1. When the score is meaningful, the letter should satisfy ().

A.B. C. D。

2. If the points (-5, y 1), (-3, y2) and (3, y3) are all on the image with the inverse scaling function y= -3x, then ()

a . y 1 > y2 > y3 b . y2 > y 1 > y3

c . y3 > y 1 > y2 d . y 1 > y3 > y2

As shown in the figure, in a right-angled trapezoid, a point is the midpoint of an edge. If, the area of the trapezoid is ().

A. 25 BC

4. If the image of the function passes through the point (1, -2), then the value of k is ().

A. 2d-2 BC

5. If the area of a rectangle is 6cm2, the functional relationship between its length cm and width cm is roughly represented by an image ().

6. The quadrangle obtained by connecting the midpoints of the sides of the isosceles trapezoid in turn is ()

A. Trapezoidal rhombic rectangular square

7. If the score is 0, the value of x is ().

A.3b.3 or -3c-3d. 0

8. (Hangzhou Senior High School Entrance Examination in 2004) Both parties start from two places at the same time. If they go in opposite directions, they will meet one hour later; If you go in the same direction, then A catches up with B in B hours, then the speed of A is the speed of B ()

A times b times c times d times

9. As shown in the figure, fold a piece of parallelogram paper ABCD in half along BD. Let point C fall at point E and BE and AD intersect at point D, if ∠ DBC = 15, ∠BOD=

130 c . 140d . 160

10. As shown in the figure, the carpet should be laid on the surface of the stairs with a height of 3m and a horizontal distance of 4m. How long is the carpet at least (

a4 b . 5 c . 6d . 7

Second, fill in the blanks

1 1. If there is a point with sides of 7, 24 and 25 in △ABC, and the distances from P to three sides are equal, then the distance is

12. If the function y= is an inverse proportional function, then k=____, and the analytical formula of this function is _ _ _ _ _ _ _.

13. Given -= 5, the value of is

14. Take the heights of six boys from a class, and subtract 165.0cm from each data (unit: cm). The results are as follows:

1.2,0. 1,? 8.3, 1.2, 10.8,? 7.0

The difference between the highest height and the lowest height among the six boys is _ _ _ _ _ _ _ _; The average height of these six boys is about _ _ _ _ _ _ _ (the result is kept to the first place after the decimal point).

15. As shown in the figure, point P is a point on the inverse proportional function, and the PD⊥ axis is at point D, then the area of △POD is

Third, answer questions.

16. Simplify before evaluating:, where x=2.

17. (Ningxia senior high school entrance examination in 2008) Wenchuan earthquake touched the hearts of hundreds of millions of people all over the country. A school launched a donation activity of "Giving Our Love" for the earthquake-stricken areas. Fifty students from Class 8 (1) actively participated in this donation activity. The following table is a statistical table of Xiao Ming's donation to the class:

Donation (RMB) 10 1530

50 60

No.3 6 1 1

13 6

Because two places were accidentally polluted by ink, I can't see clearly, but it is known that the average person in the class donated money to 38 yuan.

(1) According to the above information, please help Xiao Ming to calculate the data of the pollution site and write out the solution process.

(2) What is the model and median of the donation amount of this class?

18. It is known that the side BC of rectangular ABCD is on the X axis, e is the midpoint of diagonal BD, and the coordinates of point B and point D are respectively

Images of b (1, 0), d (3 3,3) and inverse proportional function y = pass through point a,

(1) Write the coordinates of point A and point E;

(2) Find the analytical formula of inverse proportional function;

(3) Judge whether the point E is on the image of the function.

19. It is known that CD is the height on the hypotenuse of,,, (as shown in the figure).

Verification:

Reference answer

1.D 2。 B 3。 A 4。 D 5。 C 6。 B 7。 C 8。 C 9。 C 10。 B

1 1.3

12.- 1 or y=-x- 1 or y=

13. 1

14. 19. 1 cm, 164.3 cm.

15. 1

16.2x- 1，3

17. Solution: (1) The number of people in the polluted area is 1 1.

If the number of donations from polluted places is yuan, then

1 1 + 1460=50×38

Solution =40

Answer: (1) number of people in polluted areas 1 1, and the number of donations in polluted areas is 40 yuan.

