First, multiple-choice questions (this big question 12 small questions, 3 points for each small question, ***36 points) give four answers code-named A, B, C and D under each small question, of which only one answer is correct.
1, simplification equals ()
A, B, C, D,
2, a job, A alone to do an hour to complete, B alone to do B hours to complete, then A and B need () hours of cooperation.
A, B, C, D,
3, the following proposition is incorrect ()
A a triangle with the degree ratio of three angles 1: 3: 4 is a right triangle.
B A triangle with the ratio of degrees of three angles of 1:: 2 is a right triangle.
A triangle with the ratio of the lengths of three sides of c 1:: 2 is a right triangle.
D a triangle with the ratio of three sides:: 2 is a right triangle.
4. The figure shows three inverse proportional functions,
The image above the x axis, from which the size can be observed.
The relationship is ()
A, B, C, D,
5. As shown in the figure, point A is a point on the inverse proportional function image, and the AB⊥y axis is at point B,
Then the area of △AOB is ()
a、 1 B、2 C、3 D、4
6, in the triangle with three sides of the following length, which one is not a right triangle ().
a，5 13， 12 B，2，3，C，4，7，5 D， 1，
7, the following properties, parallelogram does not necessarily have is ()
A, the opposite sides are equal b, the opposite sides are parallel c, the diagonal lines are complementary d, and the sum of internal angles is 360.
8. A set of quadrilaterals with parallel opposite sides and vertical diagonal lines is ()
A, diamond or rectangle b, square or isosceles trapezoid c, rectangle or isosceles trapezoid d, diamond or right-angled trapezoid
The average of 9, ... is the average of A, ... is the average of B, then, ... is ().
A, B, C, D,
10, when five integers are arranged from small to large, the median is 4. If these five numbers
The unique modulus of is 6, then the maximum possible sum of these five integers is ().
a、2 1 B、22 C、23 D、24
1 1 As shown in the figure, in a square grid consisting of 4×4 small squares,
The ratio of shadow area to square ABCD area is ()
a、3:4 B、5:8 C、9: 16 D、 1:2
12, it is known that the diagonal of the quadrilateral ABCD intersects with O, and the following five conditions are given:1ab ‖ CD2AD ‖ BC3AB = CD4 ∠ Bad = ∠ DCB. Choose two conditions from the above four conditions as a group, and it can be concluded that the quadrilateral ABCD is a parallelogram ().
A6 Group B.5 Group C.4 Group D.3 Group
Fill in the blanks (there are 10 small questions in this big question, with 2 points for each small question and 20 points for * * *).
13, calculate (x+y)? =___________.
14, as shown in the figure, in □ABCD, AE⊥CD is in E, ∠ B = 55, then ∠ D = 0, ∠ DAE = 0. 15, as shown in the figure, △ABC, △ACE and △ Ec. .
16. Cut the 40cm long batten into four sections to form a parallelogram, so that the ratio of long side to short side is 3:2, the long batten is cm, and the short batten is cm.
The mode of 17 and data 1, 2, 8, 5, 3, 9, 5, 4, 5, 4 is _ _ _ _ _ _ _; The median is _ _ _ _ _ _ _.
18. It is known that a worker produces parts, which is scheduled to be completed in 30 days. If five more parts are produced every day, it will be completed in 26 days, and 15 more parts will be produced. How many parts did the worker originally plan to produce every day? If the original plan is to produce X pieces a day, the equation can be listed according to the meaning of the question.
19. If y is inversely proportional to x and the image passes through the point (-1, 1), then y=. (expressed by an algebraic expression containing x) 20. It is known that in △ABC, AB = 1, AC =, ∠ B.
2 1, as shown in the figure, △OPQ is an equilateral triangle with a side length of 2. If the image of the inverse proportional function passes through point P, its analytical formula is _ _ _ _ _ _.
22. In quadrilateral ABCD, if AB‖CD is known, quadrilateral ABCD can be transformed into parallelogram by adding conditions.
Iii. Answer questions (***64 points). Please write down the necessary calculus process or reasoning steps when answering.
23.( 1)(5 points) Calculation:.
(2)(5 points) Solve the fractional equation.
24(5 points) Before answering the questions, please read the following calculation process:
= (1)
= = (B)
=x-3-3(x+ 1) (C)
=-2x-6 (deep)
(1) In the above calculation process, from which step did the error occur: _ _ _ _ _ _ _ _ _ _ _ _
(2) Whether B to C are correct. If not, the reason for the error is _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
Please answer correctly.
26.(7 points) It is known that the function Y = Y 1-y2, Y 1 is inversely proportional to X, y2 is directly proportional to X-2, and when x = 1, y =-1; When x = 3 and y = 5. When x = 5, find the value of y.
27.(8 points) It is known that in □ABCD, diagonal AC intersects BD at point O, and quadrilateral AODE is a parallelogram. It is proved that quadrilateral ABOE and quadrilateral DCOE are parallelograms.
28.(8 points) Teachers and students of a school plant trees on the roadside 20 kilometers away from the school. Teachers and students in Class A ride bicycles first. After 45 minutes, the teachers and students of Class B set off by bus. As a result, the teachers and students of the two classes arrived at the same time. As we all know, the speed of a car is 2.5 times that of a bicycle. What is the speed of the two cars?
29.(7 points) As shown in the figure, it is known that the isosceles trapezoid ABCD, AD‖BC, diagonal AC ⊥ BD, AD = 3cm, BC = 7cm, and DE ⊥ BC is in E. Try to find the length of DE.
30.(9 points) Teacher Zhang conducted 10 test in order to choose one of the two students, Wang Jun and Zhang Cheng, who are particularly outstanding in mathematics in the usual class, and give guidance to these two students. The test scores of two students are recorded in the following table:
1 second, third, fourth, fifth, sixth, seventh, eighth and ninth 10
Wang Jun 68 80 78 79 8 1 77 78 84 83 92
Zhang Cheng 86 80 75 83 85 77 79 80 80 75
Average score median model
Wang Jun 80 79.5
Zhang Cheng 80 80
Use the data provided in the table to answer the following questions:
(1) Fill in the following table:
(2) Teacher Zhang got the variance of Wang Jun 10 test score from the test score record table =33.2. Please ask Mr. Zhang to help calculate the variance of Mr. Zhang Cheng 10 test scores;
(3) According to the above information, please use your statistical knowledge to help Mr. Zhang make a choice and briefly explain the reasons.
3 1, (10 minute) As shown in the figure, a wooden stick (AB) with a length of 2a leans against the wall (ON) perpendicular to the ground (OM), and let the midpoint of the wooden stick be P. If the A end of the wooden stick slides down along the wall, the B end slides to the right along the ground.
(1) Please judge whether the distance from point P to point O changes during the sliding of the stick, and briefly explain the reasons.
(2) When the stick slides, where is the largest area of △AOB? Briefly explain the reason, and sum, 1,