1. If m >- 1, the error in the following categories is ().

a . 6m >-6 b .-5m 0d . 1-m < 2

2. It is known that a > b > 0, so the following inequalities have no solution ().

A.B. C. D。

3. Inequality 14x-7 (3x-8)

A.a & gt0 B.a & lt0c . a & gt； -2009d . a & lt； -2009

4. A car driving on the highway, after two turns, is still driving in parallel in the original direction, then the angles of these two turns may be ().

(a) Turn right 50, then turn right 40 (b) Turn right 50, then turn left 40.

(c) Turn right 50, then turn left 130 (d) Turn right 50, then turn left 50.

5. The equation solved is ()

A.B. C. D。

6. As shown in the figure, in △ABC, ∠ABC=500, ∠ACB=800, BP shares ∠ABC, CP shares ∠ACB, then the scale of ∠BPC is ().

A. 1000？ B. 1 100？ C. 1 150？ D. 1200？

( 1) (2) (3)

7. The lengths of the four line segments are 3, 4, 5 and 7 respectively, so the number of different triangles that can be formed from end to end is ().

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

8. In a polygon with equal internal angles, if an external angle is equal to an internal angle, then the number of sides of the polygon is ().

A.5 B.6 C.7 D.8

9. As shown in the figure, △A 1B 1C 1 is obtained by shifting △ABC to the direction of BC by half the length of BC. If the area of △ABC is 20 cm2, then the area of quadrilateral A 1dc 1 is ().

A. 10 cm2 B. 12 cm2 C. 15 cm2 D. 17 cm2

10. At rest, the positions of Xiaohua, Xiaojun and Xiaogang are as shown in figure 1. Xiaohua said to Xiaogang that if my position is represented by (0,0) and Xiaojun's position is represented by (2, 1), then your position can be represented by ().

A.(5，4) B.(4，5)？ C.(3，4)？ d .(4.3)

Fill in the blanks: (4 points for each small question, * * * 20 points)

1 1. If the lengths of three sides of a triangle are 3, 4 and x- 1 respectively, then the value range of x is.

12. The solution set of inequality 5x-9≤3(x+ 1) is _ _ _ _ _.

13. If point P(a, 2) is in the second quadrant, then point Q(-3, a) is in the _ _ _ _ _ quadrant.

14. If you drive from A to B at 60 east-north direction, and then drive from B to C at 20 west-south direction, then ∠ ABC = _ _ _ _ _ _

15. Give the following regular polygons: ① regular triangle; ② Square; ③ Regular hexagon; ④ Regular octagon. Can fill the ground with one of the regular polygons is _ _ _ _ _ _ _. (Fill in the serial numbers of all answers)

Three. Problem solving: (16 ~ 19 5, 20 ~ 24 6)

16. Solve the inequality group: and express the solution set on the number axis.

17. Solve the equation:

18. As shown in the figure, AD∨BC and AD share ∠EAC equally. Can you determine the quantitative relationship between ∠B and ∠C? Please provide a justification for the answer.

19. As shown in the figure, it is known that D is a point on the BC extension line beside △ABC, DF⊥AB meets AC at F and E, ∠ A = 35, ∠ D = 42, and the number of times to find ∠ACD.

20. As shown in the figure, it is known that A(-4,-1), B(-5, -4), C(- 1, -3) and △ABC are translated to get △ a ′ b ′ c ′ and △ ABC (x 1).

(1) Please make △ a ′ b ′ c ′ in the drawing;

(2) Write the coordinates of points A', B' and C'; ?

(3) Find the coordinates of △ a ′ b ′ c ′.

2 1. In order to know the time of social practice activities of 0/000 students in the mathematics department of a normal university, 50 students in this department were randomly investigated. The results are as follows:

Time/date 4 5678910111213

No.124571186442

The following frequency distribution table and frequency distribution histogram are drawn.

Percentage of grouping frequency

3.5~5.5 3 6%

5.5~7.5 18%

7.5~9.5 18 36%

9.5~ 1 1.5

1 1.5~ 13.5 6 12%

Total 50 100%

According to the information provided above, answer the following questions:

(1) complete frequency distribution table;

(2) completing the frequency distribution histogram;

(3) Please estimate how many students in the Department of Mathematics of our school participate in social practice activities for at least 10 days each semester.

