2x- 1)& lt； 4(x- 1)

14)2-6(x-5) is greater than or equal to 4(3-2x).

15)7+3x & lt； 5+4 times

16)5-x(x+3)>2 (x- 1)

1 7) x-2 (1in x+2) is less than or equal to 1-3( 1-x).

18)3(x- 1)+2( 1-3x)& lt； five

19) 1x- 1

20) 6 (65438+2x of 0-3) < 2+51(10-15x)

Parentheses are the answer

1、5 \ 7x+2 \ 3 & lt； x+ 12\2 1

2、4(x 2)>2(3x + 5)

3, in order to know the equation about X, y 3x+y = k+1,x+3y=3, if 0.

4. When 2 (a-3): the solution set of x-a.

Two teachers will lead some students to travel abroad. Both travel agencies quoted 100 yuan/person, and both said that they offered discounts: A travel agency offered 30% discount to both teachers and students, and B travel agency offered full-price discount to teachers and 50% discount to students. Which travel agency is cost-effective?

6. When m is what value, the solutions x and y of equation (6x+2y = 2m+14x+3y =11-m) are both positive numbers.

7. What is the value of k? Is the solution of equation 3x-3k=5(x+k)+2 about x positive?

8、3x >2x+ 1

9 、-2x+3 >-3x+ 1

10、3x-2(x+ 1)>0

1 1. It is known that the solution of equation 3k-5x =-9 about x is nonnegative, so find the range of k.

12. The meteorological data of a certain place show that the average temperature at the foot of the mountain is moderate, 22. From the foot of the mountain, the temperature drops moderately by 6 degrees for every increase of 1000 meters. Plant a plant with an average temperature of 18 to 20, and plant the plant at the foot of 1. The set of known inequalities about x is:

3-2X>- 1()。

2. If the solution set of inequality set 2x-a < 1 is-1 < x < 1, then the value of (A+ 1)(B- 1) is equal to.

X-2B>3()。

3. when a > 0 and b > 0, the solution set of inequality group x < a is X.

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?

2 1. If both positive integers p and p+2 are prime numbers greater than 3, then verify: 6 | (p+ 1).

22. Let n be the smallest positive integer satisfying the following conditions, which is a multiple of 75 and has exactly

23. There are several stools and chairs in the room. Each stool has three legs and each chair has four legs. When they are all seated, * * * has 43 legs (including everyone's two legs). How many people are there in the room?

24. Find the integer solution of the indefinite equation 49x-56y+ 14z=35.

25. Eight men and eight women dance in groups.

(1) If there are two substations, male and female;

(2) If men and women stand in two rows, in no particular order, only consider how men and women form a partner.

How many different situations are there?

26. 1, 2, 3, 4, 5, how many numbers are greater than 34 152?

27.A train is 92 meters long and B train is 84 meters long. If they travel in the opposite direction, they will miss each other after 1.5 seconds. If they travel in the same direction, they will miss each other in six seconds. Find the speed of two trains.

28. The two production teams of Party A and Party B grow the same vegetables. Four days later, Team A will finish the rest alone. It will take two more days. If Party A finishes all the tasks by itself three days faster than Party B, how many days does it take to ask Party A to finish it by itself?

29. A ship starts from a port 240 nautical miles apart, and its speed decreases by 65,438+00 nautical miles per hour before reaching its destination 48 nautical miles. The total time it takes after its arrival is equal to the time it takes for the whole voyage when its original speed is reduced by 4 nautical miles per hour, so that we can find out the original speed.

30. Last year, two workshops A and B of a factory planned to complete tax profits of 7.5 million yuan. As a result, workshop A exceeded the plan 15%, workshop B exceeded the plan 10%, and two workshops * * * completed tax profits of 8.45 million yuan. How many million yuan of tax profits did these two workshops complete last year?

3 1. It is known that the sum of the original prices of two commodities is 150 yuan. Due to market changes, the price of the first commodity decreased by 10%, and the price of the second commodity increased by 20%. After the price adjustment, the sum of the unit prices of the first and second commodities decreases by 1%. What are the original unit prices of the first and second commodities respectively?

