Math test questions
Volume 1 (30 points for multiple-choice questions)
1. Multiple choice questions (only one of the four options in the following questions meets the meaning of the question, with 3 points for each small question and 30 points for * * *).
1, (20 12 Anhui) The result of calculating-1-2 is
A.- 1 B. 1 C.-3 D. 3
2. The following equation holds
a . a2+a3 = a5 b . a3-a2 = a c . a2 . a3 = a6 d .(a2)3 = a6
3.(20 12 Anhui) If the two sides of an isosceles triangle are 5cm and 6cm respectively, then the circumference of the triangle is
A.15cm B.16cm C. 17cm D.16cm or17cm.
4.(20 12 Anhui) The following calculations are correct.
A.B.
C.D.
5.(20 12 Anhui) it is known that one root of the equation x2+bx+a=0 about x is -a(a≠0), so the value of a-b is
A.- 1 B.0 C. 1 D.2
6.(20 12 Anhui) As shown in the figure, if AE∨BD, ∠ 1 = 120, ∠ 2 = 40, then the degree of ∠C is
10
7.(20 12 Anhui) Fill in "+"or "-"in the space of x2□2xy□y2 respectively. In the obtained algebraic expression, the probability of forming a completely flat mode is
A. BC 1 year
8.(20 12 Anhui) In the known quadratic function y=ax2+bx+c, some corresponding values between the function y and the independent variable x are shown in the following table:
x…0 1 2 3 4…
y…4 1 0 1 4…
Points A(x 1, y 1) and B(x2, y2) are both on the image of the function, so when 1
The correct relationship between size is
A.y 1 & gt； y2 b . y 1 & lt； y2 C. y 1 ≥ y2 D. y 1 ≤ y2
9.(20 12 Anhui) As shown in the figure, the circumference of △ABC is 30cm. Fold the side AC of △ABC in half, so that the vertex C coincides with the point A, the crease passes through the BC side at the point D, and the AC side passes through the point E to connect the AD. If AE=4cm, the circumference of △ABD is.
A. length 22cm, width 20cm, height18cm, width15cm.
10 and (20 12 Anhui) are three views of a certain geometry and related data, so the following judgment is correct.
A.a & gtc B. b & gtc c a2+4 B2 = C2 d a2+B2 = C2
Volume 2 (70 points for non-multiple choice questions)
Second, fill in the blanks (3 points for each small question, *** 15 points; Only the final result is needed)
1 1, (20 12 Anhui) The images of the inverse proportional function are in the first and third quadrants, so the range of m is.
12, (20 12 Anhui) If the quadratic function y=x2-4x+5 is transformed into the form of y=(x-h)2+k, then y=.
13, (20 12 Anhui) As shown in the figure, in Rt△ABC, ∠ C = 90, BC=4cm, with point C as the center and 3cm as the radius, the positional relationship between ∵ C and AB is.
14, (Anhui, 20 12) As shown in the figure, observe the arrangement law of black regular hexagons in each figure, and there are four black regular hexagons in the 10 figure.
15, (20 12 Anhui) As shown in the figure, in the equilateral triangle ABC, D and E are two moving points on the sides of AB and BC respectively, and always make AD=BE, AE and CD intersect at point F, and AG⊥CD intersect at point G, then.
Iii. Answering questions (***55 points, the answer should specify the explanation, proof process or deduction steps)
16, (5 points) (20 12 Anhui) calculation:
17, (5 points) (20 12 Anhui) As shown in the figure, in the parallelogram ABCD, the diagonal AC and BD intersect at the O point, and the straight line EF⊥BD crosses the O point, and intersects with AD and BC at the E point and F point respectively, which proves that the quadrilateral BEDF is a diamond.
18, (6 points) (20 12 Anhui) After the accident of Fukushima nuclear power plant, the State Oceanic Administration of China paid close attention to the development of the situation, and urgently mobilized maritime inspection vessels to carry out on-site monitoring and seawater sampling in relevant sea areas, and timely analyzed and evaluated the impact of nuclear leakage on the marine environment in extreme cases. As shown in the figure, at 9: 00 am, the maritime ship was located in A, and it was observed that a port city P was located at 67.5 northwest of the maritime ship. The maritime ship was traveling at a speed of 265,438+0 knots and arrived at B at 2: 00 pm. At this time, it was observed that the city P was located at 36.9 southwest of the maritime ship. What is the distance between B where the maritime ship is located and P?
(Reference data:
, , , )
19, (6 points) (20 12 Anhui) A junior high school wants to recommend a student to a higher school. According to the prescribed recommendation procedure: firstly, 200 students of this grade will vote democratically, and each student can only recommend one person (without abstention), and the one with the most votes will choose three people. Figure 1 shows the statistics of ticket results:
Secondly, three candidates were given a written test and an interview. The following table shows the achievements:
Test scores/scores of test items
Methyl ethylene propylene
Written test 92 90 95
Interview 85 95 80
Figure 2 is an incomplete bar chart drawn by a classmate according to the above table.
