20 14-20 15 school year ninth grade last semester final mock exam.
Mathematics Test
Volume one multiple-choice questions (***40 points)
First, multiple-choice questions (4 points for each small question, 40 points for * * *)
1, the vertex coordinates of the image with function y = x2-2x+3 are
A.( 1，-4) B.(- 1，2) C.( 1，2) D.(0，3)
2. Among the following equations, the unary quadratic equation * * *
①3 x2+x = 20； ②x2+y2 = 5； ③; ④x2 = 1； ⑤.
A.5 B.4 C.3 D.2
3. In the picture below, which one is both axisymmetric and centrosymmetric?
A B C D
4. The following events are inevitable.
A. Pull out a ball from a jar with blue and white balls, and the pulled ball is a white ball.
B. Xiao Dan's bicycle tire was punctured by a nail.
C. Xiaohong must get full marks in mathematics in the final exam.
D. Drop the oil into the water and it will float on the water.
5. If the unary quadratic equation 3x2+k = 0 about X has a real root, then
A.B. C. D。
6. The radius of a sector is 24 cm. If the radius of the cone bottom surrounded by this sector is 10 cm, then the area of this sector is
a . 120πcm2 b . 240πcm2 c . 260πcm2 d . 480πcm2
7. As shown in the figure, the chord AB of ⊙P contained in ⊙O and ⊙O cuts ⊙P, AB∨OP at point C,
If the area of the shaded part is 9π, the length of the chord AB is
A.3 B.4 C.2 D.3
8. In the following statement, ① the diameter of the bisector is perpendicular to the chord; (2) the right-angled chord is the diameter; (3) The arcs of equal chords are equal;
(4) The chords of equal arcs are equal; ⑤ The circumferential angle is equal to half of the central angle; ⑥ x2-5x+7 = 0 The sum of two roots is 5.
The number of correct propositions is
A.0 B. 1 C.2 D.3
9. Xiaojun observed the following information from the given quadratic function image: ① a < 0; ②c = 0；
③ The minimum value of the function ∠ 3; ④ y > 0； when ④x < 0; ⑤ y 1 > y2 when 0 < x1< x2 < 2.
What do you think is the correct number?
A.2 B.3 C.4 D.5
10. As shown in the figure, in △ABC, AB = 10, AC = 8, BC = 6, and the moving circle passing through point C and tangent to AB intersects with CA and CB at point P. Q, then the minimum length of line PQ is
A.4.8 B.4.75 C.5 D
Volume 2 is a multiple-choice question (* *110)
Fill in the blanks (***5 small questions, 4 points for each small question, ***20 points)
1 1. It is known that one root of the equation x2+3x+K2 = 0 about x is-1, then k =.
12. When there are many experiments, the frequency of the same event is stable in the corresponding neighborhood, so we can use the same event to estimate the probability of the event after many experiments. (Fill in "Frequency" or "Probability")
13. given points A (2a+3b, -2) and B(0, 3a+2b) are symmetrical about the origin, then A+b =.
14. The image with parabola y = 2 (x- 1) 2+3 is first translated by 3 unit lengths to the left and then by 4 single lengths downward. The analytical formula of the new parabola is as follows.
15. Make two cards as shown in Figure ① with two congruent 30-degree right triangles. The radius of the sector in both cards is 1, and the center of the sector is the midpoint of the long right angle and the vertex of the 30 angle respectively. The A card and the B card are alternately placed in the order of A first and then B, and the pattern as shown in Figure ② is obtained. If you put this pattern, use two cards. If you put two cards in this pattern (2n+ 1) (n is a positive integer), the sum of the shadow areas in this figure is. (The result remains π).
Iii. Answer questions (***2 questions, 8 points for each question, *** 16 points)
16. Solve the following unary quadratic equation:
( 1)(x-2)2 = 2x-4(2)2x 2-4x- 1 = 0
17. It is known that the image of quadratic function Y = 2x2+BX+C passes through two points: A (0, 1) and B (-2, 1). (1) Find the analytical expression of this function;
(2) Transform the function into the form of y = a (x-h) 2+k by collocation method.
4. Answer questions (***2 questions, 8 points for each small question, *** 16 points)
18. As shown in the figure, the side length of each small square in the square grid is 1, and the vertex of each small square is called the grid point. The three vertices A, B and C of △ABC are all on the grid points. Rotate △ ABC 90 clockwise around point A to get △ AB ′ C ′.
(1) In the square grid, draw △ ab ′ c ′;
(2) Calculate the swept area of line segment AB when it is transformed into AB'.
