1. Fill in the blanks. (There are *** 15 small questions in this question, with 3 points for each small question and 45 points for each small question. Only one of the four options given below is correct. Please fill in the letters before the correct option in the corresponding box on the answer sheet.
() 1. The sum of "and" can be expressed as:
(A) (B) (C) (D)
() 2. In the geometric figure on the right, the upper and lower bottom surfaces are parallelograms and each side surface is trapezoidal, so the straight line parallel to the lower and middle bottom surfaces in the figure is:
1 (B)2 (C)4 (D)8
() 3. All right.
The size relationship is:
(A) (B) (C) (D)
() 4. If, it is equal to:
(A) 18 14.55(B) 1824.55(C) 1774.45(D) 1784.45
() 5. In the parallelogram ABCD ∠B= 1 10O, extend AD to F, extend CD to E, and connect EF, then ∠ e+∠ f =: (a)1/kloc-0.
() 6. As shown in the figure, a circle is inscribed with a quadrilateral ABCD, and AB= 16 and CD= 10, then the perimeter of the quadrilateral is:
50 (B)52 (C)54 (D)56
() 7. A couple who love sports gave their 12-month-old baby three building blocks with "20", "08" and "Beijing" written on them respectively. If the baby can be arranged in "Beijing 2008" or "Beijing 2008", they will reward the baby. Assuming that the baby can arrange the building blocks horizontally and vertically, then the baby can get them.
(A) (B) (C) (D)
() 8. Maglev train is a new type of high-tech means of transportation, which has the advantages of high speed, strong climbing ability and low energy consumption. The average energy consumption of each seat is only one third of that of an airplane seat and 70% of that of a car seat. Then, the average energy consumption of each seat in a car is that of an airplane seat: (A) (B) (C) (D).
() 9. The largest area in the picture below is:
(a) A square with a side length of 5; (b) A circle with a radius of.
(c) A right triangle with a side length of 68 10; A regular triangle with a side length of 7.
() 10. If the simplified result is, the value range of is:
(a) is an arbitrary real number (B) (C) (D)
() 1 1. If it is the root of an unary quadratic equation, the relationship between the discriminant and the completely flat pattern is:
The relationship between (a), (b), (c) and (d) cannot be determined.
() 12. Given a linear function, if it decreases with the increase of, the image of the function passes through:
(a) the first, second and third quadrants, (b) the first, second and fourth quadrants.
(c) second, third and fourth quadrants (d) first, third and fourth quadrants
() 13. The following four conclusions are given: ① The internal angles of equilateral polygons are all equal; ② The isosceles trapezoid is both an axisymmetric figure and a centrally symmetric figure; ③ The inscribed circle and circumscribed circle of triangle are concentric circles; If the distance from the center of the circle to a point on a straight line is exactly equal to the radius of the circle, then this straight line is the tangent of the circle. The number of correct conclusions is: (A)0 (B) 1 (C)2 (D)3.
() 14. As shown in the figure, in the isosceles, AC=BC, with the hypotenuse AB as one side, so that point C and point D are on the same side of AB; Then take one side of CD as an equilateral, so that point C and point E fall on the opposite side of AD. If AE= 1, the length of the CD is:
(A) (B) (C) (D)
() 15. When drawing a quadratic function image by tabular method, list a table first. When the values of independent variables in the table increase at equal intervals, the corresponding values of the function are: 20, 56, 1 10, 182, 274, 380, 506.
Fill in the blanks. (There are 5 small questions in this question, 4 points for each small question, and 20 points for * * *)
16. When, the value of the score is zero.
17. The sum of two numbers is 6, and the difference (note that it is not a product) is 8. Take these two figures.
One-dimensional quadratic equation with roots is
18. As shown in the figure, the chessboard is placed in the plane rectangular coordinate system, and the white chess is ②.
The coordinate of is, and the coordinate of white chess is, then
The coordinates of black chess ① should be.
19. The school canteen sells two kinds of cakes with the same thickness but different sizes. The cake has a small diameter and costs 30 cents. The diameter of the pie is 40 cents. You like to buy pies because.
20. If four circles with the same radius are placed as shown in the figure, the distance between the intersections of two adjacent circles is equal, and the shortest distance between two points on two non-adjacent circles is equal to 2, that is to say, the shadow area in the figure is equal to. (accurate to 0.0 1).
