2. Let A, B and C be rational numbers, then at least one of X, Y and Z has a value ().
A. greater than 0 b. equal to 0 c. not greater than 0 d. less than 0.
3. A supermarket offers the following preferential schemes: (1) There is no discount if the shopping amount does not exceed 200 yuan; (2) Enjoy a 10% discount for shopping in 200 yuan but not more than 600 yuan; (3) Anyone who shops in 600 yuan will enjoy a 20% discount. Xiao Ming's mother paid 168 yuan and 423 yuan respectively for the two purchases. If Xiaoming's mother buys goods with the same value as the last two times in the supermarket at one time, Xiaoming's mother should pay () yuan.
560.40 C.5 10.40 D.472.80
4. If both A and B are positive numbers and satisfy12345 = (11+a) (11-b), can the relationship between A and B be determined? If yes, write down the reasoning process, if not, explain the reasons.
Solution:
5. The password on the password box is a set of three digits, and the digits on each digit can be selected from 10 digits from 0 to 9. When someone randomly presses a three-digit number, the probability of just opening the box is only _ _ _ _. If this person doesn't remember the last digit of the password correctly, then the probability that he presses the last digit of the password at will on the basis of dialing the first two digits of the password is _ _ _ _ _ _.
6. The probability of two consecutive dice being divisible by 3 ()
A.B. C. D。
7. Choose any two numbers from 0 to 9 10, and the probability that the sum of these two numbers equals 8 is _ _ _ _.
8. There are seven white balls and three black balls in a pocket. These balls are exactly the same except the color. Find the probability that two balls are black balls. When two coins are thrown on the ground, the probability of one positive and one negative is _ _ _ _ _; When three coins are thrown on the ground, the probability of a head and two tails is _ _ _ _ _; When four coins are thrown on the ground, the probability of two heads and two tails is _ _ _ _.
9. The passenger train runs between Harbin and Station A, stopping at five stations along the way, so it is necessary to arrange () different tickets between Harbin and Station A. ..
2 1 D.42
10. Xiaoming and Xiao Bin play a ball-touching game: put seven white balls and three black balls in one pocket. These balls are exactly the same except for the different colors. Everyone touches three balls. Of the three balls touched, the white ball won. Before touching the ball, choose the scheme: (1) Touch one ball at a time, write down its color, put it back and mix it evenly, and then touch the next ball. Do you think the two schemes have the same probability of winning? Which scheme do you choose?
Solution:
1 1. There are 1 red balls, 1 yellow balls and two small cubes in a bag. The two balls are the same except for their different colors. One of the two cubes is painted red and the other is painted yellow, but they are all the same. Take out a ball and a cube from the bag. The following statement is wrong.
A. there are four possible outcomes. B. The probability of finding both red is 1/4.
C. The probability of finding two yellows is 1/4 d. The probability of finding one red and one yellow is also 1/4.
12. The probability that two pairs of socks with different colors are randomly taken out is _ _ _ _ _.
13. There is a way to play sports lottery somewhere. Please calculate, if you bet, what is the theoretical probability of winning?
Solution:
14. When x=-7, the value of the algebraic expression is 7, where a, b and c are constants. When x=7, can you find the value of this algebraic expression?
Solution:
15. As shown in the figure, in △ABC, ∠ BAC = 90, AB=AC, AE is a straight line passing through A, B and C are on opposite sides of AE, BD⊥AE is in D, and CE⊥AE is in E.
(1) verification: BD=DE+CE.
Solution:
(2) If the straight line AE rotates around the point A to the position shown in Figure (2), (BD
Solution:
(3) If the straight line AE rotates around point A to the position shown in Figure (3), (BD & gtCE), other conditions being the same, what is the relationship between BD and DE and CE? Write the results directly without proof.
Solution:
16. It is known that the two sides of ∠A and ∠B are parallel, and the degree of ∠A is twice that of ∠B and less than 30, then the degree of ∠B is _ _ _ _ _ _ _.
17. If x, y and z are integers, then the value is _ _.
A.0 B. 1 C.2 D.4
18. If one side of △ABC is twice as big as the other side and the other inner angle is equal to 30, then △ ABC is ().
A. acute triangle or right triangle B. right triangle or obtuse triangle
C. acute triangle or obtuse triangle D. right triangle or obtuse triangle or acute triangle
19. during the winter vacation, in order to enrich the amateur cultural life of teachers and students, the municipal theater held a special concert. There are two kinds of ticket offices: group tickets and retail tickets, in which 10 or more people (including 10 people) are group tickets, and each person is 20 yuan; If you buy a retail ticket, every teacher is in 30 yuan and every student 10 yuan. Six teachers and several students from a school attended the concert. How to save money by purchasing tickets?
20. Article: a※b=, then 2 ※ 5 = _ _ _ _.
2 1.A = 9 and B =-8, then the last digit is _ _ _ _ _.
22. In ABC, AB=5 and AC=9, then the value range of the midline AD is _ _ _ _ _ _.
23. As shown in the figure, if AB=AC, ∠BAD=α and AE=AD, then ∠EDC is equal to ().
A. B.C.
24. In ABC, AB=AC, and the acute angle formed by the intersection of AB's vertical line and AC's straight line is 50, then the base angle ∠B=____.
25. As shown in the figure, two points A and B are on the same side of a straight line MN, and a point P is found on MN, so that (1) is the smallest, (2) is the largest, and (3) PA+Pb is the smallest.
Solution:
Volume b
1. Given that the coordinates of the intersection of the image of a linear function with the X axis and the Y axis are (-2,0) and (0,4) respectively, the analytical formula of the function is _ _ _ _ _ _ _ _ _ _ _ _ _. (The chapter to which the test questions belong: Chapter 11 Linear Function)
2. as shown in figure 1, point c is on the AB line, DA⊥AB, EB⊥AB, FC⊥AB. and DA=BC, EB=AC, FC=AB, ∠ AFB = 5 1, and find ∠. (Chapter of the test: Chapter 13 congruent triangles)
3. Factorization:
①x2-3xy- 10 y2+x+9y-2；
②x2-y2+5x+3y+4
(Chapter of the test questions: Chapter 15 Algebraic Expressions)
4. Simplify before evaluating: (xx -2+xx+2 )÷4xx -2 (where x=2007).
Solution:
(Chapter to which the test questions belong: Chapter 16 Score)
5. Known, the value of.
Solution:
(Chapter to which the test questions belong: Chapter 21 Quadratic Radical)
6. Know the value of: and find:.
Solution:
(Chapter to which the test questions belong: Chapter 21 Quadratic Radical)
7. As we all know:
Solution:
(Chapter to which the test questions belong: Chapter 21 Quadratic Radical)
8. As shown in the figure, AB∨EF∨CD is known. If AB=6 cm and CD=9 cm, please find EF. Is this ok?