First, multiple-choice questions (this big question * *10 small questions, 3 points for each small question, out of 30 points)
1.(3 points) Among the following figures, the one that is both axisymmetric and centrally symmetric is ().
A. isosceles trapezoid B. parallelogram C. square D. regular Pentagon
2.(3 points) The following categories: ① X2+X3 = X5; ②a3？ a2 = a6③ ; ④ ; ⑤ (π- 1) 0 = 1, where the correct one is ().
A.④⑤? B. ③④ C. ②③ D. ①④
3.(3 points) The following types of secondary roots are ()
A.b? C. D。
4.(3 points) The following propositions are false, and those are ()
A.？ A quadrilateral with four equal angles is a rectangle.
B.？ A parallelogram with equal diagonal lines is a rectangle.
C.？ The quadrilateral with vertical diagonal is a diamond.
D.？ The parallelogram with vertical diagonal is a diamond.
5.(3 points) As shown in the figure, in △ABC, AB=4, AC=3, and AD and AE are its angular bisector and midline respectively. If the intersection point C is CG⊥AD in F, and AB and EF in G are connected, the length of segment EF is ().
A.？ B. 1？ c？ D. 7
6.(3 points) Move point P (﹣ 2,3) up by 3 units to get point P 1, and point P2 and point P 1 are symmetrical about the origin, so the coordinate of P2 is ().
A.(2，6) B. (2,﹣6) C. (2,﹣3)？ D. (2，0)
7.(3 points) I hope that the middle school will carry out a survey with the theme of "my favorite occupation", and get a set of data through a random sampling survey of students, as shown in the figure, which is an incomplete statistical chart drawn according to this set of data. The following statement is incorrect ().
A.？ 200 students were surveyed.
B.？ Among the students surveyed, 40 like teaching.
C.？ Among the students surveyed, 40% like other occupations.
D.？ In the pie chart, the central angle of the civil servant part is 72.
8.(3 points) As shown in the figure, quadrilateral ABCD, BEFD and EGHD are all parallelograms, in which C and F are on EF and GH respectively. If the areas of the quadrilateral ABCD, BEFD and EGHD are A, B and C respectively, which of the following is correct about the size relationship of A, B and C? ()
A.a > b > c B. b > c > a？ C. c>b>a？ D. a=b=c
9.(3 points) As shown in the figure, divide a disk into four parts and mark four areas with I, II, III and IV respectively. Only zone I is the sensing zone, and the sector AOB with a central angle of 60 rotates around zero point, and a sensing device with an indicator light is installed on its radius OA. When the sector AOB overlaps with the I area (except the origin), the indicator light will be on, otherwise it will not be on.
A.？ B? c？ D.
10.(3 points) As shown in the figure, in the rhombic ABCD, AB=2, ∠ A = 120, and points P, Q and K are arbitrary points on line segments BC, CD and BD respectively, then the minimum value of PK+QK is ().
A. 1? 2 BC? D. + 1
Fill in the blanks (***8 small questions, 3 points for each small question, out of 24 points)
According to the data of 1 1. (3 points), the number of college graduates this year has reached 7.27 million, an increase over last year. The data of 7.27 million people are expressed by scientific notation.
12.(3 points) Translate the straight line y= x up by one unit to get the straight line Y = X+7.
13.(3 points) If one side of a parallelogram is 3 and the lengths of the two diagonals are 4 and respectively, its area is.
14.(3 points) If the inequality group has three integer solutions * * * about x, the range of a is.
15.(3 points) In the rectangular paper ABCD, it is known that AD=8, AB=6, E is the point on the side of BC, and the paper is folded with AE as the crease, so that point B falls on point F and is connected with FC. When △EFC is a right triangle, the length of BE is.
16.(3 points) If the unary quadratic equation (k﹣ 1)x2+2x﹣2=0 has unequal real roots about x, then the range of k is.
17.(3 points) Xiaoming just bought several bags of milk in the supermarket with 10 yuan last Wednesday. When he went to buy it again on Sunday, it happened that there was a discount in the supermarket. Every bag of the same milk is cheaper than Wednesday, 0.5 yuan. As a result, Xiao Ming only used more 2 yuan money than last time, but bought two more bags of milk than last time. If he bought X bags of milk last Wednesday, the equation is as follows according to the meaning of the question.
18.(3 points) As shown in the figure, in the plane rectangular coordinate system, squares with unequal sides are arranged in sequence, and each square has a vertex falling on the image of function y = X, the coordinate of a vertex A in the third square from left to right is (8,4), and the area of the shadow triangle is marked as S 1, S2, S3, ...
Third, the calculation problem (full mark of this question 12)
19.( 12 points) (1) Solve the equation: x2+2x-6 = 0.