3. Answer the questions. (This question is 6 small questions, with a score of ***55. The answer should be written in the proof process or deduction steps.
2 1. (The full score for this short question is 7)
We have studied similar triangles, and we know that if two geometric figures have the same shape but not necessarily the same size, we call them similar figures. For example, if all the elements such as the sides and diagonals of two squares are proportional, we can call them similar figures.
The following four pairs of geometric figures are given: ① two circles; ② Two diamonds; ③ Two rectangles; ④ Two regular hexagons. Please point out which pairs are similar figures and which pairs are not, and briefly explain the reasons.
22. (The full score for this short question is 8)
In the plane rectangular coordinate system, point A (2 1) is known, and O is the coordinate origin. Please determine the point p on the coordinate system to make AOP an isosceles triangle. Find all such points P in a given coordinate system, draw solid points, and mark them with P 1, P2, ..., PK, (if there are K points, mark them to PK.
23. (The full score for this short question is 8)
It is known that the AC section ⊙O at A and CB intersects with the ⊙O at D and B in turn, with AC=6 and BD=5, connecting AD, AD AD AB.
(1) Proof: Δ δCAD∽δCBA
(2) Find the length of line segment DC.
24. (Full score for this small question 10)
In recent years, the number of freshmen enrolled in Hongzhi High School has increased year by year, reaching 550 last year, including students in Hongzhi class and ordinary class. Due to the limitation of space and teachers, this year's enrollment is at most more than last year's 100, in which ordinary students can recruit 20% more, and students in Hongzhi class can recruit 10% more.
25. (Full score for this small question 10)
In order to participate in the exhibition of the municipal science and technology festival, the students made a
Three kinds of squares are used in the tunnel model with parabolic cross-section.
The shape of the steel bracket. When drawing a design, if you sit at right angles.
In the coordinate system, the resolution function of parabola is,
Side length of square ABCD and side length of square EFGH
5: 1 ratio, find:
(1) The value of the constant in the parabolic analytical formula;
(2) The side length of a square MNPQ.
26. (The full score of this short question is 12)
In triangle ABC, the existing moving point P starts from point A and moves in the direction of point B along ray AB; Moving point q starts from point c and moves in the direction of point b along ray CB. If the speed of point P is/sec and the speed of point Q is/sec, they start at the same time, and it is found that:
(1) After a few seconds, the area of Δ δPBQ is half that of ABC?
(2) On the premise of (1), what is the distance between P and Q?
Reference answer:
1.D 2。 C 3。 A 4。 B 5。 D 6。 B 7。 C 8。 C 9。 B 10。 B 1 1。 A 12。 B 13。 A 14。 D 15。 C 1 6.3 17. 18。 (-3,-7) 19. Large; Because the pie is 40 л/min, and the cake is 30 л/min. 20.； 4.7 1 2 1.① ④ The reason is slightly 22. ,,,,,, 23.(2) 4 24.ABC at least 10 people 25. The value of the (1) constant is (2) the side length δPBQ of the square is 26. (65448).
Mathematics examination questions in Hangzhou in 2007.
1. Choose carefully (this question 10 is a small question, with 3 points for each small question and 30 points for * * *).
Only one of the four options given in each question below is correct. Please fill in the letters before the correct option.
In the corresponding box on the answer sheet. Please note that there are many different ways to choose the right answer.
1. In the result of the following operation, () is positive.
A.B. C. D。
2. If the point is in the second quadrant, the distance to the axis is 4 and the distance to the axis is 3, then the coordinate of the point is ().
A.B. C. D。
3. As shown in the figure, enlarge the figure with a magnifying glass, which should belong to ()
A. Similarity transformation B. Translation transformation
C. Symmetric transformation D. Rotational transformation
4. A set of data is as follows: 3, 6, 5, 2, 3, 4, 3, 6. So this group
The median of the data is ()
A.3 or 4 B.4 C.3 D.3.5
5. The result of factorization is ()
A.B. C. D。
6. As shown in the figure, the regular triangle is inscribed in the circle, and the moving point is on the lower arc of the circle, which is equal to ()
A.B. C. D。
7. As shown in the figure, the elevation angle of the roof measured at the front point of the tall building is, 60 meters to this point, and the elevation angle is, then the height of the tall building is about ().
