A.{x|x？ 3} B.{x|x？ 2}
C.{x|2？ x & lt3} D.{x|x？ 4}
Analysis B={x|x? 3}. Draw several axes (as shown below) and select B. 。
Answer b
2. Given the set A={ 1, 3,5,7,9} and b = {0,3,6,9, 12}, then a? B=()
A.{3，5} B.{3，6}
C.{3，7} D.{3，9}
Analysis A={ 1, 3,5,7,9}, B = {0,3,6,9, 12}, A and B have the same elements 3,9, Answer? B={3，9}。 So choose D.
Answer d
3.50 students participated in two sports activities, A and B, and each student participated in at least one. There are 30 students in A and 25 students in B, so the number of students who only take part in one activity is _ _ _ _ _.
analyse
Assuming that there are X people involved in both events, then (30-x) people only participate in item A, (25-x) people only participate in item B, and (30-x)+x+(25-x)=50. x=5。
? There are 25 people who only participate in item A and 20 people who only participate in item B.
? There are 45 people who participated in only one activity.
Answer 45
4. Given the sets A={-4, 2a- 1, a2} and B={a-5, 1-a, 9}, if A? B={9}, find the value of a.
Analysis ∵A? B={9}，
? 9? First,? 2a- 1=9 or a2=9? Is A=5 or A= 3.
When a=5, a = {-4,9,25} and b = {0 0,4,9}.
At this time, one? B={-4，9}？ {9}. Therefore, a=5 is discarded.
When a=3, B={-2, -2, 9}, and it is rejected if it does not meet the requirements.
The test shows that a=-3 meets the meaning of the question.
First, multiple-choice questions (5 points for each small question, 20 points for * * *)
1. set A = {0 0,2,a}, B = {1, a2}. If a? B={0, 1, 2,4, 16}, then the value of a is ().
A.0 B. 1
C.2 D.4
Analysis ∵A? B={0， 1，2，A，a2}，A？ B={0， 1，2，4， 16}，
? {a，a2}={4， 16}，？ A=4, so choose D.
Answer d
2.let s = { x | 2x+ 1 >； 0}，T = { x | 3x-5 & lt； 0}, then s? T=()
A.？ B. { x | x & lt- 12}
C.{ x | x & gt53} D.{x|- 12
Analysis of s = {x | 2x+ 1 >; 0 } = { x | x & gt- 12}，T = { x | 3x-5 & lt； 0} = {x | x & lt53}, then s? T={x|- 12
Answer d
3. known set a = {x | x >；; 0}，B={x|- 1？ x？ 2}, then a? B=()
A.{x|x？ - 1} B.{x|x？ 2}
C.{x|0
Analysis sets A and B are represented by the number axis, as shown in the figure.
Answer? B={x|x？ -1}. so choose a.
Answer a
4. meet m? {a 1, a2, a3, a4} and m? The number of sets m with {a 1, a2, a3}={a 1, a2} is ().
A. 1
C.3 D.4
The analysis set m must contain the element a 1, a2, but not the element a3, so M={a 1, a2} or M={a 1, a2, a4}. So I chose B.
Answer b
Fill in the blanks (5 points for each small question, *** 10)
5. known set A={x|x? 1}，B={x|x？ A}, and a? B=R, then the range of real number A is _ _ _ _ _ _.
Analysis A=(-? ， 1]，B=[a，+？ ), to get one? B=R, just
Answer? 1.
Answer a? 1
6. Satisfy {1, 3}? The number of all sets A with A={ 1, 3,5} is _ _ _ _ _.
Analysis due to {1, 3}? A={ 1, 3,5}, so a? {1, 3,5}, at least one element in A is 5, so the remaining elements in A can be elements of a subset of the set {1, 3}, and {1, 3} has four subsets, so the number of A's that meet the conditions is 4. They are {5} and {653} respectively.
Answer 4
Third, solve the problem (each small question 10, ***20)
7. Given the set A={ 1, 3,5}, B={ 1, 2, x2- 1}, if a? B={ 1, 2, 3, 5}, find x and a? B.
Analysis by a? For B={ 1, 2, x2- 1}, X2- 1=3 or x2- 1=5.
If x2- 1=3, then x=? 2;
If x2- 1=5, then x=? 6;
To sum up, x=? 2 or? 6.
When x=? 2, B={ 1, 2, 3}, at this time a? B={ 1，3 }；
When x=? At 6 o'clock, B={ 1, 2,5}. At this time, one? B={ 1，5}。
8. Is it known that A={x|2a? x？ A+3}, b = {x | x <-1or x & gt5}, if one? B=？ Find the range of a.
Analysis by a? B=？ ,
(1) If A=? ,
Have 2a & gta+3? a & gt3.
(2) if a,
As shown in the figure:
? The solution is-a? 2.
To sum up, the value range of a is {a|-? Answer? 2 or a & gt3}.
9.( 10) There are 36 students in a class who participate in extracurricular inquiry groups of mathematics, physical chemistry, and each student can participate in at most two groups. It is known that the number of participants in the math, physics and chemistry groups is 26, 15 and 13, respectively. There are 6 participants in the math and physics groups and 4 participants in the physics and chemistry groups.
The student who takes part in mathematics alone is X, the student who takes part in mathematical chemistry is Y, and the student who takes part in chemistry alone is Z.
According to the meaning of the question, x+y+6=26, y+4+z= 13, x+y+z=2 1, and the solution is x= 12, y=8 and z= 1.
? There are eight students taking part in mathematical chemistry at the same time.