Question number one, two, three is the total score.
1~8 9~ 16 17~ 18 19~20 2 1~22 23~24 25
score
First, multiple-choice questions: (This big question is ***8 small questions, each with 3 points and * * * 24 points. Of the four options given in the small question, only one meets the requirements of the topic. )
1, the following is a definite event (regardless of other factors) is (b)
Turn on the TV, the news is playing. B, three lines form a triangle.
C, throw a cube dice, the number of points is 8 D, and meet an old friend in another country.
2. The following figure is not an axisymmetric figure (D)
3. Understand the disappearance of the city on the first day, and randomly select the eyesight of 500 students, so the sample refers to (D).
A, all junior high school students in our city b, 500 students randomly selected.
C, the visual status of all first-year students in our city d, the visual status of 500 students randomly selected.
4, the existing length of 2cm, 3cm, 4cm, 5cm, take any three sticks, can form a triangle number is
(4)
a、 1 B、2 C、3 D、4
5. It is known that there is (c)
A, B, C, D,
6. As shown in figure ∠ cab = ∠ DBA, it cannot be determined that △ ABC △ bad is (b) under the following circumstances.
a、AC=BD B、BC=AD
c、∠ABC=∠DAB D、∠ACB=∠BDA
7. A commodity imported from 800 yuan was sold at a price of 1.200 yuan. Later, due to the backlog of goods, it was ready to be sold at a discount. If the profit margin of the commodity is exactly 5%, the commodity should be marked with (c).
A, 60% off B, 70% off C, 80% off D, 10% off
8, in the following statement, the wrong is (b)
A is a solution of the equation;
B, the equation can be changed to;
C, not a binary linear equation;
D, when it is a known number, the solution of the equation is;
Fill-in-the-blank question: (This big question is ***8 small questions, each with 3 points and * * * 24 points, and fill in the answers on the horizontal lines in the questions)
9, understand the favorite TV programs of middle school students in China is suitable for sampling survey _ _ _.
10, please write the binary linear equation _ _ _ _ 2x-y =1_ _.
1 1, as shown in figure, ∠ 1+∠ 2+∠ 3+∠ 4 = _ _ 360 degrees.
There are some fish in the pond. In order to estimate the number of fish in the pond, the fish farmers caught 40 fish from the net for the first time, all the fish were marked and then put back into the pond. After a period of time, after the marked fish and fish were completely mixed together, I fished three nets from the pond for the second time, and I fished 65438+ with one * * *.
13, as shown in the figure, where AB=AC, AB = AC, DE is the middle vertical line of AB, the perimeter of BCE is 14, and BC = 6, then the length of AB is _ _ 12 _ _.
14. To process 300 parts, Party A will work alone for 6 hours, and then work with Party B for 5 hours to complete the task. If A processes X parts per hour, B processes Y parts per hour, and A processes 5 more parts per hour than B, then the equation obtained according to the meaning of the question is _ _ _ _ _ _ _ _.
15, as shown in the figure, when △AB=AC, AB=AC, ∠ A = 40, D and E are points on AB and AC respectively, BD = BC, then ∠ CDE = _ _ 35 _ _.
16, as shown in the figure, ∠ E = ∠ F = 90, B = C, AE = AF, and the following conclusions are given: ① ∠1= ∠ 2; ②BE = CF； ③△CAN?△ABM； ④ CD = DN, and the correct conclusion is _ _ _ ① ② _ _ _ _. (Note: Fill in the serial numbers of all the conclusions you think are correct)
Third, the solution: this big question is ***9 small questions, ***72 points, and the answer should be written in words or calculus steps.
(For this big topic, ***2 small topics, the score is 17 12, the score is 18, 8, ***20).
17, solving the equation (group):
( 1) (2)
Solution: Both sides start with 24.
4(2x+ 1)-3(5x- 1)=24
8x+4- 15x+3=24
-7x=24-4-3
-7x= 17
X=-7/ 17
18, when solving the equations, due to carelessness, A misread A in the equations, and the solution obtained is; B misread b in the equation and got an understanding.
(1) Find the correct values of A and B;
(2) Find the solution of the original equations.
