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Math problems in eighth grade
I. Fill in the blanks (2 points for each question, 30 points for * * *)

1."The difference between 2 times of x and 3 is not less than 0", which is expressed as _ _ _ _ _ _ _ _ _.

2. When x _ _ _ _ _ _ _ _ _ _ the score is meaningful.

3.

4. The positive integer solution of inequality is _ _ _ _ _ _ _ _

5. The solution set of inequality is _ _ _ _ _ _ _ _

6. Factorization: ()

7. Point C is a point on AB line, AC=2, BC=3, then AB: AC =

8. Known line segment AB= 10cm, C is AB with golden section, AC >;; BC, then AC = _ _ _ _ _ _ _

9. As we all know:

10. If: known, then _ _ _ _ _ _ _

1 1. In an isosceles right triangle, the ratio of the right side to the hypotenuse is _ _ _ _ _ _ _.

12. Xiaoming bought 30 notebooks and pens with 100 yuan. In view of each notebook 2 yuan and each pen 5 yuan, Xiao Ming can buy _ _ _ _ _ _ _ pens at most.

13. Known: function, when x _ _ _ _ _ _ _ _ _ y≥0.

14. If: is a completely flat mode, the value of m is _ _ _ _ _ _ _.

15. The computer production workshop originally planned to manufacture X parts every day, but later, in order to meet the supply needs, B parts were manufactured every day, which can be completed _ _ _ _ _ _ _ _ days in advance.

Second, multiple-choice questions (3 points for each question, *** 18 points)

1. The following deformation from left to right belongs to factorization ().

A.B.

C.D.

2. There are four groups of line segments, the length of each group is as follows: ① 2, 1,

② 3,2,6,4 ③, 1, 4 1, 3,5,7 can form a ratio ().

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

3. If both A and B in the score are expanded by 3 times, then the value of the score must be ().

A.it's three times as much as before. B.it's five times as much as before.

C. Is the original D. unchanged?

4. If the solution set of inequality group is x>3, then the range of m is ().

A.m≥3 B.m≤3 C.m=3 D.m solution; 3x+3 is derived from (2): 2x≥8.

2x>6 x ≥ 4...2 points

X & gt3... 1 point

..... 4 points

The solution of the original inequality group is x ≥ 4...5 points.

2.( 1) Solve the formula = a (x-y)+b (x-y)+c (x-y) ...1fraction.

= (x-y) (a+b+c)...4 points.

(2) The solution of the original formula =...2 points.

=...4 points

3. Solution: Both sides of the equation are multiplied at the same time.

The test substitutes x=-3 into the left side of the original equation = = right side ... 4 points.

∴x=-3 is the solution of the original equation ... 5 points.

2x=-6

X =-3...3 points.

4.( 1) Solution formula =...2 points

Replace ... 4 points with x=5.

(2) Original solution =... 1 point

=...3 points

=...4 points

=

(3) The solution of the original formula: ... 2 points.

=

=...5 points

Fourth, the application questions

1. Suppose Mr. Wang's walking speed is x km/h, then his cycling speed is 3 x km/h ... 1 point.

According to the meaning of the question: ... 4 minutes and 20 minutes = hours.

Solution: x = 4...5 points.

It is proved that x=4 is the solution of the listed equation.

∴ 3x = 4× 3 = 12...6 points.

2. Solution: If the number of people taking part in the tour is X, the charge of travel agency A is y 1 yuan, and the charge of travel agency B is y2 yuan, then according to the meaning of the question, you will get: ……2 points.

Y1= 4×100-(x-4 )×100× = 50x+200 ... 4 points.

Y2 =...6 points.

X =10 = y1= 70x of y2.

By y1> Y2: 50x+200=70x Solution: X

By y 1 < Y2: 50x+200=70x solution: x >;; 10 ...9 points

To sum up, when the number of people x= 10, the charges of the two travel agencies are the same.

When the number x

When the number of X is> 10, the charge of travel agency A is more favorable.