20 1 1 Mathematical simulation test questions for the senior high school entrance examination?

In 2009, the mathematics entrance examination simulated examination questions seven.

Instructions for candidates:

1, the test paper is divided into two parts: the test paper and the answer sheet. Full score 120, test time 120 minutes.

2. Before answering the questions, you must fill in the class, name, student number, examination room number and seat number on the answer sheet.

3. All answers must be made in the position marked on the answer sheet, and attention must be paid to the serial number of the test questions and the serial number of the answers.

Just hand in the answer sheet after the exam.

Please use a pencil to black out the brackets or boxes corresponding to the admission ticket number and subject name on the answer sheet, and then begin to answer the questions.

Choose one carefully first (this question 10 sub-question, 3 points for each sub-question, * * * 30 points).

The absolute values of 1 and -3 are ()

A.-3 B.3 C.- 1/3 D. 1/3

2, a city in 2007 the highest temperature is 39℃, the lowest temperature is minus 7℃, then calculate the temperature difference of the city in 2007, the following statement is correct ().

A.(+39)-(-7) B. (+39)+(-7)

C.(+39)+(+7) D. (+39)-(+7)

3. In the rectangular coordinate system, the coordinate of the point m (1, 2) which is symmetrical about the Y axis is ().

A.( 1，-2) B.(2，- 1)c .( 1，-2)d .( 1，2)

4. The main view of the geometry in the picture on the right is ()

In 2007, the Chinese lunar exploration project "Chang 'e-1" satellite was launched and flew to the moon. It is known that the earth is about 384,000 kilometers away from the surface of the moon, so this distance is expressed as () in scientific memory, and three significant figures are reserved.

a . 3.840× 104km b . 3.84× 104km c . 3.84× 105km d . 3.84× 106km。

6. It is known that the internal angle of an isosceles triangle is 30, so the vertex angle of this isosceles triangle is ().

A.75 b. 120 c.30 d.30 or 120.

7. In the plane rectangular coordinate system, after the straight line y=2x is shifted to the right by one unit length, the analytical formula of the straight line is ().

A.y = 2x+ 1b . y = 2x- 1c . y = 2x+2d . y = 2x-2

8. The result of factorization of x2-4 is ()

A.(X-2)2b .(X+4)(X-4)C .(X-4)2d(X+2)(X-2)

9. As shown in the figure, in ⊙O, the chords AB and CD intersect at point E, and it is known that ∠ ECB = 60.

∠ AED = 65, then the degree of∠∠ ADE is ()

A.40 B. 15 C. 55 D. 65

10. In China's stock market transactions, 7.5% of various fees are charged for each transaction. An investor bought 1000 shares of a Shanghai stock at the price of10 yuan per share, and sold them all when the stock rose to 12 yuan. The actual profit of investors is ().

A.2000 yuan B. 1925 yuan C. 1835 yuan D. 19 10 yuan.

Fill in carefully (6 questions in this question, 4 points for each question, 24 points for * * *).

1 1, the intersection of parabola +3 and coordinate axis has a * * *.

12, p is the golden section point of line segment AB=8cm, then AP= cm.

13, the integer solution of the inequality group is

14. It is known that the unary quadratic equation m2x2+(2m- 1)x+ 1=0 has two unequal real roots, so the range of m is

From 15 and 1 to 10, the probability that their products are greater than 10 is.

16 as shown in the figure on the right, in the right triangle ABC, ∠ C = 90, ∠ A = 30, point 0 is on the hypotenuse AB, and ⊙O with a radius of 2 passes through point B, tangent to the AC side at point D and intersecting with the BC side at point E, then the area of the hidden shadow part surrounded by line segments CD, CE and arc DE is.

Three. Comprehensive answer (8 small questions in this question, ***66 points)

17. (6 points for this question) Find the following values:

(1)+(2) Given, find the value of.

18 (6 points in this small question) takes the O point as the similarity center and reduces the figure with the similarity ratio of 2: 1. Please draw a similar picture of O on the other side.

19, (6 points for this question) There are 15 playing cards on the table. Party A and Party B take turns to take at least one card at a time and at most three cards at a time. Whoever gets the last card wins.

(1) Is this game rule fair to both parties?

(2) Who wins first or who wins later? What's the secret of winning?

(3) What if the above 15 card is replaced by n cards (n is a positive integer not less than 4)?

20. There are only four points on the plane, and these four points have a unique property: the distance between each two points is only two lengths, such as the four vertices A, B, C and D of a square ABCD, and AB=BC=CD=DA and AC=BD. Please draw four other different figures with this unique attribute and mark the equal line segments.

2 1, (8 points in this question) As shown in the figure, a telecommunications company plans to build a cable connecting B and C. The surveyors measured the elevation angles of B and C at the foot of the mountain at 30 and 45 respectively, and the elevation angle of B and C at 60 respectively. It is known that C is 200m higher than A. Find the length of cable BC (the root number is reserved as a result).

