The final simulation test paper 1 of the first volume of mathematics in the second day of junior high school. Choose carefully (this topic is entitled *** 10, with 3 points for each topic and 30 points for * * *).
Please select the carefully selected option in the box below. If you choose wrong, don't choose. If you choose too many, you won't score.
1, the point (-1, 2) is located at ()
(a) first quadrant (b) second quadrant (c) third quadrant (d) fourth quadrant
2. What if? 1 and? 3 is the inner angle of the same side. 1=78 degrees, then the following statement is correct ()
(1)? 3=78 degrees (b)? 3= 102 degrees (c)? 1+? 3= 180 degrees (d)? The degree of 3 cannot be determined.
3. As shown in the picture, you know? 1=? 2, then the following conclusion must be correct ()
(1)? 3=? 4 (B)？ 1=? Ad 3 AB//CD (D) AD//BC
Xiao Ming, Xiao Qiang and Xiao Gang are at points A, B and C in the figure, and their connecting lines just form a right triangle. The distance between B and C is 5km, and Xinhua Bookstore is located at the midpoint D of oblique BC, so the distance between Xinhua Bookstore D and Xiaoming's home A is ().
(A)2.5 km (B)3 km (C)4 km (D)5 km
5. It can be concluded that △ABC is an isosceles triangle ()
(1)? A=30？ 、? B=60？ (B)？ A=50？ 、? B=80？
(C)AB=AC=2, BC=4 (D)AB=3, BC=7, and the circumference is 13.
6. A tourist climbed 2km/hour to watch the sunrise, and rested for 0.5 hour/hour 1 hour to climb to the top of the mountain. The functional relationship between the mountain height h and the time taken by tourists to climb the mountain t is roughly graphically represented as ()
7. The following inequality must be established ()
(A)4a >3a(B)3-x & lt； 4-x(C)-a & gt； -3a(D)4a & gt； 3a
8. As shown in the figure, the rectangular ABCD can be divided into seven small rectangles with the same shape and size. If the area of the small rectangle is 3, then the circumference of the rectangle ABCD is ().
(A) 17(B) 18(C) 19(D)
9. The image with linear function y=x is moved down by 2 unit lengths and then moved to the right by 3 unit lengths, and the corresponding functional relationship is ().
(A)y = 2x-8(B)y = 12x(C)y = x+2(D)y = x-5
10. Seven squares are placed in sequence on the straight line L. It is known that the areas of the three squares placed obliquely are 1, 2 and 3 respectively, and the areas of the four squares placed sequentially are S 1, S2, S3 and S4, so S 1+2S2+2S3+S4=.
5 (B)4 (C) 6 (D)、 10
Second, fill in carefully (3 points for each small question, 24 points for * * *)
1 1. The coordinates of the point P(3, -2) about the y axis symmetry are.
12. The lengths of two sides of a given isosceles triangle are 3 and 5 respectively, and its circumference is.
13.Rt△ABC, CD and CF are the middle and high school lines on the side of AB. If AC=4 and BC=3, then CF =；; CD=。
14. It is known that the midline of the waist of an isosceles triangle divides its circumference into two parts, 9cm and 6cm, so the length of the base of this isosceles triangle is _ _
15. If the linear function y=kx+b satisfies 2k+b=-1, its image must pass through a point whose coordinates are.
16. Given the coordinate origin O and point A( 1, 1), try to find the point P on the X axis, make △AOP an isosceles triangle, and write the coordinates of the point P that meets the conditions.
17. As shown in the figure, in △ABC,? C=90？ The median line DE of AB intersects AB at E and BC at D. If AB= 10 and AC=6, the circumference of △ABC is.
18. As shown in the figure, eight congruent right-angled triangles are spliced into a quadrilateral ABCD and a small quadrilateral MNPQ in the middle, and the quadrilateral EFGH is obtained by connecting EF and GH. Let s quadrilateral ABCD=S 1, s quadrilateral EFGH=S2, s quadrilateral MNPQ=S3, if S 1+S2+S3, then S2.
Three, carefully draw a picture (6 points)
19.( 1) Given line segments A and H, use a ruler and compasses as an isosceles triangle ABC, with the base BC = A and the height on the side of BC being H.
└─────┘a └──────┘h
(2) As shown in the figure, if △ABC is known, please draw the figure of △ABC about X axis symmetry, and write the point coordinates of A, B and C about X axis symmetry.
Four, do it with your heart (40 points)
20. (6 points in this question) Solve the following inequalities (groups) and express their solution sets on the number axis.
( 1)x+ 16 & lt； 5-x4 + 1 (2) 2x >x+2； ①
x+8 & gt； x- 1； ②
2 1. (5 points in this question) As shown in the figure, it is known that AD∨BC, 1=? 2. Explain? 3+? 4= 180? , please complete the explanation process and fill in the corresponding basis in brackets:
Solution:? 3+? 4= 180? , for the following reasons:
∫AD∨BC (known),
1=? 3( )
∵? 1=? 2 (known)
2=? 3 (equivalent substitution);
? ∥ ( )
3+? 4= 180? ( )
22. As shown in the figure, in △ABC, points D and E are on the side of BC, AB=AC, and AD=AE. Please explain why BE=CD.
23. (6 points in this question) A software company has developed a book management software, and all kinds of expenses invested in the early stage totaled * * * 50,000 yuan. After each set of software is sold, the software company also needs to pay 200 yuan for installation and debugging, and set the number of sales sets X (sets).
(1) Try to write the functional relationship between the total cost y (yuan) and the number of sales sets x (sets).
