mathematics
(Examination time *** 120 minutes, full mark in the whole paper 120 minutes)
The first volume (multiple choice questions, ***24 points)
Precautions:
1. The experimental area of curriculum reform and the experimental area of non-curriculum reform use different test papers. Please check whether the obtained test questions are correct.
2. Before answering the questions, candidates must first fill in their names and admission ticket numbers at the left sealing line of the test paper with a blue-black ink pen or ballpoint pen.
3. The first volume is from page 1 to page 2. When answering questions, please use 2B pencil to fill in the correct answer number of each small question in the corresponding question number on the answer sheet. If you need to change it, be sure to clean it with an eraser and fill in other answer numbers. The answer on the test paper is invalid.
1. Multiple-choice questions: (This topic is entitled ***8 small questions, with 3 points for each small question, out of 24 points; Of the four options given in each question, only one is correct, and each question gets 3 points for correct answer, 0 points for wrong answer, and none or more choices are made).
The reciprocal of 0 1. -3 is ().
A, B, C, D,
02. The correct result of calculating (-1)+(-2) is ().
a 、- 1 B 、-3 C、 1 D、3
03. The solution of equation 2x-4 = 0 is ().
a、x= 1 B、x=- 1 C、x=2 D、x=-2
04. The sum of the internal angles of a hexagon is equal to ().
a、 180 B、360 C、540 D、720
05. As shown in the figure, imagine that the cross-section cut along the position shown by the dotted line is ().
06. The following figure, must be central symmetry is ().
A, parallelogram b, isosceles triangle c, trapezoid d, right triangle
07. As shown in the figure, there are three switches A, B and C and a small light bulb on the circuit diagram. Close switch C or both switches A and B at the same time to make the light bulb glow. Now, if one of the switches is turned on at will, the probability of the light bulb emitting light is equal to ().
A, B, C, D,
08. Xiao Huang went upstairs and counted the steps as he walked. From the first floor to the fourth floor, * * * took 54 steps. If the steps between each floor are the same, then the number of steps he has to take from the first floor to the eighth floor is ().
a、 108 B、 1 14 C、 120 D、 126
Examination papers of Liuzhou and Beihai in 2007 (used in the experimental area of curriculum reform)
mathematics
Volume 2 (multiple choice questions, ***96 points)
Precautions:
1. The experimental area of curriculum reform and the experimental area of non-curriculum reform use different test papers. Please check whether the obtained test questions are correct.
2. Before answering the questions, candidates must first fill in their names and admission ticket numbers at the left sealing line of the test paper with a blue-black ink pen or ballpoint pen.
3. The second volume is from page 3 to page 10. Please fill in the answers directly on the test paper with a blue-black ink pen or ballpoint pen.
2. Fill in the blanks: (This topic is entitled *** 10, with 2 points for each topic, out of 20 points).
09. If walking 50 meters north is marked as +50 meters, then walking 38 meters south should be marked as _ _ _ _ _ _ _ meters.
10. Calculation: x4 ÷ x2 = _ _ _ _ _ _ _ _
1 1. Factorization: x2-9 = _ _ _ _ _ _ _ _ _ _ _ _
12. The value range of the independent variable x in the function is _ _ _ _ _ _ _ _ _.
13. A school launched a book donation activity in poverty-stricken areas. The number of books donated by 10 students was 2, 3, 2, 4, 5, 3, 3, 6, 3, 7 respectively, so the model of this set of data is _ _ _ _ _ _ _ _.
14. The average number of times the earth is struck by lightning every year is about1600,000 times, which is expressed as _ _ _ _ _ _ _ by scientific notation.
15. As shown in the figure, point O is the point on the straight line AB, and oc bisects ∠AOD, ∠ BOD = 30, then ∠ AOC = _ _ _ _ _ _ _
16. If two sides of a triangle are 23cm and 10cm respectively, and the third side is equal to one of them, then the length of the third side is _ _ _ _ _ _ _ _.
17. A cylindrical pen holder with a height of 10cm and a bottom circle radius of 5cm has a side area _ _ _ _ _ _ _ _ _ cm2.
18. As shown in the figure, four rectangles A, B, C and D are combined into a square EFGH, and the shadow in the middle is a square. Given that the sum of the areas of the four rectangles A, B, C and D is 32cm2 and the area of the quadrilateral ABCD is 20cm2, the sum of the perimeters of the four rectangles A, B, C and D is _ _ _ _ _ _ _.
Three. (This big title is ***2 small questions, full score 12)
19. (The full mark of this question is 6)
Solve the inequality 3x+( 13-x) > 17, and express its solution set on the given axis.