19. In order to get close to and feel nature, a school organized students to walk 6 kilometers from school to Zigong Huahai for fun. When they came back, they walked 1 km less than when they went. As a result, they spent half an hour more when they went back, in order to ask the students to walk faster when they went back.
V. Answer questions (***2 questions, each with 10 score and ***20 score)
20. As shown in the figure, a residential area plans to build three equal-width paths on a rectangular site with a length of 32 meters and a width of 20 meters, so that two of them are parallel and one is parallel, and the rest are planted with grass. If the lawn area is 570 square meters, how wide should the path be?
2 1. There are four cards with the same shape, size and texture, with A, B, C, D and an equation written on the front respectively. Wash the backs of these four cards evenly, draw one card at random (don't put it back), and then draw another card at random.
⑴. Use tree diagram or list to represent all possible situations when drawing two cards (the results are represented by A, B, C and D).
(2) Xiaoming and Xiao Qiang play games according to the following rules: If the equations on the two cards are not established, Xiaoming wins; If at least one equation holds, Xiao Qiang wins. Do you think this game is fair? If it is fair, please explain the reasons; If it is unfair, who benefits from this rule? Why?
6. Answer the question (full mark of this question 12)
22. if x 1 and x2 are two roots of the unary quadratic equation Ax2+BX+C = 0, then x 1+X2 =- and X65438+X2 =. This is the relationship between the roots and coefficients of a quadratic equation, and we can use it to solve the problem: let X 1 and X2 be the equation X2. Find the value of x 12+x22. The solution can be as follows: ∫x 1+X2 =-6, x 12+x22 =-3, then = (-6) 2-2× (-3) = 42. Please solve the following problem according to the above solution: X65 is known. (2) The value of x1-x2.
Seven, answer (this question full score 12 points)
23. As shown in Rt△ABC, let AC be the diameter ⊙O, D midspan AB, O midspan OE∨AB and E midspan BC.
(1) verification: ED is the tangent of ⊙O;
(2) If the radius of ⊙O is 1.5 and ED = 2, find the length of AB.
(3) Under the condition of (2), find the area of △ADO.
Eight, answer (this question full score 14 points)
24. As shown in the figure, in the plane rectangular coordinate system, the image of quadratic function y = x2+bx+c intersects with the X axis at two points A and B, with point A on the left side of the origin, point B at (3,0) and point P at point C (0,3) below the straight line BC.
(1) Find the expression of this quadratic function.
(2) COnnect PO and PC, and fold △POC along Co to get quadrilateral POP'C. Is there a point P that makes quadrilateral POP' C a diamond? If it exists, request the coordinates of this point p; If it does not exist, please explain why.
(3) When point P moves to what position, the area of quadrilateral ABPC is the largest? Find the coordinates of point P and the maximum area of quadrilateral ABPC at this time.
Ask the university (physical chemistry) to leave an email for the final exam.
I think it is enough to memorize the formulas in the book and understand the topics in the textbook. It's not appropriate for you to think about sea tactics now.
In 2004, the sixth grade math final exam questions, math graduation review questions 1, fill in the blanks. 1, () 2 = () () 0.7+99× 0.7 = () 2,8848.13m is pronounced as () m, and rounded to the nearest ten thousand places is about () m. 3. 3,800,000 is written as () million in units of "million". 7.497 Keep two decimal places (). 4. The meter means to divide 1 meter into () parts, that is, () parts; It can also mean dividing () into () parts, which means () parts. 5, 3 meters = () 12 ÷ () = (): 8 = ()% = = 6, a square pool with a length of 3 meters, the area of this pool is (), if it is only filled with water, the volume of water is (). 7. Draw the largest circle in a square with a side length of 2 cm. The area of a circle is (), and the circumference of a circle is ()% of the square. 8. Xiaohong deposited 500 yuan's money in the bank for a fixed period of 2 years, with an annual interest rate of 2.25%. The interest at maturity is () yuan, and 20% interest tax is deducted according to regulations, so the actual principal and after-tax interest can be * * () yuan. 9. The distance between a group of opposite sides on the right is 4.5 cm, and the adjacent sides are 4 cm and 6 cm respectively. The area of this parallelogram is (). 4 10, in order to reflect Xiao Fang's performance in the primary school mathematics school year exam, the statistical chart () should be selected. 6 1 1, there are () pairs of triangles with equal areas in the trapezoid. 12, it is known that x and y are directly proportional, and the wrong formula is (). ① X: Y = 4: 3 ② ③ 3x = 4Y 13, when x = (), (2x-6 )× 42 = 0 14, cylinder, radius 2 cm, height 1 decimeter, bottom area () and lateral area surface area (). 