163 C.52 D.70
8. If the image of function sum intersects with a point, the point should be located in ().
A. first quadrant B. second quadrant C. third quadrant D. fourth quadrant
9. The point in the background on the right is the vertex of a small square with the same size, in which there are two quadrangles. The following statement is correct ().
A. The areas and perimeters of these two quadrangles are different.
B. The areas and perimeters of these two quadrangles are the same.
C These two quadrangles have the same area, but the circumference of I is greater than that of II.
D These two quadrangles have the same area, but the perimeter of I is smaller than that of II.
10. At the same time, three even regular hexahedral dice marked with 1, 2, 3, 4, 5 and 6 are thrown, and the numbers appear respectively, so the probability that they are exactly three sides of a right triangle is ().
A.B. C. D。
Fill in carefully (6 questions in this question, 4 points for each question, 24 points for * * *).
Pay close attention to the conditions and contents of the questions and fill in the answers as completely as possible.
1 1. The radii of two circles are 3 and 5 respectively. When these two circles intersect, the range of center distance is.
12. Take a sample with a capacity of 150 from a school and measure it.
After the students are tall, the histogram of height frequency distribution is obtained, as shown in the right picture.
Knowing that there are 1500 students in this school, we can estimate the height of this school.
Students aged between 10 and 15 are about
People.
13. If one outer angle of an isosceles triangle is equal to, then three angles of the triangle should be equal to.
14. The vertex of the parabola is, and the area of the triangle surrounded by the linear function image and the two coordinate axes is.
15. Three students answered, "If the solution of the equations is affirmative, find the solution of the equations." Put forward your own ideas. A said, "It seems that the conditions are not enough to solve this problem"; B said: "Their coefficients have certain rules, you can try"; C said, "Can you divide the two sides of the second equation group by 5 and substitute it for the solution?" . Referring to their discussion, do you think the solution to this problem should be.
16. As shown in the figure, it is a semicircular cardboard with a radius of 1. Cut a semicircle with radius at the lower left end of the cardboard to get a figure, and then cut a smaller semicircle (whose diameter is the radius of the previous semicircle) in turn to get a figure. Note that the area of the cardboard is, try to calculate it. ; Guess.
Three. Comprehensive answer (8 small questions in this question, ***66 points)
You should write a written explanation, proof process or derivation steps for the solution. If you find some problems a bit difficult, you can also write some writable solutions.
17. (Full score for this small question)
Given the following series of scores:, (where
(1) What rules do you find when you divide any score by the previous one?
(2) According to the law you found, try to write the seventh score in a given series.
18. (Full score for this small question)
We have studied quadrangles and some special quadrangles, and the picture on the right shows their relationship under certain conditions.
If ① and ② conditions are respectively: ① two groups of opposite sides are parallel; ② One and only one group of opposite sides are parallel. Then please write down the corresponding conditions of the other six numbers on the tag.
19. (Full score for this small question)
The picture on the right is a side view of a food packaging box.
(1) Please write down the polyhedral shape name of this packing box;
(2) Please calculate the side area and total area of this polyhedron (the sum of the side area and the areas of two matrixes) according to the dimensions marked in the drawing.
20. (The full score for this short question is 8)
In social practice, 15 ninth-grade middle school students investigated the means of transportation used by 500 Hangzhou citizens to travel to work one morning. The results are shown in the fan-shaped statistical chart below.
(1) Please change this statistical chart into a polyline statistical chart;
(2) According to this survey, please make suggestions to the government on urban traffic.
2 1. (Full score for this small question)
The right picture shows the left view of a machine part, and the arc is the radius.
One lap.
Please only use a ruler and compass to enlarge this part drawing at the ratio of 2:1.
Draw it. It is required to write out the drawing method and keep the drawing traces.
22. (Full score for this small question 10)
As shown in the figure, it is known that the median perpendicular intersects with the point and intersects with the point, and there are four conclusions as follows:
(1) ray is the angular bisector;
② isosceles triangle;
③ ∽ ;
④ ≌ 。
(1) What are the correct conclusions?
(2) choose a conclusion that you think is correct to prove.
23. (Full score for this small question 10)
During the summer vacation, Xiao Zhang's family in go on road trip experienced the quality of life and planned to drive the same distance every day. If the car travels 19 kilometers more than originally planned every day, the 8-day journey will exceed 2200 kilometers; If the daily journey of a car is less than 12km, it will take more than 9 days for it to travel the same distance. Find the original planned daily travel range of the car (unit: km).
