(Examination scope: Chapter 1-Chapter 2 Examination time: 120 minutes, full mark 120 minutes)
Title number
one
two
three
Total score
Take the lead
Choose one carefully first (3 points for each small question, 30 points for * * *).
Title number
1
2
three
four
five
six
seven
eight
nine
10
election
1. In,, ()
(A) (B) (C) (D)
2. The shape and size of the parabola are the same as the opening direction, only the parabola with different positions is ().
A.B.
C.D.
3. In, the opposite sides of ∞, ∠ and ∠ are respectively, so the following formula must be true ().
(A) (B) (C) (D)
4. If there are two points (3, -8) and (-5, -8) on the image of quadratic function, then the symmetry axis of this parabola is ().
A. line = 4 b. line = 3 c. line =-5 d. line =- 1
5. If yes, the following statement is incorrect ()
(a) increase with the increase; (B)cos decreases with the decrease of;
(C)tan increased with the increase of; 0< sin< 1.
6.∞, ∞ and ∠ Yes are three internal angles, and the following types are correct ().
(A)(B)(C)(D)
7. As shown in the figure, the middle is the height,,,,
Then the length of AD is ()
Paragraph 1, paragraph 2, paragraph 3, item 4
8. The parabola image passes through the origin, which is ()
a . 0 b . 1 c .- 1d . 1
9. Represent quadratic function with vertex ()
A.B. C. D。
10. The image of the known inverse proportional function is shown on the right, and the image of the quadratic function is roughly ().
C.
Second, fill in patiently (3 points for each small question, 24 points for * * *)
1 1. As shown in the figure, if CD is the height on the hypotenuse of RT δ ABC, AD=3 and CD=4, then BC = _ _ _ _.
12. When m, the function is quadratic.
13. The picture on the right is a schematic diagram of fixing a telephone pole with a stay. Known: CD⊥AB, clean development mechanism,
∠ CAD =∠ CBD = 60, then the length of cable AC is _ _ _ m.
14. In,,, and then.
15. The symmetry axis of the function image is; Vertex coordinates are.
16. As shown in the figure, it is known that the side length of the square ABCD is 2. If the line segment BD rotates around the point B and the point D falls on the point D' on the CB extension line,' is equal to _ _ _ _ _ _ _.
17. Open the function up, and then.
18. If the parabola passes through the point (3,5), then =.
Third, do it seriously (19, 6 points, 20-25, each small question 10, * * * 66 points).
19.(6 points) Yes,,.
20.(6 points)
2 1.(8 points) As shown in the figure, the cross section of the reservoir dam is trapezoidal, the width of the dam top is, the height of the dam is, and the slope is I' = 1: 1. Find the angle, width and length of the slope.
22.(8 points) The image of quadratic function is shown in the figure. In these four formulas, please judge the symbols of their values respectively and explain the reasons.
23.(8 points). As shown in the picture, there is a reef area within 20 nautical miles around Island A, and a cargo ship sails from east to west. At point B, it sees Island A in the north of due west. After sailing for 24 nautical miles, it reached point C, and it saw that Island A was due west by north. Is it dangerous for the cargo ship to continue sailing westward?
24.(8 points) A businessman can sell 100 pieces of goods in 8 yuan at10 yuan every day. Now he increases profits by raising the sales price and reducing the purchase quantity. It is known that the sales volume of this kind of goods will decrease by 1 0 for every price increase of1yuan. Ask him how much the price (X) is. And get the maximum profit.
25.( 10) As shown in the figure, in a triangular area ABC, ∠ c = 90, the side AC=8m, BC=6m, and now a rectangular pool deFG is to be built in △ABC. The design scheme shown in the figure is to make DE on AB.
(1) Find the height h on the side of AB in △ABC;
⑵ Let DG = X, and what is the value of x, and the area of the pool DEFG is the largest?
26.( 10 minute) Typhoon is a natural disaster. It takes the typhoon center as the center of the circle and forms a cyclone storm within dozens of kilometers, which is extremely destructive. According to meteorological observation, there is a typhoon center at B, 220km south of a coastal city. Maximum wind force in the center 12. Every 20 kilometers away from the typhoon center, the wind will weaken by one level. The center of the typhoon is 60 meters away.
(1) Will this city be affected by this typhoon? Why? (Hint: Pass A as AD⊥BC in D).
(2) If it is affected by a typhoon, how long will the typhoon affect the city?
(3) What is the maximum wind force affected by typhoon in this city? ,
Senior three math test paper
(Note: The examination time of this volume is 90 minutes, with full mark 100).
1. Multiple choice questions: (This big question 10, 3 points for each small question, 30 points for * * *).
Each small question gives four answers, only one of which meets the requirements of the topic. Please fill in the selected answer number on the answer sheet 1, otherwise it will not be scored.
1, "Life is full of knowledge" As shown in the figure, the positional relationship between the two circles where glasses lenses are located is ().
