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

1, if the formula is meaningful in the real number range, the value range of x is ().

A.x≥ B.x C.x≥ D.x

2. Among the following quadratic roots, the one that cannot be simplified is ()

A.B. C. D。

3. In the triangle with the following groups as sides, there is a right triangle ().

( 1)3,4,5; (2) , , ; (3)32,42,52; (4)0.03,0.04,0.05.

1。

4, and the straight line y=2x+ 1 about x axis symmetry is ().

a . y =-2x+ 1 b . y =-2x- 1 C D

5. As shown in the figure, in a square ABCD with a side length of 2, m is the midpoint of the side length AD, MD extends to point E to make ME=MC, de is the side to make a square DEFG, and point G is on the side CD, so the length of DG is ().

A.B. C. D。

6. For the function y=﹣5x+ 1, the following conclusions are drawn: ① The image must pass through the point (﹣ 1, 5); ② When the image passes through the first, second and third quadrants; ③ When x 1, the value of Y04y increases with the increase of the value of x,

A 0 B 1 C 2 D 3

7. As shown in the figure, it is known that OP bisects ∠AOB, ∠ AOB = 60, CP = 2°, CP∨OA, PD⊥OA at point D and PE⊥OB at point E. If point M is the midpoint of OP, the length of DM is ().

The second century BC.

8. Eight squares with a side length of 1 are placed in a plane rectangular coordinate system as shown in the figure. A straight line L passing through point P divides eight squares into two parts with equal areas. The analytical formula of the straight line L is ()

A B C D

9. As shown in the figure, in quadrilateral ABCD, AB=CD, diagonal AC and BD intersect at point O, AE⊥BD intersects at point E, and CF⊥BD intersects at point F, connecting AF and CE. If DE=BF, the following conclusions are obtained: ① CF = AE; ②OE = OF； ③ The quadrilateral ABCD is a parallelogram; ④ There are four pairs of congruent triangles in the graph * * *. The number of correct conclusions is ().

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

10, Xiao Ming and Xiao Yu set out from school to participate in the calligraphy competition in the Youth Palace. After Xiao Ming walked for a while, Xiao Yu rode his bike along the same route, and both of them advanced at a constant speed. The functional relationship between their distance difference S (meters) and Xiao Ming's departure time T (minutes) is shown in the figure. The following statement: ① Xiaoyu went to the Youth Palace first; ② Xiaoyu's speed is three times that of Xiaoming; ③a = 20； ④b=600。 The correct one is ().

A.①②③ B.①②④ C.①③④ D.①②③④

10 diagram, sheet 9.

Second, write your conclusion and fill in the blanks perfectly! (3 points for each small question, ***24 points)

1 1. For the proportional function, the value of decreases with the decrease of the value of, and the value of is.

12. For long-distance calls from A to B, 2.4 yuan will be charged within 3 minutes (including 3 minutes). After 3 minutes, each additional call time of 1 minute will be charged at 1 yuan (if the call time is less than 1 minute, it will be charged at 1 minute). If anyone has 12 yuan, they can make a phone call.

17 map 18 map

13, write a straight line through the first, second and fourth quadrants.

14 When five integers are arranged from small to large and the number of digits is 4, if the unique mode of this set of data is 6, then the maximum value of the sum of these five numbers is.

15, as shown in the figure, the diagonal AC and BD of quadrilateral ABCD intersect at point O, and the conditions are as follows: ①AO=CO, bo = do2ao = bo = co = do. Among them, the condition that ABCD is rectangular is (fill in the serial number).

16, the known value is.

17, height of cylindrical box without top cover 10cm, circumference of 32cm, and point A is 3cm away from the bottom. An ant located at point A on the outer surface of a cylindrical box wants to climb to the midpoint B opposite to the inner surface of the box, so the length of the shortest path that the ant needs to crawl is cm.

18. It is known that in the plane rectangular coordinate system, point O is the coordinate origin, the straight line OM passing through O passes through point A (6 6,6), the straight line A is a square ABCD, there is a point E on the straight line OA, the side length of the square ABCD is 2, and the side length of the square EFGH is 3, so the coordinate of point F is.

