The second volume of the seventh grade

beijing normal university publishing house

Workbook answer

Chapter 1 Multiplication and Division of Algebraic Expressions

1. 1 algebraic expression

1.( 1)C、D、F； (2)A、B、G、H； (3)A、B； (4)G； (5)E、I； 2.； 3.； 4. Four, four, -Ab2c,-25; 5. 1,2; 6.a3b2c7.3x 3-2 x2-x； 8.； 9.d； 10.a； 1 1.B？ 0? 1; 12.d； 13.c； 14.； 15 . a =； 16 . n =； Four. - 1.

Addition and subtraction of algebraic expression 1.2

1.-xy+2x2y 2； 2.2 x2+2x2y； 3.3; 4 . a2-a+6； 5.99 c-99a； 6.6x2y+3x2y 2- 14y 3； 7.； 8.； 9.d； 10.d； 1 1.d； 12.b； 13.c； 14.c； 15.b； 16.d； 17.c； 18. solution: original formula =, when a =-2 and x = 3, original formula = 1.

Solution: x=5, m=0, y=2, and the original formula =5.20. (8a-5b)-[(3a-b)- ]=, when a= 10 and b=8, there are 29 passengers on the train. 38636.8886888866 1

22. Solution: (1) 1, 5,9, that is, the last one has four more squares than the previous one.

(2) 17，37， 1+4(n- 1)。

Solution: In the three pictures, the required ropes are 4a+4b+8c, 4a+4b+4c and 6a+6b+4c respectively.

Therefore, the rope in (2) is the shortest and the rope in (3) is the longest.

1.3 Multiplication of the same radix power

1., ; 2.2x5，(x+y)7； 3. 106; 4.3; 5.7, 12, 15,3 ; 6. 10; 7.d； 8.B？ 0? 1; 9.d； 10.d； 1 1.b； 12.( 1)-(x-y) 10； (2)-(a-b-c)6； (3)2x 5； (4)-xm

13. Solution: 9.6×106×1.3×108 ≈1.2×10/5 (kg).

14.( 1)① ,② .

(2)①x+3=2x+ 1，x=2 ②x+6=2x，x=6。

15.-8x7y 8； 16. 15x=-9，x=-。

Four. 105.

The power of the product of the power sum of 1.4

1., ; 2.； 3.4 ; 4.； 5.； 6. 1,- 1; 7.6, 108; 8.37; 9.a、D； 10.a、C； 1 1.b； 12.d； 13.a； 14.b； 15.a； 16.B. 17。 ( 1)0; (2) ; (3)0.

18. (1) 241(2) 540019., so it is .20. -7;

2 1. Original formula =,

Another known last digit is the same as the last digit of 33, which is 7, while the last digit of is 5.

The last digit of the original formula is 15-7=8.

Four. 400.

1.5 Division of the same radix power

1.-x3，x； 2 . 2 . 04× 10-4kg； 3.≠2; 4.26; 5.(m-n)6； 6. 100 ; 7.； 8.2; 9.3? 0? 1,2,2; 10.2m = n； 1 1.b； 12.b； 13.c； 14.b； 15.c； 16.a；

17.( 1)9; (2)9; (3) 1; (4) ; 18.x=0，y = 5； 19.0; 20.( 1) ;

(2) .2 1.；

Four. 0, 2, -2.

Multiplication of 1.6 algebraic expression

1. 18 x4 y3z 2； 2.30(a+b) 10； 3.-2x3y+3x2y 2-4xy 3； 4 . a3+3a； 5.-36; 6.a4？ 0? 1- 16; 7.-3x 3-x+ 17； 8.2,3 9.； 10.c； 1 1.c； 12.c； 13.d； 14.d； 15.d； 16? 0? 1.b； 17.a； 18.( 1)x =； (2)0;

19.∵ ∴ ;

20.∫x+3y = 0 ∴x3+3x2y-2x-6y=x2(x+3y)-2(x+3y)=x2？ 6? 10-2? 6? 10=0,

2 1. From the meaning of the question, 35a+33b+3c-3=5,

∴35a+33b+3c=8，

∴(-3)5a+(-3)3b+(-3)c-3=-(35a+33b+3c)-3=-8-3=- 1 1，

22. The original formula =-9, and the value of the original formula has nothing to do with the value of a. 。

23.∵ ,

= ,

= .

∴ divisible by 13.

4. There is a positive integer of 14.

1.7 square difference formula (1)

1.36-x2，x2-； 2.-2 a2+5b； 3 . x+ 1； 4.b+c，b+ c； 5.a-c，b+d，a-c，b+d； 6., 15999 1; 7.d； 8.c； 9.d； 10.- 1; 1 1.5050 ; 12.( 1) ,-39 ; (2)x = 4； 13. Original formula =; 14. Original formula =. 15. These two integers are 65 and 63.

