1. Multiple choice questions (3 points for each question, 30 points for * * *)

Of the four options given in each question, only one meets the requirements of the topic.

The reciprocal of 0 1. ().

a、2 B、2 C、D、

02. The solution of equation X- 1 = 1 is ().

a、x=- 1 B、x=0 C、x= 1 D、x=2

03. As shown in the figure, straight lines A and B are cut by straight line C. If a‖b, then ().

A, ∠ 1>∠2 B, ∠ 1=∠2 C, ∠ 1 ",=" or "fill in the blanks.

13. The value range of the independent variable x of the function is _ _ _ _ _ _.

14. Decomposition factor: A3+A2 = _ _ _ _ _ _ _ _ _ _ _ _

15. The height of Liang Xiao is1.6m. At a certain moment, the length of his shadow on the horizontal ground is 2m. If the shadow length of the ancient pagoda nearby on the horizontal ground at the same time is 18m, the height of the ancient pagoda is _ _ _ _ _ _ _ m. 。

16. As shown in the figure, in an 8×8 grid, the vertices of each small square are called grid points, and the vertices of delta △OAB are all on the grid points. Please draw a potential diagram of △OAB in the grid, so that the two diagrams are centered on O, and the potential ratio of the drawn diagram to △OAB is _ _ _ _ _ _ _ _.

17. Xiao Ming wants to enclose a conical paper cap with a fan-shaped paper with a central angle of 120 and a radius of 27cm (as shown in the figure), and the diameter of the bottom surface of the paper cap is _ _ _ _ _ _ _ _ _ _ _ _. (Do not leave any materials, excluding seams).

18. The image of quadratic function y = x2+bx+c passes through points A (- 1 0) and B (3 3,0). Its vertex coordinates are _ _ _ _ _ _ _ _.

19. As shown in the figure, the side length of the square ABCD is cm, the diagonal AC and BD intersect at point O, the crossing o is OD 1 ⊥ AB at D1,and the crossing D 1 is D 1D2⊥BD at D2.

20. Form a triangle with five thin sticks with lengths of 2, 3, 4, 5 and 6 (unit: cm) (connection is allowed, but breaking is not allowed). Among all triangles, the area of the triangle with the largest area _ _ _ _ _ _ _ _ _ cm2.

Three. Answer the question (this big question contains 9 small questions, with ***80 points)

2 1. (The full score of this small question is 7) Solve the inequality group: and indicate that its solution set is on the number axis.

22. (The full score of this small question is 8) Simplify first, then evaluate:, where a =-4.

23. In order to solve the problem of expensive medical treatment for ordinary people, the municipal government decided to reduce the price of some drugs. The original price of a drug is 1.25 yuan/box. After two consecutive price reductions, the price is 80 yuan/box. Assuming that the percentage of price reduction is the same every time, find the percentage of price reduction of this medicine every time.

24. (The full score of this small question is 8) As shown in Figure 1, in the isosceles trapezoid ABCD, AB‖CD, E and F are two points on the side of AB, AE = BF, and de and CF intersect at a point O in the trapezoid ABCD.

(1) verification: OE = of

(2) As shown in Figure ②, when ef = CD, please connect DF and CE to judge what kind of quadrangle DCEF is and prove your conclusion.

25. In order to know the reading situation of junior high school students in a certain area, the education department randomly investigated the number of extracurricular books read by 500 junior high school students in this area in one semester and drew a statistical chart as shown in the figure. Please answer the questions according to the information reflected in the statistical chart.

(1) Among these extracurricular books, which kind of books are read the most?

(2) How many extracurricular books do these 500 students read each semester on average? (accurate to 1 serving)

(3) If there are 20,000 junior high school students in this area, please estimate the total number of extracurricular books they read in one semester.

26. (Full score for this small question is 9) This year's National Day for Helping the Disabled, young volunteers from a certain unit went to a welfare home 6 kilometers away from the unit to participate in a "charity donation activity". Some people walk, others ride bicycles, and they walk along the same route. As shown in the figure, l 1 and l2 respectively indicate that the distance y (km) from pedestrians and cyclists to their destinations changes with time x (minutes).

(1) Find the functional expressions of l 1 and l2 respectively;

(2) How long does it take for cyclists to catch up with pedestrians?