(2) The median donation amount is 40 yuan, and most donations amount is 50 yuan.

18. solution: (1) A (1, 3), E (2 2,32)

(2) Let the functional relationship be y = kx.

Substitute x = 1 and y = 3 to get: k = 3× 1 = 3.

∴ y = 3x is an analytical formula.

(3) When x = 2, y = 32.

Point e (2, 32) is on the image of this function.

19. Proof: Left

In a right triangle,

in other words

frontage

Facts have proved that:

People's education printing plate eighth grade second volume mathematics final examination questions 2

1. Fill in the blanks carefully and make a final decision (only one of the four options given in each question is correct, please choose the correct option and fill it on the answer sheet).

The title is123455678911112.

answer

1. As we all know, beehives built by bees are strong and save materials. Do you know the thickness of the hive? In fact, the thickness of the hive is only about 0.000073m, and this data is expressed as () by scientific counting method.

A, B, C, D,

2. If the two diagonals of a quadrilateral are equal, it is called a diagonal quadrilateral. The figure below is not a diagonal quadrilateral ()

A, parallelogram b, rectangle c, square d, isosceles trapezoid

3. The statistics of the maximum temperature in a certain place 10 day are as follows:

Maximum temperature (℃) 22 23 24 25

Days 1 234

The median and mode of this set of data is ()

a、24、25 B、24.5、25 C、25、24 D、23.5、24

4, the following operations, the correct is ()

A, B, C, D,

5. In the following groups, triangles with side lengths of A, B and C are not Rt△ but ().

a、a=2、b=3、c = 4 B、a=5、b= 12、c= 13

c、a=6、b=8、c = 10D、a=3、b=4、c=5

6. The range of a set of data 0,-1, 5, x, 3 and -2 is 8, so the value of x is ().

A, 6 B, 7 C, 6 or -3 D, 7 or -3

7, known point (3,-1) is a point on the hyperbola, then the following points are not on the hyperbola is ().

a、B、C 、(- 1，3) D 、( 3， 1)

8. The following statements are correct: (a) The mode, median and average of a set of data cannot be the same number.

B, the average value of a set of data cannot be equal to any number in this set of data.

The median of a set of data may not be equal to any data in this set of data.

D, mode, median and average describe the fluctuation of a set of data from different angles.

9. As shown in figure (1), it is known that the length of the diagonal of a rectangle is that the midpoints of all sides are connected to form a quadrilateral, so the perimeter of the quadrilateral is () a, b, c, d,

10, the equation about x has no solution, and the value of m is ().

a 、-3 B 、-2 C 、- 1 D、3

1 1. In a square ABCD, diagonal AC=BD= 12cm, and point P is any point on the side of AB, then the sum of the distances from point P to AC and BD is () A, 6cm B, 7cm C, cm D and cm.

12 As shown in Figure (2), the area of rectangular ABCD is 10, and its two diagonal lines intersect at a point, AB and its adjacent side are parallelograms, and AB and its adjacent side are parallelograms, ..., and so on, the area of parallelogram is ().

a、 1 B、2 C、D、

Fill it out carefully, I believe you can fill it out quickly and accurately.

13, if the image of the inverse proportional function decreases with the increase of x in each quadrant, then the value of k can be _ _ _ _ _ (just write a qualified k value).

14. Two classes of Grade One and Grade Two in a middle school took the same math exam. The average score and variance of the two classes are points and points respectively, and the score is _ _ _ _ _ (fill in "Class A" or "Class B").

15. As shown in Figure (3), in □ABCD, e and f are points on the sides of AD and BC respectively. If you add a condition _ _ _ _ _ _ _ _ _ _ _, the quadrilateral EBFD is a parallelogram.

16, as shown in figure (4) is a broken line statistical chart of a group of data. The average of this set of data is, and the range is.

17, as shown in figure (5), there is a right-angled trapezoidal part ABCD, AD∨BC, oblique waist DC= 10cm, D∞= 120, then the length of the other waist AB of this part is _ _ _ _ _ cm.

18, as shown in Figure (6), the quadrilateral is a diamond with a perimeter, and the coordinates of the points are, so the coordinates of the points are.

