Shandong education publishing house mathematics first semester final examination questions 1. Multiple choice questions (this big question is a small question of *** 12, and each question has 4 points ***48 points. Only one of the four options given in each small question meets the requirements of the topic. )
1. The following are the logo diagrams of four kinds of cars, among which the axisymmetric diagram is
1。
2. The result of expressing the number 0.000043 by scientific notation is as follows.
A.4.3？ 10-4 B.4.3？ 10-5 C.4.3？ 10-6 D.43？ 10-5
3. The binary linear equation with solution is
A.B. C. D。
4. As shown in the figure, the vertex A passing through △ABC is the height on the side of BC. The following is correct.
A.B. C. D。
5. The following calculation is correct ()
A.a2？ a3=a5 B.a2+a3=a5 C.(a3)2=a5 D. a3？ a2= 1
6. As shown in the figure, AB∨CD is known, if? A=25？ ,? E=40？ And then what? C equals
.40 caliber? B.65？ C. 1 15？ D.25？
7. As shown in the figure, AD is the bisector of △ABC, and point O is on AD, OE? BC is at point e, BAC=60？ ,
? C=80？ And then what? The degree of EOD is
.20 caliber? B.30？ C. 10？ D. 15？
8. Calculate (13)0? The result of 2-2 is ()
a . 43 B- 4 c-43d . 14
9. Xiaoming accidentally broke a triangular glass into three pieces, as shown in Figures ①, ② and ③. He wants to go to the glass shop to match a glass of the same size and shape. Do you think he should take it with him?
A. 1b.2c.3d.① and ②
10. As shown in the figure, in △ABC,? BAC= 100？ , DF and EG are the perpendicular lines of AB and AC respectively, then? DAE equals
.50 caliber? B.45？ C.30？ D.20？
1 1. Of the following operations, the correct one is
A.(x+2)2=x2+4 B.(-a+b)(a+b)=b2-a2
C.(x-2)(x+3)=x2-6 D.3a3b2？ a2b2=3ab
12. As shown in the figure, in △ABC, p is a point above BC, P R? AB, the vertical foot is r, PS? AC, vertical foot is s, AQ=PQ, PR=PS. The following three conclusions: ① As = Ar; ②QP∑AR； ③△BRP?△CSP。 What is correct is that
A.① and ②
B.② and ③
C.① and ③
D.①②③
Volume 2 (non-multiple choice questions * * 102)
Precautions:
1. Volume 2 is a multiple-choice question. Candidates should use a blue-black pen (signature pen) or a ballpoint pen to answer directly on the test paper.
2. Before answering the question, please fill in the test center, name, admission ticket number and seat number in the specified position of the test paper.
Scoring reviewer
Fill-in-the-blank question (This big question has 6 small questions, each with 4 points and ***24 points. Fill in the answers on the lines of the questions. )
13. Calculation: (x+3) (2x-4) = _ _ _ _ _ _ _ _.
14. A bread 2 yuan and a bread 2.5 yuan are known. Someone bought X kinds of bread and Y kinds of bread, and * * * spent 30 yuan. Please list the binary linear equations about X and Y according to the meaning of the question _ _ _ _ _ _ _.
15. Given that two sides of a triangle are 3 and 6 respectively, the value range of the third side length x is _ _ _ _ _ _ _ _.
16. As shown in the figure, the straight line a∨b,? C=90？ , then = _ _ _ _ _ _ _ _ _ _.
17. As shown in the figure, points F and C are on the line segment BE, but? 1=? 2, BC=EF, if you want to make △ ABC△ def, you must add a condition _ _ _ _ _ _ _ _ _. (Write only one condition)
18. As shown in the figure, the side length of equilateral △ABC is 1, and there is a point P on the side of AB, Q is a point on the extension line of BC, CQ=PA, and point P is PE? E point AC, connecting PQ and D point AC, then the length of DE is _ _ _ _ _ _ _ _.
Third, solve the problem (this big problem ***9 small problems, ***78 points. The solution should be written in proof process or calculus steps. )
Scoring reviewer
19. (The full score for this short question is 7)
( 1)(-a)2？ (a2)2？ a3
(2) Simplify before evaluating: (2a+1) 2-(2a-1) (2a+1), where a=-34.
Scoring reviewer
20. (The full score for this short question is 7)
(1) Solve the equation x+y= 12x+y=2.
