I. 1-5, CDAAC 6- 10, DDBDC.

2. 1 1.x≥-0.5 and x ≠1; 12、2-√3 2-√3; 13、-3; 14、4.5;

15, (1) Original formula = 4-(√ 48 ÷ 3+√12 ÷ 3) = 4-(4+2) =-2.

(2) The original formula = (√ 5)-(√ 2)-(3-2 √ 6+2) = 3-3+2 √ 6-2 = 2 √ 6-2.

(3) The original formula =√x-√x=0.

(4) Original formula = 1.5ab√3a

16. The original formula ==(x+ 1-2)=(x- 1)

∫x- 1 =√3

∴ Original formula =(√3)=3

17. As can be seen from the figure, a is a positive number, greater than 1 and less than 2. Original formula =a- 1-(a-2)= 1.

18. The original formula =2/xy is substituted into x=2 and y=3 to get 2/xy=2/2√3=√3/3.

19.( 1) According to the Pythagorean theorem, c = √ a+b = (2 √ 3+1)+(2 √ 3-1) = √ 26.

(2)。 s△=(2√3+ 1)(2√3- 1)= 5.5

Mathematics world II

1- 10.BCDCB 6- 10BBBDA

1 1.5; 12.√2a； 13.8√5; 14. 12 or 7+7

15.

16.:△ BMP is a right triangle,

And from the meaning of the title, BM=8×2= 16, BP= 15×2=30,

From Pythagorean theorem,

So MP2 =162+302 = 256+900 =1156.

That is MP=34 nautical miles.

A: The distance between P Island and M Island is 34 nautical miles.

17.

= 12.5; Perimeter =3√5+3√2+√ 13 (2) No.

18.

Mathematics Tiandi San

1-5.DAAAA 6- 10BDCBA

1 1. 125; 12. 1.2; 13.7; 32; 14.8

15.∵ is a parallelogram, ∴∠BAD ∠ADC are complementary,

∫AE bisects ∠BAD, ∠ADC bisects ∠ADC∴∠ADO and ∠DAO are complementary.

∴∠AOD is 90 degrees, so DO is perpendicular to AE,

And ∠ADO equals ∠cd0, ∠AOD equals 90 degrees, d0 equals ∴ triangle ADO is congruent with triangle DOE,

∴AO equals OE, so AE is divided vertically.

16.∠∠DCE+∠ECB = 90∠DCE:∠ECB = 1:3∠DCE = 22.5，∠ ECB = 67.5 ∠ BDD。

17.∵CD=BD, ∴RT△CDE are all equal to rt△bde；; ∴CE=BE∵

DE bisects BC vertically, ∴AE=EB,: ACE is a 60-degree isosceles triangle, so: AC=CE=AE.

Af = ce = ae, ∠DEB=∠AEF=∠BAC=60 degrees, ∴△AEF is 60 degrees isosceles △∴AF=AE=EF.

Therefore: AC=AF=EF=CE, so the quadrangle ECAF is rhombic.

18.( 1)∵E is the midpoint of ae⊥bc BC, that is, AE is the middle vertical line of AB = AC BC.

And ∵ABCD is a diamond, ∴△ABC is an equilateral triangle, so ∠ BAC = 60,

∵AB=AC=4∴ Area ABCD = 2 △ Area of ABC =2×( 1/2)×4×4=8√2.

(2) Connect AC, because E is the midpoint of BC, AE⊥BC, so AE is the vertical line of BC, so AC=AB=BC, so △ABC is an equilateral triangle, so ∠ B = ∠ D = 60, so ∠ Bad = 180-.

Because AE⊥BC and AF⊥DC, ∠ BAE = ∠ DAF = 30, ∠ EAF = ∠ bad-∠ BAE-∠ DAF = 60.

, because AE‖CG, ∴ ECG = 90, ∠ Cha =180-∠ EAF =120.

19.( 1) ∵ quadrilateral ABCD is a parallelogram ∴∠B=∠CDN, AB=CD, AD=BC.

And M.N is the midpoint of AD. ∴bn=dm=am=cn. BC ∴△ABN is equal to△ △CDM.

