Zhejiang education publishing house, eighth grade, volume 2, mathematics final exam 1. Multiple-choice questions (this big question * * consists of 6 small questions, each with 3 points, * * 18 points).
1. The following questions are not suitable for comprehensive investigation (▲)
A. Understand the weekly physical exercise time of the whole Class B. Security check before boarding.
C. the school recruits teachers and interviews candidates. D. understand the daily pocket money of urban primary and secondary school students.
2. The following equation is ()
A.- B.- =-0.6 C. =- 13 D. =？ six
3. The following statement is incorrect ()
A. know about new corn varieties? Agricultural University 108? The output of is suitable for sampling survey.
B. I know that the hobbies of the students in Class Two, Grade Eight in our school are suitable for the general survey.
C. tomorrow's weather must be sunny or random.
D. In order to know the scores of 20,000 students in a city, 500 students were randomly selected for statistical analysis, with a sample size of 500 students.
4. For the inverse proportional function, the following statement is incorrect ()
A. the point (-2,2) is on its image B. Its image is in the second and fourth quadrants.
C. when, it decreases with the increase of d, and when, it increases with the increase of.
5. As shown in the figure, in the square ABCD, E is the point on the DC side. Connect BE and rotate △BCE clockwise by 90? Get △DCF, connect EF. What if? BEC=60？ And then what? The degree of EFD is ()
A. 10？ B. 15？ C. 18？ D.20？
6. Held in a city? Donate for a day? For the activity, Party A and Party B each donated 30,000 yuan, you know? Suppose there are x people in unit B, then the equation can be obtained. The missing condition should be supplemented by ()
A. The per capita donation of unit A is more than that of unit B. The number of people in unit B is 20% more than that of unit A..
B. The per capita donation of unit A is more than that of unit B. 20 yuan, and the number of people in unit A is 20% more than that of unit B..
C. The per capita donation of unit B is more than that of unit A by 20 yuan, and the number of people in unit A is 20% more than that of unit B..
The per capita donation of D.B unit is more than that of A unit by 20 yuan, and the number of people in B unit is 20% more than that of A unit.
Fill in the blanks (there are 10 small questions in this big question, with 3 points for each small question and 30 points for * * *).
The simplest common denominator of 7 is.
8. When a=, the simplest quadratic radical is the same quadratic radical.
9. If one root of the equation is 1, then the other root of the equation is.
10. In 2000, 2000, 2000, 2009.
1 1. Xiaoming wants to input a 24,000-word social survey report into the computer. The functional relationship between the time t (minutes) for completing input and the speed v (words/minute) for inputting words can be expressed as follows.
12. If +=0, then+=
13. Suppose the equation about has no solution, and the value of m is.
14. In recent years, a city has increased its investment in education in order to develop education. 20 1 1 invested 30 million yuan and 20 13 invested 36.3 million yuan.
15. As shown in the figure, in △ABC, points D, E and F are on the sides of BC, AB and CA respectively, and DE∨CA and DF∨BA. The following four statements are put forward: ① Quadrilateral AEDF is a parallelogram; 2 if? BAC=90？ , the quadrilateral AEDF is a rectangle; ③ What if AD is divided equally? BAC, then the quadrilateral AEDF is a diamond; 4 if AD? BC and AB=AC, then the quadrilateral AEDF is a square. Among them, there are correct ones.
16. As shown in the figure, point A is a hyperbola (x >；; 0) move a little, pass a as AC? The vertical foot on the Y axis is point C, the middle vertical line of AC intersects the hyperbola at point B, and the X axis at point D. When point A moves from left to right on the hyperbola, Xiao Ming lists four possibilities for the area change of quadrilateral ABCD: ① decreasing gradually; ② From big to small and then from small to big; ③ From small to large and then from large to small; (4) unchanged. What do you think is right? (Fill in serial number)
Third, answer the question (this big question * * has 10 small questions, *** 102 points. Write down the necessary steps when answering)
17. (The full mark of this question is 12) Calculation:
( 1) ; (2) .
18. (The full mark of this question is 8) Solve the following equation:
( 1) ; (2) .
19. (The full mark of this question is 8) There are three red, white and blue balls with the same color in a black box, including four red balls and white balls 10. After mixing the balls evenly every time, take out any ball, write down the color and put it back in the black box. After a lot of repeated touching experiments, it is found that the frequency of touching the red ball is stable at 20%.