27. (Full score for this small question 10) As shown in the figure, there are two unified turntables that can rotate freely. The turntable A is divided into three sectors with equal area, and the turntable B is divided into four sectors with equal area, and each sector is colored. When two turntables rotate at the same time, if the pointer of one turntable points to red and the pointer of the other turntable points to blue, it is purple. If one of the hands points to the dividing line, the two dials need to be rotated again.

(1) Find the probability that dials A and B turn purple at the same time by listing or drawing a tree diagram;

(2) Xiao Qiang and Xiao Li want to play games with these two turntables. They proposed the following two rules of the game:

(1) Turn two turntables, and when they stop, they turn purple, and Xiao Qiang wins; Otherwise Xiaoli wins;

(2) Turn the two turntables, and when the pointer stops, it points to red, and Xiao Qiang wins; The hands all point to blue, and Xiaoli wins.

Judge the fairness of the above two rules and explain the reasons.

28. In math class, students explore the correctness of the following proposition: an isosceles triangle with a vertex angle of 36 has a property, and it can be divided into two small isosceles triangles by a straight line of its vertex. So please answer the question (1).

(1) It is known that in △ABC, AB = AC, ∠ A = 36, and the straight line BD bisects ∠ABC at point D. It is proved that △ABD and △DBC are isosceles triangles;

(2) After proving this proposition, Xiaoying found that the following two isosceles triangles also have this feature. Please draw a straight line in Figure ② and Figure ③ respectively, divide it into two isosceles triangles, and mark the degrees of the two bottom angles of the isosceles triangle in the figure;

(3) Then Xiaoying found that right triangles and some non-isosceles triangles also have such characteristics. For example, the midline on the hypotenuse of a right triangle can divide them into two small isosceles triangles. Please draw a schematic diagram of two triangles with this feature, and mark the degree of the internal angle of the triangle in the diagram.

Note: the two triangles required to be drawn are not similar, neither isosceles triangle nor right triangle.

29. As shown in the figure, in the plane rectangular coordinate system, the vertex o of □ABCO is at the origin, the coordinate of point A is (-2,0), the coordinate of point B is (0,2), and point C is in the first quadrant.

(1) Write the coordinates of point C directly;

(2) Rotate □ABCO counterclockwise around the O point so that OC falls on the positive semi-axis of the Y axis, as shown in Figure ②, and get □ DEFG (point D coincides with point O). FG intersects AB side and X axis at Q point and P point respectively. Let the area of overlapping parts of two parallelograms before and after rotation be S0, and find the value of S0;

(3) If the □DEFG obtained in (2) is translated along the positive direction of the X axis, let the coordinate of the moving point D be (t, 0) and the area of the overlapping part of □DEFG and □ABCO be S, and write the functional relationship between S and T (0 < t ≤ 2). (Write the results directly).

Reference Answers of Mathematics Examination Questions in Taiyuan City, Shanxi Province in 2007

1. Multiple choice questions (3 points for each question, 30 points for * * *)

Title 01020304 05 06 07 08 0910

Answer A D B C B D D B A C

Fill in the blanks (2 points for each small question, 20 points for * * *)

1 1.9

12.-x, and x > 2 is obtained.

Solve the inequality and get x≤4.

Therefore, the dimension of the solution set of the original inequality group is 2 < x ≤ 4.

Represented on the number axis as

22. Solution: Original formula =

= ?

=

When a =-4, the original formula = 3.

23. solution: let the percentage of price reduction of this drug be x, according to the meaning of the question

125( 1-x)2=80

By solving this equation, we get X 1 = 0.2, X2 = 1.8.

∫x = 1.8 doesn't matter, so leave it out.

∴x=0.2=20%

A: The price of this medicine is reduced by 20% every time.

24. It is proved that (1)∵ trapezoid ABCD is an isosceles trapezoid, AB‖CD.

∴AD=BC,∠A=∠B

AE = BF

∴△ADE≌△BCF

∴∠DEA=∠CFB

∴OE=OF

(2)DC and DC = EF

∴ Quadrilateral DCEF is a parallelogram

△ ade△ BCF is obtained by (1).

∴CF=DE

The quadrangle DCEF is a rectangle.

25. Solution: (1) Among these kinds of extracurricular books, novels are read the most.

(2) (2.0+3.5+6.4+8.4+2.4+5.5) ×100 ÷ 500 = 5.64 ≈ 6 (Ben)

A: These 500 students read an average of 6 extracurricular books each semester.