(2) solution: ∫m is the midpoint of AD, ∠ and = 90, ∴MN=MD= 12 AD, ∴ 1 = ∠ MND,

∫ BC ∨, ∴1= ∠ CND,

∫≈ 1 =∠2，∴∠MND=∠CND=∠2，∴PN=PC，

∵CE⊥MN，∴∠CEN=90，∴∠2=∠PNE=30，

∫PE = 1，∴PN=2PE=2，∴CE=PC+PE=3，∴CN= CEcos30 =2√3，

∵∠ MNC = 60, CN=MN=MD, ∴△CNM is an equilateral triangle,

√△ABN?△CDM，∴AN=CM=2√3。

Mathematics Tiandi IV

1-5.BBACB 6- 10。 DBCDB

1 1 . y = 6x-2； 12.-8/3; 13 . y =-5x/2-4；

Two. Three. Four. 14 . y = 2x+3 =- 1.5 >- 1.5

15.( 1) solution: y-2 is directly proportional to x, that is, y=kx+2. When x= 1 and y=7, then: k=5.

Then the functional relationship between y and x is: y=5x+2.

(2) When x=4, y=5×4+2=22.

(3) In terms of meaning, 5x+2 >；; 0，x & gt-0.4

The point 16 B is the intersection of the straight line y= 1/2+3 and the y axis.

∴ Let x=0, y=3, and the coordinate of point B is (0.3).

Let this linear function be y=kx+b, and the image passes through point A (2. 1) and point B (0.3).

∴ 1 = 2k+b, 3=0k+b, the solution is b=3, k=- 1. ∴y=-x+3.

17. solution: (1) from the meaning of the question.

Let the linear functional relationship between y and x be

replace

Solution:

∴

(2) When two piles are stacked, * * * has 1 1.

X= 1 1 and y=2 1.

∴ This pile of bowls is 2 1cm high.

19. Solution: (1) Fill in according to the picture: 60,150,300.

(2) According to the information provided by the image, we can know that point M is the midpoint of on,

∵MK∥NE,∴OK=

1

2

OE=2.5,∴CK=OK-OC= 1.5.

That is, it takes 1.5 hours for the car to catch up with the truck.

Eighth grade summer homework: the world of mathematics

(3) According to the information provided by the image, we can know that m is the midpoint of CD, MK∨DF,

∴CF=2CK=3.

∴OF=OC+CF=4.

∴EF=OE-OF= 1.

That is, the car arrives earlier than the truck 1 hour.

20. (1) Ya =1.2x+900 (x ≥ 500, x is an integer);

Y b = 1.5x+540(x≥500, x is an integer);

(2) Make an image with the function Y A = 1.2x+900, Y B = 1.5x+540(x≥500),

The intersection of two function images is p (1200,2340).

As can be seen from the image, when 500 ≤ x

When x= 1200 copies, the charges of the two factories are the same;

When x> 1200 copies, it is more cost-effective to choose a factory.

Mathematics Tiandi Wu

I.1-5 bdbac6-10 cabad

Second, 1 1, 15+08.

12、50×48+46×49.8+55×50.2+48×49.5+52×5 1+54×50.3/50+46+55+48+52+54.50.0

13、89.7

14、7+4√3

Three, 15, make more shoes of size 24 and less shoes of size 20, 2 1, and make the following formula according to the actual situation.

16、≈86.93

17, a mean 1 1.45 variance 0. 1 1 range 0.93 B mean 18.50 variance 0 range 0.

18, (1)A's `average value ≈ 71.67b ≈ 68.33c = 70: A's average value is greater than B's and C's average value ∴ A will be accepted; (2) If the average value of A is greater than the average value of B, then A ≈ 74.17b ≈ 73.33c ≈ 75.83: C will be accepted.

19 and (1) median (2)≈ 132.90 did not appear.

20.( 1) A 70 B 68 C 62

(2) A 7 1.8 B 7 1.6 C 65

∫7 1.8 & gt； 7 1.6 >65

∴ A will be hired, and his score is 71.8,21,(1) 1.2 7 7 7.5 (2).