19. As shown in Figure (7), use two pieces of isosceles right-angled triangular paper with the same size to make a puzzle, and get the following figures: ① parallelogram (excluding rectangle, diamond and square); ② Rectangular (excluding square); ③ Square; ④ equilateral triangle; (5) isosceles right triangle, which must be able to spell the graphics are _ _ _ _ _ _ _ (only fill in the serial number).

20. Any positive integer n can be decomposed into: (s, t is a positive integer, s≤t). If in all these decompositions of n, the absolute value of the difference between the two factors is the smallest, we call it the optimal decomposition and stipulate that. For example, 18 can be decomposed into 1× 18, 2×9 and 3×6, and there it is. Combined with the above information, the following statements are given: ①; ② ; ③ ; (4) If n is a complete square number, then the correct statement is _ _ _ _ _ _ _. (Fill in serial number only)

Third, use your head, and you will be sure to get it right (the answer should be written in words, proof process or derivation steps)

2 1, solving the equation

22. Simplify first and then evaluate, where x=2.

23. Fifty students from Class 8 (1) of a school took part in the 2007 Jining Mathematics Quality Monitoring Examination. The results of the whole class are as follows:

Grade (score) 7174 78 80 82 83 85 86 88 90 9192 94

Number 12354553784332

Please answer the following questions according to the information provided in the table:

(1) What is the mode and median of the students in this class?

(2) Zhang Hua scored 83 points in this class. Can you say that Zhang Hua's grades are above average in the class? Try to explain why.

24. As shown in Figure (8), five small squares with the same size are arranged in the shape of the figure. Now, move one of the small squares, please click.

Graphs meeting the following requirements are drawn in Figure (8- 1), Figure (8-2) and Figure (8-3) respectively. (shadow)

(1) makes the obtained graph become an axisymmetric graph instead of a centrally symmetric graph;

(2) making the obtained figure change from an axisymmetric figure to a centrally symmetric figure;

(3) The obtained graph is both axisymmetrical and centrosymmetric.

25. A youth research institution randomly investigated the amount of winter vacation pocket money (the amount is integer yuan) of 0/00 students in a school, in order to study, analyze and guide students to establish a correct consumption concept. Now, according to the survey data, make a frequency distribution table as shown in the following figure.

(1) Please complete the frequency distribution table and frequency distribution histogram;

(2) The research thinks that students who spend more than 150 yuan should be advised to be frugal and reasonable. How many students in this school 1200 should be advised to spend this advice?

(3) What information can you get from the chart below? (Write at least one)

Median frequency in grouping (meta) groups

0.5~50.5 25.5 0. 1

50.5~ 100.5 75.5 20 0.2

100.5~ 150.5

150.5~200.5 175.5 30 0.3

200.5~250.5 225.5 10 0. 1

250.5~300.5 275.5 5 0.05

Total 100

26. As shown in Figure (9), the image of the linear function and the image of the inverse proportional function intersect at points M and N..

(1) According to the conditions in the figure, the analytical expressions of inverse proportional function and linear function are obtained;

(2) When x is what value, the value of the linear function is greater than that of the inverse proportional function?

27. As shown in figure (10), fold one side AD of the rectangular ABCD in half, so that the point D falls on the point F on the side BC. It is known that AB = 8 cm and BC = 10 cm. Find the length of CE?

28. As shown in the figure (1 1), in the trapezoidal ABCD, AD∨BC, ∠ B = 90, AD=24 cm, BC=26 cm, and the moving point P moves from point A at a speed of 1cm/s along the AD direction. Point P and point Q start from point A and point C respectively, and when one of them reaches the end point, the other point stops moving.

How long did it take (1) quadrilateral PQCD to make a parallelogram?

(2) How long did it take for the quadrilateral PQBA to become a rectangle?

(3) How long did it take for the quadrilateral PQCD to be an isosceles trapezoid?

The answer to the eighth grade math problem

First, multiple-choice questions (3 points × 12=36 points)

The title is123455678911112.

The answer is BAADA, bad, CAD, taxi, bad.

