First, multiple-choice questions (30 points for this question, 3 points for each small question)
There are four options for each question below, and only one of them fits the meaning of the question.
The square root of 1 Yes ()
A.
D.
2.=( )
D.
3. When is, the value of is ()
A.
D.
4. If the score is zero, the value of is ().
A.
D.
5. The event of "throwing a uniform coin face up and landing" is ()
A. inevitable events B. random events C. definite events D. impossible events
6. In the figure below, the axis symmetry is ().
A B C D
7. The degree of the sum of the internal angles of a Pentagon is ().
A. 180
From 540 to 720 A.D.
8. As shown in the figure, put the right-angle vertex of the triangular ruler on the straight line A,
The degree is ()
80 years
C.60 D.50
9. As shown in the figure, points A, D, C and F are known to be on the same straight line.
AB=DE, BC=EF, so △ ABC △ def,
Another condition that needs to be added is ()
A.∠B =∠E B∠BCA =∠F
C.BC∨EF d .∠A =∠EDF
10. As shown in the figure, there are four cards with real numbers written on them. Choose one of them.
The probability of the irrational number is ()
C.
D. 1
II. Fill in the blanks (the score for this question is *** 15, with 3 points for each small question)
1 1. If it makes sense, the value range of is.
12. Calculation.
13. If the two sides of an isosceles triangle are 4cm and 8cm respectively, the circumference of the triangle is.
14. In the isosceles right angle △ABC, BC =AC = 1, with hypotenuse AB.
And the side bb 1 with the length1is a right-angled side.
Right angle △ABB 1, as shown in the figure, if the structure goes on like this,
AB3 =； ABn=。
15. For two non-zero real numbers A and B, it is specified that if, the value of x is.
Third, the answer (this question ***4 small questions, each small question 5 points, ***20.
16. Calculation:.
Solution:
17. If the sum is reciprocal, find the value of.
18. Solve the equation:.
19. Simplify first, then evaluate.
Solution:
Four, painting questions (this question out of 6 points)
20. The vertices of small squares in this paper are called grids. Points A and B are grids, and their positions are as shown in the figure.
(1) In the figure 1, determine the grid point c to make △ABC a right triangle, and draw such △ ABC;
(2) Determine the grid point D in Figure 2 so that △ABD is an isosceles triangle and draw such △ Abd;
(3) There are _ _ _ _ _ lattice points d in Figure 2 that satisfy the condition of problem (2).
2 1. A school decided to buy a math curriculum standard for compulsory education (hereinafter referred to as the standard) for all math teachers, and at the same time, everyone bought an explanation of the math curriculum standard (hereinafter referred to as the explanation). The explained unit price is more than the standard unit price by 25 yuan. If the school spent 378 yuan to buy the standard, buy it.
Vi. Answering questions (there are 3 small questions in this question, *** 17)
22. (6 points in this small question) State and prove the theorem of triangle interior angle sum.
Requirements can write theorems, know, verify, draw charts, and write proof process.
Theorem:
Known:
Verification:
Prove:
23. (5 points for this small question) As shown in the figure, in △ABC, AB=AC, ∠ BAC = 36.
(1) Make a bisector BD of ∠ABC with a ruler and compasses, and intersect with AC at point D..
(traces of drawing are reserved, and writing is not required);
(2) Please find out all isosceles triangles (represented by letters and written on the horizontal line, without proof) in the graph obtained after completing the question (1).
24. (6 points in this small question) As shown in the figure △ABC, ∠ ACB = 45, AD⊥BC is at D, CF is at F, BF connects AC to E, ∠BAD =∠FCD.
Verification: (1) △ Abd △ CFD; (2)BE⊥AC.
Prove:
Seven, ask questions (this question out of 6 points)
25. As shown in the figure, when △ABC, ∠ ACB = 90, if △ABC is folded along the straight line DE,
Make △ADE and △BDE coincide.
(1) When ∠ A = 35, find the degree of ∠CBD.
(2) If AC =4 and BC =3, find the length of AD.
(3) when AB = m (m >); 0), when the area of △ABC is m+1, find the perimeter of △BCD.
