Senior three mathematics final quality inspection examination paper.
A, multiple-choice questions (this big question * * 10 small question, each small question 4 points, ***40 points. ) each item gives four options, code a, b, c and d, and only one option is correct. Please write the code name of the correct option in brackets after the item, and get 4 points for each option. If you don't choose, choose wrong or choose more than one code (whether written in brackets or not), you will get 0 point.
1. In the isosceles right triangle ABC,? C =90？ , then Sina is equal to ()
A. BC 1 year
2. The symmetry axis of parabola is ()
A. line x=-8 B. line x=8 C. line x=3 D. line x=-3.
3. If A: B = 3: 5 and B is the median in the ratio of A to C, then the value of B: C is ().
A.3:2 B. 5:3 C. 3:5 D. 2:3
4. In the following functions, when x>0 increases, it decreases ().
A.y=3x B. C. D. y=2x2
5. in Rt△ABC,? C =90？ ,? B =35？ , AB=7, then the length of BC is ()
A. 7th century BC.
6. It is known that two circles with radii of 4㎝ and 7㎝ intersect, so their center distance may be ().
a . 1㎝b . 3㎝c . 10㎝d . 15㎝
7. The parabola is translated by 2 units to the left, and then by 1 unit, then the analytical formula of the parabola is ().
a . y = x2+4x+3 b . y = x2+4x+5 c . y = x2-4x+3d . y = x2-4x+5
8. As shown in the figure, in △ABC, point D is on line segment AB, and? Bad =? C then the following conclusion must be correct ()
A.AB2=AC？ BD B. AB？ AD=BD？ Ab2 BC = BC? BD D. AB？ AD=BD？ laser record
9. As shown in the figure, the quadratic function y=ax2+bx+c(a? 0), Hu Jiao observed the following four items.
Information: (1)(a? 0)B2-4ac & gt； 0; (2)c & gt； 1; (3)2a-b & lt； 0; (4)a+b+c & lt； 0. What information do you think is wrong ()
A.4 B.3 C. 2 D. 1
10. At the 7th Middle School Track and Field Games in Tongcheng, Han Xiao ran at a constant speed on the ground, as shown in figure 1. He started from point A and ran to point C in the direction indicated by the arrow, which took 30 seconds. His coach chose a fixed position to observe Han Xiao's running process. Let Han Xiao run for T (unit: seconds), and he and Han Xiao run together.
A.M, b, n, c and PD. Ask.
2. Fill in the blanks (4 small questions in this big question, 5 points for each small question, out of 20 points)
1 1. As shown in the figure, AB is the tangent of ⊙O, with radius OA=2, and OB passes through ⊙O in C,? B=30？ , the length of the bad arc AC is
(the result was retained? )。
12. As shown in the figure, AD and AC are the diameter chords of ⊙O, respectively, and? CAD=30？ ，OB？ If OB=5, the length of the chord AC is equal to.
13. We have learned the translation transformation of function images.
For example: 5 units to the left and 5 units up.
Pan 5 units to the left and 5 units up.
Pan 5 units to the left and 5 units up =.
It can be analogized as follows: 5 units to the left and 5 units up.
14. As shown in the figure, put the rectangular piece of paper OABC in the plane rectangular coordinate system, so that OA and OC fall on the X axis and Y axis respectively, connect AC, and fold the rectangular piece of paper OABC along AC, so that point B falls on the position of point D. If B( 1 2), the abscissa of point D is.
score
commentator
Three. (This topic is entitled ***2 small questions, with 8 points for each small question, with a full score of 16).
15. evaluation: sin60? + 2sin30？ tan30？ -tan45？
16. Known parabola
(1) Determine its vertex coordinates and symmetry axis by matching method;
(2) when x is taken, y
Four. (This topic is entitled ***2 small questions, with 8 points for each small question, with a full score of 16).
17. As shown in the figure, each small square in the grid paper is a square with a side length of 1 unit. After the plane rectangular coordinate system is established, the vertices of △ABC are all on the grid points, and the coordinates of point C are (4,-1). Rotate △ABC 90 counterclockwise around the origin o? Get △A 1B 1C 1, draw △ a1b1,and write the coordinates of C 1.