Xiaohong bought two children's toothbrushes and three toothpastes in the shop last summer vacation, and just used up all the money she had with her. It is known that each toothpaste is more than each toothbrush 1 yuan. This summer, she took the same money to the store and bought the same toothbrush and toothpaste. Because each toothbrush rose to 1.68 yuan this year and the price of each toothpaste rose by 30%, Xiaohong had to buy two toothbrushes and two toothpastes, and she got back 40 cents. How much is each toothpaste?

33. If a shopping mall sells goods with a unit price of 8 yuan per piece 12 yuan, it can sell 400 pieces every day. According to experience, if each piece is sold less 1 yuan, you can sell more than 200 pieces every day. How much should each piece be reduced to get the best benefit?

34. The distance from Town A to Town B is 28 kilometers. Today, A rode his bike at a speed of 0.4km/min, and set out from Town A to Town B. After 25 minutes, B rode his bike to catch up with A at a speed of 0.6km/min. How many minutes does it take to catch up with A?

35. There are three kinds of alloys: the first contains 60% copper and 40% manganese; The second type contains manganese 10% and nickel 90%; The third alloy contains 20% copper, 50% manganese and 30% nickel. Now a new alloy containing 45% nickel is composed of these three alloys, and its weight is 1 kg.

(1) Try to express the weight of the second alloy by the weight of the first alloy in the new alloy;

(2) Find out the weight range of the second alloy in the new alloy;

(3) Find out the weight range of manganese in the new alloy.

Theme of Pythagorean Theorem

Reward score: 0- analysis time: April 2009-1116: 41.

As shown in the figure, in Rt△ABC, ∠ c = 90, AD and BE are the median lines on BC and AC respectively, and AD=8, BE=6, so find AB.

1. It is known that A, B and C are three sides of △ a, B and C respectively, and |a-3|+( 10-2b)? +c？ -8c+ 16=0, try to judge the shape of △ABC.

2. In RT △ ABC, ∠ C = 90, D and E are the midpoint of BC and AC respectively, and AD=5, BE=2 radical 10. Find the length of AB.

-√ 1 2/3 ÷√5/54

√2/3 ÷√ 1/3

√2x squared y squared /5 \\( √- 3 squared xy/m)

√3b √ 3 √ b/2.65438 squared +0/2 √ 2b/3

1.225

2. The 6th power of110 (that is, the 6th power of10, but it can't reach = =).

3. 12 1/ 144

4.9/36 1

You can use the following method to calculate the square root of a positive number. The calculation method is as follows: choose a positive number at will, and press the following formula to calculate:. Similarly, start from: and deduce: step by step. When the value of n is large, a more accurate approximation can be obtained. According to the above method, design a calculation algorithm to calculate the square root of a positive number.

Use VB language

First, fill in the blanks:

1. A square root of a positive number, represented by the symbol "_ _ _ _ _ _ _", where A is _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _.

2. The number whose square root equals itself is _ _ _ _ _ _ _ _, and the number whose arithmetic square root equals itself is _ _ _ _ _ _ _ _ _.

3. _ _ _ _ _ _ has two square roots, _ _ _ _ has only one square root, and _ _ _ _ _ has no square root.

The arithmetic square root of 4.0.25 is _ _ _ _ _.

The arithmetic square root of 5.9 is _ _ _ _ _, and the arithmetic square root of 5.9 is _ _ _ _ _.

The square root of 6.36 is _ _ _ _ _, and if it is, then x = _ _ _ _ _ _

7. The square root of is _ _ _ _ _ _, the square root of is _ _ _ _ _, and the arithmetic square root of is _ _ _ _ _ _.

The square root of 8.8 1 is the square root of _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _.

9. Then x = _ _ _ _ _ _

10. When a _ _ _ _ _, it makes sense.

Second, judgment and explanation.

1 squared. It is 9; ( )

2. The square root of1is1; ( )

The square root of 3.0 is 0; ( )

4. Irrational numbers are numbers with radical signs; ( )

5. The square root of is; ( )

6. It is the square root of 25; ( )

7. The square root of a positive number is less than its square; ( )

8. Any number except zero has two square roots; ( )

9. The square root of is; ( )

10. No square root; ( )

1 1. Zero is the smallest real number; ( )

12.23 is the arithmetic square root. ()

Third, multiple-choice questions:

1. The following statement is true ().

The arithmetic square root of a is the square root of B.