(3) 20000× 6 = 120000 (copies) or 2× 6 = 12 (ten thousand copies)

A: The total number of extracurricular books they read in a semester is 654.38+0.2 million.

26. Solution: (1) Let the expression of l 1 be y1= k1x.

The intersection of l 1 is known from the image (60, 6)

∴60k 1=6,k 1=

∴y 1= x

Let the expression of l2 be y2 = k2x+B2.

From the image, we know that l2 passes through points (30,0) and (50,6).

Get a solution

∴y2= x-9

(2) When the cyclist catches up with the pedestrian,

Y 1 = y2, that is, X = x= x-9.

∴x=45

45-30 = 15 (minutes)

A: It takes cyclists 15 minutes to catch up with pedestrians.

27. Answer: (1) List all possible outcomes:

A

Red, red, blue and blue.

Red (red, red) (red, red) (red, blue) (red, blue)

Yellow (yellow, red) (yellow, red) (yellow, blue) (yellow, blue)

Blue (blue, red) (blue, red) (blue, blue) (blue, blue)

As can be seen from the list, there are 12 possible situations in which dials A and B rotate at the same time, and four of them can be matched with purple.

P (purple) = =

(2) According to (1), p (unmatched purple) = ≠ p (matched purple)

Rule 1 is unfair.

P (all pointing to red) = =

P (all pointing to blue) = =

Rule (2) is fair.

28. Proof: (1) In △AB=AC, AB=AC.

∴∠ABC=∠C

∠∠A = 36

∴∠ABC=∠C= ( 180 -∠A)=72

∫BD equal division ∠ABC

∴∠ 1=∠2=36

∴∠3=∠ 1+∠A=72

∴∠ 1=∠A,∠3=∠C

∴AD=BD,BD=BC

△ Abd and △BDC are isosceles triangles.

(2) As shown in the figure below:

(3) As shown in the figure below:

29. Solution: (1) c (2,2);

(2)∫A(-2，0)，B(0，2)

∴OA=OB=2

∴∠BAO=∠ABO=45

√□EFGD is formed by the rotation of □ □ABCO.

∴DG=OA=2,∠G=∠BAO=45

* EFGD

∴FG‖DE

∴∠FPA=∠EDA=90

In Rt△POG, op = og? sin45 =

∠∠AQP = 90-∠ Bao =45

∴PQ=AP=OA-OP=2-

S0= (PQ+OB)？ OP= (2- +2)？ =2 - 1

(3)

When □DEFG moves to point F on AB, as shown in Figure ①, t=2 -2-2.

& lt 1 & gt； When 0 < t ≤ 2-2, as shown in Figure ②, S =-t2+t+2- 1.

& lt2> when 2-2 < t ≤, as shown in figure ③, S =-T2+4-3.

& lt3> when < t ≤ 2, as shown in figure ④, S =-t+4-2.

In 2007, Henan experimental area took the senior high school entrance examination in mathematics.

First, multiple-choice questions (3 points for each small question, *** 18 points)

None of the following questions has four answers, only one is correct. Fill in the brackets with the code letters of the correct answer.

1. The result of calculation is ()

A.— 1 B. 1 C

2. Is the value range of X that makes the score meaningful ()

3. As shown in the figure, if △ABC and △ A ′ B ′ C ′ are symmetrical about a straight line, then △ B ′

The degree is ()

A.30o B.50o C.90o D. 100o

4. In order to know the water consumption of residents in a residential area, the monthly water consumption of 10 households is randomly selected, and the results are as follows:

Monthly water consumption (ton) 4 5 6 9

Number of families 3 4 2 1

So in the following statement, the monthly water consumption of this 10 household is incorrect ()

A.the median is 5 tons. B. the model is 5 tons. C. the range is 3 tons. The average is 5.3 tons

5. The top view of the geometry composed of some small cubes with the same size is as shown in the figure, where the numbers in the square represent the number of small cubes in this position, then the left view of this geometry is ().

6. The image of quadratic function may be ()

Fill in the blanks (3 points for each small question, 27 points for * * *)

The reciprocal of 7 is _ _ _ _ _ _ _.

8. Calculation: _ _ _ _ _ _.

9. Write the expression _ _ _ _ _ _ _ _ _ _ of the function of an image passing through the point (1,-1).

10. as shown in the figure, PA and PB are tangent to ⊙O at point a and point b, point c is a point above ⊙O, and ∠ACB = 65o, then ∠ p = _ _ _ _ degrees.

