1. the real numbers a and b are known, if A >；; B, then the following conclusion is wrong (D)
A.a-5 >b-5b . 3+a & gt； b+3
C.a5 & gtb5 D.-3a >-3b
2. If the point P(x, y) is on the coordinate axis, then (c)
A.x=0 B.y=0
C.xy=0 D.x+y=0
3. From the following four diagrams, it cannot be deduced that ∠2 equals ∠ 1 (B).
4. In order to understand the extracurricular homework burden of junior high school students in a school 1 000, if sampling survey is adopted, which of the following survey methods is representative? (3)
A. Investigate all girls B. Investigate all boys
C. Investigate students in Grade 7, Grade 8 and Grade 9 100. D. survey all students in grade nine.
5.At 2 0 1799 1，3. 14 1 592 65， 13，-6，-37，0，36，&； pi； The number of irrational numbers in 3 is (c)
A. 1
6. If the solution sets of inequality groups 2-x≥-3 and x- 1≥-2 are represented on the number axis, the corresponding graph is (b).
A. rectangle B. line segment C. ray D. straight line
7. Under the condition, it can be judged that the straight lines parallel to each other are (C)
a . a∑b
b . m∑n
C. a∨b and m∨n
D. none of the above is true.
8. There are four propositions as follows: ① the vertex angles are equal; ② The complementary angles of equal angles are equal; 3 if b∨a and c∨a, then b ∨ c; (4) If two sides of an angle are parallel to two sides of another angle, then the two angles are equal or complementary. Among them, there is a true proposition (a)
A.4 B.3 C.2 D. 1
9. If the solutions of the equations x+y=★, 2x+y= 16 are x=6 and y=■, then the two numbers covered by ★ "and ■" are (a) respectively.
A. 10，4 b . 4 10 c . 3 10d . 10，3
10. (Huangshi senior high school entrance examination) when 1≤x≤2, AX+2 >；; 0, the value range of a is (a)
A.a & gt- 1 b . a & gt； -2
C.a & gt0d . a & gt； -1 and a ≠0
Fill in the blanks (3 points for each small question, 24 points for * * *)
The cube root of 1 1.64 is 2.
12. There is a certain point A outside the straight line M, the distance from A to the straight line M is 7 cm, and B is any point on the straight line M, then the length of the line segment AB is AB≥7 cm. (Fill in "
13. As shown in the figure, there are 6 pairs of congruent angles, 4 pairs of internal dislocation angles and 4 pairs of internal angles on the same side.
14. (Mid-term of Gangnan District) As shown in the figure, on the chessboard, if "Jiang" is at (1,-1) and "Che" is at (-3,-1), then "Ma" is at (4.
15. Xiao Ming, Class 1, Grade 7, learned five important steps of statistical investigation according to the topic of "Talking about water saving from data" this semester: ① Collecting data; ② Design a questionnaire; ③ estimate the population with samples; (4) sorting out data; ⑤ Analyze the data. But he didn't arrange five steps correctly. Please help him order it correctly as 2 14533. (Fill in serial number)
16. If the straight line l 1∑L2 is known and the right-angled triangular plate with an angle of 30 is placed as shown in the figure, ∠ 1 = 25, then ∠2 is equal to 35.
17. According to the account records of a supermarket, 39 toothbrushes and 2/kloc-0 toothpaste were sold on the first day, and the income was 396 yuan; Selling the same 52 toothbrushes and 28 boxes of toothpaste at the same price the next day should earn 528 yuan.
18. Given points A (-2,0), B (3 3,0), C and S triangle ABC= 10 on the Y axis, the coordinates of point C are (0,4) or (0,4).
Iii. Answering questions (***66 points)
19.(8 points) Calculation:
( 1)4-38+3- 127;
Solution: The original formula =2-2+(- 13)=- 13.
(2)2(2-3)+|2-3|.
Solution: The original formula =22-23+3-2=2-3.
20.(8 points) (1) Solve the equation: 2x+5y=25, ① 4x+3y =15; ② (2) Solving inequality: 2x-13-1≤ 5x+12.
Solution: ①× 2,4x+10y = 50. ③ Solution: 2(2x- 1)-6≤3(5x+ 1) after the denominator is removed.
③-②，7y=35，y=5。 Without brackets, 4x-2-6≤ 15x+3.
Substitute y=5 into ①, and x=0. Move the item to 4x- 15x≤3+2+6.
The solution of the original equations is x=0 and y=5. -11x ≤11.
If the coefficient is 1, x≥- 1.
2 1.(6 points) Vertices A (0 0,5) and B (-2,2) of triangle ABC in the grid as shown in the figure are known.
