A, fill in carefully (this big question * * 12 small question, each small question is 3 points, ***36 points, and the answer is directly filled in the horizontal line in the question).
1. As shown in the figure, in the straight lines A, B and C, A∑B, if ∠ 1=700, then ∠ 2 = _ _ _ _ _ _.
2. As shown in the figure, straight lines AB and CD intersect at point O, OE⊥CD, ∠BOD= 1200, then ∠ AOE = _ _ _ _ _ _
3. As shown in the figure, in △ABC, the bisectors of ∠ B and ∠ C intersect at point O. If ∠ a = 60, ∠ BOC = _ _ _ _ _ degrees.
4. As shown in the figure, it is a broken-line statistical chart drawn according to the total industrial output value of a town from 2004 to 2008. Observing the statistical chart, we can see that the year of growth rate has increased by 1 100 million yuan over the previous year.
5. Move the point P(2,-1) to the right by 3 unit lengths, and the coordinate of the point P is _ _ _ _ _ _.
6. Given point A (3, -4), the distance from point A to Y axis is _ _ _ _ _ _ _.
7. The lengths of two sides of an isosceles triangle are 7 and 3 respectively, so the length of its third side is _ _ _ _ _ _ _.
8. If the solution of the equation is non-negative, then the value range of is.
9. The inequality corresponding to "the difference between half and two is not greater than" is.
10. In a sample, 50 data are divided into 5 groups, and the frequencies of 1, 3, 4 and 5 groups are respectively
Is 3, 19,15,5, then the frequency of the second group is _ _ _ _.
1 1. Write a system of binary linear equations, the solution of which is _ _ _ _ _ _ _.
12. As shown in the figure, in the following patterns with black and white squares, there are _ _ _ _ _ white squares in the nth pattern.
Seventh grade math ***6 pages, 1 page.
Second, choose carefully (this big title is ***6 small questions, 4 points for each small question, * * * 24 points. Of the four options given in each question, one and only one is correct. Please put the letter of the correct option in brackets.)
13. In the plane rectangular coordinate system, the point (-1, 1) is in ().
A. first quadrant B. second quadrant C. third quadrant D. fourth quadrant
14. The following are applicable to comprehensive investigation ()
A. Understand the eyesight of seventh-grade students in China B. Understand the service life of a batch of light bulbs.
C. Understand the math test scores of a D class and understand the per capita income of families in Hanjiang District.
15. given a>b, then the following inequality is correct ().
A.2a & gt2b B .-2a & gt； -2b c . 2-a & gt； 2-b D . >
16. If the solution of the equation of x and y is, then the value of is ().
A.-2 B .- 1 C.0 D. 1
17. As shown on the extension line of AC in Figure E, it can be judged that AB∨CD is () under the following conditions.
A.∠3 =∠4 b .∠ 1 =∠2 c .∠D =∠DCE D .∠D+∠ACD = 1800
Question 17, question 18
18. As shown in the figure, in △ABC, ∠ A = 50, and D and E are points on the sides of AB and AC respectively. Cut off one corner of the triangle along DE to get a quadrilateral BCED, so ∠ 1+∠2 is equal to ().
A. 120 b . 150 c . 220 0d . 230 0
3. Be patient (this big topic is *** 1 1 small question, with a score of ***90, and the answer should be written in necessary words to prove the process or calculus steps).
19.(6 points) Solving equation: 20. (6 points) Solving inequalities:
And the solution set is expressed on the number axis.
Seventh grade mathematics ***6 pages, page 2.
2 1.(6 points) As shown in the figure, four identical small rectangles and 1 small squares are inlaid into a square pattern. It is known that the perimeter of the pattern is 28, and the perimeter of the small square is 12. If x and y represent the length of two sides of a rectangle (x >: Y), find the values of x and y.
22.(8 points) As shown in the figure, BC and DE intersect at point O, and the following three conclusions are given: ①∠B=∠E, ②AB∨DE, ③BC∨EF.
Please take two of them as the conditions and one as the conclusion, make up a proof question and prove it.
