20 18 seventh grade volume 2 math final examination paper 1, multiple-choice questions (3 points for each small question, * * * 30 points).
1. As shown in the figure, AC∨DF, AB∨EF, and points D and E are on AB and AC respectively. What if? 2=50? And then what? The size of 1 is ()
.30 caliber? B.40？ C.50？ D.60？
2. Calculate (-8m4n+ 12m3n2- 4m2n3)? The result of (-4m2n) is equal to ()
A.2m2n- 3mn+n2 B.2m2- 3mn2+n2
C.2m2- 3mn+n2 D.2m2- 3mn+n
3. Observe the graph and judge that the fourth graph from left to right is () according to this rule.
4. The following statement is correct ()
(1) Two triangles with the same shape are congruent triangles; (2) In two triangles, equal angles are corresponding angles and equal sides are corresponding sides; (3) The height, median line and bisector of the corresponding angle on the corresponding side of congruent triangles are equal respectively.
A.3 B.2
C. 1 D.0
5. TV station? Go to the grassroots? A reporter in the column drove to the countryside 360 kilometers away. The first part of the whole journey is the expressway, and the second part is the country road. If the car travels at a certain speed on the highway and the country road respectively, and the relationship between the distance Y (unit: km) traveled by the car and the time X (unit: h) is shown in the figure, then the following conclusion is correct ().
A. the speed on the expressway is100 km/h.
B. The total length of rural roads is 90 kilometers.
C.the speed of this car on the country road is 60 kilometers per hour.
D. the reporter arrived at the interview site 4.5 h after departure.
6. Five cards with the numbers 0,-1,-2, 1, 3 written on them, all the same except the numbers. If you draw a card, the probability of drawing a negative number is ().
A.B.
C.D.
7. As shown in the figure, in △ABC, AQ=PQ, PR=PS,? RAP=？ SAP，PR？ R point AB, PS? If AC is at point S, the following three conclusions are drawn: ① As = Ar; ②QP∑AR； ③ In △ BPR △ QPS ()
A. All are correct B. Only ① and ② are correct.
C. Only ① is correct D. Only ① and ③ are correct.
8. As shown in the figure, the pattern of the kite is an axisymmetric figure with the straight line AF as the axis of symmetry. The following conclusion may be incorrect ().
A.△ABD?△ACD
B.AF bisects EG vertically
C. the intersection of straight lines BG and ce is on AF.
D.△DEG is an equilateral triangle.
9. Mathematics is everywhere in our life. Even a small pool table has math problems, as shown in the picture. 1=? 2. What if? 3=30? In order to make the white ball bounce and the black ball hit the bag directly, you must make sure that when you hit the white ball? 1 Yes ()
.60 caliber? B.30？
C.45？ D.50？
10. As shown in the figure, OD=OC, BD=AC,? O=70？ ,? C=30？ And then what? The OAD is equal to ()
.30 caliber? B.70？ C.80？ D. 100？
Fill in the blanks (4 points for each small question, 32 points for * * *)
1 1. If the algebraic expression x2+3x+2 can be expressed as (x- 1)2+a(x- 1)+b, the value of a+b is.
12. Party A and Party B play poker games. The rules of the game are: randomly draw one card from three cards with brand numbers of 4, 8 and 9, put it back in its original place, and then randomly draw another card. If the sum of the two card numbers drawn is odd, Party A wins; If the sum of the numbers of the two cards drawn is even, then B wins the game. Is it fair? Or? Unfair? )
13. As shown in the figure, in △ABC,? ABC=？ ACB？ A=40？ P is a point in △ABC, and? 1=? 2, and then what? BPC=。
14. In April, Liang Xiao helped her mother to budget the household electricity bill. The following table shows the readings of Liang Xiao Electric Meter every morning for 8 consecutive days in early April:
Date 1 2 3 4 5 6 7 8
meter reading
(kWh) 2 1 24 28 33 39 42 46 49
(1) The variables reflected in the table are, the independent variables are and the dependent variables are.
(2) It is estimated that the household electricity consumption in Liang Xiao will be kWh in April. If the electricity bill per kilowatt-hour is 0.49 yuan, it is estimated that the electricity bill payable by his family in April will be RMB.