24. (The full score of this short question is 12)
In a right-angled trapezoid, it is high (as shown in figure 1). The moving point starts from the point at the same time, and the point moves and stops from point to point, and the speed of the two points is the same. And when the point reaches the point, the point just reaches the point. Let's assume that the time from the point at the same time is and the area is (as shown in Figure 2). Establish rectangular coordinate system with abscissa and ordinate respectively. When a point moves from to sum on the edge, the function image of sum is the line segment in Figure 3.
(1) Find the length of the trapezoid respectively;
(2) Write the coordinates of two points in Figure 3;
(3) Write the functional relationship between and when a point moves on the edge and on the edge respectively (indicate the range of independent variables), and complete the approximate image of the functional relationship in the whole movement in Figure 3.
Reference Answers of Hangzhou Mathematics College Entrance Examination in 2007
1. Choose carefully (this question 10 is a small question, with 3 points for each small question and 30 points for * * *).
1、C 2、C 3、A 4、D 5、B 6、B 7、A 8、C 9、D 10、C
Fill in carefully (6 questions in this question, 4 points for each question, 24 points for * * *).
1 1、 12、300 13、 14、 1 15、
16、
Three. Comprehensive answer (8 small questions in this question, ***66 points)
The laws of 17 and (1) are: any fraction is constant except the previous one;
(2) The seventh score should be.
18, ③ An inner angle is a right angle; ④ A group of adjacent edges are equal; ⑤ A group of adjacent edges are equal; 6. An internal angle is a right angle;
⑦ Two waists are equal; 8 One waist is vertical to the bottom.
19, (1) This polyhedron is a hexagonal prism; (2) The transverse area is: The total area is
20, (1) omitted; (2) If public transportation is preferred; Or promote that walking is good for health.
2 1, sketch
22.( 1) The correct conclusions are ①, ②, ③; (2) Omit the proof.
23, set the original plan daily trip for kilometers, by this meaning, there should be:
Solution:
Therefore, the original planned daily mileage of this car is 256 km to 260 km.
24.( 1) When the point reaches the point and the point just reaches the point two seconds after the start of the moving point, then
(seconds)
Then;
(2) The available coordinates are
(3) When the point is above,;
When the point is at the top,
Image ellipsis
In 2006, all kinds of senior high school entrance examinations in Hangzhou.
mathematics
Instructions for candidates:
1. This paper is divided into two parts: test paper and answer sheet. Full score 120, test time 120 minutes.
2. When answering questions, the school name, name and admission ticket number must be stated in the sealed area of the answer sheet.
3. All the answers must be in the marked position on the answer sheet, and we must pay attention to the corresponding relationship between the serial number of the test questions and the serial number of the answer sheet.
4. After the exam, hand in the test paper and answer sheet.
test paper
1. Multiple choice questions (this question 15, 3 points for each question, * * 45 points) Only one of the four options given in each question below is correct. Please fill in the letters of the correct options in the corresponding boxes on the answer sheet.
1.
A.-2 B.0 C. 1 D.2
2. In order to make the formula meaningful, the value of the letter X must meet the following requirements.
A.x> B.x≥ C.x> D.x≥
3. Is the solution of the equation AX-Y = 3, then the value of A is
a . 5 B- 5 c . 2d . 1
4. In the figure below, both the central symmetric figure and the axisymmetric figure are
A. equilateral triangle B. diamond C. isosceles trapezoid D. parallelogram
5. The result of calculation is
A. 1 B.a C. D.a 10
6. It is known that △ABC is displayed on the right, so in the following four triangles, similar to △ABC,
Before a game, the coach predicted that our team had a 50% chance to win the game. In contrast, which of the following four situations, we can say that the coach is more accurate.
A.this team really won the game.
C If the game can be repeated 10, the team wins 6 games.
D If the game can be repeated 100 games, the team wins 5 1 game.
8. When a square with a side length of 4 rotates around one side, the transverse area of the obtained geometric figure is equal to
a . 16 b . 16πc . 32πd . 64π
9. It is known that y is a linear function of x, and some corresponding values are listed in the right table, so m is equal to.
