Chapter VI One-dimensional Linear Equation

6. 1 From practical problems to equations

I. 1.d2.a3.a

2. 1 . x =-6 2.2x- 15 = 25 3 . x = 3( 12-x)

3. 1. Solution: If the production and operation water consumption is x billion cubic meters, the household water consumption is (5.8-x) billion cubic meters, and the equation can be listed as follows:

5.8-x=3x+0.6

2. Solution: If an apple buys X kilograms, the equation can be listed as: 4x+3(5-x)= 17.

3. Solution: Let the number of the original extracurricular math group be X, then the equation can be listed as:

6.2 Solve the linear equation of one variable (1)

I. 1.d2.c3.a

2. 1.x =-3, x= 2. 10 3. x=5。

Three. 1 . x = 72 . x = 43 . x = 4 . x = 5 . x = 36 . y =

6.2 Solving the linear equation of one variable (2)

I. 1. B 2。 D 3。 A

Two. 1.X =-5，y = 3 ^ 2。 3.-3

Three. 1.( 1)x =(2)x =-2(3)x =(4)x =-4(5)x =(6)x =-2。

2.( 1) Suppose the table tennis team in Class Two, Grade One * * has X people, and get: 9X-5 = 8x+2. Get: X = 7 (2) There are 48 people.

3.( 1)x=-7 (2)x=-3

6.2 Solving the linear equation of one variable (3)

I./kloc-0 1.C2.D3.B4.B

Second, 1. 1 2.3. 10

Three. 1.( 1)x = 3(2)x = 7(3)x =– 1(4)x =(5)x = 4(6)x =

2.3( x-2) -4(x- )=4 and x =-3 3. 3 yuan.

6.2 Solving the linear equation of one variable (4)

I. 1. B 2。 B 3。 D

Two. 1.5 2., 3.4. 15

Three. 1.( 1) y = (2) y = 6 (3) (4) x =

2.x= is obtained from equation 3(5x-6)=3-20x, and a =-8 is obtained by substituting x= into equation a- x=2a+ 10x.

When a=-8, Equation 3(5x-6)=3-20x has the same solution as Equation a- x=2a+ 10x.

3. Solution: x=9

6.2 Solve the linear equation of one variable (5)

I. 1.a2.b3.c

2.1.2 (x+8) = 402.4,6,8 3.2x+10 = 6x+54.155.160 yuan.

3. 1. Suppose person X goes to A, and 27+x=2[ 19+(20-x)] is obtained according to the meaning of the question. Solution: x= 17.

2. Suppose the user's water consumption in May is x tons, which is1.2× 6+2 (x-6) =1.4x according to the meaning of the question.

X=8。 So 1.4x= 1 1.2 (yuan).

When the number of students is X, the fees charged by the two travel agencies are the same.

240+ 120 x = 144(x+ 1)，x=4。

6.3 Practice and Exploration (1)

I. 1. B 2。 B 3。 A

Two. 1.36 2.3.42,270

3. 1. Let the digits of the original two digits be x, and according to the meaning of the question, you can get.

10x+ 1 1-x = 10( 1 1-x)+x+63。 The solution is x=9. Then the original two digits are 29.

2. If X children's tickets are sold, then sell (700-x) adult tickets.

According to the meaning of the question, the score is 30x+50(700-x)=29000. If the answer is x=300, then 700-x=700-300=400 people.

Then I sold 300 children's tickets and 400 adult tickets.

6.3 Practice and Exploration (2)

I. 1. A 2。 C 3。 C

Second, 1. X+X+ 1+ 1 = X 2 . 23 . 75% 3 . 20000000005

3. 1. Suppose B processes x parts per hour, and 5(x+2)+4(2x+2)=200.

X= 14。 Then a processes 16 parts per hour, and b processes 14 parts per hour.

2. Miss Wang needs to borrow X yuan from the housing provident fund.

According to the meaning, 3.6% x+4.77% (250000-x) =10170. The solution is x= 150000.

Then Mr. Wang needs to borrow 150000 yuan from the housing accumulation fund and 100000 yuan from the ordinary housing loan.

It will take x months to complete this project just to set up the second engineering team.

The solution is x = 1.

4. Hours

Chapter VII Binary Linear Equations

7. 1 binary linear equations and their solutions

I. 1. C 2。 C 3。 B

Two. 1.2.5 3.

3. 1. Suppose A originally had X books and B originally had Y books.

