Mathematical simulation test paper
The total score of the topic is one two three four five six seven eight.
score
Math test time: 120 minutes. Full score in math test paper 150.
First, multiple-choice questions (3 points for each question, ***24 points)
1, point a (,) must not be in the plane rectangular coordinate system.
A, the first quadrant b, the second quadrant c, the third quadrant d and the fourth quadrant
2. As shown in the figure, if eight identical rectangular floor tiles are used to form a rectangle, the area of each rectangular floor tile is () a, 200cm2 B, 300cm2 C, 600cm2 D and 2400cm2 respectively.
3. As shown in the figure, the diameter ⊙O is 10cm, the chord AB is 8cm, and p is a point on the chord AB. If the length of OP is an integer, then the point p that meets the conditions has ().
a，2 B，3 C，4 D，5。
4. As shown in the figure: in equilateral △ABC, P is a point above BC, D is a point above AC, and ∠ APD = 600, BP = 1, CD =, then the side length of △ABC is ().
a、3 B、4 C、5 D、6
5. Put a small cylindrical cup filled with some water into a large cylindrical container without water in advance, and now use the water injection pipe to inject water at a uniform speed along the inner wall of the container (as shown in the figure), then the function image of water level in the small cup and water injection time is roughly ().
6, in a closed container that can change the volume, there is a certain quality of a certain gas. When the volume changes, the density of the gas also changes, which is satisfied within a certain range. When it is, its function image is ().
7. As shown in the figure, it is obtained by rotating around a point. If known, the graphic area swept by the line segment is ().
A.b.c.d None of the above answers are correct.
8. As shown in the figure, the extension lines of known, middle, middle and intersecting intersect at, and the following conclusions are drawn:
① ② ③ ④
The correct conclusion is ()
A.①②③④ B.①②③ C.①②④ D.②③④
II. Fill in the blanks (3 points for each question, ***24 points)
9. In the function, the range of independent variables is.
10, as shown in the figure, the length of the right side of an isosceles right triangle is 1, and the height on the hypotenuse is taken as the waist to make the first isosceles right triangle; Then make a second isosceles right triangle with the height on the hypotenuse of the first isosceles right triangle as the waist; ..... And so on, so that the waist length of the first isosceles right triangle is.
1 1. The math interest group wants to measure the height of a tree. In the sun, a student measured that the shadow length of a bamboo pole with a length of 1 m was meters. At the same time, another student, while measuring the height of a tree, found that the shadow of the tree did not all fall on the ground, but some fell on the wall of the teaching building (pictured), and its shadow was meters long and fell on the ground.
12, it is known that,,, folding one of its acute angles makes the vertex of the acute angle fall at the midpoint of its opposite side, and the folding seam intersects with another right angle and hypotenuse, then the circumference is.
13, as shown in the figure: at △ABC, AD⊥BC, CE⊥AB, the vertical feet are respectively D, E, AD and CE intersect at point H, please add an appropriate condition: △ AEH △ CEB.
14. Zhang bought a newspaper from the newspaper at the price of 0.4 yuan, sold one at the price of 0.5 yuan, and returned the rest to the newspaper at the price of 0.2 yuan, so Zhang obtained RMB by selling newspapers.
15, in,,, and then.
16, as shown in the figure: in ⊙O, AB and AC are two vertically equal chords, OD⊥AB and OE⊥AC, and their vertical feet are D and E respectively. If AC = 2 cm, the radius of ⊙O is cm.
Three. (8 points for each question, *** 16 points)
17, simplify first and then evaluate:, where
18, as shown in the figure, in the grid paper, the side length of each small square is 1, which is symmetrical with the center of the point.
(1) Draw that it will be translated upward by 5 units in a straight line direction;
(2) Draw a diagram obtained by rotating the point clockwise;
(3) Find the area of the quadrilateral.
Iv. (Each question 10, ***20)
19 grade 9 years 1 class two students made a preliminary statistics on a math score of their class (the score is rounded off, the full score is 100). They found that there were 17 students with more than 80 points (including 80 points), but none of them were full marks, and none of them were below 30 points. In order to better understand the exam situation in their class, they used two kinds of tests respectively.
(1)* * How many students took the exam?
(2) Fill in three blank parts in the two pictures;
(3) How many students got 85 to 89 points?
20. It is known that two cars, A and B, start from two places 300 kilometers apart at the same time and drive in opposite directions, and A returns immediately after reaching the ground. The following figure is a function image of the distance (kilometers) from their respective starting points and the driving time (hours).
(1) Please directly write the functional relationship between the distance (km) between vehicles A and B and the driving time (hours), and indicate the range of independent variables;
(2) How many times did they meet while driving? And find out the time of each encounter.
Verb (abbreviation of verb) (10 for each question, ***20 points)
2 1. In order to protect the environment, an enterprise decided to buy 10 sets of sewage treatment equipment. There are two types of equipment, A and B. The price, monthly sewage treatment capacity and annual consumption fee of each equipment are as follows:
Type a and type b
Price (ten thousand yuan/set) 12 10
Sewage treatment capacity (ton/month) 240 200
Annual consumption expense (ten thousand yuan/set) 1 1
According to the budget, the funds used by enterprises to purchase equipment are not higher than 6.5438+0.05 million yuan.
(1) Please design several purchasing schemes for this enterprise;
(2) If the amount of sewage produced by an enterprise is 2,040 tons per month, which procurement scheme should be chosen to save money;
(3) Under the condition of (2), if the service life of each equipment is 10 year, and the sewage treatment fee of the sewage plant is per ton 10 yuan, please calculate how much ten thousand yuan the enterprise will save by treating the sewage by itself compared with discharging the sewage to the sewage plant. (Note: Enterprise sewage treatment expenses include equipment purchase expenses and consumption expenses)
22. As shown in the figure, AB is the diameter ⊙O, C is the point greater than ⊙O, the bisector of ∠BAC intersects ⊙O at point D, the extension line of EF‖BC intersects with AB at point E, and the extension line of AC intersects at point F. (1) Verification: EF is ?. (2) if sin∠ABC= = and cf = 1, find the radius ⊙O and the length EF.
Six, (each question 10 points, ***20 points)
23. According to the rules of the game, please explore the mystery of the game:
(1) Use the list method to indicate the possible breakthrough;
(2) Find out the probability of success.
24. As shown in figure 12, the straight line intersects with the X axis at point A, intersects with the Y axis at point B, and point C is the moving point on ray BA.
(1) Find the value of sin∠OAB;
When △OAC is an isosceles triangle with OA as the waist, find the coordinates of point C. 。
Seven, (this question 12 points)
25. In a known quadrilateral,,,, rotates around a point, and its two sides intersect (or their extension lines intersect) respectively.
It is easy to prove when rotating around a point (as shown in figure 1).
When rotating around a point, does the above conclusion hold in both cases of Figure 2 and Figure 3? If yes, please give proof; If not, what is the quantitative relationship between line segments? Please write your guess without proof.
Eight, (this question 14 points)
26. As shown in the figure, in the plane rectangular coordinate system, the known points, points and points are on the negative and positive semi-axes of the shaft, and their lengths are two equations respectively.
(1) Find a point and its coordinates.
(2) If it exists on the plane, it is a point on the line segment, which satisfies and finds the analytical formula of the straight line.
(3) Are there points and points on the coordinate plane (points are on a straight line) so that the quadrilateral with vertices is a square? If it exists, please write down the coordinates of this point directly; If it does not exist, please explain why.