I. Fill in the blanks (2 points for each question, ***24 points)

1. It is known that the circumference of △ABC is 25cm, and among the three sides A, B and C, a=b and c∶b= 1∶2, then the length of the three sides a=,

b=，c=。

2. As shown in the figure, P is a point on the bisector OC of ∠AOB, and PD⊥OA,PE⊥OB,

The vertical feet are d and e respectively. In the figure, * * * has a pair of congruent right triangles.

They are.

3. Figure (2) is an image obtained by similar transformation of the existing graph (1), so a=,

4. In traditional wooden houses in China, windows are often decorated with various patterns, as shown in the figure, which is a common pattern.

There is an axis of symmetry.

5. As shown in the figure, △ABC is an equilateral triangle with a side length of 2cm, and D is the midpoint of BC. Rotate △ADC around point A by 600 to get △AEB, then ∠ABE=, BE=,. If DE is connected, △ADE is a triangle.

6. The right triangle is transformed similarly, and each side is enlarged to 3 times of the original, and the enlarged graphic area is _ _ _ _ _ _ _ times of the original area.

7. Design a touch game with four balls, which makes it easier to touch the white ball than the red ball. You can put a black ball, a white ball and a red ball in the box.

8. Throw an even dice, and each side of the investment is marked with 1, 2, 3, 4, 5, 6. Then the probability that the number of points less than 3 is up is.

9. Please write a set of binary linear equations with solutions.

10. It is a system of binary linear equations about x and y, so a, b=, c=.

1 1. It is known that the solution of binary linear equations is also the solution of equation 7mx-4y=- 18x, then m=.

12. Triangle ABC is an equilateral triangle (triangle with three equal sides), which means that the algebraic expression of its side length has been marked in the diagram, so the value of 2(x2+y2-xy-7) is.

Second, multiple-choice questions (2 points for each question, ***20 points)

1. As shown in the figure, △ ABC △ bad, A and B, C and D are the corresponding vertices respectively. If AB = 6 cm, BD = 7 cm and AD = 4 cm, then the length of BC is ().

A.6 cm B.5 cm C.4 cm D. Not sure.

2. Known △ ABC△ a? c？ b？ , ∠B and ∠C , ∠C and ∠B? Is the corresponding angle, then

①BC= C？ b？ ; ② The bisector of ∠ C and ∠B? The bisector is equal;

③ What is the height and a on the side of AC? b？ The height of both sides is equal; 4 the midline on the side of ab and a? c？ The median lines on both sides are equal ()

1。

3. As shown in the figure, AB‖CD, AC‖BD, then congruent triangles has () in the figure.

A.4 to B.3 to C.2 to D. 1 right.

Question 1

4. As shown in the figure, in △ABC, AD⊥BC is in C,BE⊥AC is in E, and the following statement is wrong ().

A.FC is the height of △ABC, and B.BE is the height of △ABC.

C.AD is the height of △ABC, and D. BC is the height of △ABC.

5. Among the following four kinds of graphics, the one that cannot be translated by basic graphics is ().

6. As shown in the figure, △BEF is translated by △ABC, and points A, B and E are on the same straight line.

If ∠F=700 and ∠E=680, ∠CBF is ()

AD 420 BC 680 BC 700 BC cannot be determined.

7. The possibility of buying movie tickets at will, where the seat number is a multiple of 3 and the seat number is a multiple of 5 ()

A.it is a multiple of 5. B. equal opportunities. C.it is a multiple of 3. D. can't be sure

8. There is a two-digit number, and the sum of the digits on the ten-digit number and the digits on the one-digit number is 5, so such a two-digit number has ().

A.3 B.4 C.5 D.6

9.sum is the solution of equation y=kx+b, so the values of k and b are () respectively.

A.- 1.3 b . 1.4 c . 3，2 D.5，-3

10. It is known that a ship has a deadweight of 600 tons and a volume of 2400m3. There are two kinds of goods to be loaded now, one is the volume of 7m3 per ton, and the other is the volume of 2m3 per ton of B. How to load the goods can make the best use of the load and volume of the ship. If goods A and B are x tons and y tons respectively, the equation set is ().

A.B. C. D。

Iii. Answering questions (***46 points)

1. Solve the following equation (16 points)

( 1) (2)

(3) (4)

2. As shown in the figure, given line segments A and B and ∠ α, find △ABC so that ∠B=∠α, AB=a, BC=b, (5 points).

3. As shown in the figure, in Rt△ABC, the bisector of ∠ ACB = RT ∠ and ∠ CAD intersects with the extension line of BC at point E. If ∠B=350, find the degrees of ∠BAE and ∠E (6 points).

4. The quality samples of a batch of suits are as follows:

The number of random samples is 200 400 600 80010001200.

The quantity of genuine products is180 390 576 768 9601176.

(1) What is the probability that there is a set of defects in this batch?

(2) If you want to sell 2,000 suits, how many sets should you buy at least for the convenience of customers who bought defective suits? (6 points)

5. qingyun middle school plays basketball "three-point king" game. The following table shows the test results of basketball players throwing three-pointers:

Shooting time10 50100150 200

Number of hits 9 40 70 108 144

(1) According to the above table, what is the probability of an athlete hitting a three-pointer?

(2) According to the above table, if an athlete has 50 chances to throw three-pointers, how many points is he expected to get? (7 points)

6. A milk processing factory has 9 tons of fresh milk. If sold directly in the market, you can make a profit of 500 yuan per ton. If you make yogurt, you can make a profit of 1.200 yuan per ton, and if you make milk tablets, you can make a profit of 2000 yuan per ton. The production capacity of this factory is: if it is made into yogurt, it can process 3 tons per day, and the milk slices can be processed 1 ton. Due to personnel constraints,

Option 1: Make as many pieces of milk as possible and sell the rest directly.

Option 2: Make part of it into milk slices and the rest into yogurt, which can be sold in exactly 4 days.

Which scheme do you think is more profitable? Why? (8 points)

7. When solving the equation, due to carelessness, A misread A in the equation and got the understanding, while B misread B in the equation and got the understanding.

(1) What does A see and what does B see?

(2) Find the correct solution of the original equations. (8 points)