The arithmetic square root of c is the square root of d.

2. Among the four numbers 0, 2 and 2, the one with a square root is ().

A.0 and B.0, and

C.0 and D.0, 2 and

3. If, then X is ().

65438 AD+0 BC

The square root of 4 is ().

The third century BC.

The arithmetic square root of 5 is ().

BC 16 years

6. If it makes sense, the value range of x is ().

A.x≥0 B.x>0 C.x> D.x≥

7. If the square root of a natural number is (a≥0), then the square root of the next natural number is ().

A.B. C. D。

8. The following statement is true ().

A is the square root of 7. B. The square root of11is

C. if x has an arithmetic square root, then x > 0 d.

9. Calculate the square root, and the following expression is correct ().

A.B.

C.D.

10. The correct one in the following categories is ().

A.B.

C.D.

Find the square roots of the following numbers respectively.

1.36 2.0.008 1 3. 169 4.

5.6.40000 7.8.

5. Find the arithmetic square roots of the following numbers respectively.

1.0.0 169 2.225 3. 100

4.5. 16 6.25

6. When x is, which of the following is meaningful?

1.2.3.4.

5.6.7.8 .

9. 10.

1/2x=2/x+3

Diagonal multiplication

4x=x+3

3x=3

x= 1

The fractional equation should be tested.

X= 1 is the solution of the equation.

x/(x+ 1)= 2x/(3x+3)+ 1

Multiply both sides by 3(x+ 1)

3x=2x+(3x+3)

3x=5x+3

2x=-3

x=-3/2

The fractional equation should be tested.

X=-3/2 is the solution of the equation.

2/x- 1=4/x^2- 1

Multiply both sides by (x+ 1)(x- 1)

2(x+ 1)=4

2x+2=4

2x=2

x= 1

The fractional equation should be tested.

After testing, x= 1 makes the denominator 0, which is the increase of roots and is discarded.

So the original equation has no solution.

5/x^2+x - 1/x^2-x=0

Multiply both sides by x(x+ 1)(x- 1).

5(x- 1)-(x+ 1)=0

5x-5-x- 1=0

4x=6

x=3/2

The fractional equation should be tested.

X=3/2 is the solution of the equation.

5x/(3x-4)= 1/(4-3x)-2

Multiply by 3x-4

5x =- 1-2(3x-4)=- 1-6x+8

1 1x=7

x=7/ 1 1

The fractional equation should be tested.

test

X=7/ 1 1 is the solution of the equation.

1/(x+2)+ 1/(x+7)= 1/(x+3)+ 1/(x+6)

Turn fractions into common denominators

(x+7+x+2)/(x+2)(x+7)=(x+6+x+3)/(x+3)(x+6)

(2x+9)/(x^2-9x+ 14)-(2x+9)/(x^2+9x+ 18)=0

(2x+9)[ 1/(x^2-9x+ 14)- 1/(x^2+9x+ 18)]=0

Because x 2-9x+ 14 is not equal to x 2+9x+ 18.

So1/(x2-9x+14)-1/(x2+9x+18) is not equal to 0.

So 2x+9=0.

x=-9/2

The fractional equation should be tested.

test

X=-9/2 is the solution of the equation.

7/(x^2+x)+ 1/(x^2-x)=6/(x^2- 1)

Multiply both sides by x(x+ 1)(x- 1).

7(x- 1)+(x+ 1)=6x

8x-6=6x

2x=6

x=3

The fractional equation should be tested.

X=3 is the solution of the equation.

Simplify the assessment. [x-1-(8/x+1)]/[x+3/x+1] where X=3- radical number 2.