Please answer the following questions based on the above information:
(1), complete Figure 1 and Figure 2;
(2) Please count the votes of each candidate;
(3) If each candidate has one vote 1 point, the voting, written test and interview scores shall be determined according to the ratio of 2: 5: 3, and the average scores of the three candidates shall be calculated. Those with high scores will be admitted. Who should be admitted?
Solution: (1)
(2) The number of votes of A is: 200×34%=68 (votes).
The number of votes for B is: 200×30%=60 (votes).
The number of votes for C is: 200×28%=56 (votes).
(3) The average score of A:
The average score is b:
Average score of c:
B has the highest average score; B should be admitted.
20, (7 points) (20 12 Anhui) As shown in the figure, AB is the diameter ⊙O, AM and BN are its two tangents, DE cuts ⊙O at point E, AM at point D, BN at point C, and F is the midpoint OF CD, connecting of.
(1) verification: od ∑ be;
(2) Guess: What is the quantitative relationship between OF and CD? And explain why.
2 1, (8 points) (20 12 Anhui) During the "May 1" period, in order to meet the consumption needs of the broad masses of the people,
A shopping mall plans to buy a batch of household appliances with an amount of 160000 yuan. The purchase price and sales price of these household appliances are as follows:
Category color TV refrigerator washing machine
Purchase price: 2000 1600 1000.
The price is 220018001100.
(1). If all the funds are used to buy *** 100 color TV sets and washing machines, how many color TV sets and washing machines can the store buy?
(2) If the number of washing machines does not exceed the number of color TV sets, please calculate how many purchase schemes there are if you buy three types of household appliances 160000, including the same number of color TV sets and refrigerators, within the scope of the existing funds? After selling these home appliances, which purchasing scheme can make the store get the maximum profit? Find out the maximum profit.
(Profit = selling price-buying price)
22, (8 points) (20 12 Anhui) Last winter and this spring, Jining suffered the worst drought in 200 years. In order to solve the problem of drought resistance, a township should build a water pump station in a river to supply water to Zhang Cun A and Licun B on the same side of the river. After on-the-spot investigation, the engineer established a rectangular coordinate system with the bridge O on the river as the coordinate origin and the straight line where the river is located as the X axis when designing the drawings (as shown in the figure). The coordinates of the two villages are A (2 2,3) and B (12,7) respectively.
(1), from the perspective of saving money, how far is the pump station from the O bridge?
Where can the shortest water pipeline be used?
(2) How far is the water pump station from O Bridge, and it can reach Zhang Cun and Licun.
Equal distance?
23.( 10) (20 12 Anhui) As shown in the figure, in the first quadrant, ⊙C with a radius of 2 is tangent to the Y-axis, with a diameter of AD, the tangent L passing through the D-point is tangent to ⊙C, the X-axis intersects with the B-point, and P is a fixed point on the straight line L.
(1) Let the ordinate of point p be p, and write the functional relationship between p and change.
(2) If ⊙C intersects with PA at point M and with AB at point N, there is △AMN∽△ABP wherever the moving point P is on the straight line L (except point B). Please prove the similarity of two triangles when point P is in the figure.
(3) Is there a k value that makes the area of △AMN equal? If yes, request a matching k value; If it does not exist, please explain why.
Jining 20 1 1 senior high school entrance examination
Reference answers to math test questions
First, multiple choice questions
The title is 1 23455 6789 10.
Answer c d d c a b c b a d
Second, fill in the blanks:
1 1, m > 1 12, y=(x-2)2+ 1 13, intersection 14,13.
Third, answer questions:
16, solution: original formula = ... 2 points.
=..........................4 points.
= 5 points.
17, it is proved that the ∵ quadrilateral ABCD is a parallelogram.
∴ AD ∨ BC, OB = OD ...........................1min.
∠ edo = ∠ FBO，∠ OED = ∠ ofb ...............................................................................................................................
∴△OED≌△OFB
∴ Germany = BF ................................ 3 points.
∫ED∨BF is here again
∴ Quadrilateral is parallelogram. ........................... 4 points.
∵EF⊥BD
A parallelogram is a diamond. 5 points: 5 points
18, solution: let the passing point p be PC⊥AB, the vertical foot be C, and let PC=x nautical miles.
In Rt△APC, ∫ tan ∠ a = ∴ AC = ………………………………………………………….
In Rt△PCB, ∫tan∠b =∴BC = .........
∫ AC+BC = AB = 21× 5 ∴+= 21× 5, and the solution is x=60.
∫sin∠b = ∴pb= = 50×= 100 (in the sea)
∴ The distance between City B and City P where the ship is located is 100 nautical mile. ........................ scored six points.
19, solution: (1)…2 points.
(2) The number of votes of A is: 200×34%=68 (votes).
The number of votes for B is: 200×30%=60 (votes).
The number of votes for C is: 200×28%=56 (votes). ..................................................................................................................................................
(3) The average score of A:
The average score is b:
Average score of c:
B has the highest average score; B should be admitted. ........................ scored six points.