Third, answer the question.

19, calculation (6 points)

20(8 points). In the plane rectangular coordinate system, it is known that the intersection of a straight line and a straight line is in the fourth quadrant, and the value of an integer is found.

2 1, (8 points) A middle school conducted a sampling survey on voluntary donation activities for the disabled, and obtained a group of data on student donations. The following figure is a statistical chart drawn according to this set of data. The height ratio of the rectangle in the figure from left to right shows that the number of people who donated 15 yuan and 20 yuan was ***39.

(1) How many people did they randomly check?

(2) What is the mode and median of this set of data?

(3) If the school has 1500 students, please estimate the donations of all students.

Question 22

22(8 points), as shown in the figure, in the parallelogram ABCD, e is a point on the side of BC, connecting AE and BD, and AE=AB.

(1) Verification: ∠ Abe = ∠ EAD;

(2) If ∠AEB=2∠ADB, it is proved that the quadrilateral ABCD is a diamond.

23( 12), on-the-spot investigation: In △ABC, the lengths of AB, BC and AC are,,, respectively. Find the area of this triangle. When Xiaohua solves this problem, he first draws a square grid (the side length of each small square is 1), and then draws outliers △ABC (that is, three△ ABC) in the grid.

(1) △ The area of ABC is: _ _ _ _ _ _ _ _;

(2) If the lengths of the three sides of △DEF are,,, please draw the corresponding △DEF in the square grid of figure 1 and find its area by composition method;

(3) As shown in Figure 2, a hexagonal flower bed is divided into seven parts, in which the areas of square PRBA, RQDC and QPFE are 13, 10, 17 respectively, and the areas of △PQR, △BCR, △DEQ and △AFP are equal, so as to find the hexagonal flower bed.

24.( 12) A garment factory has fabric A 70m and fabric 52m, and plans to produce 80 sets of M and N fashions with these two fabrics. It is known that making a set of M-style fashions requires 0.6m fabric A and 0.9m fabric B, which can make a profit in 45 yuan.1.20060.000000000606

(1) Find the functional relationship between Y and X, and find the range of the independent variable X;

(2) In the production of this batch of fashions, how many sets of N-type fashions are produced, and the garment factory gains the most profit? What is the maximum profit?

25( 12 minutes), as shown in the figure, in the plane rectangular coordinate system, the side length of the square OABC is a. The straight line y=bx+c intersects with the X axis in E, and intersects with the Y axis in F, and A, B and C satisfy respectively.

(1) Find the analytical formula of the straight line y=bx+c and directly write the coordinates of the intersection point d of the diagonal of the square OABC;

(2) The straight line y=bx+c translates along the positive direction of the X axis at the speed of 1 unit length per second. Let the translation time be t seconds, and ask whether there is a value of t, so that the straight line EF bisects the area of the square OABC. If it exists, request the value of t; If it does not exist, please explain the reason;

(3) Point P is the moving point on the diagonal AC of the square OABC (except endpoints A and C), and PM⊥PO and intersection AB are at m ... Find the value of ...

This paper navigates to 1, home page 2, and the final examination paper of the second volume of mathematics in grades 2 -2.

Attachment: Reference answer

I. 1- 10a DBBD BC ABB

Two. 1 1, 2 12, 12 13, 2 14, 50 15, 20 16, (9, 6)

Three. 17( 1) (4 points) (2) 2 (4 points)

18, (1) cross c is CE∑DA, AB is e,

∴∠A=∠CEB

∠A=∠B again.

∴∠CEB=∠B

∴BC=EC

And ∵AB∨DC CE∨DA.

∴ Quadrilateral AECD is a parallelogram

∴AD=EC

∴AD=BC (4 points)

(2) The inverse proposition of (1): In trapezoid ∠A=∠BCD, AB∨DC, if AD=BC, it is proved that ∠ A = ∠ B.

Proof: cross c as CE∨DA and AB as e.