Four. Omit.

1.7 square difference formula (2)

1 . B2-9 a2； 2.-a- 1； 3 . n-m； 4.a+b， 1； 5. 130+2 , 130-2 , 16896; 6.3x-y2； 7.-24 ; 8.- 15; 9.b； 10.d； 1 1.c； 12.a； 13.c； 14.B. 15。 Solution: Original formula =.

16. solution: the original formula =16y4-81x 4; 17. Solution: Original formula = 10x2- 10y2. When x =-2 and y = 3, the original formula =-50.

18. Solution: 6x=-9,∴x=.

19. solution: the area of this vegetable field is:

(2a+3)(2a-3)=(2a)2-9=4a2-9(cm2)，

20. Solution: The volume of the swimming pool is (4a2+9b2)(2a+3b)(2a-3b).

= 16a4-8 1b4 (m3)。

2 1. solution: original formula =-6xy+ 18y2,

When x =-3 and y =-2, the original formula =36.

A change: solution: from the title:

m =(-4x+3y)(-3y-4x)-(2x+3y)(8x-9y)

=(-4x)2-(3y)2-( 16x 2- 18xy+24xy-27 y2)

= 16 x2-9 y2- 16 x2-6xy+27 y2 = 18 y2-6xy。

4.2n+ 1。

1.8 complete square formula (1)

1.x2+2xy+9y2，y- 1； 2.3a-4b，24ab，25，5； 3 . a2+B2+C2+2ab-2ac-2bc； 4.4ab？ 0? 1,-2, ; 5.6; 6 . x2-y2+2yz-z2； 7.2cm8.d； 9.b； 10.c； 1 1.b； 12.b； 13.a；

14.∫x+= 5 ∴(x+)2 = 25, namely x2+2+ =25.

∴x2+ =23 ∴(x2+ )2=232, that is, +2+ =529, that is, =527.

15.[(a+ 1)(a+4)][(a+2)(a+3)]=(a2+5a+4)(a2+5a+6)=(a2+5a)2+ 10(a2+5a)+24

= .

16. Original formula = a2b3-ab4+2b. When a = 2 and b =- 1, the original formula =- 10.

17.∫a2+B2+C2-a b-BC-ca = 0

∴2(a2+b2+c2-ab-bc-ca)=0

∴(a2-2ab+b2)+(b2-2bc+c2)+(a2-2ac+c2)=0

That is, (a-b)2+(b-c)2+(a-c)2=0.

∴a-b=0,b-c=0,a-c=0

∴a=b=c.

18.left =[(A+C)2-B2](A2-B2+C2)=(A2+B2+C2)(A2-B2+C2)

=(a2+c2)2-b4= +2a2c2-b4=。

Ab+bc+ac=-。

1.8 Complete Square Formula (2)

1.5y； 2.500; 2; 250000+2000+4; 252004.3.2; 4.3a6abB2； 5.-6; 6.4; 7.2xy2xy

8.,4; 9.d； 10.d； 1 1.b； 12.b； 13.c； 14.b；

15. solution: original formula =2a4- 18a2. 16. Solution: Original formula =8x3-2x4+32. When x=-, the original formula =.

17. solution: let m= 1234568, then 1234567 = m- 1, 1234569 = m+ 1,

Then a = (m-1) (m+1) = m2-1,and b = m2.

It is obviously M2- 1

18. Solution:-(x2-2) 2 > (2x)2-(x2)2+4x，

-(x4-4x2+4)>4x2-x4+4x，

-x4+4x 2-4 & gt； 4x2-x4+4x，

-4 & gt； 4x,∴x<； - 1.

19. Solution:

From ①: x2+6x+9+y2-4y+4 = 49-14y+y2+x2-16-12,

6x-4y+ 14y=49-28-9-4，

6x+ 10y=8, that is 3x+5y=4, ③.

From ③-②× ③: 2y=7,∴y=3.5,

Substitute y=3.5 into ② to get: x=-3.5- 1=-4.5,

∴

20. solution: c=8-b is obtained from b+c=8, and it is obtained by substituting bc=a2- 12a+52.

b(8-b)=a2- 12a+52，8b-b2=a2- 12a+52，

(a-b)2+(b-4)2=0，

So a-6=0 and b-4=0, that is, a = 6 and b = 4,

Replace c=8-b with b=4, and c=8-4=4.

C = b = 4, so △ABC is an isosceles triangle.

( 1) 200 12+(200 1× 2002) 2+20022 = (200 1× 2002+ 1) 2.