2. Each big piece is packed in X cans, and each small piece is packed in Y cans.

3. There are X cars and Y classmates, according to the meaning of the question.

7.2 Solutions of Binary Linear Equations (1)

I. 1. D 2。 B 3。 B

Two. 1.2, omitting 3. 20

Three. 1.2.3.4.

7.2 Solutions of Binary Linear Equations (2)

I. 1. D 2。 C 3。 A

Second, 1. , 2. 18, 12 3.

Three. 1.2.3.4.

4. Assume that the planting area of two kinds of vegetables, A and B, is x and y mu respectively.

Solve this system of equations

7.2 Solutions of Binary Linear Equations (3)

I. 1.b2.a3.b4.c

Two. 1.2.9 3. 180,20

Three. 1.2.3.

If there are X gold medals and Y silver medals respectively, there will be (y+7) bronze medals.

According to the meaning of the question, the equations can be solved, so y+7 = 2 1+7 = 28.

7.2 Solutions of Binary Linear Equations (4)

I. 1.d2.c3.b

Two. 1.2.3, 3.- 13

Three. 1. 1.2.3.4.5.6.

Suppose Xiaoming booked X tickets and Y tickets for Class B and Class C respectively.

According to the meaning of the problem, we can solve this system of equations.

7.2 Solutions of Binary Linear Equations (5)

I. 1. D 2。 D 3。 A

Two. 1.24 2.6 3.28 yuan, 20 yuan

Three. 1.( 1)

Processing type

Project finishing and rough machining

Processing days (days)

Profit (RMB) 6000x 8000y

(2) Derived from (1): obtained by solving.

A: This batch of vegetables * * * has 70 tons.

2. Set a basketball for each yuan and a B basketball for each yuan, depending on the meaning of the question.

solve

3. If you don't buy 1 A goods and 1 B goods at a discount, you need to use X yuan and Y yuan respectively, depending on the meaning of the question.

Solve this equation group and get 50× 16+50×4-960=40 (element).

7.3 Practice and Exploration (1)

I. 1. C2.D3.A

Two. 1.722.3. 140,280,000

3. 1. Assume that the original selling prices of A and B are X yuan and Y yuan respectively.

solve

2. sandbags will be scored when they land in area a, and scored according to the meaning of the question when they land in area B.

Xie ∴ A: Xiao Min's total score of four times is 30 points.

3.( 1) Let the price of type A washing machine be X yuan, and the price of type B washing machine be Y yuan.

According to the meaning of the problem, the equation can be solved.

(2) The actual amount paid by Xiao Li: (yuan); Actual amount paid by Xiao Wang: (Yuan).

7.3 Practice and Exploration (2)

I. 1.a2.a3.d

Two. 1.55m/min, 45m/min 2. 20, 18 3.2, 1

3. 1. Let this plantation harvest X kilograms of "Feizixiao" litchi and Y kilograms of "seedless No.1" litchi this year. According to the meaning of the problem, we can solve this system of equations.

2. Set a gram of one-yuan coins and a gram of five-yuan coins. According to the meaning of the question:

Suppose the original plan is to produce x tons of wheat and y tons of corn.

The solution is10× (1+12%) =1.2 (ton), 8× (1+10%) = 8.

4. slightly 5. 40 tons

Chapter VIII One-dimensional One-time Inequality

8. 1 Cognitive inequality

I. 1. B 2。 B 3。 A

Ii) 1.; > ; > 2.2x+3 3; (2)a+7 < 0； (3) 2+ 2≥0; (4)≤-2; (5)∣ -4∣≥ ;

(6) The solution of-20. 2.

8.2 Solving the one-dimensional inequality (2)

I. 1. B 2。 C 3。 A

Second, 1. >;

Third,1.x > 3; 2.x≥-2 3.x< 4。 x>5

Four. Figure x ≥-1; 5.( 1) (2) (3)

8.2 Solving the one-dimensional inequality (3)

I. 1. C 2。 A

2. 1.x ≤-3 2.x ≤-3.k > 2

Three. 1.( 1)x >-2(2)x ≤- 3(3)x ≥- 1(4)x

2.x≥ 3。 eight months

8.2 Solving the one-dimensional inequality (4)

I. 1. B 2。 B 3。 A

2. 1.-3, -2, - 1 2.5 3.x≤ 1 4。 24.

Three. 1. Solving inequality 6(x- 1)≤2(4x+3) leads to x≥-6, so the values of all negative integers x whose value of 6(x- 1) is not greater than 2(4x+3) are -6 and -5.

2. Suppose that the company can print at most X advertisements, and get 80+0.3x≤ 1200 and x≤3733 according to the meaning of the questions.

A: The company can print up to 3733 advertising leaflets.