∴∠A=∠CEB

And AB∨DC CE∨DA

∴ Quadrilateral AECD is a parallelogram

∴AD=EC

Once again: AD = BC

∴BC=EC

∴∠CEB=∠B

∴∠A=∠B (4 points)

19、

Proof: link BD,

∫△ACB and △ECD are isosceles right triangles,

∴∠ECD=∠ACB=90，∠E=∠ADC=∠CAB=45，EC=DC，AC=BC，AC2+BC2=AB2，

∴2AC2=AB2.∠ECD-∠ECB=∠ACB-∠ECB，

∴∠ACE=∠BCD.

In △AEC and △BDC,

AC=BC

∠ACE=∠BCD

EC =DC

,

∴△AEC≌△BDC(SAS).

∴AE=BD,∠AEC=∠BDC.

∴∠BDC= 135，

That is ∠ ADB = 90.

∴AD2+BD2=AB2，

∴AD2+AE2=2AC2.(8 points)

20. Proof: (1) in parallelogram ABCD, AD∨BC,

∴∠AEB=∠EAD，

AE = AB，

∴∠ABE=∠AEB，

∴∠abe=∠ead； (3 points)

②∫AD∨BC，

∴∠ADB=∠DBE，

∠∠ Abe =∠∠ AEB = 2 ∠ ADB,

∴∠ABE=2∠ADB，

∴∠abd=∠abe﹣∠dbe=2∠adb﹣∠adb=∠adb，

∴AB=AD，

The quadrilateral ABCD is a parallelogram,

The quadrilateral ABCD is a diamond. (5 points)

2 1 and ∵ straight line y = ∵ x+8, which intersect with X axis and Y axis at points A and B respectively.

When x=0, y = 8；; When y=0, x=6.

∴OA=6,OB=8

∵CE is the middle vertical line of line segment AB.

∴CB=CA

Let OC=, then

Solution:

The coordinate of point ∴c is (∴ 0); (6 points)

∴△abc∴△ Region S= AC×OB= × ×8= (2 points)

22. Solution: (1) According to the lattice number, we can know that the area is s = 3× 3-=; (2 points)

(2) The drawings are as follows

Calculate the correct result s △ def = 3; (3 points)

(3) Calculate S△PQR= by synthesis method.

△PQR, △BCR, △ Dirk and △ AFP have the same area.

The calculated area of hexagonal flower bed ABCDEF is s square PRBA+S square RQDC+S square QPF+4s △ PQR =13+10+/7+4x = 62. (5 points)

23. Solution: (1) Fill in the form as follows:

Transfer to position

Fertilizer dosage (ton)

Total number of transfers from Township A and Township B.

A city x 300﹣x 300

B City 260-x240-(300-x200)(3 points)

Total 260,240,500

(2) According to the meaning of the question:

y=20x+25(300﹣x)+25(260﹣x)+ 15[240﹣(300﹣x)]=﹣ 15x+ 13 100； (3 points)

(3) because y =-15x+13100, y decreases with the increase of x,

According to the meaning of the question,

Solution: 60≤x≤260,

So when x=260, y is the smallest, y=9200 yuan.

At this time, the plan is as follows: 260 tons of fertilizer will be transported from City A to Township A, 40 tons from City A to Township B, 20 tons from City B to Township A and 200 tons from City B to Township B (4 points).

24.( 1) From the meaning of the question, the analytical formula of the straight line y=bx+c is: y=2x+8.

D (2，2)。 (4 points)

(2) When y=0, the coordinates of points X =-4 and-E are (-4,0).

When the straight line EF translates across the point D, it just bisects the area of the square AOBC.

Let the translated straight line be y=2x+b, and substitute the coordinates of point D to get b=﹣2.

At this time, the coordinate of the intersection of the straight line and the X axis is (1, 0), and the translation distance is 5, so t=5 seconds. (8 points)

(3) NQ∑OA, GH∑CO, CO and AB in N and Q, CB and OA in G and H.

It is easy to prove that △ oph △ mpq, quadrilateral CNPG is a square.

∴PG=BQ=CN.

That's it. (12)