Second, fill in the blanks (3 points ×8=24 points)

13, k > any value 4 (the answer is not unique); 14, _ _ class _ _ _ A 15, the answer is not unique; 16、 46.5 , 3 1 ;

17、cm； 18、 (0,3) ; 19、__①③⑤__; 20、 __①③④__.

Three, use your head, you can do it right (***60 points)

2 1, (6 points) solution: multiply both sides of the equation:

Solution:

Test: Substitution =0

So -2 is the root of the original equation, and the original equation has no solution.

22.(6 points) Solution: Original formula =

Substitute x=2 into the original formula =8.

23.(8 points) (1) mode 88, median 86;

(2) No, the reason is very short.

24.(6 points)

25.(9 points)

(1) omitted

(2) (name)

(3) Omission

26.(8 points) Solution: (1) The inverse analytic function is:

The analytical formula of linear function is:

(2) When the value of OR linear function is greater than the value of inverse proportional function.

27.(8 points) CE=3

28.(9 points) (1)(3 points) Let the quadrilateral PQCD be a parallelogram, that is, PD = CQ, so it is obtained.

(2)(3 points) Suppose that the quadrilateral PQBA is a rectangle, that is, AP = BQ, so.

(3)(3 points) Suppose that the quadrilateral PQCD is an isosceles trapezoid.

People's education printing plate eighth grade second volume mathematics final examination questions 3

First, multiple-choice questions (2 points for each question, ***24 points)

1, in the following categories, the number of scores is ()

、 、 、 、 、 、 、

a，2 B，3 C，4 D，5。

2. If both x and y in are magnified by 5 times, then the value of the score ().

A, expand by 5 times B, keep constant C, shrink by 5 times D, and expand by 4 times.

3. It is known that the coordinate of the intersection of an image with the proportional function y=k 1x(k 1≠0) and the inverse function y= (k2≠0) is (-2,-1), then the coordinate of the other intersection is A. (2,

In a strong typhoon, a big tree broke off and fell 5 meters above the ground, and the fallen part made an angle of 30 with the ground. What is the height of this big tree before it breaks?

A. 10m B. 15m C.25 D.30

5. A set of quadrilaterals with parallel opposite sides and vertical diagonal is ()

A, diamond or rectangle b, square or isosceles trapezoid c, rectangle or isosceles trapezoid d, diamond or right-angled trapezoid

6. Both sides of the fractional equation are multiplied by (x-2) at the same time, and the denominator is removed to get ().

a . 1-( 1-x)= 1 b . 1+( 1-x)= 1 c . 1-( 1-x)= x-2d . 1+( 1-x)= x-2

7. As shown in the figure, if the side length of a small square is 1, the △ABC in the square grid is ().

A, right triangle B, acute triangle C, obtuse triangle D, none of the above answers are correct.

(Question 7) (Question 8) (Question 9)

8. As shown in the figure, in the isosceles trapezoid ABCD, if AB∨DC, AD=BC=8, AB= 10, and CD=6, the area of the trapezoid ABCD is ().

A, B, C, D,

9. As shown in the figure, the images of the linear function and the inverse proportional function intersect at point A and point B, so the value range of x that makes the value of the inverse proportional function smaller than that of the linear function in the figure is ().

A, x 2c,-1 < x < 0, or x > 2d, x

10. In a science and technology knowledge contest, the scores of two groups of students are as follows. Through calculation, we can know that the variance of the two groups is. The following statements: ① The average value of the two groups is the same; ② The scores of students in group A are more stable than those of students in group B; ③ The achievement mode of group A is greater than that of group B; ④ The median score of both groups was 80, but the number of people in group A who scored ≥80 was more than that in group B. From the median point of view, the score of group A was generally better than that of group B; ⑤ There are more people in group B with scores higher than or equal to 90 points than in group A, and group B with high scores is better than group A. The correct * * * is ().

Score 50 60 70 80 90 100

mankind

No. a group 25 10 13 14 6

Group b 4 4 16 2 12 12.

(A)2 species (B)3 species (C)4 species (D)5 species.

1 1. Xiaoming usually goes uphill to school, and the average speed on the way is m km/h. When he comes home from school, the average speed is n km/h, so the average speed on his way to and from school is () km/h.

