First, multiple-choice questions (3 points for each small question, ***24 points)
1. Among the following four numbers, the one less than 0 is
(1) -2. (B)0。 (C) 1。 (D)3。
2. The geometry on the right consists of five cubes with the same size. Its front view is as follows.
3. Inequality 2x-6
(A)x & gt； 3.(B)x & lt； 3.(C)x & gt； -3.x & lt-3.
4. The radii of the two circles are 2 and 5 respectively, and the center distance is 7, so the positional relationship between the two circles is
(1) external. (b) external. (c) cross. (d) internal.
5. In a "Love and Mutual Assistance" donation activity, the amount donated by seven students in the first group of a class (unit: yuan) is 6, 3, 6, 5, 5, 6 and 9 respectively. The median and mode of this set of data are respectively
(A)5.5。 Article 6, paragraph 5. (c) Articles 6 and 6. (d) Articles 5 and 6.
6. As shown in the figure, rotate △ ABC 80 counterclockwise around point A to get △ AB ′ C ′. If ∠ BAC = 50,
∠CAB' degree is
(A)30。 Forty years old. (C)50。 (D)80。
7. The position of the rhombic OABC in the plane rectangular coordinate system is shown in the figure. ∠ AOC= 45, OC=, then the coordinates of point B are
(A)(， 1)。 (B)( 1，)。 (C)( + 1， 1)。 (D)( 1，+ 1)。
8? As shown in the figure, the moving point P starts from point A, moves along the AB line to point B, and immediately returns by the original road. The speed of point P is constant during the movement. Then the function image between the area S of a circle with point A as the center and the length of straight line AP as the radius and the movement time T of point P is roughly as follows.
Fill in the blanks (3 points for each small question, *** 18 points)
9. Calculation: 5a-2a=.
10. Put three tickets for Jingyuetan Park and two tickets for Chang Ying Century City in five identical envelopes. Xiao Ming randomly chooses an envelope, and the probability that the envelope just contains the tickets for Jingyuetan Park is.
1 1. As shown in the figure, point C is on ⊙O with AB as the diameter, AB= 10, ∠ A = 30, then the length of BC is.
12. as shown in the figure, l‖m, the vertex b of the rectangular ABCD is on the straight line m, then ∠ α = degrees.
13. Use regular triangles and regular hexagons to spell out the patterns as shown in the figure, that is, starting from the second pattern, each pattern has one regular hexagon and two regular triangles more than the previous pattern, then the number of regular triangles in the nth pattern is (expressed by algebraic expressions containing n).
14. As shown in the figure, the side lengths of the four small squares in the grid paper are all 1, so the sum of the areas of the three small sectors in the shaded part in the figure is (the result is π).
Iii. Answering questions (5 points for each small question, 20 points for * * *)
15. Simplify first, then evaluate:, where x=2.
16. In two opaque boxes, there are only three balls of different colors: red, white and black. Randomly draw a ball from each box. Please draw a tree diagram (or list) and find out the probability that two balls are the same color.
17. As shown in the figure, in the rectangular ABCD, points E and F are on the sides of AD and DC, respectively, △ABE∽△DEF, AB=6, AE=9, DE=2, and find the length of EF.
18. An engineering team undertook the task of repairing roads for 3000 meters. Repaired 600 meters, introduced new equipment, and the work efficiency doubled. It took 30 days to finish the task. How many meters of roads were built on average every day before the introduction of new equipment?
4. Answer questions (6 points for each small question, *** 12 points)
19. Figures ① and ② are 7×6 square grids with three points A, B and C.
(1) Determine the grid point d in Figure ① and draw a quadrilateral with vertices A, B, C and D to make it an axisymmetric figure. (Draw any one) (3 points)
(2) Determine the grid point E in Figure ②, and draw a quadrilateral with vertices A, B, C and E to make it a figure with center symmetry. (Draw any one) (3 points)
20. As shown in the figure, two straight lines AB and CD intersect at point O, and ∠AOC is 36. Command center m is located in OA section, with a distance of 18km. In an operation, police officer Wang led a team to start from it and travel in the direction of OC. Officer Wang and the command center are equipped with walkie-talkies, and the two walkie-talkies can only be outside 10km.
Reference data: sin36 =0.59, cos36 =0.8 1+0, tan36 =0.73.
