1. In the following groups, the inverse number is (▲).
A.3 and B.3 and -3 C.3 and-D.3 and-
2. As shown in the figure, if the straight line AB∨CD, A = 70, C = 40, then E is equal to ().
30-40 A.D.
3. The daily maximum temperature of a city for five consecutive days in May is 23, 20, 20, 265, 438+0 and 26 (in degrees Celsius) respectively. This set of data
The median and mode of is ()
A.22C，26 B. 22C，20 C. 2 1C，26 D. 2 1C，20 C
4. The solution set of inequality group is ()
A.B. C. D。
5. Put a cylindrical water cup and a rectangular chalk box on a horizontal platform (right), and its front view is ().
A. Figure1B. Figure 2 C. Figure 3 D. Figure 4
6. If the image of the inverse proportional function passes through the point, then the image of this function must pass through the point ().
A.B. C. D。
7. The picture shows a round artificial lake. The string AB is a bridge on the lake. Known AB bridge length 100m, measured ACB is 45.
The diameter of this artificial lake is ()
A.B.
C.D.
8. A large sunshade can be approximately regarded as a cone when the umbrella surface is unfolded.
As shown in the figure, its bus length is 2. 5 meters, its bottom radius is 2 meters, so do it.
The fabric area required for placing sunshade is () square meters (excluding seams).
A.B. C. D。
9. As shown in the figure, it is a square matrix of algebraic expression about X. If the value of the second item in line 10 is 1034,
Then the value of x at this time is ()
A. 10 B. 1 C. 5 D. 2
10. It is known that in △ABC, d and e are the midpoint of AC and AB sides, BDCE and.
At point f, ce = 2, BD = 4, and the area of △ABC is ().
A.B.8 C.4 D.6
Volume II
Fill in the blanks (6 small questions in this question, 4 points for each question, * * * 24 points)
The range of the independent variable x in the 1 1. function is.
12. Decomposition factor:.
13. As shown in the figure, in ABC, m and n are the midpoint of AB and AC respectively.
And A +B= 136, then ANM=
14. Five identical balls except the color are marked with the numbers 1, 2, 3, 4 and 5 respectively.
Put it in an opaque bag and mix well. Touch a ball from your pocket, write down the number and put it down.
Come back. After stirring, touch a ball from any one of them, and the sum of the numbers on the two touched balls is 5.
The interest rate is
15. (Yangzhou, 20 12) As shown in the figure, the rectangular ABCD is folded along CE, and the point B just falls on it.
The f of marginal advertising. If yes, the value of tanDCF is _ _ _ _ _ _ _ _.
16. (Original title) In the known plane rectangular coordinate system, O is the coordinate origin.
The coordinates of point A are (0,8), point B is (4,0), and point E is a straight line.
A moving point on a straight line y=x+4, if EAB=ABO, then this point
The coordinates of e are.
Third, solve the problem (8 small questions in this question, ***66 points, each small question should write the problem-solving process).
17. (6 points for this question) Calculation: sin45-|-3|+
18. (6 points for this question) Solve the equation:.
19. (6 points in this question) As shown in the figure, in the plane rectangular coordinate system xOy, the straight line AB intersects with the X axis at point A (-2,0), and intersects with the image of the inverse proportional function in the first quadrant at point B (2,n), connecting BO and if.
(1) Find the analytical expression of the inverse proportional function;
(2) If the intersection of straight line AB and Y axis is c, find the area of △OCB.
20. (8 points in this question) As shown in the figure, AB is the diameter ⊙O, CD is the tangent ⊙O, and the tangent point is c, BECD, and the foot is vertical.
E. connect AC and BC.
(1) Verification: BC is equally divided.
(2) If ABC=30 and OA=4, find the length of CE.
2 1. (8 points in this question) The Fourth Plenary Session of the 13th Zhejiang Provincial Committee proposed that it is an important decision to control sewage, prevent floods and drainage, ensure water supply and save water. In order to improve students' enthusiasm for learning "Five Waters", a middle school held a knowledge contest about "Five Waters", and all the participating students won the first, second and third prizes respectively.
(1) How many students are there in this knowledge contest?
(2) The Fourth Plenary Session of the 13th Zhejiang Provincial Committee proposed that major decisions should be made on sewage treatment, flood control, drainage, water supply and water saving, and the degree of fan-shaped central angle corresponding to the second prize should be used to completely supplement the bar chart;
Xiaohua took part in the knowledge contest. Please help him find out the probability of winning the first prize or the second prize.
Huayu Company is authorized to produce some Olympic souvenirs. According to market research and analysis, the functional relationship between the sales volume (ten thousand pieces) and the price (yuan/piece) of souvenirs is shown in the figure. The output of company souvenirs (ten thousand pieces) and the price of souvenirs (yuan/piece) roughly meet the functional relationship. If the price of each souvenir is not lower than that of 20 yuan and not higher than that of 40 yuan.
Please answer the following questions:
(1) Find the function relation of sum and write out the value range;
(2) When the price is what value, the production and sales of souvenirs are balanced (production equals sales);
(3) When the output is lower than the sales volume, the government often increases the output by subsidizing the souvenir price difference to the company to promote the new balance between production and sales. If the sales volume reaches 460,000 pieces in the new balance of production and marketing, how much should the government subsidize each souvenir?
23.( 10) Xiaohua uses two isosceles right-angled equilateral triangles to place the figure.
(1) As shown in Figure ①, two isosceles right angles △ABC and △DBE intersect at point F, connecting BF and AD, which proves that BF = AD.