18. As shown in the figure, it is known that AB is ⊙ O in diameter, points C and D are above ⊙O, and point E is outside ⊙O, and EAC=? D=60？ .
(1) Q? Degree of ABC;
(2) Prove that AE is the tangent of ⊙ o.
V. (For this big topic ***2 small questions, each small question 10, out of 20 points)
19. Fill the balloon with a certain mass of gas. When the temperature is constant, the pressure P (kPa) of the gas in the balloon is an inverse proportional function of the volume V (m3) of the balloon, and its image is as shown in the figure (kPa is the pressure unit).
(1) What is the analytical expression of this function?
(2) When the volume of the balloon is 0.6 m3, what is the pressure of the gas in the balloon?
(3) When the air pressure in the balloon is greater than 168 kPa, the balloon will explode. What is the volume of gas for safety reasons?
20. A shop bought a batch of winter thermal underwear, each set of purchase price 100 yuan, price 130 yuan, and it can sell 80 sets every week. Now that the Spring Festival is approaching, the merchants have decided to cut prices and promote sales. According to the market research, every time the price of 5 yuan is reduced, 20 sets can be sold every week.
(1) What is the sales profit of the week before asking the merchants to reduce their prices?
(2) After the price reduction, how much price should the seller set to maximize the weekly sales profit? What is the maximum sales profit?
Six, (full mark for this question 12)
Seven, (this question is full 12)
22. Among the known △ABC,? C=90？ ，AC=4，BC=3。
(1) As shown in figure 1, the square DEFG is inscribed on △ABC, where DE is on AB, G is on AC, and F is on BC. Try to find the side length of square DEFG;
(2)① As shown in Figure 2, if there are two congruent squares side by side in a triangle, and the rectangle they form is inscribed in △ABC, the side length of the square is:
(2) As shown in Figure 3, if there are three congruent squares side by side in a triangle, and the rectangle they form is inscribed in △ABC, then the side length of the square is:
(3) As shown in Figure 4, if there are n congruent squares side by side in a triangle, and the rectangle they form is inscribed in △ABC, then the side length of the square is:
Eight, (full mark for this question 14)
23. Mathematical thinking methods such as analogy transformation and from special to general are often used in mathematics learning and research. The following is a case, please complete it.
Original title: As shown in figure 1, in the parallelogram ABCD, point E is the midpoint of BC side, point F is a point on AE line, and the extension line of BF intersects with CD at point G, if, the value of.
(1) Try to explore
In figure 1, if the intersection e is EH∑AB and BG are at point h, the quantitative relationship between AB and EH is, and the quantitative relationship between CG and EH is, and the value of is.
(2) analogy extension
Under the condition of the original problem, if (m>0), try to find the numerical value (expressed by an algebraic expression containing m, and write out the solution process).
(3) expanding immigration
As shown in Figure 2, in trapezoidal ABCD, ABCD, point E is the midpoint of BC side, and point F is a point on AE line. If the extension line of BF intersects with CD at G point, the value of is. Represented by an algebraic expression containing m and n, without proof.
Answers to the quality test questions at the end of the third year of mathematics.
1 2 3 4 5 6 7 8 9 10
B C C B B C A C D B
1 1 12 13 14
15
15.
16.( 1), vertex coordinate (), and the symmetry axis is a straight line;
(2)x & lt； -2 or x>.
17. As shown in the figure, the coordinate is C 1 (1, 4).
18.( 1)600; (2) ellipsis.
19.( 1) ; (2) 140 kPa; (3) Not less than 0.5m3..
20.( 1)2400 yuan;
(2) the price is reduced by X yuan, and the weekly sales profit is Y yuan.
When X=5, the maximum sales profit should be 125 yuan.
2 1.62㎝.
22.( 1) ; (2)① ; ② ; ③ 。
23.( 1) AB=3EH，CG=2EH，.