(2) Simplify first, then evaluate: ⊙, where x2 ÷ 9 = 0.
Iv. Answer questions (0/2 for each small/kloc, 24 for * * *)
20.( 12 points) Four balls marked with the numbers 1, 2, 3, 4 are packed in an opaque pocket. There is no difference between balls except the numbers. Every experiment should be stirred evenly.
(1) If you take any ball from it, what is the probability that the number on the ball is even?
(2) If you take any ball from it (without putting it back), and then take any ball from it, please draw a tree diagram or list grid to find out the probability that the sum of the numbers on two balls is even.
(3) If a game plan is designed and two balls are randomly selected, and the absolute value of the difference between the numbers on the two balls is 1, it is the first victory, otherwise it is the second victory. Is this game plan fair to both parties? Explain why.
2 1.( 12 points) It is known that x 1, x2 is two real roots of quadratic equation x2-2 (m+ 1) x+m2+5 = 0.
(1) If (x1-1) (x2-1) = 28, find the value of m;
(2) Given that the length of one side of the isosceles △ABC is 7, if x 1 and x2 are just the side lengths of the other two sides of △ABC, find the perimeter of this triangle.
Verb (abbreviation of verb) problem solving (22 questions 10, 23 questions 12, ***22)
22. (65,438+00 points) Manager Li bought 2,000 kilograms of mushrooms in our city at a market price of 65,438+00 yuan/kg and stored them in the cold storage. It is predicted that the market price of this kind of mushroom will increase by 0.5 yuan per kilogram every day, but the cost of storing these mushrooms in the cold storage will be charged by 340 yuan every day, and the mushrooms will be stored in the cold storage for at most 120 days, and at the same time, 6 kilograms of mushrooms will be damaged every day and cannot be sold.
(1) If this batch of mushrooms is sold once after being stored for x days, the total sales will be:
(2) How many days will it take to store and sell these mushrooms in Li Jing? (Profit = total sales-acquisition cost-various expenses)
23.( 12) Xiaoming and his father do mountaineering. They started from the foot of the mountain at the same time and went up the mountain at a constant speed along the same route. Xiaoming climbed to the top of the mountain in 8 minutes, and his father was 280 meters away from the starting point. Xiao Ming climbed to the top of the mountain and immediately descended at a constant speed. After meeting his father, he and his father returned to the starting point at the original downhill speed. During the exercise, the distance between Xiao Ming and his father from the starting point was y 1.
(1) in the diagram, a=, b =；;
(2) Ask Xiao Ming's father to go down the mountain.
6. Answer the question (full mark of this question 12)
24.( 12 points) As shown in the figure, in the square ABCD, point E is on the edge of AD, point F is on the extension line of BC, connecting EF intersects with CD edge at point G, connecting BE intersects with diagonal AC at point H, AE=CF, Be = EG.
(1) Verification: ef ∑ ac;
(2) Find the size of ∠BEF;
(3) If EB=4, the area of △BAE is.
Seven, answer (this question full score 12 points)
25.( 12 point) As shown in the figure, it is known that △ bad △ BCE, ∠ bad = ∠ BCE = 90, ∠ Abd = ∠ BEC = 30, point M is the midpoint of DE, and the straight line intersecting with ray AM parallel to AD passes through point E.
(1) As shown in figure 1, when A, B and E are on the same straight line, it is judged that the quantitative relationship between AC and CN is;
(2) When △BCE in figure 1 rotates counterclockwise around point B to the position in figure 2, does the conclusion in (1) still hold? If so, try to prove it; If not, please explain the reasons;
(3) Rotate △BCE in figure 1 counterclockwise around point B. Can △ be an isosceles right triangle during the rotation? If you can, write the rotation angle directly; If not, explain why.
Eight, answer (this question full score 14 points)
26.( 14 point) As shown in the figure, in the plane rectangular coordinate system, the coordinates of point A are (6,0), and the coordinates of point B are (0,8). The moving point P starts from point A and moves along the dotted line AO-OB-BA, and the moving speed of point P on A0, OB and BA is 3 per second respectively. That is to say, l∑OA remains unchanged during the movement, and intersects with OB and AB at E and F respectively. At the same time, let the moving time be t seconds. When point P intersects point F, point P and line L stop moving at the same time.
The expression of the straight line where (1) line segment AB is located is: the abscissa of point F is (expressed by algebraic expression of t);
(2) Let the area of △APE be S(S≠0), and find the functional relationship between S and T when point P and straight line L move;
(3) During the movement of point P and straight line L, make a symmetrical point of point P about straight line L, and record it as point Q. If the quadrilateral PEQF is a diamond, please write the value of t directly.