(1) Try to find the value of a;
(2) Choose a ball from it, the following events: ① The ball is a red ball; ② The ball is white; This ball is a blue ball. Try to estimate the possibility of these three events, and arrange the three events in the order from small to large (events are represented by serial numbers).
20. (The full mark of this question is 8) As shown in the figure, the coordinates of the three vertices of △ABC are known as A (-6,0), B (-2,3) and C (- 1, 0) respectively.
(1) Please use point B to directly write the coordinates of the symmetry point B 1 relative to the coordinate origin o;
(2) Rotate △ABC 90 counterclockwise around the coordinate origin O? Draw the corresponding
△A？ b？ c？ Figure, write the corresponding point A directly? Coordinates of;
(3) If quadrilateral A? b？ c？ d？ For parallelogram, please write the fourth vertex d directly. The coordinates of.
2 1. (The full mark of this question is10) What is April 23rd? World Book Day? What is the theme of this year's World Reading Day? Reading makes our world richer? A school randomly surveyed some students, so? What's your favorite book category? (Choose only one item) Make a survey on students' extracurricular reading, and draw the following statistical chart after counting the survey results. Please answer the following questions according to the information provided by the statistical chart:
Investigation and statistics of junior middle school students' extracurricular reading
Category frequency
Cartoon painting a 0.45
Shi Wen magazine b 0. 16
Martial arts novels 100 c
Literary masterpiece
(1) In this random survey of students, d= Please complete the statistical table;
(2) If this statistical table is used to draw a fan-shaped statistical chart, the corresponding central angle of the martial arts novel is;
(3) Try to estimate how many of the 1500 students in this school like literary classics best?
22. (full mark of this question 10) The quadratic equation of one variable about X is known.
(1) If the equation has two equal real roots, find the value of a and the root of the equation at this time;
(2) If the equation has two unequal real roots, find the range of a. 。
23. (Full score of this question 10) As shown in the figure, point E and point F are two bisectors of the line segment BD, and the quadrilateral AECF is a diamond.
(1) Try to judge the shape of quadrilateral ABCD and prove it;
(2) If the perimeter of diamond AECF is 20 and BD is 24, try to find the area of quadrilateral ABCD.
24. (Full mark for this question 10) A store bought a batch of clothes, each of which was 50 yuan. If you sell it in 60 yuan, you can sell 800 yuan; If each piece is sold in 5 yuan at a higher price, its sales will be reduced by 65,438+000 pieces. If the store wants to make a profit 12000 yuan by selling these clothes, what should the price of this kind of clothes be? How many pieces of this kind of clothes should the store buy?
25. (The full mark of this question is 12) As shown in the figure, the linear function y=k 1x+b intersects with the X axis at point A, and the inverse proportional function y= intersects with points B and C. If the intersection point C is a CD perpendicular to the X axis, the vertical foot is D. If the abscissa of point C is 2, OA=OD, then △COD.
(1) Find the relationship between inverse proportional function and linear function;
(2) According to the given conditions, please directly write the inequality k 1x+b? Solution set of;
(3) If points p (,) and q (,2) are two points on the function image, and >; , for.
Value range (direct write result).
26. (The full mark of this question is 14)
In Figure 1 to Figure 3, point B is the midpoint of line segment AC and point D is the midpoint of line segment CE. Quadrilateral BCGF and CDHN are both squares. The midpoint of AE is m, and the midpoint of FH is p.
(1) As shown in figure 1, the three points A, C and E are on the same straight line. Fill in the blanks according to the picture:
①△BMF is a triangle;
② The positional relationship between MP and FH is, and the quantitative relationship between MP and FH is;
(2) Rotate CE in Figure 1 clockwise by an acute angle around point C to get Figure 2, and answer the following questions:
① Prove that △BMF is an isosceles triangle;
(2) Is the conclusion of the positional relationship and quantitative relationship between MP and FH still valid in (1)? Prove your conclusion;
(3) The CE in Figure 2 is shortened to the CE in Figure 3. (2) Are the three conclusions in? (You don't need to explain why it is established, you need to explain why it is not.)