A. exogenous B. exogenous C. endogenous D.
2. As shown in figure 1, the left view of the cylinder is C.
Figure 1 A B C D
3. As shown in the figure, in the diamond ABCD, P and Q are the midpoint of AD and AC, respectively. If
PQ=3, then the circumference of diamond ABCD is ()
18 C.24 D.30
4. In the same coordinate system, the image of function sum may be roughly as follows
A B C D
5. It is known that α is the acute angle of isosceles right triangle, so cosα is equal to.
A.B. C. D。
6. In the following four functions, when x >; The function of 0, y decreasing with the increase of x is
a、y=2x B、C、D、
7. The image of the inverse proportional function in the first quadrant is shown in the figure, and the point m is a point on the image.
MP is perpendicular to the X axis at point P. If the area of △MOP is 1, the value of k is
A. 1
8. Translate the parabola y = x2 by 3 units to the left, and then by 2 units downward. The expression of the parabola is ().
a、y=(x+3)2+2 B、y=(x-3)2+2
c、y=(x-2)2+3 D、y=(x+3)2-2
9. Wash three cards marked with numbers 2, 3 and 4 and put them face up on the table. If one card is randomly selected as the tenth number (not put back) and the other card is the unit number, the probability that the two cards selected form a two-digit number is 42.
A, yes; B, yes; C, yes; d .
10. As shown in the figure, AB is the diameter ⊙O, points D and E are the bisectors of a semicircle, and the extension lines of AE and BD intersect at point C. If CE=2, the area of the shaded part surrounded by line segments BD, BE and arc d E in the figure is
aπ-bπ
cπ-dπ
Figure 5
Two. Fill in the blanks: (3 points for each question, *** 18 points, please fill in the second answer sheet, otherwise no points will be deducted)
1 1, the diagonal parallelogram is a square.
12. At the same time, the height of the object is proportional to the length of the shadow. Xiaoli measured that the shadow length of the experimental building is 6 meters, at the same time.
He measured that the shadow length of a classmate whose height is 1.6 meters is 0.6 meters, and the height of the comprehensive building is meters.
13. As shown in the figure, if the generatrix AB=6 of the cone is 6 and the bottom radius CB=2 is 2, then
Central angle α = fan-shaped degree of side expansion diagram.
14, any one of the three numbers-1, 1, 2, as the value of a of quadratic function y=ax2+3,
Then the probability that the parabolic opening is upward is.
15. In two concentric circles, if a chord with a length of 250px is tangent to a small circle, the area of the circle surrounded by the two concentric circles is.
At 16 and the quadratic function y=ax2+bx=c, 2a-b=0, and its image crossing point (-3,25), find y=. When x= 1
Answers to the third grade math exam.
1. Multiple choice questions: (This big question 10, 3 points for each small question, * * * 30 points).
Answer sheet 1
Title number
1
2
three
four
five
six
seven
eight
nine
10
answer
Two. Fill-in-the-blank question: (This topic is entitled ***6 blanks, with 3 points for each blank, and * *18 points).
Answer sheet 2
Title number
1 1
12
13
14
15
16
answer
Third, answer questions:
17, (4 points) Simplified calculation: 6tan 230-sin60-2sin45.
Solution: Original formula =
18. (6 points for this question)
The Consumers Association received some complaints last week, and now it is classified and counted and drawn into a statistical chart as shown in the figure (the angle in the figure is the degree of the central angle of the fan). Among them, there were 30 complaints about "home appliance repair". Please answer the following questions according to the information in the statistical chart:
(1) What is the number of complaints about "others"? What is the percentage of the total?
(2) How many complaints about "real estate rental and sale" did Consumers Association receive last week?
(3) According to the calculation of 52 weeks a year, what is the total number of consumer complaints that the Consumer Association expects to receive this year?
(4) What kind of statistical chart is more reasonable and intuitive to show the number of all kinds of complaint calls?
Solution:
19, (8 points) Xiao Li, Xiao Hong, Grade 8 students of a school went to a supermarket to participate in social practice activities. During the activity, they participated in the sales of a certain fruit and learned that the purchase price of the fruit was 8 yuan/Jin. The following is their conversation after the activity.
Xiaoli: If we sell it at the price of 10 yuan/kg, we can sell 300 kg every day.
Xiao Qiang: If you sell it at the price of 13 yuan/kg, you can make a profit in 750 yuan every day.
Xiaohong: Through investigation and verification, I found that there is a functional relationship between daily sales volume Y (kg) and sales unit price X (yuan).
(1) Find the functional relationship between y (kg) and x (yuan) (x > 0);
(2) Assuming that the daily profit of this fruit sold in this supermarket is W yuan, what is the maximum profit that can be obtained every day when the unit price is what? What is the maximum profit?
Solution:
20.(8 points) As shown in the figure, in trapezoidal ABCD, ABCD and AB=2CD, E and F are the midpoint of AB and BC, respectively, and EF and BD intersect at point M. 。
(1) Verification: △ EDM ∽△ FBM;
(2) If DB=9, find BM.