(2) The company plans to sell at the price of each set in 400 yuan, and the company is still responsible for installation and debugging. How many sets of software did the software company sell, and the revenue exceeded the total cost?
24. (8 points for this question)? Eleventh golden week? One day, Xiaogang's family took a bus from home at 8 am and went to a famous tourist attraction, with a distance of 180 km. The relationship between the distance s (kilometers) and the time t (hours) from home can be represented by the dotted line on the right. According to the information provided in the picture, answer the following questions:
(1) How many hours did the Xiaogang family play in the tourist attractions?
(2) Find the functional relationship between s (km) and time t (hour) in the whole process, and find the value range of the corresponding independent variable t. ..
(3) When did the Xiaogang family leave home? When will you go home?
25. (Subject 10) As shown in the figure, it is known that the straight line Y =-34 x+3 intersects the X axis and the Y axis at points A and B respectively, and the line segment AB is a right-angled side, and the isosceles Rt△ABC is made in the first quadrant. BAC=90？ .
(1) Find the area of △AOB;
(2) Find the coordinates of point C;
(3) Point P is a moving point on the X axis, let P(x, 0).
① Please use the algebraic expression of X to represent PB2 and PC2.
② Is there such a point p that the value of |PC-PB| is the largest? If it does not exist, please explain the reason;
If it exists, request the coordinates of point p.
The reference answer of the final simulation test paper of the first volume of junior two mathematics 1. Choose carefully (this topic is entitled *** 10, with 3 points for each topic and 30 points for * * *).
Please select the carefully selected option in the box below. If you choose wrong, don't choose. If you choose too many, you won't score.
The title is 1 23455 6789 10.
Answer B D D A B D B C D C
X k B 1。 chief operating officer
Second, fill in carefully (3 points for each small question, 24 points for * * *)
11.(-3,2)12.11or 3.
132.5,2.4143 or 7
15 (2,- 1) 16 ( 1,0) (2,0) (2 ,0) (- ,0)
17 14 18 203
Three, carefully draw a picture (6 points)
19.( 1) The sketch is correct, 2 points, and the conclusion 1 point.
(2) Solution: 2 points for a1(2,3) b1(1,-1) c1(3,2); Drawing score 1.
Four, do it with your heart (40 points)
20. (6 points in this question) (1) solution: remove the denominator to get 2 (x+ 1) < 3(5-x)+ 12.
Move the items without brackets to get 2x+3x.
Merge similar projects to get 5x.
Divide both sides of the equation by 5 to get X.
? The solution set of the original inequality is x < 5 as shown in the figure:
(2) solution: obtained by ①, x >; 2
From ②, x
? The solution set of the original inequality is 2.
2 1. (5 points for this question) Solution:? 3+? 4= 180? , for the following reasons:
∫AD∨BC (known),
1=? 3 (two straight lines are parallel and the internal dislocation angle is equal);
∵? 1=? 2 (known)
2=? 3 (equivalent substitution);
? EB∨DF (same angle, two straight lines are parallel)
3+? 4= 180? (Two straight lines are parallel and complementary to the fat inner angle)
W W W W x K b 1 c o M
22. (5 points for this question) Solution: ∵AB=AC, AD=AE
ABC=？ ACB？ ADC=？ AEB (equilateral)
Also, in △ABE and △ACD,
? ABC=？ ACB (certification)
? ADC=？ AEB (certification)
AB=AC (known)
? △ABE?△ACD(AAS)
? BE=CD (the corresponding sides of congruent triangles are equal)
23. (6 points for this question)
Solution (1): let the total cost y (yuan) and the number of sales sets x (sets),
According to the meaning of the question, the functional relationship is obtained: y = 50000+200 x.
Solution (2): A software company must sell at least X sets of software to ensure no loss.
Yes: 400x? 50000+200x solution: x? 250
A: Software companies must sell at least 250 sets of software to ensure no loss.
24. (8 points for this question)
Solution: (1)4 hours
② ① When 8? t？ At 10,
Let s=kt+b cross points (8,0) and (10, 180) to get s=90t-720.
② 10? t？ 14，s= 180。
③ When 14? T time is over (14, 180), (15, 120).
? s=90t-720(8？ t？ 10) s= 180( 10？ t？ 14)s =-60t+ 1020( 14？ t)
(3)① When s= 120 km and 90t-720= 120, t=9, that is, 9: 20.
T = 1020 = 120 of -60t.
② When s=0 -60t+ 1020=0, t= 17.
A: I left home at 9: 20 or 15 and got home at 120㎞ and 17.
25. (This question 10)
(1) from the straight line y=- x +3, let y=0, OA=x=4, let x=0, OB=y=3,
(2) Make a CD at point C? X axis, vertical foot is d,
∵? Bao+? CAD=90？ ,? ACD+？ CAD=90？ ,
Bao =? ACD，
AB = AC，？ AOB=？ CDA=90？ ,
? △OAB?△DCA，
? CD=OA=4, AD=OB=3, then OD=4+3=7,
? C(7，4)；
(3)① According to (2), PD=7-x,
In Rt△OPB, PB2=OP2+OB2=x2+9,
In Rt△PCD, pc2 = pd2+Cd2 = (7-x) 2+16 = x2-14x+65,
(2) there is such a p point.
Let point b be symmetric about x, which is b? , then b (0, -3),
Connect CB? Set a straight line b? The analytical formula of c is y=kx+b, and b? Substitute the coordinates of two points, c, and you get
b =-3；
7k+b = 4；
k= 1
The solution is b=-3.
So, line B? The analytical formula of c is y=x-3,
Let y=0 and get p (3 3,0). At this time, the value of |PC-PB| is the largest.
So the answer is: (3,0).