Mathematics midterm examination questions in the second volume of the eighth grade 1. Multiple choice questions (this topic is entitled ***8 small questions, with 3 points for each small question and 24 points for * * *). There are four options for each small question, and fill in the code of the correct answer in the corresponding position on the answer sheet).
1. The number of the following beautiful patterns that are both axisymmetric and centrally symmetric is ()
1。
2, the following events, belong to the random event for ()
A. the high tide can lift a ship. B. wait for the rabbit. C. fishing for the moon in water. Winter gave place to spring.
3. The score in,,, and is ()
1。
4. The following approximate view is correct ()
A.B. C. D。
5. Among the known □ABCD,? B=4？ So it's a? D=()
A. 18？ B.36？ C.72？ D. 144？
6. As shown in the figure, P is a moving point on the side AD of the rectangle ABCD, and the lengths of the two sides AB and BC of the rectangle are 3 and 4 respectively.
Then the sum of the distances from point P to the two diagonal lines AC and BD of the rectangle is ()
The CBI is not sure
7. As shown in the figure, the side length of rhombic ABCD is 4, the intersection points A and C are perpendicular to diagonal AC, and the extension lines of CB and AD intersect at E and F respectively, AE=3, so the perimeter of quadrilateral AECF is ().
A.22 b . 18 c . 14d . 1 1
8. As shown in the figure, take a point E outside the square ABCD and connect AE, BE and de. The vertical line crossing point A is regarded as AE crossing point P, if AE=AP= 1, PB=. The following conclusions are drawn: ① △ APD △ AEB; ② The distance from point B to straight AE is: 3eb? ED； ④S△APD+S△APB = 1+； ⑤S squared ABCD=4+.
The serial number of the correct conclusion is ()
A.①③④ B.①②⑤ C.③④⑤ D.①③⑤
2. Fill in the blanks (this big question * * 10 small question, 2 points for each small question, 20 points for * * *)
9. When x=, the value of the score is 0.
10. It is known that the value of algebraic expression is
1 1. There are five cards printed with patterns of circle, isosceles triangle, rectangle, diamond and square respectively (all cards are the same except for different patterns). Now put the patterned side down at will and draw a card randomly from it. The probability of drawing a card with a central symmetrical pattern is _ _ _ _ _ _ _ _.
12. As shown in the figure, diagonal lines AC and BD of rectangular ABCD intersect at points O, CE∨BD, DE∨AC. If AC=4,
Then the perimeter of the quadrilateral code is _ _ _ _ _ _ _.
13. As shown in the figure, in □ABCD, BD is diagonal, and E and F are the midpoint of AD and BD respectively, connecting EF. If EF=3, the length of the CD is.
14. As shown in the figure, in the rectangular ABCD, AB=3, BC=5, and the diagonal intersection O is OE? AC crosses AD at point e, and then
The length of AE is _ _ _ _.
15. If the fractional equation about has no solution, then =.
16. As shown in the figure, in the equilateral triangle ABC, BC=6cm, ray ABC, point E distance.
Starting from point A, it moves along the ray AG at the speed of 1cm/s, starting from point B, and moving along the ray Ag at point F..
Line BC moves at a speed of 2 cm/s. If point E and point F start at the same time, set the moving time.
T(s), when t= s, the quadrilateral with vertices A, C, E and F is a parallelogram.
17. In quadrilateral ABCD, diagonal AC? If BD and AC=6, BD=8, and E and F are the midpoint of AB edge and CD edge respectively, then EF=.
18. in the plane rectangular coordinate system xOy, the squares A 1B 1O, A2B2C2B 1, A3B3C3B2,? , as shown. Point A 1, A2, A3,? It is also divided into B 1, B2, B3,? On the straight line y=kx+b and the x axis respectively. Given C 1( 1,-1) and C2 (,), the coordinate of point A3 is _ _ _ _ _ _ _.
3. Short answer questions (this big topic is ***8 small questions, and the score is ***56. The answer needs to be written with necessary words or calculation steps. )
19. Calculation or simplification: (3 points for each small question, ***6 points)
(1) Calculation: (2)
20. (3 points for this question) Solve the equation:
2 1. (4 points in this question) As shown in the figure, in the rectangular coordinate system, a (0 0,4) and c (3 3,0).
