Test paper p8- 17 for the next semester of the second day of junior high school.

(a) multiple-choice questions (3 points for each small question, ***30 points)

1. In order to know the weight of 400 students in grade three of a school, 50 students were randomly selected for statistical analysis. In this question, it is generally expressed as ().

A.400 students

B. Select 50 students

C. Weight of C.400 students

D. the weight of the 50 students taken away.

Answer: c

2. Among the following polynomials, the one that cannot be decomposed by the square difference formula is ().

Answer: b

A.2 B. 3 C. 4 D.5

Answer: c

Answer: d

As shown in the picture, there is a pond between A and B. Choose a point C outside AB, connect AC and BC and take their bisectors M and N respectively. If Mn = 38m, the length of AB is ().

A.152m

Answer: b

6. The following types of deformation from left to right are incorrect ()

Answer: d

7. It is known that the bisector of ∠ABC and ∠ACB intersects with O in △ABC, then ∠BOC must be ().

A. less than right angle B. Equal to a right angle

C. greater than right angle D. greater than or equal to right angle

Answer: c

8. As shown in the figure, in rectangular ABCD, if point E is any point on AD, there is ().

A. perimeter of A.△ Abe+perimeter of △ CDE = perimeter of △ BCE.

B. Area of △ Abbe+area of △ CDE = area of △ BCE.

C.△ABE∽△DEC

D.△ Abe ∽△EBC

Answer: b

A: A.

Answer: b

2. Fill in the blanks (3 points for each small question, ***24 points)

Answer:,,

Answer:

13. As shown in the figure, the extension line where CD bisects ∠ACB, AE ∠ DC intersects BC is at point E, and if ∠ ACE = 80, ∠ CAE = _ _ _ _ _ _ _ _ _

Answer: 50

Answer:

15. As shown in the figure, in the equilateral triangle ABC, points D and E are on the sides of AB and AC, respectively, and DE‖BC, if BC = 8cm, AD: AB = 1: 4, then the circumference of △ADE is equal _ _ _ _ _ _ _ _ _ cm.

Answer: 6cm

16. In order to adapt students to the new requirements of physical education examination, a school randomly selected the heights of some junior two boys. After sorting out and analyzing, it is estimated that about 80% of the junior two boys in this school are above 160cm (including 160cm). The following is the frequency distribution table when sorting out the analysis, where a = _ _ _ _ _ _ _ _ _

Answer: 0.2

17. Full score in a math exam 100 (unit: minutes), average score in a class of 75, variance 10. If each student's grade is converted according to full mark 120, the converted average score and variance are _ _ _ _ _ _ _ _ _.

Answer: 90, 14.4

18. In trapezoidal ABCD, AD‖BC, AC and BD intersect at O. If AD: BC = 1: 3, the following conclusion is correct ().

Answer: c

Three. Problem solving (6 points for each small question, *** 12 points)

Answer:

Answer: No solution.

4. (8 points for each small question, *** 16 points)

2 1. As shown in the figure, after the rectangular paper ABCD is folded along EF, the point D coincides with the point B, and the point C falls on the position of the point C. If ∠ 1 = 60, AE = 1.

(1) Number of times to find ∠2 and ∠3;

(2) Find the area s of rectangular paper ABCD.

Answer: (1) ∠ 2 = 60, ∠ 3 = 60; (2)

22. The two banks of a river are parallel. There is a tree every 5 meters on this side of the river, and there is a telephone pole every 50 meters on the other side of the river. Looking at the other side 25 meters away from the shore, I saw two poles adjacent to the other side just covered by two trees on the shore, separated by three trees, seeking the width of the river.

A: The river is 37.5 meters wide.

V (8 points for each small question, *** 16 points)

23. Some students from a middle school participated in the national junior high school mathematics competition and achieved excellent results. The instructor counted the scores of all the students participating in the competition (the scores are all integers, and the full score is 120), and drew a "histogram of frequency distribution" (pictured).

