Mathematics examination paper (questionnaire)

Precautions:

1. This volume has ***4 pages. Full marks 150, and the examination time 120 minutes. You can use a calculator during the exam.

2. Before answering questions, candidates must fill in their name, admission ticket number, examination room number and seat number in the position specified in the examination paper.

3。 After selecting the answer to each question in multiple-choice questions, black out the replacement label of the corresponding question on the answer sheet with 2B pencil. If you need to change it, clean it with an eraser, and then choose to apply other answer labels. You can't answer on the test paper. Non-multiple choice questions must be written on the answer sheet with a 0.5 mm black pen, with neat font and clear handwriting.

4. Non-multiple choice questions must be answered in the answer area of each question on the answer sheet in the order of the question number. Answers written outside the answer area or written in other question answer areas are invalid. In the draft paper, this paper is invalid;

5. You can draw with 2B pencil first. After confirmation, it must be blacked out with a 0.5mm black pen.

6. After the exam, return this paper together with the answer sheet.

First, multiple-choice questions (this big question * * l0 small questions, 4 points for each small question. * * * 40 points) Only one option per question meets the requirements of the topic.

1. Is an irrational number.

A. come on c . 3. 14D。

2. as shown in the figure, the real number corresponding to point a and point b on the number axis is a.b.

A.B. C. D。

3. The following operation is correct

A.B. C. D。

4. Warehouse A and Warehouse B * * * store 450 tons of grain, 60% of which are shipped from Warehouse A and 40% from Warehouse B. As a result, the remaining grain in Warehouse B is 30 tons more than that in Warehouse A. If Warehouse A initially stores X tons of grain and Warehouse B initially stores Y tons of grain, then there will be.

A.B.

C.D.

5. The resolution function of the image obtained by translating the straight line to the right by L units is

A.B. C. D。

6. The bar chart on the right describes the number of parts processed in a workshop on the heating day, so the average, median and mode of the number of parts processed on the heating day are respectively

A.6.4， 10，B.6，6，6

7. Lulu cuts out a circle and a fan-shaped piece of paper (as shown in the picture), which can just form a cone model. If the radius of the circle is 1 and the central angle of the sector is equal to 120, the radius of the sector is

A.3d.6 BC

8. If one root of the quadratic equation of X is 0, then the value of the real number A is

A.b.0 c. 1 d. or1

9. As shown in the figure, in trapezoidal ABCD, ad∨BC, AB=CD, AC⊥BD is at point O, and ∠ BAC = 60. If BC=, the area of this trapezoid is

The second century ad.

10. As shown in the figure, the side length of equilateral triangle ABC is 3, point P is a point on the side of BC, BP= 1, and point D is a point on the side of AC. If APD = 60, the length of CD is

A. BC 1

Second, fill in the blanks (this big question is ***5 small questions, each small question is 4 points, ***20 points) and fill in the answers directly in the answer position of the answer sheet.

1 1. If the algebraic expression is meaningful in the real number range, then the value range of x is _ _ _ _ _.

12. As shown in the figure, AD and BC intersect at point O, AB∨CD, if ∠ B = 30 and ∠ D = 60, then ∠ BOD = _ _ _ _ _ _ _

13. The coordinates of one intersection of the image of the direct proportional function and the image of the inverse proportional function are (), and the coordinates of the other intersection are _ _ _ _ _ _ _ _.

14. In order to know the monthly average number of plastic bags used by 100 households in a residential area, the monthly number of plastic bags used by 10 households was randomly investigated, and the results are as follows (unit: only).

65 70 85 74 86 78 74 92 82 94

According to this statistical situation, it is estimated that the average monthly usage of plastic bags in this 100 household in this community is _ _ _ _ _.

15. The operation is as follows:

It is also stipulated that the program runs to "whether the result is greater than 65" as one operation, and stops the operation after four times. Then the number of integers X that can be entered is _ _ _ _ _ _ _ _ _

Third, the answer (big questions I-V, ***9 small questions, ***90 points) should be written in the corresponding position on the answer sheet.

ⅰ. (The full score of this question is 15, the score of 16 is 7, and the score of 17 is 8).

16. Simplify before evaluating:, where.

17. Solve the equation:

Two. (This question is out of 30 points. Question l8 is 8. Question l9 is l2. The 20th question is 10).

18. For example, at △ABC, ∠ ACB = 90, AC=BC, BE⊥CE at point E, and AD⊥CE at point D.

Verification: △ BEC △ CDA

19. A shopping mall sells a table lamp at the purchase price of 20 yuan/set. After investigation, it is found that the daily sales volume W (Tai) of desk lamps is in line with the sales unit price X (RMB).

Suppose the profit of selling this kind of desk lamp every day is Y (yuan).

(1) Find the functional relationship between y and x;

(2) When the sales unit price is set at RMB, what is the maximum profit per day? What is the maximum profit?

(3) On the premise that the sales volume is as large as possible, the mall still wants to make a profit every day 150 yuan. How much should the sales unit price be set?