(1)① Draw a line segment AB, whose line segment AC is symmetrical about y;
(2) Rotate the line segment CA clockwise by an angle around the point C to get the corresponding line segment CD, so that the line segment CD can be drawn for the AD∨x axis;
(2) If the straight line y=kx bisects the area of the quadrilateral ABCD in (1), please write the value of the real number k directly.
22. (6 points in this question) The heavy academic burden of students will seriously affect their learning attitude. To this end, the education department of our city conducted a sample survey on the learning attitude of eighth-grade students in some schools (the learning attitude is divided into three grades, A: very interested in learning; Grade b: more interested in learning; Grade C: not interested in learning), and draw the survey results into the statistical charts in Figure ① and Figure ② (incomplete). Please answer the following questions according to the information provided in the chart:
(1) In this sampling survey, * * * students surveyed;
(2) Supplementary picture ①;
(3) Find the degree of the central angle occupied by Grade C in Figure ②;
(4) According to the results of the sampling survey, please estimate how many of the nearly 8,000 eighth-grade students in our city have reached the standard of learning attitude (including Grade A and Grade B).
23. (5 points for this question) As shown in the figure, in □ABCD, AE=CF, and M and N are the midpoint of BE and DF respectively.
Explain that quadrilateral MFNE is a parallelogram.
24. As shown in the figure, in the diamond ABCD, diagonal AC and BD intersect at point O, MN intersects with point O, and intersects with edges AD and BC at points M and N respectively.
(1) Please judge the quantitative relationship between OM and ON and explain the reasons;
(2) When the intersection D is the extension line where DE∑AC intersects BC at E, AB=5 and AC=6, find the perimeter of △BDE.
25. (8 points for this question) Yixing is near Taihu Lake. What are lilies made of? Taihu ginseng? After Lily went on the market this year, supermarket A and supermarket B bought lilies of the same quality at the same purchase price of 12000 yuan. Supermarket A's sales plan is to classify and package lilies, among which 400 kilograms of high-quality lilies are selected and sold at twice the purchase price, and the rest are sold at a price higher than the purchase price 10%. Supermarket B's sales plan is not to classify lilies.
(1) How much is the purchase price of lily per kilogram?
(2) How much profit does Supermarket B make? And compare which sales method is more economical.
26. (9 points for this question) As shown in the figure, the edges OA and OC of the square ABCO are on the coordinate axis, and the coordinates of point B are (6,6). Rotate the square ABCO counterclockwise around point C? (0? & lt？ & lt90? ), the intersection AB of square CDEF and ED is at point g, and the intersection OA of ED is at point h, connecting CH and CG.
(1) Verification: △ CBG △ CDG;
(2) Q? Degree of HCG; And judge the quantitative relationship between line segments HG, OH and BG, and explain the reasons;
(3) Connect BD, DA, AE and EB to get a quadrilateral AEBD. Can quadrilateral AEBD be rectangular during rotation? If yes, request the coordinates of point H; If not, please explain why.
27. (8 points in this question) Figure ① is a rectangular piece of paper, take a little on the edge and a little on the edge, and fold the paper in half along the edge to make it intersect with the points, as shown in Figure ②.
(1) If, find the degree.
(2) Can the area be less than? If there is, then make it clear; If not, try to explain why.
(3) How to fold to maximize the area? Please draw a picture to explore the possible situation and find out the maximum value.
The reference answer to the examination paper of the mathematics midterm in the second volume of the eighth grade 1. Multiple choice questions (3 points for each small question, * * * 24 points).
1.C 2。 B 3。 C 4 explosive D 5。 D 6。 A seven. An eight. D
2. Fill in the blanks (2 points for each blank, ***20 points)
9 . x =- 1； 10.； 1 1.； 12.8; 13.6; 14.3.4; 15. 1 or-2;
16 .2 or 6; 17.5; 18、( , )
Three. Answer (this big question is ***8 small questions, ***56 points. )
19. Calculation or simplification:
( 1) (2)
= 1 min =? 1 point
= =2 ? 2 points =? 2 points
20 solving equations:
Solution: x (x+1)-(x+1) (x-1) = 2? .. 1 point
X= 1 1。
After testing, it is the root of the original equation, and the original equation has no solution? 1 point
2 1.( 1) sketch, per minute1; (2)k=？ 2 points
22, (1)200(2 points)
(2) Correct graphics (1) (omitted)
(3) Degree of central angle occupied by Grade C: 360? 15%=54? ( 1)
(4) The number of people meeting the standards is about 8,000 (25%+60%) = 6,800 (person) (2 points).