[X- 1-(8/X+ 1)]/[(X+3)/(X+ 1)]

= {[(X- 1)(X+ 1)-8]/(X+ 1)}/[(X+3)/(X+ 1)]

=(X^2-9)/(X+3)

=(X+3)(X-3)/(X+3)

=X-3

=-Root number 2

8/(4x^2- 1)+(2x+3)/( 1-2x)= 1

8/(4x^2- 1)-(2x+3)/(2x- 1)= 1

8/(4x^2- 1)-(2x+3)(2x+ 1)/(2x- 1)(2x+ 1)= 1

[8-(2x+3)(2x+ 1)]/(4x^2- 1)= 1

8-(4x^2+8x+3)=(4x^2- 1)

8x^2+8x-6=0

4x^2+4x-3=0

(2x+3)(2x- 1)=0

x 1=-3/2

x2= 1/2

Substitution test, x= 1/2 makes denominator 1-2x and 4x 2- 1 = 0. refuse

So the original equation solution: x=-3/2.

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

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

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

1/(x+2)+ 1/(x+7)= 1/(x+3)+ 1/(x+6)

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

(x+3-(x+2))/(x+2)(x+3)=(x+7-(x+6))/(x+6)(x+7)

1/(x+2)(x+3)= 1/(x+6)(x+7)

(x+2)(x+3)=(x+6)(x+7)

x^2+5x+6=x^2+ 13x+42

8x=-36

x=-9/2

X=-9/2 is the root of the equation.

(2-x)/(x-3)+ 1/(3-x)= 1

(2-x)/(x-3)- 1/(x-3)= 1

(2-x- 1)/(x-3)= 1

1-x=x-3

x=2

The fractional equation should be tested.

X=2 is the root of the equation.

Topic: Two fixed points on AB and AC on the side of △ABC, find a point M on BC to make the circumference of △MEF shortest.

Triangle ABC and AEC are equilateral triangles. Verify DC=BE

Problem supplement: The straight line CD and BE intersect at point O, connecting DB, BC and EC. DB is one side of the equilateral triangle ABD and CE is one side of the equilateral triangle ACE. Verify that CD equals BE.

In △ABC, AB=AC, E is a point on the reverse extension line of AC, and AF=AE is intercepted on AB. What is the positional relationship between EF and BC? Give reasons

A two-digit number, the unit number is A, and the ten-digit number is 3 larger than the unit number, so this two-digit number is ().

The number on Xiao Ming's shirt is 8 1, so this number is in the mirror.

Mid-term examination paper of mathematics in the eighth grade last semester

(Examination time: 120 minutes) Volume: Yi Zhu, New China.

Fill in the blanks (1 ~ 10 is 1,1~14 is 2, * * 28).

1, (1) in □ABCD, ∠A=44, then ∠B=, ∠C=.

(2) If the circumference of □ABCD is 40cm and AB:BC=2:3, then CD=, AD=.

2. If the side length of the cube is expanded by 2 times, the volume will also be expanded by 2 times.

Enlarge the volume of a ball by 27 times, and the radius will be enlarged by 10 times.

3. The side length of a square with diagonal length of 2 is: Its area is.

4. Simplification: (1) (2), (3) = _ _ _.

5. Estimation: (1)∽_ (error is less than 1), (2)∽_ (accurate to 0. 1).

The square roots of 6 and 5 are, the square root of 0 is, and the cube root of -8 is.

7. As shown in figure 1, 64 and 400 are square areas respectively, then the square area represented by the letters in the figure is.

8. As shown in Figure 2, the length of the unknown side of the right triangle =.

9. As we all know, a triangle with three sides is a triangle.

10, the minute hand on the clock rotates around the axis. /kloc-After 0/5 minutes, the minute hand angle is.

1 1, as shown in Figure 3, right-angled trapezoid, ∠ b = 90, AD ‖ BC, AB = BC = 8, CD = 10, then the area of the trapezoid is.

12. As shown in Figure 4, given that AC = AD and ∠ B = 72 in ABCD, ∠ AC=AD = _ _ _ _ _ _ _

13. In Figure 5, how did Figure A become Figure B: _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _.

14. You can spell _ _ _ _ _ _ _ kinds of parallelograms with two identical trigonometric rulers (the one with an angle of 30).

