Selected mathematical problems in the first volume of the second day of the second day of the People's Education Edition

2008-2009 school year second semester eighth grade mathematics final examination questions

(The full marks of the four major questions in this volume are 150, and the examination time is 120 minutes. )

1. Multiple choice questions (this big question 10 small question, 4 points for each small question, ***40 points) Under each small question, four answers codenamed A, B, C and D are given, and only one is correct. Please put the code of the correct answer in brackets after the question.

1. In the rectangular coordinate system, the point p (3 3,6) is shifted to the left by 4 unit lengths and then moved down by 8 unit lengths, and the obtained point is located at ().

A, the first quadrant b, the second quadrant c, the third quadrant d and the fourth quadrant

2. In the plane rectangular coordinate system, multiply the abscissa of point A (1, 2) by-1, and the ordinate remains unchanged, so as to get point A? What about point a and point a? The relationship between them is ()

A, about x axis symmetry b, about y axis symmetry

C. with respect to the origin symmetry d, translate point a to the negative direction of the x axis by one unit.

3, the following statement is wrong ()

A. The quadrilateral bisected by two diagonal lines is a parallelogram; B, two quadrangles with equal diagonals are rectangles;

C A rectangle with two diagonal lines perpendicular to each other is a square; Two diamonds with equal diagonal lines are squares.

4. In order to face the 2008 Beijing Olympic Games, Liu Xiang has made great efforts in the training of 1 10 meter hurdles. The coach made a statistical analysis of his 10 training results. To judge whether his performance is stable, the coach needs to know Liu Xiang's 10 score ().

A, mean b, median c, mode d, variance

5. The axis coordinate of point P (3 3,2) is ().

a 、( 3，-2) B 、( 3，2) C 、( 3，-2) D 、( 3，2)

6. A parallelogram with three vertices and three midpoints of a triangle as vertices * * * has: ()

a， 1 b，2 c，3 d，4

7. As shown in the figure, two points on the side of "Yes" are known, and the size of "Yes" is ().

A, B, C, D,

8. As shown in the figure, the area at □ABCD is 12, points E and F are on AC, AE = ef = FC, then the area of △BEF is ().

a、6 B、4 C、3 D、2

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

9. As shown in the figure, the diagonal BD of the rectangle ABCD passes through the coordinate origin, the sides of the rectangle are parallel to the coordinate axis respectively, and the point C is on the image of the inverse proportional function. If the coordinates of point A are (-2, -2), then the value of k is ().

a . 4 B- 4 c . 8d .-8

10, as shown in the figure, in the square ABCD, take points E and F on the AD extension line so that DE=AD and DF=BD, and connect BF and CD, CE and H and G respectively. Draw the following conclusions:

①EC = 2DG； ② ; ③ ; ④ There are 8 isosceles triangles in the picture. The correct one is ()

a、①③b、②④c、①④d、②③

Fill-in-the-blank question: (There are 10 small questions in this big question, with 3 points for each small question and * * 30 points) Please fill in the answer directly on the horizontal line after each small question.

1 1. If the score is zero, the value of x is.

12, known as 1 nm, the diameter of a nanoparticle is 35 nm, which can be expressed as _ _ _ _ _ _ _ _ _ meters by scientific counting method.

13, as shown in the figure, it is known that OA=OB, point C is on OA, point D is on OB, OC=OD, and AD and BC intersect at point E, then congruent triangles in the figure is right.

(question 13) (question 14) (question 17)

14, as shown in the figure. To make it, you need to add a condition, which can be.

15, known and proportional, when,; And then when ...

16, given samples x, 99, 100,10/,the average value of y is 100, and the variance is 2, then x=, y=.

17 as shown in the figure, the image of the sum of functions is known to intersect at point p, then the solution of the binary linear equations is.

18 As shown in the figure, put the right vertex E of the right triangle EFG in the parallelogram ABCD, with vertices F and G on AD and BC respectively, and if, then = _ _ _ _ _ _ _.

