Mathematics Test
Precautions:
1. This exam is divided into two parts, Volume I and Volume II, with pages of *** 10. Volume one or two multiple-choice questions, 36 points, volume two or eight non-multiple-choice questions, 84 points; *** 120 points. Examination time 120 minutes.
Before answering the first volume, you must scribble your name, test number and test subjects on the answer sheet. After selecting the answer for each question, you must blacken the answer label (ABCD) of the corresponding question on the answer sheet with 2B pencil. If you need to change it, be sure to clean it with an eraser before scribbling other answers.
3. When answering the second volume, fill in the items in the sealed line clearly, fill in the seat number on the right side of page 8, and answer directly on the test paper with a pen or ballpoint pen. After the exam, the test questions and answer sheets are taken back together.
The first volume (multiple choice questions ***36 points)
First, multiple-choice questions (only one of the four options in the following questions meets the meaning of the question, with 3 points for each small question and 36 points for * * *).
The reciprocal of 1 Yes.
A.B. - C. 2 D.-2
2. As shown in the figure, in △ABC, ∠ A = 70, ∠ B = 60, the extension of point D in BC.
Online, then ∠ACD is equal to
A.b . 100 c . 130d . 150
3. Of the following operations, the correct one is
A.B. C. D。
4. Through ground magnetic survey, Shandong Bureau of Geology and Mineral Resources estimates the inherent economic resources of Jining magnetic anomaly iron mine as follows.
10 800 000 000 tons. This data is represented by scientific symbols as follows
A. 108× 10 8 tons
C.1.08×1010 ton.
5. In the figure below, the axis symmetry and center symmetry is ().
A.B. C. D。
(Question 5)
6. In the function, the value range of the independent variable X is
a、x≠0 B、x>3 C、x ≠ -3 D、x≠3
7. As shown in the figure, in a rectangle with a length of 8 cm and a width of 4 cm, cut off a rectangle and leave it.
The rectangle (shaded in the figure) is similar to the original rectangle, so the area of the left rectangle is ().
A.2 cm2 B. 4 cm2 C. 8 cm2 D. 16 cm2
8. Known as a real number, it is equal to
A. BC-1 year
9. Fold a square piece of paper in the following order, and then cut off the small right triangle on the last folded paper along the dotted line (the center line of the right triangle).
Expand the remaining pieces of paper, and the resulting figure is
10. "Zhao Shuangxian Diagram" is a big square composed of four congruent right triangles with a small square in the middle. As shown in the figure, it is a "Zhao Shuangxian Diagram" dart board, and the lengths of the two right angles of a right triangle are 2 and 4 respectively. Xiao Ming throws darts into the dartboard at a certain distance (assuming that all the darts thrown are tied to the dartboard), and then he throws them once and sticks them in the small square area in the middle (including).
A.B. C. D。
Three views of the 1 1. geometry are displayed on the right, so the transverse area of the geometry is
A.4π B.6π C. 8π D. 12π
12. Xiao Qiang observed the following five pieces of information from the quadratic function image as shown in the figure: (1); (2) ; (3) ; (4) ; (5) What do you think is the amount of correct information?
A.2 B.3 C.4 D.5
Jining senior high school entrance examination in 2009
Math test questions
Volume 2 (84 points for non-multiple choice questions * *)
Second, fill in the blanks:
13. Decomposition factor:.
14. Given that the radii of two circles are 2 and 3 respectively and the center distance is 6, the positional relationship between the two circles is.
15. In the isosceles trapezoid ABCD, if AD ‖ BC, AD = 3cm, AB = 4cm, and ∠ B = 60, the length of the bottom BC is
Centimeter.
16. As shown in the figure, ⊙A and ⊙B are tangent to the X axis and the Y axis, respectively, and the centers are A and B..
B is the inverse proportional function on the image, and then the shaded part in the figure.
Area equal to
17. Please look at the following poem: "A group of crows are perched on a tree, and there are countless crows, three of them.