Second, multiple-choice questions (15 ~ 25 questions, 2 points for each question, ***22 points)

15, which of the following movements belongs to rotation is ()

A. Basketball in the process of rolling B. Pendulum swing of clocks and watches

C. the movement of the balloon in the air D. the process of folding a figure in half along a straight line

16, as shown in Figure 6, is a rectangular concrete playground in our school. If a student wants to walk from Angle A to Angle C, he should at least walk ().

140

17, the following statement is true ()

A. rational numbers are only finite decimals. Irrational numbers are infinite decimals

C. infinite decimals are irrational numbers. D. scores

18. Among the following conditions, the condition that a quadrilateral ABCD cannot be judged as a parallelogram is ().

A.AB‖CD，AB=CD B. AB‖CD，AD‖BC

C.AB=AD，BC=CD D

19, in the following array, the number that is not Pythagoras is ().

A 3、4、5 B 9、 12、 15 C 7、24、25 D 1.5、2、2.5

20. The number one-to-one corresponding to the points on the number axis is ()

A. natural number B. rational number C. irrational number D. real number

2 1. Xiaofeng's mother bought a 29-inch (74 cm) TV set. The following statement is about 29 inches.

The correct one is ()

A. Xiaofeng thinks it refers to the length of the screen; B Xiaofeng's mother thinks it refers to the width of the screen;

C. Xiaofeng's father thinks it refers to the circumference of the screen; D. The salesman thinks it refers to the diagonal length of the screen.

22. Xiaogang intends to measure the depth of a river. He inserted a bamboo pole into the bottom of the water 1.5m from the shore. The bamboo pole is 0.5m higher than the water surface, and the top of the bamboo pole is pulled to the shore. The top of the pole is just flush with the water on the shore, so the depth of the river is ().

A.2m； B. 2.5mC. 2.25mD. 3m。

23, diagonal vertical and equal quadrilateral must be ().

A, square b, rectangle c, diamond d, whose shapes cannot be determined.

24, the following statement is incorrect ()

The square root of A. 1 is1B. The cube root of–1is-1.

C is the square root of 2. D.–3 is the square root.

25, the length of the two diagonal lines and one side of the parallelogram can be taken in turn ().

A.B. 6，4，3 C. 6，4，6 D. 3，4，5

III. Answers (26 ~ 33 questions ***50 points)

26.(4 points) Fill in the following figures in the corresponding set (only fill in the serial number).

( 1)3. 14(2)- (3)- (4) (5)0

(6) 1.2 122 1222 1… (7) (8)0. 15

Irrational number set {…};

Rational number set {…}

27. Simplification (3 points for each small question *** 12 points)

( 1).(2).

(3).(4).

28, painting questions (6 points)

As shown in the figure, the side length of each small square in the square grid is 1, and some line segments can be obtained by arbitrarily connecting the vertices of these small squares. Please draw such a line segment in the picture.

29.(5 points) Use 250 square floor tiles of the same size to pave a living room of 40 square meters. What is the side length of each square floor tile?

30.(5 points) When a fire broke out in a high-rise residential building, the fire truck immediately rushed to the place 9 meters away from the building (from the back of the building to the wall of the building) and lifted the ladder to the fire window, as shown in the figure. It is known that the length of the ladder is15m, and the bottom of the ladder is 2m from the ground. How high is the window of the household where the fire broke out?

3 1, (6 points) Xiaozhen came up with a method to measure the width AB of the pond: first, draw two straight lines AC and BC from both ends A and B of the pond to intersect at point C, then take two points E and G from BC to make BE = CG, and then pass E and G as EF‖GH‖AB, and AC intersects at F and H to measure EF. Why?

32.(5 points) Given the quadrilateral ABCD, choose any combination of three conditions from the following conditions to make the quadrilateral ABCD rectangular, and write all the situations: (only fill in the serial number)

( 1)AB‖CD(2)BC‖AD(3)AB = CD(4)∩A =∩C(5)∩B =∩D

(6)≈A = 90(7)AC = BD(8)≈B = 90(9)OA = OC( 10)OB = OD

Please write five groups,,,,.

33.(7 points) Xiaodong thinks that it is the same after learning, so he thinks that a simplified process: = is correct.

(3 points) Do you think his simplification is correct? If not, please write the correct simplification process.