1 1. As shown in the figure, AB‖CD, AD⊥CD,

AB = 1㎝, AD = 2㎝, CD = 4㎝, then BC = _ _ _ _ _ _\\.

12. Given that X is an integer and satisfies, then X = _ _ _ _ _ _ _ _

13. Divide the regular hexagon shown in Figure ① to get Figure ②, then divide the smallest regular hexagon in Figure ② to get Figure ③ in the same way, and then divide the smallest regular hexagon in Figure ③ in the same way …, then there are _ _ _ _ _ _ _ regular hexagons in the nth figure.

14. As shown in the figure, the quadrilateral OABC is a diamond, and points B and C are centered on point O,

If OA = 3, ∠ 1 = ∠2, the area of the sector OEF is _ _ _ _ _.

15. As shown in the figure, point P is a point on the bisector of ∠AOB, and the intersection point P is PC‖OA and OB.

Point C. If ∠ AOB = 60o and OC = 4, then the distance PD from point P to OA is equal to _ _ _ _ _ _ _.

Iii. Answering questions (8 small questions in this big question, ***75 points)

16.(8 points) Solve the equation:

17.(9 points) As shown in the figure, points E, F, G and H are the midpoints of the sides AB, BC, CD and DA of the parallelogram ABCD respectively.

Verification: △ BEF △ DGH

18.(9 points) The following chart is a fan-shaped statistical chart and an incomplete bar-shaped statistical chart based on the number of students in various schools in a province in 2006.

It is known that the number of students in colleges and universities in this province in 2006 was 974 1 10,000. Please answer the following questions according to the information provided in the statistical chart:

(1) What was the total number of students in various schools in this province in 2006? (accurate to 10000 people)

(2) completing the bar graph;

Please write a rationalization proposal.

19.(9 points) Two students, Zhang Bin and Wang Hua, each designed a plan to get tickets to watch the football match:

Zhang Bin: As shown in the figure, a turntable which can rotate freely is designed. When the pointer points to the shaded area, Zhang Bin gets the admission ticket. Otherwise, Wang Hua gets the admission ticket;

Wang Hua: Mark three identical balls with the numbers 1, 2 and 3 respectively, put them in an opaque bag, randomly take out the last ball from it, and then put it back in the bag; After mixing evenly, take out a small ball at will. If the sum of the numbers on the balls taken out twice is even, Wang Hua gets the admission ticket; Otherwise, Zhang Bin got the ticket.

Please use your knowledge of probability to analyze whether the design schemes of Zhang Bin and Wang Hua are fair to both parties.

20.(9 points) As shown in the figure, ABCD is a square with a side length of 1, in which the centers of, and are.

It's a, b and C.

(1) Find the route length from point D to point G along three arcs;

(2) Judge the positional relationship between straight line GB and DF, and explain the reasons.

2 1.( 10) Please draw an isosceles △ABC with BC as the base, so that the height on the base is AD = BC. ..

(1) find the values of tan B and sinB;

(2) In your isosceles △ABC, suppose the base BC = 5m, and find the waist height be.

22.( 10) A shopping mall bought two kinds of goods, A and B, for 360,000 yuan. After the sale, * * * made a profit of 60,000 yuan. The buying price and selling price are as follows:

A b

Purchase price (RMB/piece) 1200 1000

Price (RMB/unit) 1380 1200

(Note: profit = selling price-buying price)

(1) How many A and B products did the mall buy?

(2) For the second time, the mall bought two kinds of goods, A and B, at the original purchase price. The number of pieces in B remains the same, while the number of pieces in A is twice that in the first time. A sells at the original price and B sells at a discount. If these two commodities are sold, the profit of the second business activity should be no less than 865,438+0, 600 yuan. What's the lowest price for b?

23.( 1 1) As shown in the figure, a parabola with a straight axis of symmetry passes through points A (6 6,0) and B (0 0,4).

(1) Find the parabolic analytical formula and vertex coordinates;

(2) Let point E (,) be the moving point on the parabola, located in the fourth quadrant, and the quadrilateral OEAF is a parallelogram with OA as the diagonal. Find the functional relationship of the area s sum of parallelogram OEAF, and write the range of independent variables.

① When the area of the parallelogram OEAF is 24, please judge whether the parallelogram OEAF is a diamond?