20. (The full mark of this question is 6 points)
As shown in the picture, the shadow of a paratrooper who is about to land on the ground under the light is AB. Try to locate the light source P and draw the shadow ef of the stake standing on the ground. (Keep drawing traces and do not require writing methods. )
4. (This big topic is ***4 small questions, with a full score of 32 points)
2 1. (The full mark of this question is 8)
In the process of urban and rural cleaning, a proofreader's assessment of classroom hygiene in each class includes the following items: blackboard, doors and windows, tables and chairs, and floor. One day, the hygiene scores of the two classes are shown in the following table: (unit: minutes)
Blackboard, door, window, desk and chair, floor.
1 class 95 85 89 9 1
Category 2 90 95 85 90
(1) What is the average score of the two classes?
(2) According to the evaluation requirements of the school, the four scores of blackboard, doors and windows, desks and chairs, and floor are calculated according to the ratio of 15%, 10%, 35%, and 40% in turn. So which class has a high health score? Please explain the reason.
22. (The full mark of this question is 8)
As shown in the figure, ∠ ADB = ∠ ADC and BD = CD.
(1) verification: △ Abd △ ACD;
(2) Let E be the moving point on the AD extension line. When the point E moves to what position, the quadrilateral ACEB is a diamond. State your reasons.
23. (The full mark of this question is 8)
As shown in the figure, images with linear functions y = x and y = x+ 1 all pass through point p.
(1) Find the expression of the inverse proportional function of the image passing through point P;
(2) Try to determine whether the point (-3,-1) is on the image of the obtained inverse proportional function.
24. (The full mark of this question is 8)
On May Day, Xiao Jia and his classmates went to the playground to play the big Ferris wheel. The radius of Ferris wheel is 20m, and it takes 12 minutes to rotate at a constant speed. Xiao Jia took the bottom carriage (0.5m). Above the ground).
(1)2 m2 minutes later, Xiao Jia arrives at Q (pictured). What is his height from the ground at this time?
(2) How long will Xiao Jia stay in the air at least 30.5 meters above the ground when the Ferris wheel rotates?
Verb (the abbreviation of verb) (this big topic is ***2 small questions, with a full score of 20 points)
25. (The full mark of this question is 10)
A city adjusted the water price from 1 this year, and the water fee per cubic meter rose. It is understood that the water fee of a school in this city was1800 yuan in last year1October, while the water fee in March this year was 3,600 yuan. If the water consumption of this school in March this year is higher than last year, it is 165438+.
(1) What is the water price in this city this year?
(2) The school carried out the theme activity of "saving every drop of water" and took effective measures to save water. In May this year, the water consumption decreased by 20% compared with that in March, so how much should the school pay for water in May this year?
26. (The full mark of this question is 10)
As shown in the figure, AB = AC, AB is the diameter ⊙O, and AC and BC intersect ⊙O at E and D respectively, connecting ED and BE.
(1) Try to judge whether DE and BD are equal, and explain the reasons;
(2) If BC = 6 and AB = 5, find the length of BE.
Six. (The full mark of this question is 12)
27. (The full mark of this question is 12)
As shown in the figure, in the plane rectangular coordinate system, the image of parabola y =-x2+bx+c intersects the X axis at point A and point B (A is on the left side of B), and intersects the Y axis at point C. 。
(1) Try to judge whether the product of b and c is positive or negative. Why?
(2) If ab = 4 and the image of parabola y =-x2+bx+c moves to the left by one unit, its vertex is on the y axis.
① Find the expression of the original parabola;
② Let P be a moving point on the line segment OB and the intersection point P be the intersection parabola of the PE⊥x axis at point E. Q: Is there a point P that makes the straight line BC divide the △PCE into two parts with the area ratio of 3∶ 1? If it exists, find the coordinates of point P; If it does not exist, please explain why.
Hainan province junior high school graduation entrance examination in 2007.
Mathematics subject examination questions
(Full score 1 10, test time 100 minutes)
Special reminder:
1. Multiple-choice questions should be filled in with 2B pencils, and all other answers should be filled in with black pens on the answer sheet, which is invalid if written on the test paper.
Please read the test questions and related instructions carefully before answering the questions.
Please arrange the answer time reasonably.
First, multiple-choice questions (this big question scored 20 points, and each small question scored 2 points)
Of the four alternative answers to the following questions, only one is correct. Please use 2B pencil to black out the letter code of the answer you think is correct on the answer sheet as required.