Please answer:

(1) How many students took part in this middle school math contest?

(2) If more than 90 students win the prize, what is the winning rate of the students in this middle school?

(3) In which score segment does the median score of this competition fall?

(4) The picture provides other information, such as the students who didn't get full marks in this middle school, and so on. Please write two more messages.

Answer: (1) 32;

(2)43.75%;

(3)80~90;

(4)& lt； 1 & gt； Fail below 70 points, with a passing rate of 87.5%; & lt2> There are no students with a score of 120.

24. An engineering team wants to recruit two jobs 150 people. The monthly wages of two types of workers are 600 yuan and 1000 yuan respectively. At present, the number of workers in Class B is required to be not less than twice that of Class A. When asked how many people are recruited in the same type of work in Class A and Class B, can the monthly salary be the least?

Solution: There are X people in group A and (150-x) people in group B.

The monthly salary is:

When x = 50, the minimum monthly salary is 130000.

25. Verification: the sum of the angles in the triangle is equal to 180 (drawing is required, and the process of understanding, verification and proof is written).

A: Omit.

26. The calculation method of water fee of a water supply company is as follows: if the monthly water consumption of each household does not exceed 5m3, it will be charged per cubic meter 1.5 yuan; If the monthly water consumption of each household exceeds 5m3, a higher fixed fee will be charged for the excess. In June 5438+10, the water consumption of the Zhang family was that of the Li family. The monthly water consumption of the Zhang family is 17.5 yuan, and that of the Li family is 27.5 yuan. What is the charge per cubic meter for the part exceeding 5m3?

Solution: If it exceeds 5m3, X yuan will be charged.

27. Topic: As shown in the figure, in the rectangular ABCD, AB = 12 cm, BC = 6 cm, point P moves from point A to point B at a speed of 2cm/ s along the AB edge, and point Q moves from point D to point A at a speed of 1cm/ s along the DA edge. If p and q start at the same time, t (seconds) is used. (5 points)

Solution: Let AP = 2t, AP = 2t.

∫△AQP∽△ABC

Or:

∴ When t = 1.2, 3 seconds, △AQP∽△ABC

Simulated test questions

I. Fill in the blanks (30 points)

1. The condition of the proposition "the complementary angles of equal angles are equal" is _ _ _ _ _ _ _ _, and the conclusion is _ _ _ _ _ _ _ _.

2. If the inequality group has no solution, the value range of m is _ _ _ _ _ _ _ _.

3. Decomposition factor _ _ _ _ _ _ _ _.

4. As shown in the figure, DE‖BC, AD = 15cm, BD = 20cm, then _ _ _ _ _ _ _.

5. A factory has stored1100,000 tons of coal for 3 days. In order to use the coal stored for d days more than the scheduled time, it should save _ _ _ _ _ _ _ tons of coal every day.

6. The sum of three consecutive natural numbers is less than 15, and such a natural array * * * has _ _ _ _ _ _ _ _ groups.

7. It is most natural and appropriate for a TV host to stand in the prime time of the stage when hosting a program. If the length of the AB stage is 20m, it is more appropriate for the host to walk at least _ _ _ _ _ _ _ m from point A. ..

8. It is known that the fractional equation about x has an increasing root, so the value of k is _ _ _ _ _ _ _ _.

9. Simplify _ _ _ _ _ _ _.

10. Two students, A and B, scored the following in five math exams:

A: 89,85,965,438+0,95,90;

B: 98, 82, 80, 95, 95.

_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _.

2. Multiple choice questions (30 points)

1. If it is a completely flat mode, the value of k is ().

A.6 B. 6 C. 12 D. 12

There are 70,000 students taking the senior high school entrance examination in a city. In order to know the math test scores of these 70,000 students, the math scores of 1000 candidates were selected for analysis. The following statement is correct ().

A this 1000 candidate is a sample of this group.

B. Each candidate is an independent individual.

C. This survey method is a general survey.

D.70,000 candidates' math scores are overall.

