The answer to the seventh grade summer vacation life guidance (Shandong Education Press)

1. Mathematical answers to summer vacation life

1.×

2.√

3.√

Two.

1.B

2.B

3.B

4.D

5.A

Three.

1.∠BCE=∠ABC

2. No.55, south by west

3. Equal vertex angle, equal generation, equal generation, equal generation, equal generation, equal generation, etc.

4.25

Four.

1. Solution: ∫∠2+∠3 = 180.

∴a‖b (the inner angles on the same side are complementary and the two straight lines are parallel)

∵∠3=∠4

∴c‖d (same angle, two parallel straight lines)

∫a‖b

∴∠ 3 =∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠

∵∠3+∠5= 180

∠3=60

∴∠5= 120

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3. The evidence is as follows:

∵AB⊥BC

∴∠ABC=90

∵BC⊥CD

∴∠BCD=90

∠∠ABC = 90∠BCD = 90

∠∠BCD =∠ABC∠ 1 =∠2∠2+∠FBC =∠ABC∠ 1+∠BCE =∠BCD

∴∠FBC=∠BCE

∠∠FBC =∠BCE

∴BF‖CE (internal dislocation angles are equal and two straight lines are parallel)

4. Solution: AB‖CD

The reason for this is the following：

∫ Average score ∠ABD

∴∠ABD=2∠ 1

Desplit bottom dead center

∴∠BDC=2∠2

∵∠ 1+∠2=90

∴∠ABD+∠BDC= 180

1. Lines perpendicular to the same line are parallel.

Draw a vertical line

Two vertical lines are parallel if they are equal in length.

3. Use parallel lines with equal internal angles: two mirrors are parallel, so 90-∠2=90-∠3, so ∠2=∠3, then ∠1+∠ 2 = ∠ 3+∠.

One.

1.√

2.×

3.√

4.×

Ii. 1. A

2.D

3.A

4.B

5.B

6.D

VII .. b

8.D

9.B

Three.

1.3 6

2. Second

3.- 1

4. 10

5. The time for A to chase B is 1 1.25 hours.

It takes 4.5 hours to meet.

It takes 12 hours for A to chase B.

6.

Equation set 32(x+y)=400

180(x-y)=400

7. 10

8. Because the two values are different, a number is negative.

When x is negative, x+y = 4 | x |+y | =-x+y = 7.

X=- 1.5 y=5.5 x-y=-7。

When y is negative, x+y = 4 | x |+y | = x-y = 7.

x=5.5 y=- 1.5 x-y=7

Four.

1.

leave out

3. If the rectangular ABCD is AB = 6 and AD = 4. Then take a little E on AB to make AE = 2；; Take a little f on AD to make AF= 1. Points E and F are parallel lines EM and FN of AD and AB respectively, which intersect at point O, that is, O is the origin, EM is the X axis, and FN is the Y axis, so the coordinate of point D is (-2, -3).

The coordinates of the other three points are A (-2, 1), B (4, 1) and C (4 4,3) respectively.

4. Substitute x=2 and y= 1 into the two formulas respectively, and there are

2a+b=3，2b+a=7

By solving this binary linear equation, b= 1 1/7 and a=5/7.

5.4x+3y=7( 1)

kx+(k- 1)y=3(2)

x=y(3)

Because x=y is substituted (1)

7x=7y=7

So x=y= 1.

Substitute (2)

k+k- 1=3

2k=4

k=2

6.x=3，y=4。 Stay in a1x+b1y = c1,a2x+b2y=c2, right.

3a 1+4b 1=c 1

3a2+4b2=c2 ( 1)

3a 1x+2b 1y = 5c 1

3a2x+2b2y=5c2

Divide both sides of the equation by 5 to get:

3/5a 1x+2/5b 1y = c 1

3/5a2x+2/5b2y=c2 (2)

Compare equations (1) and (2).

There are 3x/5 = 32y/5 = 4.

So x = 5 and y = 10.

7. Let the speed and length of the train be V and S respectively.

800+s=45

800-s=35 gives v=20 s= 100.

1. Solution: 1. If the planned new school building is x square meters, the demolished school building is 7200-X square meters.

List the equations according to the meaning of the question:

80% X+( 1+ 10%)(7200-X)= 7200

8X+ 1 1(7200-X)= 72000

3X=79200-72000

X=2400

Planned demolition of school buildings: 7200-X=7200-2400=4800 (m2)

A: It is planned to build 2,400 square meters of new school buildings and demolish 4,800 square meters of school buildings.

2.

Fund for the proposed new school building: 700 * 2400 = 1 680,000 yuan.

Fund for planned demolition of school buildings: 80 * 4,800 = 384,000 yuan.

School building construction and demolition plan funds * * *: 65,438+0,680,000+384,000 = 2,064,000 yuan.

Actual fund for new school building: 80% * 2400 * 700 =1344,000 yuan.

Actual funds for demolishing school buildings: (1+10%) * 4,800 * 80 = 42,240 yuan.