(represented by an algebraic expression containing m)
Shijingshan district 20 12-20 13 school year first semester final exam.
Math reference answer for grade two in junior high school
Tag description:
For the convenience of marking papers, the derivation steps in the solution questions are written in detail, and candidates only need to explain the main process in detail. If the candidate's solution is different from this solution, the correct one can be scored with reference to the scoring reference, and the score marked on the right hand side can be answered, indicating the accumulated score that the candidate should get if he does this step correctly.
First, multiple-choice questions (this question is a small question of * *10, with 3 points for each small question and 30 points for * * *).
The title is 1 23455 6789 10.
Answer A C A D B B C B A C
2. Fill in the blanks (5 small questions in this question, 3 points for each small question, *** 15 points)
The title is112131415.
Answer a question.
20 (the first space is 1 and the second space is 2)
Iii. Answering questions (there are 4 small questions in this question, with 5 points for each small question and 20 points for * * *).
16. Solution: 3 points for the original formula.
Five points.
17. solution: you can get 2 points from what you know;
Solve it, so ..................................................................................... 5 points.
18. Solution: ................................................................................ scored 2 points.
.
...................................................., 4 points.
Test: it is the simplest common denominator, so it is rooted.
∴ The original equation has no solution. ....................................... scored 5 points.
19. Answer: = = ........................................................... 4 points.
When, the original formula = = ............................................ 5 points.
Four, painting questions (this question out of 6 points)
20. Solution: (1) Draw a triangle .......................... in the following figure 1, with 2 points.
(2) Draw a triangle, as shown in Figure 2 below. ............................. scores 4 points.
(3) 4. (The reason is shown in Figure 2) 6 points.
Five, column equation to solve the application problem (this question out of 6 points)
2 1. solution: if the standard unit price is x yuan, the unit price is (x+25) yuan ... 1.
According to the meaning of the question, get =, ... 3 points.
Solution, x =14 .................................................................... 4 points.
It is verified that x= 14 is the solution of the listed equations, which accords with .....................................................................'s score of 5.
∴x+25=39.
Answer: The standard unit price 14 yuan, which means the unit price 39 yuan. ................................................................................................................................................
(Note: If you don't take the test, you won't be deducted 1 point)
Vi. Answering questions (there are 3 small questions in this question, *** 17)
22. Solution: Theorem: The sum of the three internal angles of a triangle is equal to180 ..........................1minute.
It is called △ABC (pictured).
Verification: ∠ A+∠ B+∠ ACB = 180 ................................................................................................................................
Proof: extend BC to D, and pass C .................................................................................... 3 points for CE//AB.
∴ ∠ 1=∠A，
∠2=∠B。
∫≈ 1+∠2+∠ACB = 180
∴∠ A+∠ B+∠ ACB =180 ......................... 6 points.
23. (5 points for this short question)
Solution: (1) 2 points as shown in the right figure.
(2) Delta Agricultural Bank, Delta ADB, Delta DBC .................................... 5 points.
(65438+ 0 point for each item)
24. (6 points in this small question) Solution:
Proof: (1)∫ad⊥bc, ∴∠ ADB = ∠ CDF = 90.
∠ ACB = 45, ∴∠ ACD = ∠ DAC = 45 ...........................1min.
∴ AD = CD ......................................................... 2 points.
In △ABD and △CFD,
∴△ Abd△ CFD ............................................... 3 points.
(2) ∴ BD = FD ................................................................... 4 points.
∫∠fdb = 90 ,∴∠fbd=∠bfd=45。
≈ACB = 45 ,∴∠ceb=90。
∴ Yes ⊥ 6 points for AC ....................................................................
Seven, ask questions (this question out of 6 points)
25. Solution:
(1) 20 .........................1min.
(2) Let AD=x, and BD = x；; CD=4-x。
In △BCD, ∠ c = 90. According to Pythagorean theorem, we get x2 = (4-x) 2+32. ........................................................................................................................
The solution is x = Advertising = .................................. 3 points.
(3) let AC=b, BC=a,
From the known m2=a2+b2, and ... and ...
You can get a+b = m+2...................5 points.
Because a+b is the circumference of △BCD,
So the circumference of △BCD is m+2.....................6 points.