(This big question has two small questions, each with 6 points, *** 12 points)
19, as shown in the figure, straight lines respectively represent JASON ZHANG Highway and Feng Gang Highway in our city, and A and B are two factories. Now it is planned to build a warehouse C, so that the distance from the warehouse to the two expressways is equal, and the distance to the factories in A and B is also equal. Please use a ruler and compasses to determine the position of point C (keep drawing traces).
on paper
20. There are the following types of regular polygons: ① regular triangles; ② Square; ③ Regular hexagon; ④ Regular dodecagon, where two or more figures are combined into a plane ① Regular triangle; ② Square; (Every graphic can be reused:. Please design four planar mosaic schemes that meet the above conditions, and point out the number of the regular polygon used in each design scheme (there is no need to make a planar mosaic).
① Regular triangles ② Squares are inlaid into regular pentagons.
Regular quadrilateral regular icosahedron regular octagon
(This big question is ***2 small questions, each with 8 points, *** 16 points)
2 1, as shown in the figure. When △AB=AC, AB=AC, F is a point above AC, FD⊥BC is in D, DE⊥AB is in E, ∠AFD = 145, find the values of ∠ A and ∠EDF.
22. Two students, A and B, had a darts throwing contest, each throwing 10 times. The situation of hitting the target is shown in the figure below.
Please answer the following questions:
(1) Fill in the following table:
Score 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.
A (times)
(2) Write out the average, median and mode of students A and B's 10 darts throwing and catching respectively;
(3) Draw a line chart of A and B throwing and catching darts in the grid diagram below;
(4) From the trend of the line chart, please analyze which student has greater potential.
(This big question is ***2 small questions, each with 8 points, *** 16 points)
23. Use two congruent equilateral triangles △ABC and △ACD to form a quadrilateral ABCD, and superimpose a 60-degree angle triangular ruler with this quadrilateral, so that the vertex of the 60-degree angle of the triangular ruler coincides with point A, and both sides coincide with AB and AC respectively, and rotate the triangular ruler counterclockwise around point A..
(1) What conclusions can BE drawn by observing or measuring the lengths of Be and CF when the two sides of the triangular ruler intersect with the two sides of the quadrilateral BC and CD at points E and F respectively (as shown in Figure A)? And explain the reasons;
(2) When the two sides of the triangular ruler intersect with the extension lines of the two sides BC and CD of the quadrilateral at points E and F respectively (as shown in Figure B), is the conclusion you got in (1) still valid? Briefly explain why.
24. As shown in Figure 24- 1, there are two unified turntables A and B, which can rotate freely. The turntable is divided into four equal parts, each marked with four numbers: 1, 2, 3 and 4, and the turntable b is divided into six equal parts, each marked with six numbers: 1, 2, 3, 4, 5 and 6. Someone designed a game for Party A and Party B, and the rules are as follows:
① Rotate dials A and B freely at the same time. When the dial stops, the pointer points to a number (if the pointer just points to the grid line, turn it again until the pointer points to a number).
② Multiply the two numbers indicated by dials A and B, and if the product is even, A wins; If the product is odd, then B wins.
(1) Do you think this rule is fair? If it is unfair, who has the best chance to win, A or B?
(2) If you don't change the numbers in the turntable, please change the rules of the game appropriately to make the game fair to both sides;
(3) If you don't change the rules of the game in question, please change the numbers on the turntable appropriately, and mark the numbers you choose on the turntable in Figure 24-2 to make the game fair to both parties.
(The full mark of this question is 8)
Xiaoming bought a lamp for his study. There are two kinds of lamps to choose from, one is 10 watt energy-saving lamp (that is, 0.0 1 kw), and the price is 78 yuan/lamp; The other is 60 watts (i.e. 0.06 kW) at a price of 26 yuan/lamp. Assuming that the illumination brightness of the two lamps is the same, the service life can reach 2800 hours. It is understood that Xiao Ming's electricity price is 0.52 yuan per kilowatt hour.
(1) If the lighting time is x hours, please use the algebraic expression containing x to express the cost of using energy-saving lamps and the cost of using incandescent lamps (note: cost = lamp price+electricity fee);
(2) Xiao Ming chooses one of these two lamps.
(1) What is the cost of using two kinds of lamps when the lighting time is?
(2) When x = 1500 hours, the cost of selecting _ _ _ _ lamp is low; When x = 2500 hours, the cost of choosing _ _ _ _ lamp is low;
③ ① ② Guess: When the lighting time is _ _ _ _ hours, the cost of choosing incandescent lamp is low; When the lighting time is _ _ _ hours, the cost of choosing energy-saving lamps is low;
Xiao Ming wants to buy two of these lamps. The precise lighting time is 3000 hours, and the service life of each lamp is 2800 hours. Please help him design the lowest-cost lamp selection scheme and explain the reasons.