10) The point set on the coordinate axis in a rectangular coordinate system can be expressed as {(x, y)|xy=0}
1 1) If the equation 8x 2+(k+1) x+k-7 has two negative roots, then the value range of k is: k >；; seven
12) let the set A = {x |-3 < x ≤ 2}, b = {x | 2k-1< x ≤ 2k+1}, and b is included in a, then the range of real number k is:-1≤
13) It is known that the set a = {a | equation x 2-ax+ 1 = 0 has a real root}, so find a ∩ b.
Solution: a = {a | Equation with real roots about X X 2-AX+1= 0} = {A | a ≤- 2}-4 ≥ 0} = {A | A ≥ 2 or A ≤-2},
B = {a | inequality ax 2-x+1> 0 holds for all x∈R} = {a | a > 0 and 1-4a.
So a ∩ b = {a | a ≥ 2}
14) It is known that one root of the equation x 2-(k 2-9) x+k 2-6k+6 = 0 is less than 1, and the other root is greater than 2, so the value range of the real number k.
Solution:
15) let the complete set u = {x | x ≤ 5 and x ∈ n *}, set a = {x | x 2-5x+q = 0}, and b = {x | x 2-px+12 = 0.
(cua) ∪ b = {1435}, the value of the real number p q.
Solution: the complete set U = {x | x ≤ 5, x ∈ n *} = {1, 2,3,4,5}, which is obtained by b = {x | x 2-px+12 = 0}.
CuA contains 1, so A does not contain 1, and x 1+x2=5 is a = {x | x 2-5x+q = 0}, so only 2 and 3 in U meet the requirements, so A = {2,3}.
So P=3+4=7 and Q=2×3=6.
16) if the solution set of inequality x 2-ax+b < 0 is {x | 2 < x < 3}, find the solution set of inequality bx 2-ax+ 1 > 0.
Solution: the solution set of inequality x 2-ax+b < 0 is {x | 2 < x < 3}. It can be seen that the two roots of the equation x 2-ax+b = 0 are 2,3, so a=2+3=5 and b=2×3=6, so the inequality bx 2-ax+. 1/2 or x
17) set A = {(x, y) | x 2+MX-y+2 = 0}, set B = {(x, y) | x-y+ 1 = 0, and 0 ≤ x ≤ 2}, A ∩.
Value range of real number m
Solution: Substitute B into A to get the equation: x 2+(m- 1) x+ 1 = 0. Since A∩B is not empty and δ = (m- 1)-4 ≥ 0, the solution is m≥3 or m ≤-60. And 0≤x≤2, so1≤ x2+(m-1) x+1≤ 4+2 (m-1)+1= 2m+3, so 2m+3 ≥ 63.
To sum up, it can be seen that the value range of m is m≥3 or m=- 1.
18) The correct conclusion is (b)
A. when proposition p is true, propositions "p and q" must be true.
B When the propositions "P and Q" are true propositions, the proposition P must be true.
C When the proposition "P and Q" is a false proposition, the proposition P must be a false proposition.
D when proposition p is false, propositions "p and q" are not necessarily true.
19) In the inverse proposition of the proposition "If the opening of parabola y = ax 2+bx+c is downward, then {x | ax 2+bx+c < 0} ≠ empty set", the conclusion in the inverse proposition is: "If {x | ax 2".
20) A proposition and its inverse proposition have no proposition and no proposition among these four propositions (b)
A. the number of true propositions must be odd.
B. The number of true propositions must be even.
C the number of true propositions may be odd or even.
D. None of the above is true