Only one tree is alive, five have nowhere to go, five live in one tree and one is idle. Please count carefully. What is the size of the crow tree? In the poem, the crow is a bird and the tree is a tree.
18. Observe the arrangement of white triangles in each big triangle in the picture. There are three white triangles in the fifth big triangle.
Third, answer questions:
19.(6 points)
Calculation: (π- 1)++-2.
20.(6 points)
Solve the equation:
2 1.(8 points)
As an important measure to benefit farmers and strengthen agriculture in response to the current international financial crisis and stimulate domestic consumption demand, the work of "home appliances going to the countryside" was approved by the State Council and implemented in our city from 65438+ to 65438+ in February 2008. The number of refrigerators sold by a home appliance enterprise in our city from February last year to May this year is as follows:
(1) Complete the following table:
Mean variance
Sales of a certain brand/Taiwan Province 10
B Brand Sales/Taiwan Province
(2) According to the changing trend of the line chart, please make suggestions on the future purchasing situation of the marketing point.
22.(8 points)
Prince Soul Tower is located in Baoxiang Temple, Wenshang County, Shandong Province. It was built in the Northern Song Dynasty (A.D. 1 12). This is a brick octagonal building with 13 floors. The math activity group carried out extracurricular practical activities. On a sunny morning, they went to measure the height of the Prince's Soul Tower. The measuring tools they carried were: goniometer, tape measure and small mirror.
(1) Xiaohua uses a goniometer and a tape measure to measure the height of the tower. Figure 1 is a schematic diagram of Xiaohua measuring tower height. First of all, she chooses a point on the flat ground in front of the tower, measures the elevation of the tower top with a goniometer, selects a point between the point and the tower, measures the elevation of the tower top, and then measures the distance between two points with a tape measure as m, and her height as m. Please use the above data to help Xiaohua calculate.
(2) If you are a member of an activity group and are preparing to measure the tower height, and the length of the tower shadow is m (as shown in Figure 2), can you use this data to design a measurement scheme? If yes, please answer the following questions:
(1) In the measurement scheme you designed, the measurement tools you selected are:
(2) What other data are needed to calculate the height of the tower?
.
23.(8 points)
Read the following materials:
In plane geometry, we learned the definition of two parallel lines. Below we give the definition of two straight lines determined by the images of two linear functions: let the image of a linear function be a straight line and the image of a linear function be a straight line. If, and, we say that straight lines and straight lines are parallel to each other.
Answer the following questions:
(1) Find the function expression of the straight line passing through this point and parallel to the known straight line, and draw the image of the straight line;
(2) Let the straight line intersect the axis and the axis at this point. If the straight line is parallel to the straight line and intersects the axis at this point, find the functional expression about the delta area.
24.(9 points)
As shown in the figure, the center of a circle with a radius of 1 moves upward from a point at a speed of 1 unit/. Let the moving time be (unit:).
(1) When it is a value, ⊙ is tangent to;
(2) If ⊙ intersects the line segment at a point, it is proved that the quadrilateral is a parallelogram.
25.(9 points)
A sporting goods store bought a batch of skateboards. The purchase price of each skateboard is 100 yuan, and the selling price is 130 yuan, and 80 skateboards can be sold every week. The merchant decided to reduce the price and promote sales. According to market research, every time the price of 5 yuan is reduced, 20 more skateboards can be sold every week.
(1) What is the sales profit of the week before asking the merchants to reduce their prices?
(2) After the price reduction, what price should the merchants set to maximize the weekly sales profit? What is the maximum sales profit?
26.( 12 points)
In plane rectangular coordinates, the two vertices of a square with a side length of 2 are on the axis and the positive semi-axis of the axis respectively, and the point is at the origin. Now the square rotates clockwise around the point and stops rotating when the point falls on a straight line for the first time. In the process of rotation, an edge intersects a straight line, and an edge intersects an axis at a point (as shown in the figure).