Actual funds for building and dismantling school buildings * * *:1344000+4240 =1386240 (RMB).

The saved funds are: 2064000- 1386240=677760 (yuan).

Green area saved: 677,760/200 = 3,388.8 square meters.

Answer: In the actual demolition and construction project, the remaining funds are used for greening, which is 3,388.8 square meters.

2. Solution: We assume that before the activity, the first refrigerator is X and the second refrigerator is 960-X..

x( 1+30%)+(960-x)( 1+25%)= 1228

The solution is x=560.

First class refrigerator: 560 sets

Category II refrigerators: 400 sets

(2) Type I refrigerator: 560*( 1+30%)=728.

Category II refrigerators: 1228-728=500 sets.

13%(728*2298+500* 1999)

≈3.5* 10 quintic

3. 8m water pipe X and 5m water pipe Y are required.

8X+5Y= 132

Because 132-8X is a multiple of 5, the mantissa of 8X is 2 or 7 (mantissa 7 is singular, not a multiple of 8, regardless of mantissa 7).

So the mantissa of x is 4 or 9, and X≤ 132/8= 16.5.

So x can be chosen as 4; 9; 14 with a relative y of 20; 12; four

That is to say, there are three schemes: 8m 4 5m 2.

8m 9, 5m 12.

8m 14，5m 4。

Because the unit price of 8m is 50/8 yuan/meter < 5m is 35/7 yuan/meter.

Therefore, it is the most economical to choose the scheme with the maximum of 8 meters, that is, 14 blocks of 8 meters and 4 blocks of 5 meters.

1.

Price of pear:11÷ 9 =12/9 (text)

Fruit price: 4 ÷ 7 = 4/7 (text)

Number of fruits:

(12/9×1000-999) ÷ (12/9-4/7) = number of pears: 1000-343 = total price of 657 pears.

12/9× 657 = 803 (text)

Total fruit price:

4/7× 343 = 196 (text)

Solution: let pear be X and fruit be Y.

x+y= 1000

1 1/9X+4/7Y=999

Solution: x = 657Y=343

That is, there are 657 pears, and the money is: 657* 1 1/9=803.

The fruit is 343 and the money is: 343*4/7= 196.

2. Solution: Let there be X on the tree and Y under the tree, then from what is known, we can get:

y- 1/x+y= 1/3

x- 1/y+ 1= 1

The solution is x = 7；; y=5

That is, seven on the tree and five under the tree.

1.C

2.C

3. 120

4. Solution: ∠ AMG = ∠ 3

Reason: ∫≈ 1 =∠2,

∴AB‖CD (the inner angles are equal and the two straight lines are parallel).

∵∠3=∠4,

∴CD‖EF (internal dislocation angles are equal and two straight lines are parallel).

∴AB‖EF (two lines parallel to the same line are parallel).

∴∠AMG=∠5 (two straight lines are parallel and have the same included angle).

∠5=∠3,

∴∠AMG=∠3.

5.。 (1) Set up a walkman with X yuan and a schoolbag with Y yuan.

X+y=452 x=4y-8 If you substitute 2 into 1, you get 4y-8+y=452, y=92 and x=360.

(2) If you buy it in A, it will cost 452*0.8=36 1.6 yuan.

If you buy it at B, 360+(92-90)=362 yuan.

So he can buy it in supermarkets A and B, but A is cheaper.

6.A4( 16，3)

B4(32，0)

An((-2)^n,(- 1)^n*3)

Bn((-2)^n*2,0)

1.A

2.C

3.A

4. Xiaohong means that the same angle is equal and two straight lines are parallel.

Cause of floret: the internal angle is equal and the two straight lines are parallel.

Another set of parallel lines: AB//CE Reason: ∠ABC=∠ECD →AB//CE (same angle, two parallel lines)

5. If 2 yuan has X, 5 yuan has 58-20-7-X.

2x+5(58-20-7-x)+20+ 10 * 7 = 200 x = 15

2 yuan 15, 5 yuan 16.

6.( 1)sδABC = sδABP，sδAPC = sδBPC，sδAOC = sδBOP

(2)sδABC = sδABP, and the areas of triangles with the same base height are equal.

(3) Connect EC, the intersection point D is the parallel line of EC, and the parallel line intersects with CM at point F. 。

EF is the direct way to meet the requirements.

(3) reasons

Because parallel lines are parallel to EC, the height of the distance triangle ECD from point D to EC edge = the height of the distance triangle ECF from point F to EC edge.

Area of triangle = area of triangle ECF.

So,

Area of pentagonal ABCDE = area of quadrilateral ABCE+area of triangular ECD.

= area of quadrangle ABCE+area of triangle ECF.

Therefore, the straight ef meets the requirements.

That makes sense. There are 99 items in Sanduo, and one item refers to three items (also refers to three scholars), all of which are singular. There are many kinds of distribution of such problems. However, this kind is somewhat interesting, and some are just doing problems.