1. Expressed by inequality: ① a is greater than 0: _ _ _ _ _ _ _; ② No: _ _ _ _ _ _ _ _;
③ The sum of 5 and x is less than 3 times of x: _ _ _ _ _ _ _ _ _ _.
2. The solution set of inequality is _ _ _ _ _ _ _ _ _ _ _.
3. Fill in the blanks with inequalities: If.
4. When x _ _ _ _ _ _ _ _ _ the value of algebraic generation is positive.
5. The solution set of inequality group is _ _ _ _ _ _ _ _ _ _ _.
6. The positive integer solution of inequality is _ _ _ _ _ _ _ _ _ _ _ _.
The minimum value of 7 is a, and the maximum value of 7 is b, then
8. It used to take one hour to produce a certain product, but now it can save 8% to 15% due to the improvement of work efficiency. If the time needed now is b hours, it is _ _ _ _ _ _ _ _
9. Compile a set of unary linear inequalities and a set of binary linear inequalities:
One-dimensional linear inequality is _ _ _ _ _ _ _ _ _ _ _ _ _ _ _;
The set of binary linear inequalities is _ _ _ _ _ _ _ _ _ _ _ _ _.
10. If the solution set of the inequality group is an empty set, the size relationship between A and B is _ _ _ _ _ _ _ _ _.
Second, multiple-choice questions (this big question ***8 small questions, each small question 3 points, out of 24 points)
1 1. Among the following inequalities, () is a linear inequality of one variable.
A.B. C. D。
12. The solution set of inequality is ()
A.B. C. D。
13. The solution set of the unary linear inequality group is ()
A.B. C. D。
14. As shown in the figure, which inequality solution set is represented on the number axis ()?
A.B.
C.D.
15. If the solution sets of two inequalities are the same, it is called an inequality with the same solution. The following two inequalities are identical solution inequalities ().
A. And B. And
C. and D. and
16. Solve the following inequality, and the correct result is ()
A. the solution set of inequality group is; B. the solution set of the inequality group is;
C. the solution set of the inequality group is; D. the solution set of inequality group is
17. If, then A can only be ().
A.B. C. D。
18. The solution of the equation about x is non-negative, so the condition that A meets is ().
A.B. C. D。
Third, solve a linear inequality (group) and express its solution on the number axis (there are 2 small questions in this big question, 7 points for each small question, full score 14 points).
19.20.
Four, solve the following linear inequality (group) (this big question ***2 small questions, 8 points for each small question, full score 16 points)
2 1.22.
Verb (abbreviation for verb) (the full mark for this big question is 8)
23. When x is a value, the value of algebraic expression is greater than that of algebraic expression.
Intransitive verbs (the full mark of this big question is 8, the sub-topic 1 is 3, and the sub-topic 2 is 5)
24. The equations of x and y are known.
(1) Find the solution of this system of equations;
(2) When the value of m is taken, in the solution of this equation group, X is greater than 1 and Y is not less than-1.
7. List one-dimensional linear inequalities (groups) to solve application problems: (The full score of this big problem is 20 points)
25. In a promotional activity, a store stipulated that consumers could get a discount if they spent all their money in 200 yuan or 200 yuan. A classmate bought a prize for the class and was going to buy six photo albums and some pens. Given each album 15 yuan and each pen 8 yuan, how many can he buy at least to get a discount?
A private middle school plans to recruit 60 teachers. The monthly salary of all employees is as follows:
Staff management, teaching staff
Personnel structure principals, vice principals, department heads, teaching and research team leaders, senior teachers, intermediate teachers and junior teachers.
Number of employees/person 1 24 1 3
Monthly salary per person/RMB 2000017000 2500 2300 2200 2000 900
Please answer the following questions based on the information provided in the above table:
(1) If the school is going to recruit ***40 "senior teachers" and "intermediate teachers" (the number of other employees remains the same), the senior teachers should be recruited at least 13, and the monthly salary paid by the school to the senior and intermediate teachers should not exceed 83,000 yuan. According to the requirements of the school, how many recruitment schemes are there for senior and intermediate teachers?
(2 )( 1) Which scheme gives the school the least monthly salary? And explain why.
(3) When the monthly salary issued by the school is the least, the above table should be completed to find the median and mode of the monthly salary of all employees.
Reference answer
1. 1.①, ②, ③; 2.； 3.& gt，& lt，& gt； 4.； 5.； 6. 1,2,3; 7.-4; 8.85%a，92% a； 9. Omission; 10.。
Second,11~18abcaddbd.
Three. 19.20.。
4.2 1.22.。
Verb (abbreviation for verb) 23.
6.24.( 1), (2) is solved by a set of inequalities, and its meaning can be obtained.
Seven,
25. Solution 1: Suppose a classmate bought a pen.
According to the meaning of the question, you get.
Solve.
Is an integer,.
Answer: Students must buy at least 14 pens to get the discount.
Option 2: Suppose the classmate bought at least one pen.
According to the meaning of the question, you get.
Solve.
The number of pens purchased should be an integer greater than, that is, buy a pen.
Answer: Students must buy at least 14 pens to get the discount.
Note: In the solution 1, it is assumed that students will not be punished for buying at least one pen. If he does not write, he will not be punished.
26. Solution: (1) If there are senior teacher recruiters, then there are intermediate teacher recruiters.
According to the meaning of the question:
To solve this inequality:
and
Is a positive integer,
The school has three recruitment schemes: senior teachers and intermediate teachers.
(2) that is, the monthly salary of senior teachers is greater than that of intermediate teachers.
The fewer senior teachers are recruited, the less monthly salary the school pays.
Senior teachers recruit 13, intermediate teachers recruit 27, and the school pays the least monthly salary.
(3) Supplementary Form:13,27
When the school pays the least monthly salary, the median is 2 100 yuan, and the mode is 2000 yuan.