22. The ticket price of a park in Changsha is shown in the following table:

The number of ticket buyers is1~ 50,51~ 100, which exceeds100.

Ticket price 10 yuan/8 yuan/5 yuan/person.

More than 50 students from Class A and Class B 100 of Grade 9 in a school went to the park to hold a graduation party, and less than 50 students from Class A and Class B. If tickets were bought separately according to classes, the two classes would have to pay 920 yuan. If two classes buy tickets together, one class has to pay 5 15 yuan. How many people are there in Class A and Class B respectively?

23. A machinery factory has 120 production workers, and each worker can produce 50 bolts or 20 nuts every day. If a bolt and two nuts are matched into a set, how many workers are arranged to produce bolts and nuts every day, which happens to be a set of products produced every day?

24. A storage and transportation station has Class A goods 1.530 tons and Class B goods 1.500 tons. Arrange freight trains to transport these goods to Qingdao, and you can hang 50 carriages of two different specifications, A and B. It is known that 35 tons of Class A goods and 0.5 tons of Class B goods/KLOC-0 can fill a Class A truck, and so can Class A freight trains. Please design it.

answer

I. Multiple choice questions: (***30 points)

BCDDD，CBBCD

Two. Fill in the blanks: (***24 points)

1 1.2 & lt； x & lt8 12.x≤6

13.3 14.40

15.①②③

Three. Answer: (***46 points)

16. Solution: The first inequality can be simplified as

X-3x+6 ≥ 4, and its solution set is X ≤ 1.

The second inequality can be simplified as follows

2(2x- 1)-7。

The solution set of the original inequality group is -7 < x ≤ 1.

Representing the solution set on the number axis are:

17. Solution: The original equation can be transformed into

∴

Subtract the two equations and you can get 37y+74=0.

Y =-2。 Therefore.

Therefore, the solution of the original equation is

18. ∠ b = ∠ c. Reason:

∫ AD ∨ BC

∴∠ 1=∠B,∠2=∠C

∵∠ 1=∠2

∴∠B=∠C

19.？ Solution: Because ∠ AFE = 90,

So AEF = 90-A = 90-35 = 55.

So ∠ CED = ∠ AEF = 55,

So ∠ ACD =180-∠ ced-∠ d.

= 180 -55 -42=83 .

20.( 1)A′(2，3)，B′( 1，0)，C′(5， 1)。

(2) As shown on the right.

(3) As shown in the figure, the intersection point b' is the axis B'd⊥x, and the intersection point a'

Let DE be parallel to the X axis, intersect with B ′ D and C ′ at point D.

The FE⊥x axis intersects with DE at point E, and then B'D=3, DE=4,

Iron =3

S△A′B′C′= SDB′C′E-S△DB′A′-S△EA′C′-S△B′C′F

= B′C′？ DB′-DA′？ DB′-A′E？ EC′-B′F？ cost and freight

=4×3- × 1×3- ×3×2- ×4× 1

= 12- 1.5-3-2

=5.5

2 1.( 1)

Percentage of grouping frequency

3.5~5.5 3 6%

5.5~7.5 9 18%

7.5~9.5 18 36%

9.5~ 1 1.5 14 28%

1 1.5~ 13.5 6 12%

Total 50 100%

(2)

(3)

22. Solution: There are X people and Y people in Class A and Class B respectively.

According to the meaning of the question

solve

A: There are 55 students in Class A and 48 students in Class B. 。

23. Solution: Assume that X workers are arranged to produce bolts and Y workers to produce nuts every day.

solve

Answer: 20 workers are arranged to produce bolts and 65,438+000 workers to produce nuts every day, which is just a set of products produced every day.

24. Solution: If the X part of Type A cargo hold is used, the (50-x) part of Type B cargo hold is used.

The solution is 28 ≤ x ≤ 30.

Because x is an integer, x can only take 28, 29 and 30.

Therefore, the value of (5O-x) is 22,265,438+0,20.

So * * * there are three transportation schemes.

Transport scheme 1: 28 sections for A-type trucks and 22 sections for B-type trucks;

The second transportation scheme: 29 sections for type A trucks and 2 1 section for type B trucks;

The third transportation scheme: 30 sections for A-type trucks and 20 sections for B-type trucks.

May I? Hope to adopt.