(1) Find the area swept by the edge when rotating;
(2) In the process of rotation, when parallel, find the square.
Angle of rotation;
(3) Let the perimeter be in a rotating square.
Has the value changed during the process? Please prove your conclusion.
Reference answers and grading standards of mathematics test questions
First, multiple choice questions
The title is123455678911112.
Options a, b, c, d, c, d, c, c, c.
Second, fill in the blanks.
13. 14. External distance15.716.π17.20,518.6438+021.
Third, answer questions.
19. solution: original formula = 1+2+(-5)-2. ...............................................................................................................................
= 3+3-5-2 5 points 5 points.
=-2.6 points.
20. Solution: When both sides of the equation are multiplied by (x-2), you get
X-3+(X-2) =-3 ............................................. 3 points.
The solution is x =1.................................................................................... 5 points.
Test: when x= 1, x-2≠0, so 1 is the solution of the original fractional equation. .........................................................................................................................
2 1. Solution: (1) Calculate the mean and variance as follows:
Mean variance
Sales of a certain brand/Taiwan Province 10
B brand sales/Taiwan Province 10
Six points.
(2) Suggestions are as follows: From the line chart, the monthly sales volume of brand A refrigerators is on the rise, and you can buy 8 points more for brand A refrigerators when purchasing.
22. Solution: The extension line set by (1) intersects with the point, and the length is, then.
∵ ,∴ .∴ .
∵, ∴, solution
∴ The height of Prince Lingta is 4 points in ...................................
(2) ① goniometer and tape measure; (2) standing at point P to see the elevation of the tower top and its own height.
(Note: the answer is not unique) 8 points.
23. Solution: (1) Let the functional expression of the straight line L be y = k x+b. 。
∫ The line L is parallel to the line Y =-2x- 1, and∴ K =-2.
∫ The line L intersects the point (1, 4), ∴— 2+b = 4, ∴ b = 6.
The functional expression of the straight line L is y =-2x+6 .................................................. 3 points.
The image of a straight line is shown in the figure. .....................................................................................................................................................................
(2) The coordinates of the point where the ∫ line intersects the axis and the axis, and the ∴ and are (0,6) and (3,0) respectively.
The straight line is y =-2x+t.
The coordinates of point ∴C are.
*t>0,∴。
The point ∴C is on the positive semi-axis of the X axis.
When point C is to the left of point B;
When point C is to the right of point B,
∴△ The functional expression about this region is
................................., eight.
24.( 1) solution: when ⊙ is tangent to the moving edge, let the tangent point be even,
Then.
∴ ∽ .∴ .
∵ , ,
........................................................, 4 points.
(2) Proof: ∫ ∴.
When.
∴ .∴ .
∴ .
∵ ∽ ,∴ .∴ ,
∴ .∴ .
When appropriate, the quadrilateral is a parallelogram. ...................... scored 9 points.
25. Solution: (1) (130-100) × 80 = 2400 (yuan); Four points.
(2) If the selling price should be set at RMB, the sales profit is.
Six points.
..................................................., eight.
At most, there are 2500.
∴ The price should be 125 yuan, and the maximum sales profit is 2500 yuan. .........................................................................................................................................
26.( 1) Solution: ∵ Stop turning when the point falls on a straight line for the first time.
It's spinning.
∴ The area swept during the rotation is ................................................... 4 points.
(2) Solution: ∫,
∴ , .
∴ .∴ .
Do it again.
Say it again.
∴ .∴ .
In the process of rotation, when parallel, the degree of rotation of the square is
..................................................., eight.
(3) Answer: The value has not changed.
It is proved that if the intersecting axis extends to this point,
,
∴ .
Here we go again.
∴ .
∴ .
Say it again,
∴ .∴ .
∴ ,
∴ .
∴ In the process of rotating the square, the value remains the same. ............................................................................................................................................................