A, B, C, D,

12, Li Chengbao an orchard and planted 100 cherry trees, which has entered the harvest period this year. At the time of harvest, 10 cherries are selected and picked, and the mass of cherries produced by each tree is weighed as follows:

Serial number 123456789 10

Mass (kg)14212717182019231922

According to the survey, the wholesale price of cherries in the market this year is per kilogram 15 yuan. Using the statistical knowledge learned, it is estimated that the total output of cherries in this orchard and the total income of selling cherries at wholesale price this year are about () respectively.

A.2,000 Jin, 3,000 yuan b. 1.900 Jin, 28,500 yuan

C.2000 kg, 30000 yuan D. 1850 kg, 27750 yuan

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

13, x, the score is meaningless; When is, the value of the score is zero.

14, the simplest common denominator of each fraction is _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

15. Known hyperbola crossing point (-1, 3). If a () and b () are on hyperbola and < < 0, then.

16, trapezoid,,, straight line is the symmetry axis of trapezoid, which is the last point, so it is the minimum.

(question 16) (question 17) (question 19)

17. It is known that any straight line L divides □ABCD into two parts. In order to make the areas of these two parts equal, the position of the straight line L needs to meet the condition of _ _ _ _ _ _ _.

18 As shown in the figure, fold the rectangular ABCD along EF, so that point C falls on point A and point D falls on point G. If ∠ CFE = 60, DE= 1, the side length of BC is.

19 As shown in the figure, in □ABCD, e and f are the midpoint of the sides of AD and BC respectively, and AC intersects with BE and d F at G and H respectively. Try to judge the following conclusions: ① δ Abe δ CDF; ②AG = GH = HC； ③EG =④sδABE = sδAGE, in which the correct conclusion is _ _.

20. Point A is a point on the image of the inverse proportional function, and its distance to the origin is 10, and its distance to the X axis is 8, so the expression of this function may be _ _ _ _ _ _ _ _ _ _ _ _ _.

2 1, called an identity, then a = _ _ _ _ _ _ b = _ _ _ _ _ _

22. As shown in Figure, is an isosceles right triangle, and the point on the function image and the hypotenuse are all on the axis, so the coordinate of the point is _ _ _ _ _ _ _ _ _.

(Question 24)

23. Kobayashi's written math test scores in the first semester of Grade Three are: 84 points in Unit One, 76 points in Unit Two and 92 points in Unit Three; 82 points in the mid-term exam; I got 90 points in the final exam. If the weights of the usual, mid-term and final exams are 65,438+00%, 30% and 60% respectively, Xiaolin's total score in written mathematics this semester should be _ _ _ _ _ _ _ _.

24. There are seven squares on the straight line L in turn (as shown in the figure). It is known that the areas of the three squares placed obliquely are 1, 2 and 3 respectively, and the areas of the four squares placed vertically are S 1, S2, S3 and S4 in turn, so S1+S2+S3+S4 = _ _ _ _.

Iii. Answering questions (***52 points)

25.(5 points) The known real number A satisfies A2+2A-8 = 0.

26.(5 points) Solve the fractional equation:

27.(6 points) Drawing problem: As shown in the figure, in rtδABC, ∠ ACB = 90, ∠ CAB = 30, draw with compasses and straightedge, and divide into two triangles by two methods, and one of them is required to be an isosceles triangle. (traces of drawing are preserved, and writing method and proof are not required)

28.(6 points) As shown in the figure, it is known that the quadrilateral ABCD is a parallelogram, the bisector CF of BCD intersects with F, and the bisector DG of ∠ADC intersects with G.

(1) Verification: AF = GB(2) Please add another condition on the basis of the known condition to make △EFG an isosceles right triangle, and explain the reasons.