3. The number of true propositions in the following propositions is ()

(1) Two right triangles with equal acute angles are similar.

(2) The hypotenuse and right-angled edge are similar to two proportional right-angled triangles.

(3) Any two rectangles must be similar.

(4) Two diamonds with equal internal angles are similar.

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

4. It is known that if AB‖CD, ∠ D = 38 and ∠ B = 80, then ∠ P = ().

A.52 B. 42 C. 10 D. 40

5. As shown in the figure, in △ABC, p is a point above AB, which has the following four conditions: (1) ∠ ACP = ∠ b; (2)∠APC =∠ACB； (3) ; (4) AB CP = AP CB, and the condition that △APC is similar to △ACB is ().

A.( 1)(2)(3) B. ( 1)(3)(4)

C.(2)(3)(4) D. ( 1)(2)(4)

6.△ABC, BF and CF are angular bisectors, ∠ A = 70, then ∠ BFC = ().

A. 125 b . 100 c . 100d . 150

7. A classmate wants to measure the height of the flagpole. At a certain moment, he measured that the shadow length of a bamboo pole with a length of 1m was 1.5m when it was placed vertically. At the same time, when measuring the shadow length of the flagpole, because the flagpole is close to a building, all the shadows fall on the ground and some fall on the wall. He measured that the length of the shadow that fell to the ground was 2 1m, and the length of the shadow left on the wall was 0.

A. 12 b . 16 c . 10d . 15

8. Given CE⊥AD, ∠ A = 35 and ∠ C = 25, ∠ B = ().

A.25 B. 30 C. 35 D. 45

9. As shown in the figure, the quadrilateral ABCD is a parallelogram, so there are () pairs of similar triangles (except congruent triangles) in the figure.

A.2 to B. 3 to C. 4 to D.5.

10. When x = (), the value of the score is 0.

A. 2 BC

3. Painting problems:

Enlarge quadrilateral ABCD twice into quadrilateral by potential diagram method.

4. Answer the questions.

1. In an activity of measuring the height of flagpole, a group adopted the following scheme: AB stands for the distance from a classmate's eyes to the soles of his feet, CD stands for a pole, EF stands for a flagpole, and AB, CD and EF are all perpendicular to the ground. If AB = 1.6m, CD = 2m, the distance between people and poles BD = 1m, and the distance between poles and flagpoles DF = 30m, find the height EF of flagpoles.

2. In order to let students know about environmental protection knowledge and enhance their awareness of environmental protection, a middle school held an "environmental protection knowledge contest" with 900 students participating. In order to know the results of this competition, some students' scores (scores are integers, full marks are 100) are selected for statistics.

(1) Please fill in the form according to what you have learned.

Packet frequency

50.5~60.5 4 0.08

60.5~70.5 0. 16

70.5~80.5 10

80.5~90.5 16 0.32

90.5~ 100.5

Total 50 1.00

3. As shown in the figure, in △ABC, d is a point on BC, and it is known that AC = 15, BC = 9 and CD = 3. Find a point e on AC to make △CDE similar to the original triangle and prove it. (sketch is needed)

4. Known ∠ 1+∠ 2 = 180, verified: ∠ 3 = ∠ 4.

Tucki and Xiao Kai both live 3.6 kilometers away from the school. They set off for school at the same time. Tucki left 100 meters, and found that he forgot to bring his exercise book, so he immediately returned and went to school from A with his exercise book. As a result, they both arrived at school at the same time, knowing that Tucki walked 0.5 kilometers more than Xiao Kai, and asked their speed?

Test answer

1. Fill in the blanks.

1. If two angles are equal, then their complementary angles are also equal.

4.9:40

6.3 Prompt: (1, 2,3) (2,3,4) (3,4,5)

8. 1

10. A, B

2. multiple choice questions.

1.D 2。 D 3。 C 4 explosive B 5。 A

6. A seven. B 8。 B 9。 D 10。 B

3. Drawing questions.

∴ Quadrilateral A'B'C'D is what you want.