3. Suppose you buy X chairs, it is more favorable to go to Mall A.. When X > 12, we get 200×12+50 (x-12) < 0.85 (200×12+50x), so we get X < 32, so we get 650. When 0 < x ≤ 12, the solution of 200×12 < 0.85 (200×12+50x) is x >, so the integer solution of < x ≤ 12 is 9,12.

8.3 One-dimensional linear inequalities (1)

I. 1. A 2。 B

2. 1.x >- 1 2。 - 1 < x≤2 ^ 3。 x ≤- 1。

Three. 1.(1) x ≥ 6 (2)1< x < 3 (4 ≤ x <10 (4) x > 2 (omitted).

2. If there are X children in the kindergarten, there are 3x+59 toys in this batch. According to the meaning of the question 1≤3x+59-5(x- 1)≤3, the solution is 30.5≤x≤3 1.5. Because x is an integer, X = 30.

8.3 One-dimensional linear inequalities (2)

I. 1. C 2。 B3。 A

Two. 1.m ≥ 2 2。 < x

Three. 1.(1) 3 < x < 5 (2)-2 ≤ x < 3 (3)-2 ≤ x < 5 (4) x ≥13 (omitted)

2. Let the unit price of apples be X yuan.

The solution is 4 < x < 5, because x is only an integer, so x=5 (yuan).

3. The positive integer solution of-2 < x ≤ 3 is 1, 2,3.

4. With the remaining funds, you can also buy a schoolbag and a cultural shirt for each student in X Mountain Primary School, depending on the meaning of the question.

350 ≤1800-(18+30) x ≤ 400, the solution is 29≤x≤30. Because the number of people should be an integer, x=30.

5.( 1) This shipment is 66 tons. (2) 2 vehicles with a load of 5 tons and 7 vehicles with a load of 8 tons.

Chapter 9 Polygons

9. 1 triangle (1)

I. 1. C 2。 C

Second, 1. 3, 1, 1; 2. Within right angle 3. 12

Third, 1. 8; △ABC, △FDC and △ADC are acute triangles; △ABD and△△△ AFC are obtuse triangles; △AEF, △AEC and △BEC are right triangles.

(1) Omit (2) Three midlines intersect at one point, and the ratio of two line segments divided by the intersection point is 1:2.

3. No, because the sum of the angles in the triangle should be equal to 180.

4.∠A=95 ∠B=52.5 ∠C=32.5

9. 1 triangle (2)

I.1.c2.b3.a.

Second, 1. ( 1) 45; (2)20 ,40 (3)25 ,35 2. 165 3.20 4.20 5.3:2: 1

Three. 1.∠BDC should be 2 1+32+90 = 143 (hint: making ray AD).

2.70 3.20

9. 1 triangle (3)

I. 1. D 2。 A

Second, 1. 12cm 2. 3 pieces 3.5

3. 1. The length of the other two sides is 8cm 2.

9.2 sum of inner and outer angles of polygon

I. 1. C 2。 C. 3。 C 4 explosive C

2. 1.8, 1080 2. 10,1800 3.125 4.120m.

3. 1. 15 2. dodecagon 3. Nonagon, the degree of missing internal angle is 135.4. 1 1.

9.3 Splicing floors with various regular polygons (1)

I.1.b2.c.

2. 1.6 2. Regular hexagon 3. 1 1，(3n+2)。

3. 1.( 1) Because the sum of the inner angles of regular polygons put together around a point is 360. (2) No, because every inner angle of a regular octagon is 135, it cannot be divisible by 360. (3) ellipsis.

2. You should choose "8080cm2" tiles, because the length and width of a rectangular living room are integer multiples of 80cm, and 32 tiles are needed.

9.3 Splicing floors (2) with various regular polygons

I. 1. D 2。 D3。 C

Two. 1. 12

2.( 1) 123, (2) 122, 133,15,244 can be (3) 123.

Third, answer questions.

1 cannot be densely laid, because the internal angles of regular octagon, regular nonagon and regular decagon are 135, 140 and 144 respectively, and the sum of the internal angles around the same point is not equal to 360 2, so three regular triangles and two squares are needed; draw

Chapter 10 Axisymmetric

Axisymmetry in life

I.1.d2.b3.b.

Second, 1. Omit 2. Omit 3. W 17906。

Three. 1. Omit 2. (1)P2② as shown in the figure.