22.( 10) In order to promote a certain brand of sportswear, a sporting goods mall made a market survey and got the following data:

Price x (yuan/piece) 50 5 1 52 53

Sales P (pieces) 500 490 480 470

(1) Take X as the abscissa of a point and P as the ordinate, trace the data in the above table to the corresponding point in the rectangular coordinate system, observe the graph obtained by connecting the points, judge the functional relationship between P and X, and find the functional relationship between P and X;

(2) If the purchase price of this kind of sportswear is 40 yuan/piece, try to find the functional relationship between sales profit Y (yuan) and sales price X (yuan/piece) (sales profit = sales revenue-purchase expenditure);

(3) Under the condition of (2), when the selling price is what, can you get the maximum profit?

23.( 10) Cut a fan-shaped BAC as shown in the figure. It forms a central angle with a circular iron plate with a radius of 1.

(1) Find the area of this sector;

(2) If the sector BAC is surrounded by the side of the cone, what is the diameter of the bottom of the cone?

Can you cut a circle from the largest remaining ③ to make the bottom of the cone? Please explain the reason.

24.( 12) Let the parabola intersect with the X axis at two different points A (- 1 0) and B (m, 0), and intersect with the Y axis at point C. And ∠ ACB = 90.

(1) Find the value of m;

(2) Find the analytical formula of parabola and verify whether point D (1, -3) is on parabola;

(3) It is known that the straight line passing through point A intersects with the parabola of another point E. Q: Is there a point P on the X axis, so that the triangle with points P, B and D as its vertices is similar to △AEB? If it exists, request the coordinates of all points p that meet the requirements. If it does not exist, please explain why.

In 2009, the mathematics entrance examination simulated examination questions seven.

answer sheet

First, multiple choice questions

The title is 1 23455 6789 10.

answer

Second, fill in the blanks:

1 1.____________ 12.____________ 13._________________ 14.______________

15.______________ 16._________________

Three. Comprehensive answer (8 small questions in this question, ***66 points)

17. (6 points for this small question)

( 1) +

(2) Known, the value of.

18. (6 points for this small question)

19. (6 points for this small question)

20. (8 points for this short question)

2 1. (8 points for this small question)

22. (This little question is 10)

( 1)

(2)

(3)

23. (This little question is 10)

24. (This little question is 12)

In 2009, the mathematics entrance examination simulated examination questions seven.

Reference answer

First, multiple choice questions

The title is 1 23455 6789 10.

Answer B A D A C D D D C C

Second, fill in the blanks:

1 1._ _ San _ _ 12. 13。 _-2 _, - 1, 0, 1__

14. 15. 16.

Three. Comprehensive answer (8 small questions in this question, ***66 points)

17、( 1) +

= 1-+(- 1) (2 points)

=0 (1 point)

(2) Known, the value of.

Solution: ∫∴x= y( 1 min)

∴ = = (2 points)

18, (6 points in this small question) Write what is known, get 2 points for verification, 1 point for conclusion, and 3 points for figure (omitted).

19. (6 points for this small problem) (1) Unfair (2 points)

(2) Whoever wins first, (1 point)

Because in order to get the last one, A must leave zero matches for B, so in the round before the last step, A can't leave 1 or 2 or 3, otherwise B can take them all and win. If there are four games left, then B can't win them all, so no matter how many games B wins (1 or 2 or 3), A can win all the remaining games. Similarly, if there are eight matches left on the table for B to take, no matter how B takes them, A can leave four matches after this round, and finally A must win. It can be seen from the above analysis that as long as the matching numbers on the table are 4, 8, 12, 16, etc. Party A will be a shoo-in. Therefore, if the original number of matches on the table is 15, A should take three matches. (∫ 15-3 = 12)(2 points)

(3) Whoever wins first wins (1 point)

20. (8 points in this small question) There are these kinds of figures: 1, a diamond with a vertex angle of 60 degrees; 2. Square; 3. A quadrilateral line consisting of a regular triangle and an isosceles triangle with a vertex angle of 150 degrees (the bottom of the isosceles triangle is the side of the regular triangle); 4. An isosceles triangle+an interior point, so that the distance from the point to the three vertices is equal to the base; 5. The inner angle is 72 degrees, and the upper bottom is equal to the isosceles trapezoid of the waist; 6. Regular triangle+heart shape (2 points for each answer and 8 points for all four answers)

2 1. (8 points in this small question) Draw BE and CF perpendicular to AM, and the vertical feet are E and F respectively; Draw BD⊥CF on D.

Then the quadrilateral BEFD is a rectangle. Let BD=x, which is derived from the meaning of the question.

AF=CF=200, EF=BD=x, AE=200- x (2 points).

∵∠CBD=60 ,∴CD=tan60？ BD= x, BE = DF = 200-X...(2 points)

∫= tan∠BAE = tan 30 =，

That is =, ... (2 points)

The solution is x =,

∴ BC = 2x = (m)...(2 points)

22. (This little question is 10)

(1) sketch (2 points)

P is a linear function of x (1 point),

P=- 10x+ 1000 (2 points);