15. As shown in the figure, first divide a turntable into two semicircles, then divide one semicircle into five parts, and mark them with 1, 2, 3, 4, 5, and the other semicircle with 6, and then rotate the turntable at will. When the turntable stops, the probability that the pointer points to an even number is.
16. As shown in the figure, what is OE? The bisector of AOB, BD? Point d OA, AC? OB is at point C, then triangles symmetrical about the straight line OE are paired.
17. As shown in the figure,? E=？ F=90？ ,? B=？ c，AE=AF。 Give the following conclusions: ①? 1=? 2; ②BE = CF； ③△ACN?△ABM； CD = DN。 The correct conclusion is (fill in the serial numbers of all the conclusions you think are correct).
18. As shown in the figure, in △ABC, DE is the middle vertical line of AC, AE = 3cm, and the circumference of △ Abd is 13 cm, so the circumference of △ABC is cm.
Iii. Answering questions (***58 points)
19.(8 points) First simplify (2x-1) 2-(3x+1) (3x-1)+5x? (x- 1), and then choose a number you like instead of x to find the value of the original algebra.
20.( 10) A farmer friend brought a few kilograms of potatoes to the city to sell. He brought some small change for convenience. After selling some at the market price, he sold it at a reduced price. The relationship between the number of kilograms of potatoes sold and the amount of money (including change) he holds is shown in the figure. Answer the following questions with pictures:
(1) How many changes have farmers brought?
(2) What was his price per kilogram of potatoes before the price reduction?
(3) After reducing the price, he sold the surplus potatoes in 0.4 yuan per kilogram. At this time, his money (including spare money) is 26 yuan, so how many Jin of potatoes did he take with him?
2 1.( 10 minute) As shown in the figure, which angles can be measured to judge whether AB is parallel to CD? Please write three plans and explain the reasons.
22.( 10) Wash three spades in a deck of playing cards (the numbers in front of them are 3, 4 and 5 respectively) and put them face down on the table. Xiao Wang and Xiao Li play a card-touching game. The rules of the game are: first, Xiao Wang randomly draws a card, writes down the card number, puts it back in its original place, and washes it face down. Then Xiao Li randomly draws a card and writes it down. When the face numbers of two cards are different, Xiao Li wins. Now please judge whether the rules of the game are fair to both sides and explain the reasons.
23.( 10) Draw an isosceles triangle in the square grid diagram (1) and Figure (2) respectively. One vertex of each isosceles triangle is grid point A, the other vertices are selected from grid points B, C, D, E, F, G and H, and the drawn triangles are not equal.
24.( 10) In △ABC, AC=BC,? ACB=90？ Point D is the midpoint of AB, and point E is the point on the side of AB.
(1) As shown in figure (1), BF is perpendicular to CE at point F and intersects CD at point G. Try to explain AE = CG.
(2)AH is perpendicular to CE, the vertical foot is H, and the extension line intersecting with CD is at point M (as shown in Figure (2)). Find the line segment equal to the figure and explain the reason.
20 18 answers to the final examination paper of mathematics in the second volume of grade seven 1. C
2.c (resolution: (-8m4n+ 12m3n2- 4m2n3)? (- 4m2n)=- 8m4n？ (- 4m2n)+ 12m3n2？ (- 4m2n)- 4m2n3？ (-4m2n)=2m2- 3mn+n2, so C.)
3.D (Analysis: If you look at the diagram, you can see that the angle that is blacked out alone rotates clockwise, and only D is satisfied, so D is selected).
4.c (Analysis: (1) Two triangles with the same shape but different sizes are not congruent triangles, so (1) is wrong; (2) Overlapping edges in congruent triangles are called corresponding edges, and overlapping angles are called corresponding angles. If two triangles are arbitrary triangles, there may be no corresponding angles or sides, so (2) is wrong; (3) correct. Therefore, C.)
5.c (Analysis: A. What is the speed of the car on the expressway 180? 2=90(km/h), so this option is wrong; B The total length of rural roads is 360- 180= 180(km), so this option is wrong; C.the speed of the car on the country road is 90? 1.5=60(km/h), so this option is correct; D.2+(360- 180)？ [(270- 180)? 1.5]=2+3=5(h), so the reporter didn't arrive at the interview site until 5 h after his departure, so this option is wrong. Therefore, C.)