Known: (insert serial number)
Verification: (fill in serial number)
Prove:
23.(8 points) (1) As shown in figure 1, a pair of triangular plates are stacked together, so that the two right-angled sides overlap respectively, and AB and CD intersect at E. 。
Find: ∠ the degree of ∠AEC;
(2) As shown in Figure 2, keep △COD constant, rotate △AOB around point O as AOC, and find the degree of ∠AOC.
Seventh grade math * * * Page 6 Page 3 (with questions on the back)
24.(8 points) After learning statistics, Xiao Gang made a survey on the way students in this class go to school. Figure 1 and Figure 2 are two incomplete statistics he drew after collecting data. Please answer the following questions according to the information provided in the picture:
(1) Find the number of students in this class;
(2) In the figure 1, the "walking" part will be indicated.
Child completion;
(3) In the figure
In fig. 2, "walking",
Percentage corresponding to the "cycle" part;
(4) If there are 500 students in the whole grade, please
Estimate the number of students who walk to school in the whole grade.
25.(8 points) A math test with 25 multiple-choice questions. The grading standard is: a correct answer is 4 points, -65438+ a wrong answer is 0 points, and no answer is 0 points. A classmate has 1 questions unanswered. If he wants to get a score of not less than 80 points, how many questions must he answer correctly at least?
26.(8 points) As shown in the figure, in △ABC, D and E are points on the sides of AB and AC respectively. Fold the triangle along DE, and the vertex A falls at point C (point A), and ∠B=∠BCD.
(1) Judge the shape of △ABC and explain the reason;
(2) verification: DE∨BC.
Seventh grade mathematics * * * Page 6 Page 4.
27.( 10) The following figures are made of rubber bands nailed to the wall with nails, among which AB∑CD.
(1) As shown in figure 1, if ∠A=30 and ∠C=50, ∠ AEC = _ _ _ _ _ _ _ _;
(2) As shown in Figure 2, if ∠A=x and ∠C=y, ∠AEC= (expressed by a formula containing X and Y);
(3) As shown in Figure 3, if ∠A = M∠C = N, what is the quantitative relationship between ∠AEC and M and N? Please prove it.
28.( 10 point) As shown in the figure, in the rectangular OABC, O is the origin of the plane rectangular coordinate system, and the coordinates of point A and point C are respectively
A (3 3,0), C (0 0,2), and point B are in the first quadrant.
(1) Write the coordinates of point B;
(2) If the straight line passing through the point C intersects the 0A side of the rectangle at the point D, the circumference of the rectangle OABC is divided into 2: 3, and the coordinates of the point D are found;
(3) If the line segment CD in (2) is translated downwards by 3 unit lengths to get the corresponding line segment C D, draw a triangle CD C in the plane rectangular coordinate system and find its area.
Seventh grade mathematics ***6 pages, page 5.
29.( 12) A shopping mall bought 1 time products A and B for 390,000 yuan, and made a profit of 60,000 yuan after selling them. Their buying and selling prices are as follows:
(Total profit = profit per piece × sales volume)
(1) 1 time, how many A and B goods did the mall buy?
(2) For the second time, the mall bought two kinds of goods, A and B, at the original price. The number of pieces of B remained unchanged, while the number of pieces of A was twice that of the first 1 time. A sells at the original price and B sells at a discount. If these two commodities are sold, the profit of the second business activity is not less than 75,000 yuan. What's the lowest selling price of B?
Seventh grade mathematics ***6 pages, page 6.
Reference Answers for Final Quality Inspection of Grade 7 Mathematics (Scoring Rules)
I: 1.70 2.30 3. 120 4.20 5 . p(5，- 1) 6。 3 7.7 8.m ≥- 1。
9. 10.8 1 1. (None) 12. 3n+ 1
2:13.b14.c15.a16.c17.b18.d.
Three: 19. Solving equation: 20. Solving inequality groups:
And the solution set is expressed on the number axis.
Solution: ②+①: 6x = 66, x = 1 1...2. Decomposition: solving inequality ①: x.