The reciprocal of 1 be
A.B. C. D。
2. In 2007, there were113,000 students taking the entrance examination for junior high school graduation in Hainan Province. Numbers expressed in scientific notation should be recorded as
A.B. C. D。
3. The following operation is correct.
A.B. C. D。
4. As shown in figure 1, two straight lines are cut by the third straight line. If,
Then the degree is
Number 1
5. The top view of a three-dimensional figure composed of several small cubes with the same size is shown in the figure below, so this three-dimensional figure should be shown in the figure below.
Figure A B C D
6. Images of linear functions will not pass.
A. first quadrant B. second quadrant C. third quadrant D. fourth quadrant
7. In Rt, if,, the value is.
A.B. C. D。
8. As shown in the figure, it is still impossible to determine ∽ after adding one of the following conditions.
A.B. C. D。
Figure 4
9. As shown in Figure 4, the radius ⊙ is 4, and the point sum is the moving point on the ray and the straight line respectively. When the translation is tangent to ⊙, the length of ⊙ is
A.B. C. D。
10. Natural numbers,,, are arranged from small to large, where the number of digits is. If the only mode of this set of data is, the maximum value of all qualified,, and is.
A.B. C. D。
Fill in the blanks (this big question gets 24 points, and each small question gets 3 points)
1 1. Decomposition factor: =.
12. If the image of the inverse proportional function passes through a point, the relationship of the inverse proportional function is.
13. The range of independent variables of the function is.
14. As shown in the figure, it is known that the length of the midline of the isosceles trapezoid is and the length of the waist is, then the circumference of the isosceles trapezoid is.
tutu
15. As shown in the figure, after folding, the point falls on the edge. If the point is the midpoint of the edge, the degree is.
16. It is known that one root of the equation is, then.
17. There is a white ball and a yellow ball in an opaque cloth bag. They are all the same except for the different colors. If a ball is randomly drawn, the probability that it is a yellow ball is =.
18. As we all know, the lateral expansion of a cylinder is rectangular (as shown in Figure 7).
If, then the volume of the cylinder is about.
Yes (take, the result is accurate to 0. 1). Figure 7
Third, solve the problem (this big question is 66 points))
19. (Full score for this question 10, 5 points for each small question)
(1) calculation:
(2) Solving inequality groups
20. (The full mark of this question is 10) The "South of the Sea" fruit plantation has harvested * * * kilograms of "Feizixiao" and "No.1 Seedless" this year, and the income after all the sales is RMB. It is understood that the price of "Feizixiao" litchi is RMB per kilogram, and the price of "No.1 seedless" litchi is RMB per kilogram. Ask the plantation how many kilograms of these two kinds of lychees have been harvested this year.
2 1. (The full mark of this question is 10) Please answer the following questions according to the information provided by the histogram (chart) and fan chart (chart) of total annual education expenditure in Hainan Province:
tutu
(1) Annual expenditure on secondary education in Hainan Province 1 100 million yuan (accurate to 0.01);
(2) The percentage of Hainan province's annual college education expenditure to the total annual education expenditure is, and the angle of the circle center of the sector representing this expenditure in the figure is;
(3) Compared with, the annual growth rate of total education expenditure in Hainan Province is (accurate to 0.0 1%), which is twice that of the year before the establishment of the province (accurate to one place);
(4) According to the above information, please write your correct conclusions or suggestions that are beneficial to the development of education in Hainan.
22. (The full mark of this question is 10) In the grid paper as shown in the figure, the vertex coordinates of are, and respectively.
(1) about axis symmetry, and write
Coordinates of symmetric points of points, sums;
(2) symmetry about the origin, write
Coordinates of symmetric points of point, sum.
(3) Trial judgment: whether the sum is symmetrical (only write the judgment result).
23. (The full mark of this question is 12) As shown in figure 1 1, in a square, points are on the edge, rays intersect at the point, and extension lines intersect at the point.
(1) Verification:;
(2) Put forward a point and give it to the point to verify:
(3) Set, find whether there is a value, make it into an isosceles triangle, and if there is, evaluate it; If it does not exist, please explain why.
Figure 1 1 figure
24. (The full mark of this question is 14) As shown in the figure, the straight line intersects with the axis at one point and intersects with the axis at one point. It is known that the image of quadratic function passes through a point and a sum point.
(1) Find the relation of quadratic function;
(2) Let the vertex of the quadratic function image be, and find the area of the quadrilateral;
(3) There are two moving points, starting from this point at the same time, in which the point moves along the broken line at a speed of one unit length per second, and the point moves along the broken line at a speed of one unit length per second, and when the two points meet, both stop moving. Let it start from this point for two seconds at the same time, with an area of S.
(1) Are there two points during the exercise? If yes, request the value at this time; If it does not exist, please explain the reason;
(2) Find the functional relationship of S and write the range of independent variables;
③ Let be the maximum value of the function s in ②, then =.