Verb (abbreviation of verb) solving problems (6 points for each small question, *** 12 points)
2 1. As shown in the figure, the coordinate of point P is (2,), and the parallel lines passing through point P as X axis intersect with Y axis at point A and hyperbola (X >；; 0) at point n; Hyperbolic curve (x >；) intersecting PM⊥AN; 0) at point m, link AM. PN=4 is known.
(1) Find the value of k (3 points)
(2) Find the area of △APM. (3 points)
22. A city adolescent health research center randomly selected 1000 primary school students and several middle school students in this city, investigated their eyesight status, and drew the survey results into the following statistical chart. (Myopia is divided into mild, moderate and high. )
(1) Find the percentage of myopia among this 1000 pupils. (2 points)
(2) Seek the number of middle school students in this spot check. (2 points)
(3) There are 80,000 middle school students and 65,438+10,000 primary school students in this city. Estimate the number of middle school students and primary school students suffering from "moderate myopia" respectively. (2 points)
Six, answer (7 points for each small question, *** 14 points)
23. As shown in the figure, the parabola intersects with the positive semi-axis of the X axis at point A (3,0). Make a square OABC with OA as the edge above the X axis, extend the intersecting parabola of CB at point D, and then make a square BDEF with BD as the edge.
(1) Find the value of a. (2 points)
(2) Find the coordinates of point F (5 points)
24. As shown, in the parallelogram ABCD, ∠ bad = 32. Do △BCE and △DCF with BC and CD as edges respectively, so that BE=BC, DF=DC, ∠EBC=∠CDF, and extend AB intersection EC to point H, and point H is between E and C.
(1) verification: △ Abe △ FDA. (4 points)
② When AE ⊥ AF, find the degree of ∠EBH. (3 points)
Seven, answer (each small 10 points, ***20 points)
25. Class A and Class B of a certain army participated in tree planting activities. Class B planted 30 trees first, and then Class A began to plant trees with Class B. The total number of trees planted in Class A is Y A (trees), and the total number of trees planted in Class B is Y B (trees). The time for two classes to plant trees together (from Class A) is X (hours). Some function images between Y A, Y B and x are shown in the following figure.
(1) When 0≤x≤6, find the functional relationship among Y A, Y B and x respectively. (3 points)
(2) If both Class A and Class B maintain the working efficiency in the first six hours, the calculation shows that when x=8, the sum of the total number of trees planted in Class A and Class B can exceed 260. (3 points)
(3) If, after six hours, Class A maintains the work efficiency of the first six hours, Class B improves the work efficiency by increasing the number of people, and continues to plant trees for two hours, the activity is over. When x=8, there are 20 trees difference between the two classes. How many trees will be planted per hour after the number of class B is increased? (4 points)
26. As shown in the figure, straight lines intersect with X axis and Y axis at points A and B respectively; The straight line intersects with AB at point C, and intersects with the straight line passing through point A and parallel to the Y axis at point D. From point A, point E moves left along the X axis at a speed of 1 unit per second. The point passing through E is the vertical line of the X axis, which intersects with straight lines AB and OD at points P and Q, respectively, and makes a square PQMN to the right with PQ as the edge. Let the area of the overlapping part (shaded part) of square PQMN and △ACD be S.
(1) Find the coordinates of point C. ( 1)
(2) When 0
(3) Find the maximum value of S in (2). (2 points)
(4) when t >; 0, directly write out the value range of t when the point (4,) is in the square PQMN. (3 points)
Reference formula: Quadratic function y=ax2+bx+c The vertex coordinate of the image is ().
09 Changchun senior high school entrance examination mathematics question answer and grading standard
First, multiple-choice questions (3 points for each small question, ***24 points)
1.A 2。 D 3。 B 4。 B 5。 C 6。 A seven. C 8。 A
Fill in the blanks (3 points for each small question, *** 18 points)
9.3a 10。 1 1.5 12.25 13.2n+2 14。
Iii. Answering questions (5 points for each small question, 20 points for * * *)
15. Solution: Original formula =. (3 points)
When x=2, the original formula. (5 points)
16. Solution:
(3 points)
∴P (two balls with the same color are found) =39= 13. (5 points)
17. Solution: ∫△Abe∽△def, ∴ AB: de = AE: df.
That is 6: 2 = 9: DF, ∴DF=3.(3 points)
In right-angle ABCD, ∠ d = 90.
∴ in Rt△DEF, EF= 13. (5 points)
18. solution: before the introduction of new equipment, x meters of roads were built on average every day.
According to the meaning of the question, score. (3 points)
The solution is x=60.
After investigation, x=60 is the solution of the original equation, which accords with the meaning of the question.