20. Solution: (1) Proof: Connect OE
∵AM and DE are tangents of ⊙ O, and OA and OE are radii of ⊙ o.
∴∠ ADO =∠ EDO, ∠ Dao =∠ deo = 90 ...........................................................1min.
∴∠aod =∠EOD =∠AOE ......................................................................................................................................
∠∠ Abbe =∠∴∠ AOD =∠∴∴ Abbe ∴ OD ∨ Be ................................................................ 3 points.
(2) of = CD ................................ 4 points.
Reason: connecting OC
Be and CE are tangents of ⊙ O.
∴∠ OCB = ∠ OCE ............................... 5 points.
∫AM∨BN
∴∠ADO+∠EDO+∠OCB+∠OCE= 180
∠ADO=∠EDO from ( 1)
∴ 2 ∠ EDO+2 ∠ OCE = 180, that is ∠ EDO+∠ OCE = 90. .................................................................................................
In Rt△DOC, ∫f is the midpoint ............................ of DC ∴ = CD 7 points.
2 1, solution: (1) If you open a shop and buy X color TV sets, buy (100-x) washing machines.
From the meaning of the question, we get 2000 x+1000 (100-x) =160000, and we get x=60.
Then 100-x=40 (unit)
Therefore, stores can buy 60 color TVs and 40 washing machines. ........................, 3 points.
(2) Buy a color TV and buy a washing machine (100-2a).
According to the meaning of the question, it is 2000a+1600a+1000 (100-2a) ≤160000.
100-2a≤a
Solve. Because a is an integer, a=34, 35, 36, 37.
Therefore, * * * has four purchase schemes. ........................ scored six points.
The profit after the sale of the store is W yuan.
w =(2200-2000)a+( 1800- 1600)a+( 1 100- 1000)( 100-2a)。
= 200a+10000 ............................... 7 points.
∵200 & gt； 0 ∴ w increases with the increase of a.
∴ When a=37, the maximum value of W = 200× 37+10000 =17400. .................................................................................................................
So the maximum profit of the store is 17400 yuan.
22. Solution: (1) Let point B be the dual point E about the X axis and connect AE, then point E is (12, -7).
Let the functional relationship of straight AE be y=kx+b, then
2k+b=3
12k+b=-7
The solution is k=- 1.
b=5
When y=0, x=5.
Therefore, the water pump station is built 5 kilometers away from the bridge, which can make the water pipeline shortest.
(2) The median line GF of the line segment AB intersects with AB at point F and with X axis at point G..
The coordinate of point G is (x, 0).
In Rt△AGD, AG2=AD2+DG2=32+(x-2)2.
In Rt△BCG, BG2=BC2+GC2=72+( 12-x)2.
∫ag = BG∴32+(x-2)2 = 72+( 12-x)2，x=9。
Therefore, the pump station is built 9 kilometers away from the bridge, which can make it equal to Zhang Cun and Licun.
23. Solution: (1),
The y axis and the straight line l are tangents of the c.
∴OA⊥AD BD⊥AD
OA⊥OB again
∴∠AOB=∠OAD=∠ADB=90
The quadrilateral OADB is a rectangle.
∵⊙C has a radius of 2.
∴AD=OB=4
Point p is on the straight line L.
The coordinate of point p is (4, p)
Point p is also on the straight line AP.
∴p=4k+3
(2) connect DN
∫ad is the diameter of∫∴∠ C, and = 90.
∠∠AND = 90-∠DAN，∠ABD=90 -∠DAN
∴∠AND=∠ABD
And ∵∠ ADN = ∠ AMN ∴∠ Abd = ∠ AMN ............................. 4 points.
∠∠ man = ∠ BAP ............................... 5 points.
∴△ AMN ∽△ ABP ................................ 6 points.
(3) existence. Seven points
Reason: Substituting x=0 into y=kx+3 to get y=3, that is OA=BD=3.
AB=
∫S△ABD = AB？ DN= AD？ decibel
∴DN= =
∴AN2=AD2-DN2=
∫△AMN∽△ABP
That's ∴ ... eight points.
When point p is above point b,
∫AP2 = AD2+PD2 = AD2+(p B- BD)2 = 42+(4k+3-3)2 = 16(k2+ 1)
Or AP2 = Ad2+PD2 = Ad2+(BD-Pb) 2 = 42+(3-4k-3) 2 =16 (k2+1).
S△ABP= PB？ AD= (4k+3)×4=2(4k+3)
∴
After sorting, k2-4k-2=0, and the solution is K 1 = 2+K2 = 2- ............................................................................................................................
When point p is lower than point b,
∫AP2 = AD2+PD2 = 42+(3-4k-3)2 = 16(k2+ 1)
S△ABP= PB？ AD= [-(4k+3)]×4=-2(4k+3)
∴
K2+ 1=-(4k+3) is simplified and k=-2 is obtained.
Based on the above results, when k = 2 or k=-2, the area of △AMN is equal to … 10 point.