20. As shown in the figure, in ABCD, DAB = 60, AB=2AD, points E and F are the midpoint of AB and CD respectively, point A is AG∨BD, and the extension line of intersection CB is at point G..

(1) verification: the quadrilateral DEBF is a diamond;

(2) Please judge what special quadrilateral AGBD is? And prove it.

Three. (The full mark of this question is 23. The score of 2 1 question is l2, and the score of 22 questions is ll)

2l。 In a bag, there are four identical cards numbered L, 2, 3 and 4 respectively.

(1) Take two cards at random from the bag. Find out the probability that the sum of the card numbers is equal to 4:

(2) Take a card from the bag at random, write down the number of the card as A, then put it back, and then take a card from the bag at random, rank the number of the card as B, and seek the probability of satisfaction.

22. In an extracurricular activity group of a school, at the observation station A, which is 7 meters away from the lake, the elevation angle of a hot air balloon P above the lake is 37, and the depression angle of P' in the lake is 53 (P' is the symmetrical point of P about the lake). Would you please calculate the height PC of this hot air balloon P from the lake?

Note: sin37 ≈, cos37 ≈, tan 37 ≈;

Sin53 ≈，cos53 ≈，tan53 ≈

Ⅳ. (The full mark of this question is 10)

23. Xiao Wang goes from place A to place B and returns immediately after his arrival. The functional relationship between his distance Y (km) from A and the time spent x (hours) is shown in the figure.

(1) How many hours did it take Xiao Wang to return from B to A?

(2) How far is it from A to Xiao Wang after 6 hours' departure?

(3) In the friendship site C between A and B, it took Xiao Wang 2 hours and 20 minutes to pass through the site C on his way back. How far is it between a and c?

ⅴ. (The full mark of this question is 12)

24. As shown in the figure, at △ABC, ∠ B = 90, AB = 6m, BC = 8m, moving point P starts from point A at 2m/s and moves along AC to C, at the same time, moving point Q starts from point C at 1m/s and moves along CB to B ... When one of them reaches the end point.

(1)① When t=2.5 seconds, find the area of △CPQ;

② Find the functional relationship between the area s (square meters) of △CPQ and the time t (seconds);

(2) Write the value of t when △CPQ is an isosceles triangle during the movement of P and Q;

(3) When the circle with P as the center and PA as the radius is tangent to the circle with Q as the center and QC as the radius, find the value of T. ..

20 1 1 Urumqi junior high school graduates' academic level examination

Mathematical answer

First, multiple choice questions

The title is 1 23455 6789 10.

Answer d a c b b c a d b

Second, fill in the blanks

11.12.9013.14.8015.4

Third, answer questions.

16. solution: original formula =, when, original formula =

17.

18. Brief proof

19. Solution: (1)

(2)∵

When x=30, the maximum profit is RMB.

(3) according to the meaning of the question, that is

Solve.

Moreover, the sales volume decreases with the increase of unit price, so when x=25, it can not only ensure a large sales volume, but also obtain a daily profit of 150 yuan.

20.( 1) Proof is abbreviated.

(2) The quadrilateral AGBD is a rectangle. There is a simple reason.

2 1.( 1)(2)P()=

22.25 meters

23. Solution: (1) It took Xiao Wang four hours to return from B to A.

(2) Xiao Wang left for 6 hours, ∫ 6 > It can be seen that Xiao Wang is on his way back now.

Therefore, let the analytical formula of the straight line where DE is located be, which can be obtained from the image:

, solution

The analytical formula of the straight line where ∴DE is located is

When x=6, there is

Xiao Wang is 60 kilometers away from a place and will arrive in 6 hours.

(3) Let the analytical formula of the straight line where AD is located be, which is easy to find.

∴ The analytical formula of the straight line where AD is located is

Let Xiao Wang spend a few hours from C to B, then the distance from C to A is

When I came back, it took () hours from B to C.

At this time, the distance between C and A is

come from

Therefore, the distance between c and a is meters.

24. solution: in Rt△ABC, ab = 6m, BC = 8m, ∴ AC = 10m.

From the meaning of the question: AP=2t, CQ= 10-2t.

(1) PD⊥BC in D after ① P.

∫t = 2.5，AP=2×2.5=5，QC=2.5

∴PD= AB=3,∴S= ×QC×PD=3.75

② Do QE⊥PC at point E after point Q.

∴ Yi Zhi Rt△QEC∽Rt△ABC, QE=

∴S=

(2) When seconds (PC=QC at this time), seconds (PQ=QC at this time), or seconds (PQ = PC at this time) △ CPQ is an isosceles triangle;

(3) If the intersection point P is PF⊥BC at point F, there is △PCF∽△ACB.

∴, namely

∴PF=，FC=

Then in rt delta pfq,

When ⊙P and ⊙Q are circumscribed, PQ=PA+QC=3t. At this time,

Tidy up: solve

Therefore, when ≥P and ≥Q are circumscribed,;

When ⊙P and ⊙Q are inscribed, PQ=PA-QC=t, at this time,

Tidy up: solve

So ⊙P and ⊙Q are inscribed.