Substitute x= 1 1 into ① to get: 3x11+2y = 47 ... 4. Get inequality ②: x >; 1 ...4 points
Y = 7...5 points, so the solution set of the original inequality group is: 1.
So the solution of the original equation is ... 6 points ... 6 points.
2 1. Solution: According to the meaning of the question, you get … 3 points, and you get … 6 points.
22. There are three kinds:
Type 1: Type 2: Type 3:
Known: ①, ② Known: ①, ③ Known: ②, ③
Authentication: 3 … 3 points authentication: 2 … 3 points authentication: 1 … 3 points authentication.
Proof: ∫AB∨DE…4 points: ∫BC∨EF…4 points: ∫AB∨DE…4 points.
∴∠B=∠DOC…5 got 5 points, ∴∠DOC=∠E…5 got 5 points, ∴∠ B = ∠ Doc got 5 points.
∠∠B =∠E…6 points ∠∠B =∠E…6 points ∫BC∨DE…6 points.
∴∠ Doc =∠ E ... 7 score ∴∠ B =∠ Doc ... 7 score ∴∠ Doc =∠ E ... 7 points.
∴BC∥DE …8 points ∴AB∥DE …8 points ∴∠B=∠E …8 points.
23. Solution: (1) ∵∠ OAB = ∠ c+∠ AEC …1(2) ∵ ao ∨ CD … 5.
∠OAB=60, ∠C=45 …2 o'clock ∴∠AOC=∠C…6 o'clock.
∴60 =45 +∠AEC …3 o'clock, while ∠C=45 …7 o'clock.
∴∠AEC= 15 …4 points ∴∠AOC=45 …8 points.
24. 2 points for each small question (1) 40 (2) 8 (3) Walking 20%, cycling 30% (4)500×20%= 100 (name).
25. solution: suppose this classmate answers question x correctly. ... 1 score: 4x-(25- 1-x) ≥ 80...4 points.
solve
The smallest integer solution to the inequality X ≥is 2 1, …7 points, so this student should get at least 2 1 correctly. ... eight points
26.( 1) △ABC is a right triangle. ..... 1 point
∠∠ACB =∠ACD+∠BCD∠ACD =∠a，∠ BCD = ∠ B ∴∠ ACB = ∠ A+∠ B ...
∠∠ACB+∠A+∠B = 180...4 points ∴ 2 ∠ ACB =180, ∠ ACB = = 90...5 points.
(2) According to (1), ∠ACB==90, ∠ DEA = ∠ DEC = 180 = 90...6 points.
∴∠ DEA = ∠ ACB ... 7: 00 BC ∴ 8: 00 BC.
27. For questions (1) and (2), 2 points are given for each minor question, and 6 points are given for minor question (3).
( 1) ∠AEC=80，(2) ∠AEC=360 -x -y
(3)AEC = n-m...2 points.
Proof: ∫ab∨CD, ∠C=n …3 points ∴∠EFB= ∠C=n …4 points.
And ≈efb =∠a+∠AEC, ∠A=m …5 points ∴n = m +∠AEC.
∴∠ AEC = n-m...6 points.
28. (1) b (3,2) ... 2 points.
(2) The circumference of the rectangular OABC is 10 ... three minutes.
Point d is on the edge of OA, and the perimeter of rectangular OABC is put.
It is divided into two parts: 2: 3. ∫OC+OA = 5 & lt； 6 Only ∴oc+od = 4
∫ OC = 2 ∴ OD = 4-2 = 2D (2,0) ... 5 points.
(3) The triangle C D C is shown in figure …7 o'clock.
CC =3 D (2, -3)...8 points.
The area of triangle C D C is … 10 point.
29. Solution: (1) Suppose that X pieces of A goods and Y pieces of B goods are purchased. ..... 1 point
According to the meaning of the question: ... 4 points.
Solution: ... 6 cents, so I bought 200 A goods, 150 B goods. ..... 7 points
(2) Let the price of commodity B be M yuan/piece. ..... 8 points
According to the meaning of the question: ... 10.
Solution: m ≥1100 ...11.
A: The lowest selling price of B goods 1 100 Yuan/piece. ..... 12 point