23. Prove that the quadrilateral ABCD is a parallelogram? AD=BC，
AE = CF again? AD-AE=BC-CF
That is, DE=BF? 1 point
∵DE∨BF？ Is quadrilateral BEDF a parallelogram? 1 point
? BE=DF 1 point
? M and n are the midpoint of BE and DF, respectively.
? EM=BE/2=DF/2=NF？ 1 point
And em sigma nf
? Quadrilateral MFNE is a parallelogram? 1 point
24. It is proved that (1)∵ quadrilateral ABCD is a diamond.
? AD∨BC，AO=OC，
Certificate △ aom △ con? OM = on? 3 points
(2)∵ quadrilateral ABCD is a diamond,
? AC？ BD，AD=BC=AB=5，？ 1 point
? BO= =4，？ BD = 2bo = 8， 1。
∫DE∨AC，AD∨CE，？ A quadrilateral is a parallelogram of 1 point.
? DE=AC=6，
? The circumference of △BDE is: BD+DE+BE = BD+AC+(BC+CE) = 8+6+(5+5) = 241.
25. Solution: (1) Suppose the purchase price of lily is X yuan per kilogram.
According to the meaning of the question: 400 (2x-x)+(-400)? 10%x=8400？ 3 points
Solution: x = 20, 1.
It is verified that x=20 is the solution of fractional equation, which accords with the meaning of the question. 1 point
A: The purchase price of lily is 20 yuan per kilogram;
(2) The quality of lilies purchased by supermarkets A and B =600 (kg). 1 point
[2? 20+20? ( 1+ 10%)]? 2= 1 1 , 1 1? 600=6600, 1 min
∵6600 & lt； 8400,? Supermarket is more cost-effective 1 minute
26. Answer: (1) Proof: ∫ Square ABCO rotates around point C to get square CDEF.
? CD=CB，？ CDG=？ CBG=90？
In CDG and CBG.
? △CDG?△CBG(HL)，？ 2 points
(2) Solution: ∫△CDG?△CBG
DCG=？ BCG, DG=BG
In Rt△CHO and Rt△CHD.
? △CHO?△CHD(HL)OCH =？ Ohio DCH = DH 1.
? 1 point
HG=HD+DG=HO+BG 1。
(3) Solution: The quadrilateral AEBD can be rectangular.
As shown in the figure,
Connecting BD, DA, AE, EB
∵ Quadrilateral DAEB is a rectangle? AG=EG=BG=DG
AB = 6？ AG=BG=3 1 point
Let the coordinate of H point be (x, 0), then HO = X.
∵OH=DH，BG=DG？ HD=x，DG=3
At Rt△HGA.
∵HG=x+3,GA=3,HA=6﹣x
? (x+3)2=32+(6﹣x)2？ 2 points
? x=2
? The coordinate of point H is (2,0). 1 point
27. Solution: (1)∵ The quadrilateral ABCD is a rectangle. AM∨DN，KNM=？ 1,
∵? KMN=？ 1，KNM=？ KMN？ 1 point
∵? 1=70? ,
KNM=？ KMN=70？ ，MKN=40？ ; ? 1 point
(2) no,
The reasons are as follows: m point AE? DN, the vertical foot is point e,
Then ME=AD= 1, which is known from (1). KNM=？ KMN？ MK=NK，
∵ MK again Me, me =AD= 1,? MK？ 1,? 1 point
∫S△MNK =, that is, the minimum value of △MNK area is, which cannot be less than; 1 point
(3) There are two situations:
Case 1: Fold the rectangular piece of paper in half, so that point B and point D coincide, and then point K and point D coincide.
Let NK=MK=MD=x, then AM=5-x,
According to Pythagorean Theorem, 12+(5-x)2=x2,? 1 point
X=2.6 is obtained by solving.
Then MD=NK=2.6, S △ MNK = S △ MND =; ? 1 point
Case 2: Fold the rectangular paper diagonally in half, and the crease is AC.
Let MK=AK=CK=x, then DK=5-x,
Similarly, MK=AK=CK=2.6,
S△MNK=S△ACK=， 1。