(2)N2+[n(n+ 1)]2+(n+ 1)2 =[n(n+ 1)]2。

Division of 1.9 algebraic expression

1.； 2.4b3.-2x+ 1； 4.； 5.- 10× ; 6.-2yz, x (answer? 0? 1 not unique); 7.； 8.3; 9 . x2+2； 10.c； 1 1.b； 12.d； 13.a； 14.c； 15.d；

16.( 1)5xy 2-2x2y-4x-4y； (2) 1(3)2x2y 2-4x 2-6；

17. Obtained from solution;

∴ .

18.a=- 1，b=5，c=-，

∴ Original formula =.

19.；

20. Let the divisor be p and the remainder be r, then according to the meaning of the question:

80 = pa+R 1, 94 = Pb+R2, 136 = PC+R3, 17 1 = PD+R4, where p, a, b, c, d? 0? 1 is a positive integer, r≠0.

②-① 14=P(b-a), ④-③ 35=P(d-c) and (35, 14)=7.

Therefore, when P=7 or P= 1, when P=7, 80 ÷ 7 = 1 1...3 gives r=3.

When P= 1, 80÷ 1=80+0, which is inconsistent with the remainder not being 0, so P≠ 1.

The divisor is 7 and the remainder is 3.

Four. Omit.

Unit comprehensive test

1., 2.3,2; 3. 1.23× ,- 1.49× ; 4.6; 4; ; 5.-2 6? 0? 1. Single or quintic idempotent, letter A, etc. 7.25; 8.4002; 9.- 1; 10.- 1; 1 1.36; 12.a=3，b=6？ 0? 1，c = 4； 13.b； 14.a； 15.a； 16.a； 17.c； 18.d；

19. from a+b=0, cd= 1, │m│=2, x=a+b+cd- │m│=0.

Original formula =, when x=0, the original formula =.

20. orders,

∴ Original formula = (b-1) (a+1)-AB = AB-A+B-1-AB = B-A-1=.

2 1.∵

=

∴

∴ =35.

22.

= = 123×3- 12×3+ 1=334.

Chapter II Parallel Lines and Intersecting Lines

2. 1 complementary angle and complementary angle

1.×、×、×、×、×、√; 2.( 1) Complementary angle of vertex angle (2) (3); 3.d； 4. 1 10 、70 、 1 10 ; 5. 150 ; 6.60 ; 7.∠AOE∠ BOC ∠AOE∠ BOC 1 Right; 8.90 9.30 ; 10.4 and 7 pairs; 1 1.c； 12. 195 ; 13.( 1)90 ; (2)∠MOD= 150，∠AOC = 60； 14.( 1)∠AOD = 12 1； (2)∠AOB=3 1，∠DOC = 3 1； (3)∠AOB =∠DOC； (4) established;

Four. 405.

2.2 conditions for exploring parallel lines (1)

1.d； 2.d； 3.a； 4.a； 5.d； 6.64 ; 7. AD, BC, same angle, two straight lines parallel; 8, the vertex angle is equal, equivalent substitution, the same angle is equal, and the two straight lines are parallel; 9.BE‖DF (the answer is not unique); 10.AB‖CD‖EF； 11.12. FB ‖ AC, the proof is abbreviated.

Four. A ‖ B，M ‖ N ‖ L。

2.2 conditions for exploring parallel lines (2)

1.CE, BD, same angle; BC, AC, ipsilateral inner angle; CE, AC, internal angle; 2.BC‖DE (the answer is not unique); 3. Parallel, the internal dislocation angles are equal, and the two straight lines are parallel; 4.c； 5.c； 6.d； 7.( 1)∠ Bed with the same angle and two straight lines parallel; (2)∠DFC, the internal dislocation angles are equal and the two straight lines are parallel; (3)∠AFD, which is complementary to the inner angle of the side and the two straight lines are parallel; (4)∠AED, which is complementary to the inner angle of the same side and the two straight lines are parallel; 8.b； 9.c； 10.b； 1 1.c； 12. Parallel, the proof is abbreviated; 13. Omit the proof; 14. Omit the proof; 15. Parallel, the proof is abbreviated (hint: extend DC to H);

4. Parallel, hint: the parallel line passing through E is AB.

2.3 Characteristics of parallel lines

1. 1 10 ; 2.60 ; 3.55 ; 4.∠CGF, isosceles angle is equal, two straight lines are parallel, ∠F, internal angle is equal, two straight lines are parallel, ∠F, two straight lines are parallel and complementary; 5. Parallel; 6.①② ④ (the answer is not unique); 7.3; 8.d； 9.c； 10.d； 1 1.d； 12.c； 13. Omit the proof; 14. Omit the proof;

4. Parallel, prompt: the parallel line passing through C is DE, 1 10.

2.4 Draw line segments and angles with a ruler (1)

1.d； 2.c； 3.d； 4.c； 5.c； 6. Omit; 7. Omission; 8. Omission; 9. Omission;

(1) ellipsis (2) ellipsis (3) 1a2.