29.(6 points) Teacher Zhang conducted 10 test in order to choose one of the two students, Wang Jun and Zhang Cheng, who are particularly outstanding in mathematics in the usual class, and give guidance to these two students. The test scores of two students are recorded in the following table:

1 second, third, fourth, fifth, sixth, seventh, eighth and ninth 10

Wang Jun 68 80 78 79 8 1 77 78 84 83 92

Zhang Cheng 86 80 75 83 85 77 79 80 80 75

Use the data provided in the table to answer the following questions:

Average score median model

Wang Jun 80 79.5

Zhang Cheng 80 80

(1) Fill in the following table:

(2) Teacher Zhang got the variance of Wang Jun 10 test score from the test score record table =33.2. Please ask Mr. Zhang to help calculate the variance of Mr. Zhang Cheng 10 test scores; (3) According to the above information, please use your statistical knowledge to help Mr. Zhang make a choice and briefly explain the reasons.

30.(8 points) To make a product, the material needs to be heated to 60℃ before operation. Let the temperature of the material be y(℃) and the time from heating be x (minutes). It is understood that when the material is heated, the temperature y is linearly related to the time x; When the heating operation is stopped, the temperature y is inversely proportional to the time x (as shown in the figure). It is known that the temperature of the material before operation and processing is 65438 05℃, and the temperature reaches 60℃ after heating for 5 minutes. (1) The functional relations of y and x are obtained when the material is heated and stopped.

(2) According to the technological requirements, when the temperature of the material is lower than 65438 05℃, the operation must be stopped. So how long did it take * * * from the start of heating to the stop of operation?

3 1, (6 points) It takes 16 days for two engineering teams A and B to complete a project together. Now the two teams work together for 9 days. Team A is transferred due to other tasks, and Team B will work for 2 1 day to complete the task. How many days does it take for Team A and Team B to complete the task by themselves?

32.( 10) e is a point on the diagonal BD of eg⊥cd ef⊥bc ABCD square, and the steps are f and g respectively.

Reference answer:

First, multiple choice questions

1、C 2、B 3、A 4、B 5、B 6、D 7、A 8、A 9、D 10、D 1 1、C 12、C

Second, fill in the blanks

13，3 14， 15 ,& lt； 16, 17, diagonal intersection18,319,3.

20, or 2 1, a = 2, b =-2 22, (,0) 23, 88 o'clock 24, 4.

Third, answer questions.

25. Answer: =

= =

∵a2+2a-8=0,∴a2+2a=8

∴ Original formula = =

26. Solution:

Proving is not the solution of the equation.

∴ The original equation has no solution.

27. 1 can be used as the middle vertical line of BC. If AB intersects with point D, the line segment CD divides △ABC into two isosceles triangles.

You can first find the midpoint d of the AB side, and then divide △ABC into two isosceles triangles by the line segment CD.

3 can take B as the center of the circle, BC as the radius, and intersect BA at points BA and D, then △BCD is an isosceles triangle.

28.( 1) Prove that the ∵ quadrilateral ABCD is a parallelogram.

∴AB∥CD,AD∥BC,AD=BC

∴∠AGD=∠CDG,∠DCF=∠BFC

∫DG and CF are divided into∠ ∠ADC and∠ ∠BCD respectively.

∴∠CDG=∠ADG,∠DCF=∠BCF

∴∠ADG=∠AGD,∠BFC=∠BCF

∴AD=AG,BF=BC

∴AF=BG

② ∫ AD ∨ BC ∴ ADC+∠ BCD =180

∫DG and CF are divided into∠ ∠ADC and∠ ∠BCD respectively.

∴∠EDC+∠ECD=90 ∴∠DFC=90 ∴∠FEG=90

So we just need to ensure that the condition of addition makes ef = eg

We can add ∠ gfe = ∠ FGD, quadrilateral ABCD is rectangular, DG = CF and so on.

29,1) 78,80 (2)13 (3) Zhang Cheng was chosen because of his stable grades and high median and mode.

30, (1) (2)20 minutes

3 1. solution: team a and team b need x and y days to complete the task independently respectively.

Solution:

After testing, it is the solution of the equations.

A: It takes 24 days for Team A and 28 days for Team B to complete their tasks independently.

32. proof: connecting CE

∵ quadrilateral ABCD is a square.

∴AB=BC,∠ABD=∠CBD=45，∠c = 90°

∵EF⊥BC,EG⊥CD

∴ quadrilateral GEFC is a rectangle.

∴GF=EC

In △ABE and △CBE.

∴△ABE≌△CBE

∴AE=CE

∴AE=CF