② Is there a point E that makes the parallelogram OEAF square? If it exists, find the coordinates of point e; If it does not exist, please explain why.

In 2007, Henan experimental area took the senior high school entrance examination in mathematics.

Reference answer

First, multiple choice questions

Title 1 2 3 4 5 6

Answer A B D C A B

Second, fill in the blanks

Title: 78910112131415.

answer

example

50

- 1，0， 1 (3n-2)

Third, answer questions.

16. solution: multiply both sides of the equation by the same, and you get.

Solve it and get it.

Check: When,

So it is the solution of the original equation.

17. It is proved that the ∵ quadrilateral ABCD is a parallelogram.

∴∠B = ∠D，AB = CD，BC = AD。

And \e, f, g and h are the midpoint of the four sides of the parallelogram ABCD,

∴BE = DG，BF = DH。

∴△BEF≌△DGH.

18. Solution: (1) In 2006, the total number of students in various schools in this province was

97.4 1 ÷ 4.87% ≈ 2000 (ten thousand people).

(2) The number of students in ordinary senior high schools is about

2000×10.08% = 201.6 (ten thousand people).

(There is no calculation, but full marks can be given if the figure is correct)

(3) The answer is not unique, as long as it is reasonable.

19. solution: Zhang Bin design scheme:

Because P (Zhang Bin gets the ticket) =,

P (Wang Hua gets the ticket) =,

Because, therefore, Zhang Bin's design scheme is unfair.

Wang Hua's design scheme:

The list of all possible outcomes is as follows:

first time

Second time 1 2 3

1 2 3 4

2 3 4 5

3 4 5 6

∴P (Wang Hua gets the admission ticket) = P (sum is even) =,

P (Zhang Bin gets the ticket) = P (the sum is not even) = Because,

Therefore, Wang Hua's design scheme is also unfair.

20. solution: (1)∵AD = 1, ∠DAE = 90o,

∴' length,

Similarly, the length,

Length,

Therefore, the route from point D to point G is very long.

(2) Linear national standard ⊥ df.

The reasons are as follows: extend GB to DF in H.

CD = CB，∠DCF = ∠BCG，CF = CG，

∴△FDC≌△GBC.

∴∠F =∠G

∵∠F+∠FDC = 90o，

∴∠G + ∠FDC = 90o，

That is, ∠GHD = 90o, so GB ⊥ DF.

2 1. solution: as shown in the figure, draw the graph correctly.

( 1)∵AB = AC,AD⊥BC,AD = BC，

∴. That is, AD = 2BD. ..

∴ .

∴ ,

.

② BE⊥AC in E.

In Rt△BEC,

Say it again,

∴ .

Therefore (meters).

22.( 1) Suppose you buy Class A goods and Class B goods.

According to the meaning of the question, you must

Simplify and acquire

Solve it and get it.

A: The mall bought $200 A and 120 B respectively.

(2) Due to the purchase of 400 items A, the profit is

(1380-1200) × 400 = 72000 (yuan).

Therefore, the profit from selling commodity B should be no less than 8 1, 600-72000 = 9600 yuan.

Let the price of each commodity B be X yuan, then 120 (X- 1000) ≥ 9600.

X ≥ 1080 is obtained by solving.

Therefore, the lowest selling price of commodity B is 1080 yuan per piece.

23. Solution: (1) From the parabola symmetry axis, the analytical formula can be set as.

Substitute the coordinates of a and b into the above formula, and you get

Solve it and get it.

So the analytical formula of parabola is, and the vertex is.

(2)∵ Point is on the parabola, located in the fourth quadrant, and the coordinates are appropriate.

,

∴y<； 0, that is, -y > 0, and -y represents the distance from point E to OA.

∫OA is diagonal,

∴ .

Because the two intersections of the parabola and the axis are (6,0) of (1, 0), and those of the independent variable.

The value range is 1 < < 6.

According to the meaning of the question, when S = 24, that is.

Simplify, get the solution, get it

So there are two points E, namely E 1(3, -4) and E2(4, -4).

Point E 1(3, -4) satisfies OE = AE, so it is a diamond;

Point E2(4, -4) does not satisfy OE = AE, so it is not a diamond.

(2) When OA⊥EF and OA = EF, it is a square, and at this point E.

Coordinates can only be (3, -3).

And the point with coordinate (3, -3) is not on the parabola, so there is no such point e,

Make it square.

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