Study should be persistent. Beethoven became a world-famous musician because of his perseverance and fearless spirit. The following are the final exam questions about seventh grade mathematics next semester. I hope you will read them carefully!
First, fill in the blanks:
The arithmetic square root of 1 Yes.
2. As shown in the figure, points A, B and C are on a straight line, and it is known that 1=53 and 2=37, then the positional relationship between CD and CE is.
3. The sum of known numbers A and B is 42, 3 times of number A is equal to 4 times of number B, let number A be X and number B be Y, and the equations can be obtained from the meaning of the question.
4. When a0, the solution set of inequality group is.
5. In the plane rectangular coordinate system, if point A (1, 2) is symmetrical with point B (a a, 2) about the Y axis, then a=.
6. A school randomly selected 65,438+000 students to find out their favorite sports, and asked each student to choose a favorite sports and make a pie chart, as shown in the figure. Then there are some classmates who like skipping rope.
7. Given point A (-4, -6), translate point A to the right by 4 unit lengths, and then translate it by 6 unit lengths to get a, then the coordinate of a is.
8. Please construct a system of binary linear equations, which can be solved as. This system of equations is.
9. As shown in the figure, a‖b is known, and Xiao Liang puts the right-angled vertex of the triangle on the straight line B. If 1=40, the degree of 2 is.
10. As shown in the figure, the ground is paved with black and white square bricks of the same specification. Please observe the figure and answer the question: the nth figure needs black tiles. (expressed by algebraic expression with n)
Second, multiple-choice questions: (Please fill in the code of the correct answer in the brackets after the question, with 3 points for each small question and * * * 30 points).
1 1. The following operation is correct ()
A.B.(-3)2=-9 C.2-3=8 D.20=0
12. If point P( 1-m, m) is in the second quadrant, then the following relationship is correct ().
A.d. 00 m 1
13. Among the following equations, () belongs to the system of binary linear equations.
A.B.
C.D.
14. If =(x+y)2, the value of x-y is ().
A.- 1 B. 1 C.2 D.3
15. A proofreader investigated 300 seventh-grade students in the math exam. The pie chart shows scores within a certain range, and the number of scores below 75 is ().
A.75 people B. 125 people C. 135 people D. 165 people.
16. As shown in the figure, it is known that 3=4. To get AB‖CD, the condition that needs to be added is ().
A.1= 4b.3 = 2c.1= 2d.1and 2 are complementary.
17. In x=-4,-1, 0,3, the value of x satisfying the inequality group is ().
A.-4 and 0 B.-4 and-1 C.0 and 3 D.- 1 and 0.
18.△DEF (triangle) is translated by △ABC, and the point corresponding to point A (-1, -4) is D( 1,-1), then point B (1,/kloc-0).
A.(2，2)，(3，4) B.(3，4)，( 1，7)c .(2，2)，( 1，7) D.(3，4)，(2，-2)
19. It is known that the value of xy is ().
A.2 B. 1 C.- 1 D.-2
20. It is known that three different straight lines A, B and C are on the same plane, and the following four propositions:
① If a‖b, ac, then BC;
② if b‖a and c‖a, then b ‖ c;
3 if ba, ca, then BC;
4 if ba, ca, then b ‖ c.
Among them, the real proposition is ()
A.①②③ B.①② C.①②④ D.①③
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, and 4x+ 10y=50 is obtained. ③ Solution: Remove the denominator and get 2(2x- 1)-6? 3(5x+ 1)。
③-②, the result is 7y=35, and the solution is y=5. Without brackets, the result is 4x-2-6? 15x+3。
Substitute y=5 into ① to get x=0. Move the term to get 4x- 15x? 3+2+6.
? The solutions of the original equations are x=0 and y=5. After the merger, we get-1 1x? 1 1.
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 point d corresponds to point a and point e corresponds to point B.
Solution: As shown in the figure.
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？ , communication split? BCD，ACB=40？ ,? BAC=70？ .
(1) Are AD and BC parallel? Try to write reasoning process;
(2) Q? DAC and? The degree of EAD.
Solution: (1)AD is parallel to BC.
∫ communication split? BCD，？ ACB=40？ ，BCD=2？ ACB=80？ .
Again? D= 100？ ，BCD+？ D=80？ + 100? = 180? . ? BC.
(2) From (1), we know that AD‖BC, DAC=? ACB=40？ .
∵? BAC=70？ ，B=70？ .
EAD=？ B=70？ .
24.(8 points) Once? Give love and hold hands? In the donation activity, 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 donor ratio of 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 & lt200 10
C 200？ x & lt300 20
D 300？ x & lt400 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%=2 16 (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. From the meaning of the question: 80-70? 80%=24,24? 20% = 120 & gt； 100, so it's 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, get an A? 75.
His test score should be at least 75.
26. (1 2min) As shown in figure1,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, and then move them to the right by 1 unit length to get a.
(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) As shown in Figure 2, 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 write directly? OPC and? PCD，？ Quantitative relationship of POB.
Solution: (1) c (0) c (0,2), D (4 4,2).
S quadrilateral ABDC=AB? OC=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=？ POB-？ PCD
When point P moves on the extension line of DB:? OPC=？ PCD-？ POB。
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