6.B
7.b (Analysis: Because PR=PS, PR? R point AB, PS? AC is at point s, AP=AP,? RAP=？ SAP，so△ARP?△ASP，so AS=AR。 Because AQ=PQ, so? QPA=？ QAP, so? RAP=？ QPA, so QP∨AR. So ① and ② are both right. At △BPR and △QPS, only? BRP=？ QSP=90？ And PR=PS, we can't find the third condition, so we can't get △ BPR △ QPS. So only ① and ② are correct in this question, so we choose B.)
8.d (analysis: A. Because this graph is axisymmetric, it is correct; B the symmetry axis bisects the straight line connecting the corresponding points vertically, which is correct; C. According to the congruence of triangle, BG=ce, and the intersection of straight line BG and CE is on AF, which is correct; D. there is no 60 in the title? Condition, can't judge is an equilateral triangle, error. So choose D.)
Because the four corners of the billiard table are right angles, 3=30? , so? 2=60? Because? 1=? 2, so? 1=60? . So choose a.)
10.c (resolution: in △OBC, known? o，？ Is the degree of C easy to get? OBC=80？ Desire? The degree of OAD can be obtained by △ OBC △ oad? OAD=？ OBC=80？ . )
11.11(analysis: because x2+3x+2 = (x-1) 2+a (x-1)+b = x2+(a-2)
12. Unfair (Analysis: The probability that A wins is that B wins is that the two probability values are not equal, so the game is unfair. )
13. 1 10? (Analysis: Because? A=40？ ,? ABC=？ ACB, so? ABC=？ ACB=( 180？ - 40? )=70? .
Because again? 1=? 2,? 1+? PCB=70？ , so? 2+? PCB=70？ , so? BPC= 180？ - 70? = 1 10? . )
14.( 1) date, meter reading date (2) meter reading (120 58.8) has two variables: date and meter reading, the independent variable is date, and the dependent variable is meter reading; (2) What is the daily electricity consumption (49- 2 1)? 7=4 (kWh), electricity consumption in April =30? 4= 120 (kwh), because the electricity fee per kwh is 0.49 yuan, the electricity fee should be paid in April = 120? 0.49=58.8 yuan. )
15. (analysis: there are even numbers of 2, 4 and 6. Find the ratio of even area to total area, and find the probability that the pointer points to even number. )
16.4 (analysis: △BCE and △ADE, △BOE and △AOE, △OCE and △ODE, △BOD and △AOC, ***4 pairs. )
17. 123 (resolution: because? E=？ F=90？ ,? B=？ C, AE=AF, so △ Abe △ ACF. So AC=AB? BAE=？ CAF, BE=CF, so ② is correct. Because? B=？ c，？ BAM=？ CAN, AB=AC, so △ ACN △ ABM, so ③ is correct. Because? 1=? Pei- BAC，？ 2=? Cafe-? BAC，？ BAE=？ Cafe, so? 1=? 2, so ① is correct, so the correct conclusion in the question should be ① ② ③.
18. 19 (Analysis: Because DE is the middle vertical line of AC, AD=CD, AC=2AE=6 cm. And because △ABD =AB+BD+AD= 13 cm circumference, AB+BD+CD= 13 cm, that is.
19. solution: original formula = 4x2-4x+1-9x2+1+5x2-5x =-9x+2. When x=0, the original formula =2. (The answer is not unique)
20. Solution: (1) As can be seen from the image, the change brought by farmers is 5 yuan. (2)=0.5 yuan. (3)= 15 (kg), 15+30=45 (kg). A: The change brought by farmers is 5 yuan; Before the price reduction, the price he sold per catty of potatoes was 0.5 yuan; He brought 45 kilograms of potatoes.
2 1. Solution: (1)? EAB=？ d； The isosceles angles are equal and the two straight lines are parallel. (2)? BAC=？ c； Internal dislocation angles are equal and two straight lines are parallel. (3)? Bad+? D= 180？ ; The internal angles on the same side are complementary and the two straight lines are parallel.
22. Solution: The rules of the game are unfair. The reasons are as follows: The list is as follows:
As can be seen from the above table, there are nine possible results * * *, so P (the number on the card is the same) = =, P (the number on the card is different) = =. because