A.- 1
10. As shown in the figure, if the central angle ∠ ABC = 100? , circle angle ∠ ADC =
80? B. 100？ C. 130？ D. 180？
1 1. If they are known and reciprocal, the number of real numbers satisfying the conditions is
A.0 B. 1 C.2 D.3
12. As shown in the figure, △ABC, △ADE and △EFG are equilateral triangles, and D and G are the midpoint of AC and AE respectively. If ab = 4, the circumference of the periphery of the figure ABCDEFG is
a . 12 b . 15 c . 18d . 2 1
13. Given the formula of the equation, it can be expressed as follows.
A.B.
C.D.
14. as shown in the figure, translate △PQR to the position of △ p ′ q ′ r ′ along the PQ direction, and the area of their overlapping part is half that of △PQR. If PQ =, the distance PP' of this triangle is
A. BC 1 year.
15. Consider the following four propositions:
① There is an angle of 100? Two isosceles triangles are similar;
② The hypotenuse and perimeter correspond to the coincidence of two right-angled triangles;
③ Quadrilaterals whose diagonals are perpendicular to each other and equal are squares;
④ A trapezoid with equal diagonal lines is an isosceles trapezoid.
The serial number of the correct proposition is
A.①②③④ B.①③④ C.①②④ D.②③④
Fill in the blanks (5 small questions in this question, 4 points each ***20 points)
16. Factorization:
17. As shown in the figure, the five mascots "Fuwa" of the Beijing Olympic Games have all been placed on the exhibition table, and the positions of "Huanhuan" and "Beibei" have been determined, so the probability of "welcoming" is.
18. In algebraic expression operation, after any two linear binomials are multiplied, the number of terms obtained by merging similar terms can be.
19. As shown in the figure, in △ABC, AB = 12, AC = 5, ∠ BAC = 90? . If point p is the midpoint of BC, the length of line segment AP is equal to; If point P moves on a straight line BC, and the symmetry points of point B and point C with respect to the straight line AP are B'C' respectively, the length of line segment B'C' is equal to
20. As shown in the figure, it is known that the side length of the square ABCD is 2 and the delta △BPC is an equilateral triangle, then the area of delta △CDP is; The area of delta △BPD is.
Third, answer the question (this question is 6 small questions, ***55 points). The answer should be written in the proof process or deduction steps.
2 1. (The full score for this short question is 7)
The following two groups have some real numbers. Please select two rational numbers and two irrational numbers respectively, and then perform three operations on the selected four numbers with "+,-,×," to make the operation result a positive integer.
22. (The full score for this short question is 8)
As shown, in Rt△ABC, ∠ ACB = 90? , CH⊥AB, HE⊥BC and HF⊥AC.
Verification: (1) △ hef △ ehc; (2)△HEF∽△HBC
23. (The full score for this short question is 8)
Known, and. Find the value range of x and express this range on the number axis.
24. (Full score for this small question 10)
As shown in the figure, the point P is outside the circle O, the point PA is tangent to the circle O at the point A, the point OP intersects the circle at the point C, and the point B and the point A are symmetrical about the straight line PO. It is known that OA = 4 and PA =. ask
(1) ∠ degree of POA; (2) chord length ab; (3) the area of the shadow part.
25. (Full score for this small question 10)
During the remaining time of the Hangzhou World Expo, the Carnival Playground invested 6,543,800 yuan+0.5 million yuan to introduce a large-scale amusement facility. Excluding maintenance costs, it is estimated that the monthly income will be 330,000 after opening. After the amusement facilities are opened, the total maintenance cost from 1 month to 10 month is y (ten thousand yuan), Y = AX2+BX；; If the net income of the amusement park after deducting investment and maintenance expenses is called G (ten thousand yuan), G is also an analytical formula about X;
(1) If 1 month maintenance cost is 20,000 yuan, the second month is 40,000 yuan. Find the analytical formula of y about x;
(2) Find the analytical formula of the net income g of X;
(3) Q: After the facilities were opened for several months, the net income of the playground reached the maximum? In a few months, you can recover your investment.
26. (The full score of this short question is 12)
It is known that the straight line intersects the X-axis and the Y-axis at point A and point B respectively, and the isosceles Rt△ABC is in the first quadrant with the line segment AB as the right angle, and ∠ BAC = 90? . And point P( 1, a) is a moving point in the coordinate system.
(1) Find the area of triangle ABC s △ ABC;
(2) It is proved that the area of triangular BOP is a constant, which has nothing to do with whether A is a real number;
(3) Make the areas of △ABC and △ABP equal and find the value of number A. ..