(2) Fill in the reasoning reasons:
Known: as shown in figure, CD∨EF,? 1=? 2.
Prove: 3=? ACB。
Proof: ∫CD∨EF (known),
DCB=？ 2(_____________________________).
Again? 1=? 2 (known),
DCB=？ 1(_____________________________).
? GD∨CB(_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _)。
3=? ACB(_________________________)。
Scoring reviewer
2 1. (The full score for this short question is 7)
As shown in the figure, points A, B, D and E are on the same straight line, and AD=EB, BC∨DF,? C=？ F.
Proof: AC=EF.
Scoring reviewer
22. (The full score for this short question is 8)
A company adjusted its employees' monthly salary distribution plan in June+10 this year. After adjustment, the monthly salary consists of two parts: basic guarantee salary and piece-rate bonus salary (piece-rate bonus salary = bonus amount for selling each piece? Number of pieces sold). The following table shows the salary information of two employees of Party A and Party B in May this year:
Employees a and b
Monthly sales (pieces) 200 180
Monthly salary (RMB) 1800 1700
After the salary distribution scheme is adjusted, what is the basic guaranteed monthly salary of employees and the reward amount for selling each product?
Scoring reviewer
23. (The full score for this short question is 8)
As shown in the figure, it is known that AD∑BE,? 1=? C. verification:? A=？ E.
Scoring reviewer
24. (The full score for this short question is 8)
Observe the following equation and answer the questions:
①x-y = 22x+y = 1； ②x-2y = 63x+2y = 2； ③x-3y = 124 x+3y = 3； ?
(1) What quantitative relationship do you find between X and Y in the solutions of the above three equations? Please write this relationship. (Needless to say)
(2) Please construct the fourth equation group that satisfies the structural characteristics of the above equations and verify the conclusion in (1).
Scoring reviewer
25. (The full score for this short question is 9)
Known: As shown in the figure, point D is a point within △ABC, satisfying BD=CD,? ABD=？ ACD。
Proof: (1) ab = AC;
(2)AD？ BC.
Scoring reviewer
26. (The full score of this short question is 12)
As shown in figure 1, CE is equally divided? ACD, AE split equally? BAC, and EAC+ ACE=90？ .
(1) Please judge the positional relationship between AB and CD and explain the reasons;
(2) As shown in Figure 2, when? E=90？ The positional relationship between AB and CD remains unchanged. When the right vertex e moves, write? BAE and? The quantitative relationship of ECD, and explain the reasons;
(3) As shown in Figure 3, P is a fixed point on the line segment AC, Q is a moving point on the straight line CD, and the positional relationship between AB and CD remains unchanged. When point Q moves on the light CD (except point C),? CPQ+？ CQP and? What is the quantitative relationship of BAC? Write a conclusion and prove it.
Scoring reviewer
27. (The full score of this short question is 12)
It is known that point C is a point on the line segment AB, with AC and BC as sides, △ACD and △BCE as the same side of the line segment AB, respectively, CA=CD, CB=CE,? ACD=？ BCE, straight AE and BD intersect at point F.
(1) as shown in figure 1, if? ACD=60？ And then what? The degree of AFB is _ _ _ _ _ _ _ _ _ _ _;
(2) As shown in Figure 2, what if? ACD=？ And then what? AFB = _ _ _ _ _ _ _ _ _ _ _ _ _? Algebraic representation of);
(3) Rotate the △ACD in Figure 2 clockwise at any angle around point C (the intersection point F is at least on a line segment of BD and AE), as shown in Figure 3. Trying to explore? AFB and? Quantitative relationship, and prove it.
Shandong Education Publishing House refers to the answer to the final examination paper of mathematics in the first semester.
The title is123455678911112.
Answer C B C A A B A D C D B A
fill (up) a vacancy
13.2x2+2x- 12
14.2x+2.5y=30
15.3x & lt9p = " " & gt； & lt/x & lt； 9 & gt
16.25?
17.AC=DF or? A=？ D or? B =？ E
18. 12
Third, answer questions.
19. Solution: (1) Original formula =a2? a4？ A3 1 point
=a6？ A3 2 points
=a3 3 points
(2) The original formula = 4a2+4a+1-(4a2-1) 4 points.
= 4a2+4a+1-4a2+1.5 points.
=4a+2 6 o'clock
When a=-34,
The original formula =-3+2=- 1. Seven points
20. Solution: (1) ②-①, get
? X= 1。 1.