4.4 Use a ruler as the line segment and angle (2)

1.b； 2.d； 3. Omit; 4. Omission; 5. Omit; 6. Omit; 7.( 1) omitted; (2) ellipsis; (3) equality; 8. Omission; 9. Omission; 10. Omit;

Four. Omit.

Unit comprehensive test

1. 143 ; 2. The vertex angles are equal; 3.∠ACD、∠B； ∠BDC∠ACB； ∠ACD； 4.50 ; 5.65 ; 6. 180 ; 7.50 、50 、 130 ; 8.α+β-γ= 180 ; 9.45 ; 10.∠AOD∠AOC； 1 1.c； 12.a； 13.c； 14.d； 15.a；

16.d； 17.d； 18.c； 19.d； 20.c； 2 1. omit the proof; 22. Parallel, the proof is omitted; 23. Parallel, the proof is omitted; 24. Omit the certificate;

Chapter III Data in Life

3. 1 one in a million

1, 1.73× 10 ; 2,0.000342 ; 3,4× 10 ; 4,9× 10 ; 5，C； 6、D； 7，C； 8，C； 9，C； 10,( 1)9. 1× 10 ; (2)7× 10 ; (3) 1.239× 10 ; 1 1, = 10 ; 10.

3.2 Approximation and significant figures

1.( 1) approximation; (2) approximate figures; (3) accurate quantity; (4) approximate figures; (5) approximate figures; (6) approximate figures; (7) approximate figures; 2. Thousands; Ten places; Percentile; Unit; Hundreds; Thousands; 3. 13.0, 0.25 , 3.49× 104 , 7.4* 104; 4.4, 3, 4, 3, 2, 3; 5.a； 6、C； 7.b； 8.d； 9.a； 10.b；

1 1. It is possible, because the approximate number 1.8× 102cm is greater than or equal to 1.75× 102 and less than1.85×/kloc.

12.×3. 14×0.252×6 = 0.3925 mm3≈4.0× 10- 10 m3

13. Because archaeology can only measure an approximate number of years, the 800,000 years mentioned by archaeologists is only an approximate number, but the administrator regards it as an accurate number, which is really a big mistake.

Four: 1, Liang Xiao and Xiao Ming's statements are incorrect. The approximate number of 3498 accurate to thousands is 3× 103.

3.3 World Newborn Map

1,( 1)24% ; (2) below 200 m; (3)8.2%;

2. (1) 59× 2.0 =118 (ten thousand boxes);

(2) Because 50× 1.0=50 (ten thousand boxes), 59×2.0= 1 18 (ten thousand boxes), 80× 1.5= 120 (ten thousand boxes)

(3) = 96 (ten thousand cases);

Answer: In the past three years, the region sold an average of 960,000 boxes of bento every year.

3.( 1) The monthly income and expenditure chart of Mr. Wang in 200 1 year1-June.

(2)28:22:27:37:30:29;

4.( 1) This person shoots steadily and has a good mentality, so his grades are getting better and better;

(2) The average score is 8.

(3)

5. Solution: (1) The actual living consumption is decreasing year by year, the consumption of health products is increasing year by year, and the consumption of tourism is increasing year by year.

(2) The total annual consumption has increased.

(3)

6.( 1) is expanded as: 6000-500=5500(km)2.

6000÷500= 12.

(2) During the period of1960 ~1980, the land area of Shanghai urban area and suburban counties did not change much, indicating that the urbanization process was very slow.

(3) It shows that some land in suburban counties has been included in Shanghai urban area. After 1980, the total land area of Shanghai urban area and suburban counties remained almost unchanged, indicating that the total land area of Shanghai urban area and suburban counties remained almost unchanged after 1980, indicating that the urbanization process of Shanghai is getting faster and faster without expanding the total land area after 1980.

7. (1) Statistics show that the tax revenue is increasing year by year, so the tax revenue in 2000 was between 8-1300 million yuan.

(2) you can get the tax situation of each year, etc. (3) as long as it is reasonable.

Unit comprehensive test

1. 10-9; 2. 106 ; 3.333× 103; 3.0.0000502; 4. 170, 6 ; 5. Hundred, 3.3×104; 6. 1.4× 108 , 1.40× 108; 7.0.36 0.4; 8. 1.346× 105; 9.a， 10。 b， 1 1。 c， 12。 c， 13。 a， 14。 d， 15。 b， 16。 c， 17。 b， 18。