Zhejiang education printing plate eighth grade second volume mathematics final examination paper reference answer 1. Multiple-choice questions (this big question ***6 small questions, 3 points for each small question, *** 18 points).
1.d； 2.a； 3.d； 4.c； 5.b； 6.C。
Fill in the blanks (there are 10 small questions in this big question, with 3 points for each small question and 30 points for * * *).
7.； 8.5; 9.2; 10.0.75; 1 1.； 12. 1+ ; 13.-4; 14. 10﹪; 15.3; 16.④.
Three. Answer questions (*** 10 questions, 102 points. The following answers are for reference only. If you have other answers or solutions, please refer to the standard to give extra points. )
17. (The full mark of this question is 12) (1) The original formula =-(4 points) =- (6 points); (2) The original formula = (2 points) = (4 points) = (6 points).
18. (this question is full of 8 points) (1), (2 points) (3 points), test: x-2? 0 is the solution of the original equation (4 points); (2), (2), (4).
19. (This question is full of 8 points) (1)a=4? 20%=20 (3 points); (2)∵, (5 points), (7 points)? The order of possibility from small to large is: 1322 (8 points, no points will be deducted for writing correct conclusions directly).
20. (This question is full of 8 points) (1)B 1(2, -3)(2 points); (2) sketch (4 points), a? ((0, -6)(6 points); (3)(3, -5).
2 1. (the full mark of this question is 10) (1)400(2 points), 56(4 points), and the supplementary picture (slightly 6 points); (2) Right angle (or fill in 90? ) (8 points); (3) Do you like literary classics 1500? 0. 14=2 10 (name) (10 score).
22. (The full mark of this question is 10) (1)∵ The quadratic equation with one variable about X has two equal real roots. And (2 points), (3 points), the equation is -4x2-4x- 1=0, and the solution is (6 points); (2)∵ The univariate quadratic equation about x has two unequal real roots. And (8 points), and (10 points).
23. (The full mark of this question is 10) (1) The quadrilateral ABCD is a diamond. Connect the AC intersection BD to point O, and the quadrilateral AECF is a diamond. AC？ BD，AO=OC，EO=OF。 Points e and f are two bisectors of line segment BD. BE=FD，？ BO=OD，AO = OC，？ The quadrilateral ABCD is a parallelogram (4 points), ∫AC? BD，？ The quadrilateral AECF is a diamond (6 points); (2)∵ Quadrilateral AECF is a 20? AE=5，BD = 24，？ EF=8, AO=3, AC=6(8 points), (10 points).
24. (The full mark of this question is 10) Let the sales unit price be X yuan (1), which means: (4) and the solution is (7). When the unit price is 70 yuan, 600 pieces should be entered; When the unit price is 80 yuan, 400 pieces should be entered (9 points), a: (omitted) (10 point).
25. (The full mark of this question is 12) (1) When the area of △COD is 4, the coordinate of C is (2, -4). ,? (2 points); OA = OD，OD=2，？ AO=2，？ The coordinate of point A is (-2,0). ,? ,? Y=-x-2 (4 points); (2) Do you want to pass point B? If the X axis is at point E, AE=BE and AE=m, then B(-2-m, m) and m(2+m)=8, then the solution is m=2, so B (-4,2). Or,? , ,? The coordinates of point B are (-4,2) (6 points). Observing the image, we can see the inequality k 1x+b? Solution set of is -4? X<0 or X? 2(8 points); (3)y 1 & gt； 2 or y 1
26. (The full mark of this question is 14) (1)① isosceles right angle; ②MP？ FH, MP = FH(3 points)
(2)①∫B, D and M are the midpoint of AC, CE and AE respectively. MB∨CD, and MB=CD=BC = BF, △BMF is an isosceles triangle (5 points);
(2) it still holds. Proof: As shown in the figure, connect MH and MD and let FM and AC meet at Q. From ①, we can know MB∑CD, MB=CD,? Quadrilateral BCDM is a parallelogram (6 points), CBM =? CDM。
Again? FBQ =？ HDC，FBM =？ MDH，
? △ FBM△ MDH (7 points),? FM = MH，
And then what? MFB =？ FMH HMD =？ FMD-？ HMD =
? AQM-？ MFB =？ FBP = 90？ ,? △FMH is an isosceles right triangle (9 points).
P is the midpoint of FH. MP？ FH, MP= FH( 10);