Substitute x= 1 into ② to get.
2+y=2。
? Y=0。 2 points
? X= 1y=0。 3.
(2) Proof: ∫CD∨EF (known),
DCB=？ 2 (two straight lines are parallel and the same angle is equal) 4 points.
Again? 1=? 2 (known),
DCB=？ 1 (equivalent replacement) 5 points
? GD∨CB (internal dislocation angles are equal and two straight lines are parallel) 6 points.
3=? ACB (two straight lines are parallel and have the same angle) 7 points.
2 1. proof: AD = EB,
? AD-BD=EB-BD。
? AB=DE。 1.
∫BC∨DF，
CBD=？ FDB 2 points
ABC=？ France Power 3 points
In △ABC and △EDF,
∵? ABC=？ EDF？ C=？ FAB=DE。
? △ ABC△ EDF (AAS) 6 points.
? AC=EF 7 points
22. Solution: If the monthly basic guarantee salary is X yuan, and the reward amount for each product sold is Y yuan, you will get 1 point.
X+200y =1800x+180y =1700.4 points.
X=800y=5。 Seven points
Answer: The basic monthly salary is 800 yuan, and the reward amount is 5 yuan for every product sold. Eight points.
23. proof: ∫AD∨BE,
A=？ EBC 2 points
∵? 1=? c，
? DE∑AC 4 Dian
E=？ EBC 6 points
A=？ E 8 fen
24. Solution: (1)x+y=0 (or x=-y or x and y are reciprocal) 2 points.
(2) The fourth equation set is: x-4y = 205x+4y = 4; 5 points
The score of solving this system of equations is x=4y=-4. 7.
? X+y = 0.8 points
25. Proof: (1)∵BD=CD,
DBC=？ DCB 2 points
Again? ABD=？ ACD，
DBC+？ ABD=？ DCB+？ Automatic call distribution system
ABC=？ ACB 4 points
? Ab = ac.6。
(2)∫AB = AC，BD=CD，
? Point a and point d are on the vertical line of BC. Eight points.
? AD？ BC. 9 points
(2) Solution 2: Extend the intersection of AD and BC to point E. 。
In △ABD and △ACD,
BD = CD？ ABD=？ ACDAB=AC，
? △ Abd△ ACD (SAS) 7 points.
DAB=？ DAC 8 points
AB = AC，
? AE？ BC. 9 points
Namely AD? BC.
26. solution: (1)AB∑CD. 1.
Reason: ∵CE split equally? ACD, AE split equally? BAC，
ACD=2？ ACE？ BAC=2？ EAC。 2 points
Again? EAC+？ ACE=90？
ACD+？ BAC= 180？ 3 points
? AB∨CD。 4 points
(2)? BAE+？ ECD=90？ .5 points
Reason: extend AE CD to point F.
∫AB∨CD，
BAE=？ AFC 6 points
∵? AEC is the external angle of △EFC,
AEC=？ AFC+？ ECD=90？ .7 points
BAE+？ ECD=90？ .8 points
(2) Solution 2: If point E is EM∨AB, then EM∨CD is 5 points.
∫EM∨AB
BAE=？ AEM 6 points
∫EM∑CD
ECD=？ CEM 7 points
BAE+？ ECD=？ AEM+CEM=？ AEC=90？ .8 points
(3)? CPQ+？ CQP=？ BAC 9 points
Proof: ∫AB∨CD
BAC=？ ACG 10 integral
∵? ACG is the external angle of △PCQ,
ACG=？ CPQ+？ CQP 1 1 min
CPQ+？ CQP=？ BAC 12 point
27. Solution: (1) 120? .2 points
(2) 180? ―? .4 points
(3)? AFB= 180？ ―? .5 points
Proof: ACD =? BCE，
ACD+？ DCG=？ BCE+？ DCG。
ACE=？ DCB。 6 points
In △ACE and △DCB.
CA = CD？ ACE=？ DCBCE=CB，
? △ ace△ DCB (SAS) 8 points.
AEC=？ DBC 9 points
Again? EGF=？ BGC
And then what? EFG= 180？ -? AEC-？ EGF，？ ECB= 180？ ―? DBC―? BGC
EFG=？ European Central Bank 10 point
Again? ACD=？ BCE=？
EFG=？ 1 1 min
Again? AFB+？ EFG= 180？
AFB= 180？ ―? . 12 point