19. In the math activity class, Xiaoming made a trapezoidal cardboard. It is measured that the length of a bottom is 7 cm, the height is 12 cm, and the waist circumference is 15 cm and 20 cm respectively. Then the other bottom length of trapezoidal paperboard is.

20, as shown in the figure, square ABCD, point P is a point on the diagonal AC, connecting BP, cross P, PQ, cross CD and Q. If CQ=5, the area of square ABCD is _ _ _ _ _ _ _.

Three. When solving problems (there are 6 small questions in this big question, each small question has a score of 10 and a score of ***60), each small question should give the necessary calculus process or reasoning steps.

2 1, (10) (1) Calculation:.

⑵ Solve the equation

22, (10)

(1) Mathematics comes from life and serves life. Applying geometry knowledge in mathematics can help us solve many practical problems. Li Ming is going to run a supermarket in partnership with his friends. After investigation, he found that there are two large communities, A and B, near his home, and there are two intersecting roads. Li Ming wants to build the supermarket at the same distance from two residential areas and two roads, and draw the following residential areas and roads. You are very clever. Use your math knowledge to help Li Ming on the map. Please draw the location of supermarket P with a ruler (write what is known, what is sought, and do not draw, but leave traces of drawing. )

(2) As shown in the figure, O is the midpoint of diagonal AC of parallelogram ABCD, and the intersection point of a straight line O and AB and CD intersect at point M and point N respectively, while point E and point F are on the straight line MN, and OE=OF.

(1) There are several pairs of congruent triangles * * * in the picture, please write them all down;

(2) Verification: ∠MAE=∠NCF.

23.( 10) Simplified evaluation:, in which.

24.( 10) The results of 20 students in the physics interest group in the experimental operation are as follows:

Score 10987

Number of people (persons)

Q: ① Find the mode and median of the experimental operation scores of these 20 students.

② What is the average score of these 20 students' experimental operations?

(3) According to the number of people, make the score of this operation into a fan-shaped statistical chart as shown in the figure. What is the central angle of sector ①?

25.( 10) As shown in the figure, in the rhombic ABCD, e and f are points on CB and CD respectively, and BE=DF.

(1) verification: AE=AF.

(2) If ∠ b = 60, then point E and point F are the midpoint of BC and CD respectively, which proves that △AEF is an equilateral triangle.

26.( 10) On the eve of New Year's Day, in order to beautify the city and carry out urban greening activities, our city will plant new varieties of saplings. Nursery bases A and B both sell the saplings at the price of each 4 yuan, and all users who buy at least 1000 saplings at one time will get preferential treatment: the preferential policy of place A is to sell each sapling at 7.5 fold of the original price; B's preferential policy is to waive the cost of purchasing 200 saplings, and the rest saplings are sold at 10% off the original price.

(1) stipulates that this kind of sapling can only be purchased at one place in A and B, assuming that x(x≥ 1000, x is an integer) sapling is purchased at one time. If it is purchased in the seedling base of A, the cost is y 1 yuan. Write the functional relationship between y 1 and X. If it is at point B,

(2) If you buy 1 0,400 seedlings in A and B at one time, where will you spend less money? Why?

(3) If you buy a batch of this kind of seedlings in the first nursery base and another batch of this kind of seedlings in the second nursery base in a corresponding preferential way, there are 2,500 seedlings in the two batches. How much does it cost to buy 2500 seedlings at least? At this time, how many seedlings should A and B buy respectively?

Four, answer (this big question 2 small questions, each small question 10 points, ***20 points) in answering each small question, you must give the necessary calculus process or reasoning steps.

27.( 10) In the square ABCD as shown in the figure, e is the midpoint on the side of AD, A is AF⊥BE, the intersection of CD is F, M is the point on the side of AD, and BM = DM+CD.

(1) verification: point f is the midpoint of CD edge;

(2) Verification: ∠ MBC = 2 ∠ Abe.