Understanding of 10.2 Axisymmetry (1)

I. 1. B 2。 A 3。 C

Two. 1.2 2.50

Third,1.21cm2. ad = BD; AE=BE=AC 3。

Understanding of 10.2 Axisymmetry (2)

I. 1. C 2。 A 3.B. 4。 A

Second, 1. Fourth, countless; 2. The straight line where the angle bisector is located

Third,

1.2.

Understanding of 10.2 Axisymmetry (3)

I. 1. B 2。 C

Second, 1. Point B, line segment DF, median vertical line; 2.60 3.3

Three, 1. 8: 02 a. m. As shown in the figure.

Understanding of 10.2 Axisymmetry (4)

I.1.c2.d.

2. 1.2.( 1) These graphs are all axisymmetric, and the area of these graphs is equal to 4 square units.

(2) First of all, the first figure has only two symmetry axes, and the other three figures all have four symmetry axes.

Three. 1. Omit 2.

10.3 isosceles triangle (1)

I. 1. C 2。 B 3。 B 4。 D

2. 1.36 2. The median line at the bottom of the isosceles triangle coincides with the bisector with the vertex angle of 3.74. < x < 5。

Three. 1.22 cm

2.( 1)∠PCD=∠PDC, because OP is the bisector of ∠AOB, PC⊥OA, PD⊥OB, so PC=PD.

∠PCD=∠PDC。

10.3 isosceles triangle (2)

I. 1. C 2。 D

2. 1.5 2. isosceles right angle 3. three

3. 1.△OBD is an isosceles triangle, while in ∵ rectangular ABCD, ad∨BC, ∴ ODB = ∠ DBC. According to the nature of axial symmetry, ∠OBD=∠DBC, ∴.

2.ab = ac, ∴ ABC = ∠ ACB, while ∫bo shares ∠ABC, ∠ 1= ∠ABC, and similarly: ∠2= ∠ACB.

3.BF+CE=EF 4.72 5。 ∠A=∠E

Chapter 1 1 Experience Uncertainty

1 1. 1 may still be confirmed (1)

I. 1. C 2。 D

Second, 1. Uncertainty (random) 2. Necessity (certainty) 3. Uncertainty (random)

Three. 1.( 1) impossible (2) possible (3) impossible (4) possible (5) possible (6) possible 2. (omitted)

1 1. 1(2) can still be determined.

I. 1. C 2。 B

Second, 1.0, 100% 2.0 3. A

Third, 1. Not necessarily. According to Xiaoyu's statistics, it can only show that Xiaoyu's probability of taking bus 12 is greater than that of taking bus No.8, that is, the probability of taking bus 12 is not 100%. 2. incorrect. (Example omitted)

1 1.2 Equal and unequal opportunities (1)

I. 1. B 2。 B

Second, 1. 2., 3.

Three. 1.( 1) (2) (3) (4) 2.=

1 1.2 Equal and unequal opportunities (2)

I. 1. C 2。 C

Second, 1. > 2. fairness 3. unfair

3. 1. Unfair. Because there are four prime numbers in the ten integers of 1 ~ 10: 2, 3, 5, 7, the winning probability of A = =, and the winning probability of B = =.

2. Unfair, A has a great chance of winning, because there are three situations when two balls are randomly drawn: 1 and 2, or 1 and 3, or 2 and 3, and there are two situations when it is odd, that is, A has a chance of winning and B has a chance of winning.

1 1.3 Observe the uncertainty in repeated experiments (1)

I. 1. D 2。 A

Second, 1. 25% 2.3.

Three. 1.( 1)

The frequency of touching the red ball is 70% 60% 63.3% 65% 67% 68.3% 67.9% 67.5 66.7% 67%.

(2) sketch; (3)67%; (4)67%.

2.( 1)

Throwing times 200 1000 5000 10000

Positive frequency 109 480 2450 50 10.

The positive frequency was 0.545 0.48 0.49 0.50 1.

(2) sketch;

(3)50%;

(4) different; Because the results of each experiment are random and unpredictable, after 10000 coin toss experiments, the recorded frequency and frequency table may be different from this table.

1 1.3 uncertainty of repeated experiments (2)

I. 1. C 2。 D

Second, 1. 2. error 3. 24 4.

Third, answer questions.

1. The pointer is most likely to stop in red; The possibility of stopping on purple is the least; The possibility that the pointer stops on yellow is the same as that on green. Reason (omitted). If you don't do the experiment, the probability of predicting that the pointer stops on green is.

2.( 1) Estimate the number of white balls in the bag: 25% × 20 = 5; (2) The probability of hitting the red ball at this time is =.

3.( 1) 18, 0.55 (2) Omit (3)0.55

4.( 1)y= x (2)