(2) If Xiaohua places two triangular plates △ABC and △DBE as shown in Figure ②, so that the three points of D, B and C are on a straight line, the extension lines of AC and DE intersect at point F, the intersection point F is FG∨BC, and the straight line AE intersects at point G, connecting AD and FB, which proves that FG = AC+DC;
(3) Under the condition of (2), if AG= and DC=5, the vertex of a 45-degree angle coincides with point B and rotates around point B, and both sides of this angle intersect with line segment FG at two points (as shown in Figure ③). If PG=2, find the length of line segment FQ.
24.( 12) As shown in the figure, the parabola y=ax2+bx+c intersects with the X axis at points A (0 0,4) and E (0 0,2), and intersects with the Y axis at point B (2 2,0) to connect AB. The intersection point A is a straight line AKAB, and the moving point P starts from point A and moves along the ray AK at a speed of one unit length per second. Let the moving time be t seconds, the intersection point P be the PCx axis, and the vertical foot be C. Fold the △ACP in half along the AP so that the point C falls on the point D..
(1) Find the analytical formula of parabola;
(2) When point D is inside. For △ABP, the area of the non-overlapping part between △ABP and △ADP is S. Find the functional relationship between S and T, and directly write the range of T;
(3) Is there a moment to minimize the distance from moving point D to point O? If yes, find this minimum distance; If not, explain why.
Mathematical simulation test paper
Reference answer
First, multiple-choice questions (there are 10 small questions in this question, each with 3 points and ***30 points)
1-5:BADCB 6- 10:DBCDA
Fill in the blanks (6 small questions in this question, 4 points for each question, * * * 24 points)
1 1:
12:
13:44
14:
15:
16:
Third, solve the problem (8 small questions in this question, ***66 points, each small question should write the problem-solving process).
17.
18. is the solution of the original equation after testing.
19.( 1) 3 points (2) 6 points
20. (8 points in this question) Proof: Connect OC
Cut: CD: o in C.
OCCD
* BECD
OC∨BE
OCB=EBC
OC = OB
OCB=OBC
EBC=OBC
BC divides ABE4 equally.
② After ②CFAB does A in F,
∵AB is the diameter of⊙ O.
ACB=90
ABC = 30A = 60
In Rt△ACF, A=60,
Divide Abe, CFAB and ∵CEBE equally in BC.
8 points (similar solutions can also be used)
2 1. Solution: (1)200 people get 2 points.
(2)72, the number of second prize is 40, plus 5 points.
(3) 8 points
22. Solution: (1) Let the resolution function of sum be:, and substitute the point sum into:
Solution: 2 points
The functional relationship between and is: 3 points.
(2) When appropriate, there are solutions: 4 points, when appropriate, there are solutions:
When the price is 30 yuan or 38 yuan, the company's production and sales can be balanced by five points.
(3) At that time, at 6 o'clock
So, at 7: 00.
The government should subsidize 1 yuan. 8 points for each souvenir.
23. Solution: (1) Prove that △ABC and △DBE are isosceles right triangles.
△CDF is also an isosceles right triangle;
CD=CF, (1 min)
BCF = ACD = 90，AC=BC。
△ BCF△ ACD, (2 points)
BF = AD(3 points)
(2) prove that:
∫△ABC and△△△ BDE are isosceles right triangles.
ABC=BAC=BDE=45，
∫FG∑CD，
G=45，
AF = FG(4 points)
CDCF，CDF=45，
CD=CF, (5 points)
∫AF = AC+CF，
AF=AC+DC。
FG=AC+DC。 (6 points)
(3) If the crossing point B is the vertical foot H of BHFG and the crossing point P is the PKAG of point K, (7 points).
∫FG∨BC, C, D and B are in a straight line,
It can be proved that △AFG and △DCF are isosceles right triangles,
AG =，CD=5，
According to pythagorean theorem, AF=FG=7, FD=,
AC=BC=2，
BD = 3；
BHFG，
BH∑CF，BHF=90，
∫FG∨BC，
Quadrilateral CFHB is a rectangle, (8 points)
BH=5，FH = 2；
∫FG∨BC，
G=45，
HG=BH=5，BG =；
PKAG，PG=2，
PK=KG=，
bk =﹣= 4； (9 points)
PBQ=45，HGB=45，
GBH=45，
2;
* PKAG，BHFG，
BHQ=BKP=90，
△BQH∽△BPK
,
QH=, (9 points)
(10)
24, (12 points)
(1) solution:
The analytical formula of parabola is y= x2+ x+24 minutes.
(2) AC=t can be obtained from AP= t and AOB∽PCA.
PC=2t5 points
S=SABP-SADP= 2 t- 2tt
=-t2+5t6 points
The value range of t is 0.
(3) Connect the CD, and cross the AP at point G, with the crossing point as axis D Hx and the vertical foot as H..
Yi Zheng △ACG∽△DCH∽△ Bao and OB: OA: AB = 1: 2:
Because DAP=CAP, point D is always on a straight line through point A..
Linear motion, let this fixed straight line intersect with Y axis at E point.
When AC=t= 1, DC=2CG=2 =
DH=，HC=
OH=5- =
The coordinates of point D are (,) 10.
The analytical formula of straight line AD can be obtained as y=- x+, and the coordinate of point E is (0,).
AE= 1 1 can be obtained.
At this time, the height on the hypotenuse of RT△EAO is the minimum distance of OD, = 12 minutes.