28.( 10) As shown in the picture, sailing boats and sailing boats are training on Taihu Lake, which is a fixed point on the lake, and the coach boat is waiting. During training, it is required that the two boats are always symmetrical about this point. Take the origin as the point, and establish the coordinate system as shown in the figure. The axis and the positive direction of the axis represent the due east and the due north direction respectively. Suppose that two ships can be approximately regarded as moving on a hyperbola, and the lake is calm. Double sails have beautiful distant shadows. During the training, when the coach ship and two ships happened to be in a straight line, Minlang lamented and found a ship in distress on the lake. At this time, the coach measured that the ship was in the southeast direction, the included angle between the ship and the ship was, and the ship also measured the position of the ship (assuming that the position of the ship will not change, Minlang's elegy can be represented by three points respectively).

(1) When the ship was found, the coordinates of Minlang's elegy position were and;

(2) After finding the ship, Minlang elegy immediately stopped training, set off from three o'clock and went to the rescue along the shortest route. Assuming that the speed of the two ships is equal, ask the coach whether the speed of the ship is faster than that of the coach ship. Please explain the reason.

Reference answer

First, multiple choice questions

1.C 2。 B 3。 B 4。 D 5。 A six. C 7。 An eight. D 9。 D 10。 D

Second, fill in the blanks

1 1, 12, 13, 4 14, the answer is not unique.

15、7 16、98, 102 17、

18,80132cm or14c20,81.

Third, answer questions.

2 1, (1) 1 (2) x = 1, all of which are proved to be rooting, and the original equation has no solution.

22.( 1) Known: intersecting straight lines, points A and B 。

Find: point p, so that the distance from point p to a straight line is equal, pa = Pb.

(2) (1) * * There are 4 pairs: Δ ABC Δ CDA; δAMO?δCNO； δAEO?δCFO；

δAEM?δCFN； (2) It is proved that Δ δAOE?δCOF can get ∠ EAO = ∠ FCO; From ∠ Mao =∠OCN, ∠ Mao =∠NCF can be deduced.

23. Solution:

When, the original formula =.

24. Solution: (1) 1, the mode is 9, and the median is 9.

(2) Average score = =8.75.

⑶ Central angle = (1-25%-40%-20%) × 360 = 54.

25. It is proved that (1) ∵ quadrilateral ABCD is a diamond.

∴AB=AD，，

BE = DF

∴ ≌

∴AE=AF

(2) Connect the AC power supply

AB = BC，

∴ is an equilateral triangle,

E is the midpoint of BC.

∴AE⊥BC，

∴ ,

In the same way; In a similar way

∵

∴

AE = AF

This is an equilateral triangle.

26 、( 1)y 1=0.75×4x=3x，y2 = 0.9×4(x-200)= 3.6x-720；

(2) The cost of purchasing seedlings in nursery base is low.

When x= 1400, y 1=3x=4200, Y2 = 3.6x-720 = 4320. Because Y 1 < Y2, it was purchased from Party A;

(3) Set up a second place to buy a seedling of this kind, and the cost is W yuan, w = 3 (2500-a)+3.6a-720 = 0.6a+6780.

Because 1000≤a≤ 1500, and a is an integer. Because 0.6 > 0, w increases with the increase of a, so when a= 1000, w is the minimum = 7380. Seedlings purchased at A = 2500- 1000.

Answer: At least 7380 yuan. You should buy 65,438+0,500 plants of this kind in A place and 65,438+0,000 plants in B place.

Fourth, answer questions.

27. Prove: (1) AD=AB, ∠ ADC = ∠ Bad = 90 square ABCD.

∴∠ 1+∠2=90

∵AF⊥BE ∴∠3+∠2=90

∴∠ 1=∠3

In △ADF and △BAE

∴△ADF≌△BAE ∴DF=AE

AE = DE = AD AD = AB

∴DF=CF= AB ∴ Point F is the midpoint of the CD edge.

⑵ Connect BF, and extend the extension line of AC AD to N point.

∫ A.D. ∨ B.C. ∴∠4=∠N in the square ABCD.