(1) Establish a plane rectangular coordinate system in the grid according to the A and B coordinates, and write the point C coordinates (2,3);
(2) Translate the triangle ABC so that the point C moves to the point F (7, -4), and draw the translated triangle DEF, where the point D corresponds to the point A and the point E corresponds to the point B. 。
Solution:
22.(6 points) When the apple is ripe, throw an apple from the tree. As shown in the figure, from A to B, (the unit length of the grid is 1)
(1) Write the coordinates of point A and point B;
(2) When an apple falls from A to B, which two translations can be regarded as the result?
Solution: (1) A (2,4), B(- 1, -2).
(2) First translate 3 unit lengths to the left, and then translate 6 unit lengths down (or translate 6 unit lengths down, and then translate 3 unit lengths to the left)
23.(8 points) As shown in the figure, in the known quadrilateral ABCD, ∠ D = 100, AC divides ∠BCD equally, while ∠ ACB = 40, ∠ BAC = 70.
(1) Are AD and BC parallel? Try to write reasoning process;
(2) Find the degree of ∠DAC and ∠EAD.
Solution: (1)AD is parallel to BC.
∫AC bisector ∠BCD, ∠ ACB = 40, ∴ BCD = 2 ∠ ACB = 80.
∠∠d = 100，∴∠BCD+∠d = 80+ 100 = 180。 ∨ BC ∴.
(2) According to (1), AD∥BC, ∴∠ DAC = ∠ ACB = 40.
∠∠BAC = 70 ,∴∠b=70。
∴∠EAD=∠B=70。
24.(8 points) In a donation activity of "giving love and holding hands", a math interest group conducted a survey and grouping statistics on some donors in the community where the school is located, and sorted the data into the following statistics and charts (incomplete information). It is known that the ratio of donors in group A and group B is 1: 5.
Group statistics of donor families,
Group donation (x) number of families
a 1≤x & lt； 100 a
b 100≤x & lt； 200 10
c 200≤x & lt； 300 20
d 300≤x & lt； 400 14
E x≥400 4
Please combine the above information to answer the following questions:
( 1)a=2。 The sample size of this survey is 50 people;
(2) Complete the statistics and charts of the number of donors;
(3) If there are 600 households in the community, according to the above information, how many households in the whole community are expected to donate no less than 300 yuan?
Solution: (2) The statistics of the number of households who have completed the donation are as follows:
(3) 600× (28%+8%) = 600× 36% = 216 (households).
A: There are no fewer than 2 16 households in 300 yuan.
25.( 10) (Zhuzhou senior high school entrance examination) A city evaluates aesthetics and art in the comprehensive quality evaluation of senior two, and it is stipulated as follows: the comprehensive evaluation score of the evaluation consists of two parts: the test score (full score 100) and the usual score (full score 100), of which the test score accounts for 80%, and the usual score.
(1) The sum of Kong Ming's test scores and usual scores is 185, and the comprehensive evaluation score is 9 1. What's the score of Kong Ming's exam and his usual score?
(2) A student got 70 points in the exam. Is it possible for his comprehensive evaluation score to reach A? Why?
(3) If a student's comprehensive evaluation is to reach A, what is his test score at least?
Solution: (1) Let Kong Ming's test score be X and his usual score be Y.
X+y= 185，80%x+20%y=9 1。 The solution is x=90 and y=95.
Answer: Kong Ming scored 90 points, usually 95 points.
(2) impossible. According to the meaning of the question: 80-70× 80% = 24,24 ÷ 20% =120 >100, so it is impossible.
(3) Set the normal score as full mark, that is, 100, and the comprehensive score as 100×20%=20.
Let the test score be a, and according to the meaning of the question, you can get
20+80%a≥80, solution a≥75.
His test score should be at least 75.
26.( 12 points) In the plane rectangular coordinate system, the coordinates of point A and point B are (-1 0) and (3,0) respectively. Now, at the same time, move point A and point B up by 2 unit lengths respectively, and then move them to the right by 1 unit length to get point C and point D corresponding to point A and point B..
(1) Write the coordinates of points C and D, and find the area of quadrilateral ABDC;
(2) Whether there is a point F on the X axis, so that the area of the triangle DFC is twice that of the triangle DFB, and if there is, the coordinates of the point F are requested; If it does not exist, please explain the reason;
(3) Point P is a moving point on the straight line BD, connecting PC and PO. When point P moves on a straight line BD, please directly write the quantitative relationship between ∠OPC and ∠PCD and ∠POB.
Solution: (1) c (0) c (0,2), D (4 4,2).
S quadrilateral ABDC=ABOC=4×2=8.
(2) Yes, when BF= 12CD, the area of triangular DFC is twice that of triangular DFB.
∫C(0，2)，D(4，2)，
∴CD=4,BF= CD=2。
∫B(3，0)，
∴ f (1, 0) or (5, 0).
(3) When point P moves on line BD: ∠ OPC = ∠ PCD+∠ POB;
When point P moves on the BD extension line: ∠ OPC = ∠ Bob-∠ PCD;
When point P moves on the extension line of DB: ∠OPC=∠PCD-∠POB.