A: Before the introduction of new equipment, roads were built 60 meters a day on average. (5 points)
4. Answer questions (6 points for each small question, *** 12 points)
19? Solution: (1) There are the following answers for reference:
(3 points)
(2) There are the following answers for reference:
(6 points)
20? Solution: passing through point M is MH⊥OC at point H.
In Rt△MOH, sin∠MOH=. (3 points)
∫OM = 18，∠MOH=36，
∴mh= 18×sin36 = 18×0.59 = 10.62 & gt； 10.
In other words, police officer Wang Can can't talk to the command center with a walkie-talkie when he is traveling. (6 points)
Verb (abbreviation of verb) solving problems (6 points for each small question, *** 12 points)
2 1. Solution: (1)∵ The coordinate of point P is (2,),
∴AP=2,OA=。
∵PN=4,∴AN=6，
The coordinate of point n is (6,).
Substitute N(6,) into y= to get k=9. (3 points)
(2)∵k=9,∴y=。
When x=2, y=.
∴MP= - =3。
∴S△APM= ×2×3=3。 (6 points)
22. Solution: (1) ∫ (252+104+24) ∫1000 = 38%,
Among these 1000 students, the proportion of myopia is 38%. (2 points)
(2) ∫ (263+260+37) ∫ 56% =1000 (person),
Middle school students 1000 were selected this time. (4 points)
(3)∫8×= 2.08 (ten thousand people),
About 20,800 middle school students in this city suffer from "moderate myopia".
∫ 10×= 1.04 (ten thousand people),
About 10400 pupils in this city suffer from "moderate myopia". (6 points)
Six, answer (7 points for each small question, *** 14 points)
23? Solution: (1) Substitute A (3 3,0) into y=ax2-x- to get a=. (2 points).
(2)∫A(3，0)，
∴OA=3.
∵ Quadrilateral OABC is square,
∴OC=OA=3.
When y=3, that is, x2-2x-9=0.
X 1= 1+，x2 = 1-
∴CD= 1+。
In a square OABC, AB=CB. Similarly, BD=BF.
∴AF=CD= 1+，
The coordinate of point ∴f is (3, 1+). (7 points)
24.( 1) Prove: In parallelogram ABCD, AB=DC.
∫DF = DC，
∴AB=DF.
Similarly, EB=AD.
In parallelogram ABCD, ∠ABC=∠ADC.
And ? ≈EBC =∠CDF,
∴∠ABE=∠ADF，
∴△ABE≌△FDA.(4 points)
(2) Solution: ∫△ABE?△FDA,
∴∠AEB=∠DAF.
∠∠EBH =∠AEB+∠EAB，
∴∠EBH=∠DAF+∠EAB.
∵AE⊥AF,∴∠EAF=90。
∫∠BAD = 32，
∴∠DAF+∠EAB=90 -32 =58，
∴∠ EBH = 58。 (7 points)
Seven, answer (each small 10 points, ***20 points)
25? Solution: (1) Let YA =k 1x and substitute (6, 120) to get k 1=20, ∴ YA =20x.
When x=3, y A =60.
Let y b =k2x+b and substitute (0,30) and (3,60) to get b=30.
3k2+b=60。
The solution is k2= 10,
b=30。
∴y B = 10x+30。 (3 points)
(2) When x=8, y A =8×20= 160,
y B = 8× 10+30 = 1 10。
∫ 160+ 1 10 = 270 & gt； 260,
When x=8, the total number of trees planted in Class A and Class B can exceed 260. (6 points)
(3) After increasing the number of students in Class B, plant a tree every hour on average.
When B compares a variety of 20 trees in Class A, there are 6× 10+30+2a-20×8=20.
The solution is a=45.
When A is compared with 20 trees of Class B, there are 20×8-(6× 10+30+2a)=20.
The solution is a=25.
So Class B will plant an average of 45 or 25 trees per hour after increasing the number of students. (10)
26. Solution: (1) You can get a solution from the meaning of the problem.
∴C(3)。 ( 1)
(2) According to the meaning, AE=t, OE = 8-t. 。
The ordinate of point q is (8-t), and the ordinate of point p is t,
∴PQ= (8-t)- t= 10-2t。
When MN is on AD, 10-2t=t, ∴t=.(3 points)
When 0
When ≤t< <
(3) When 0
When ≤t< <
When t =, the maximum value of s =.
∵& gt； The maximum value of ∴S is. (7 points)
(4)4 & lt； T< or t & gt6.( 10)