2 1, (7 minutes) speeding is the main cause of traffic accidents. Last weekend, three students, including Tucki, tried to use their knowledge to test the speed on the mangrove section of Binhai Avenue. The observation point is located at P, which is 0/00 meter away from the highway L/KLOC-.At this time, a Fukang car is coming from west to east at a constant speed, and it takes 3 seconds for the car to travel from A to B.
∠ BPO = 45, try to judge whether the car exceeds the speed limit of 80 kilometers per hour? (Reference data: = 1.4 1, = 1.73)
Solution:
22.(9 points) As shown in the figure, △ABC is an equilateral triangle, ⊙O passes through points B and C, and intersects with the extension lines of BA and CA at points D and E respectively. The chord DF//AC intersects with ⊙O at point F, and the extension lines of EF and BC intersect at point G. 。
(1) proves that △BEF is an equilateral triangle;
(2) If BA=5 and CG=3, find the length of BF.
23.( 10 point) As shown in the figure, the image of quadratic function y =ax2+bx+c intersects with X axis at points A (6 6,0) and B (2 2,0), and intersects with Y axis at point C (0 0,0); P goes through a, b and C.
(1) Find the expression of quadratic function;
(2) Find the coordinates of the center p;
(3) Does the quadratic function have a point Q on the image of the first quadrant, so that the quadrilateral with four vertices P, Q, A and B is a parallelogram? If it exists, request the coordinates of point Q to prove that the quadrilateral is a parallelogram; If it does not exist, please explain why.
Solution:
The answer to the math test in senior three.
1. Multiple choice questions: (This big question 10, 3 points for each small question, * * * 30 points).
Answer sheet 1
Title number
1
2
three
four
five
six
seven
eight
nine
10
answer
A
C
C
A
B
B
B
D
A
B
Two. Fill-in-the-blank question: (This topic is entitled ***6 blanks, with 3 points for each blank, and * *18 points).
Answer sheet 2
Title number
1 1
12
13
14
15
16
answer
Perpendicular and equal to each other.
16
120
2/3
25π
25
Iii. 17, (the first step is every point, and the result is one point)
18, ( 1) 15, 10%; (2 points)
(2)45; (2 points)
(3)7800; ( 1)
(4) Available bar charts (1)
19, ① y =-50x+800 2 points.
② w = (x-8) (-50x+800) =-(x-12) 2+800 4 points.
∴ when X = 12 yuan, W max = 1 min in 800 yuan.
20( 1)4 o'clock
(2)3(4 points)
2 1. Let the speed of Fukang car be x kilometers per hour (1 min).
Then AB = km and AO=OP, op = ob = 0. 1km.
+0. 1=0. 1 (3 points)
X=87.6 This car exceeded the speed limit of 80km/h (3 points).
22.( 1) Prove that ∵△ABC is an equilateral triangle, ∴∠BCA=∠BAC=60? ...... 1 point
∵DF∥AC,∴∠D=∠BAC=60？ ，∠BEF=∠D=60？
∠∠BFE =∠BCA = 60？
∴△BEF is an equilateral triangle with ...................................................... 3 points.
(2) Solution: ∫∠ABC =∠EBF = 60? ,∴∠FBG=∠ABE，
∠BFG=∠BAE= 120？ ,
∴△ BFG ∽△ BAE ............................................................................... 3 points.
∴, and BG=BC+CG=AB+CG=8, BE=BF,
∴ BF2 = AB BG = 40, you can get BF= (excluding negative values) ......................... 2 points.
23.( 1) solution: let the expression of quadratic function be y = a (x-6) (x-2) .................................................. (1).
Substitute the coordinates of C(0,) into = 12a.
............... (2 points)
The expression of the quadratic function is ................... (3 points).
that is
(2) Solution: In Rt△BOC,
............. (1 min)
When BC crosses the vertical line of P, it crosses BC at D and X axis at E..
Prove BD = BC = 2:Rt△BDE≌Rt△BOC(AAS) from the vertical meridian theorem.
∴ Germany = OC =, BE = BC = 4................(2 points)
If p is used as PF, the vertical x axis is perpendicular to f, and the vertical longitude theorem BF = AB = 2,
∴ ef = be+BF = 6 ............................ (3 points)
It is also easy to prove that Rt△EFP∽Rt△EDB (two angles are equal).
∴∴ and OF=OB+BF=4.
∴P(4,) ............ (4 points)
(3) Answer: There are qualified Q points. ............. (1 min)
Solution: the image of the quadratic function of parallel lines with P as the X axis is in Q.
And to the right of Q'(Q is in Q'), it is obviously the ordinate of Q and Q'.
Same as the ordinate of p, that is,
∵Q and q' on the image of quadratic function,
Solution:,
∴Q(8,) .................. (2 points)
Q'(0,) that is not in the first quadrant is discarded.
Proof: connect PB, AQ∫PQ∨x axis. That is PQ∨BA (drawing)
PQ=8-4=4=BA
∴ Quadrilateral PQAB is a parallelogram ............................. (3 points)
(A set of opposite sides are parallel and equal) OK?