15, Xiaohong reads a book. On the first day, she finished reading the whole book, which happened to be 10 page. The next day, she finished reading the whole book. The next day, she read (). 16, two cars, A and B, started from A and B relatively and met four hours later. A car is 50 kilometers per hour, and B car is faster than A car, so ask AB () kilometers apart. What is the quotient of the difference between 17, 75 and 45 divided by their sum? The column type is (). 18, the actual electricity consumption of a factory is 600 kwh, which is 150 kwh less than planned, saving ()%. 19, Xiao Fang originally planned to read a book, reading 20 pages every day, 15 days, but actually read 125% of the original plan every day, which took () days to finish. 20. The ratio of two baskets of fruit, A and B, is 3: 2. If you take out 15 Jin from the first basket and put it in the second basket, the fruits in the two baskets are equal, so there are fruits in the first basket (). 2 1. The distance between Party A and Party B is 350km. Buses and trucks depart from Party A and Party B for 5 hours, and the distance between them is 30 kilometers. It is known that the bus speed is 45 kilometers per hour and the truck speed is () kilometers per hour. A factory produced 200 tons of cement last year. Due to technological innovation, the output in the first five months of this year was the same as last year. Please ask this factory to increase its output this year by ()% compared with last year. 23. After transferring students from Group A to Group B, the number of students in the two groups is equal, and the original Group B is equivalent to Group A ... 24. The base area of a cuboid is 15 square centimeter, the perimeter of the base is 20 centimeters, and the height is 3 centimeters. Its surface area is () and its volume is (). 25, ① This is a statistical chart (). ② The first () quarter is 80% of the first () quarter. (3) The average monthly output value is () ten thousand yuan. ④ The output in the third quarter increased by ()% compared with that in the fourth quarter. 26, 2, 3, 4, 6 and 8 are all 24 (). 1 prime number 2 divisor 3 prime number 4 prime factor 27. Distribute 3 kilograms of fruit candy to 16 children on average, and each child will get these fruit candy (). ① ② ③ The cube of KG28,65,438+0 in the figure on the right represents 65,438+0 cubic centimeters, and a cube with a length of 3 centimeters can be built by adding such a small piece as (). 29. Cut a cube into two cuboids with the same size, and the surface area of a cuboid is the original cube. 30. The sum of numbers A and B is 14.3. If the decimal point of number B is shifted to the right by one place, it is equal to number A, and number B is (). 3 1, a circle with a radius of 1 decimeter, is divided into several equal parts and cut into an approximate rectangle. The circumference of this rectangle is (). 1 3.14 2 6.28 3 7.28 4 8.28 32. Cut a wire into two sections, the first section is meters long and the second section occupies the whole length. Then (). ① The first section is longer than the second section; ③ The length of the two sections is the same; 4 can't be compared; 33. After the number of students in a class increases, it decreases; The number of people in this class (). ① More than the original ② Less than the original ③ equals to the original 34. A book has 225 pages. Xiaohong finished reading the whole book on the first day and the rest the next day. On the third day, she should start reading from page (). 35. A pile of coal has been transported away, and the remaining pile of coal is less than the remaining ()%. 36. The average value of the three numbers A, B and C is 12, and the ratio of the three numbers A, B and C is 3: 4: 5. A is () and c is (). 37. The sum of three consecutive odd numbers is 69, and the ratio of these three numbers is (). 38, a section, a team repair hours alone, team b repair hours alone, the ratio of a and b work efficiency (). 39. True or false. The number of students has increased this year, and there is no "1" unit. () ② A number is 24, and the difference between this number and 24 is 20. () ③ A ∶ B =, when A is doubled and B is multiplied by 3, the ratio of A to B is still the same. () (4) A fraction, if the numerator is magnified 5 times and the denominator is magnified 6 times, then this fraction is. () ⑤ Divided by a number that is not 0, this number will increase by 9 times () ⑤ Xiao Wang used his salary, Xiao Li used his salary, and the rest of the salary was equal, so Xiao Li's salary was more. There are two bags of rice. The weight of bag A is 15 kg. If you pour from bag B to bag A, it's the same. The original weight of bag B is 1.5 kg. 4 1, two ropes with the same length, cut rice from one of them, when the rope is (), the other rope is longer. 42. From A to B, it takes 4 hours for A and 5 hours for B to A. Party A and Party B walk opposite each other. After two hours, the distance between them is the whole journey. 43. The unit of the score is the reciprocal of the maximum true score divided by, and the quotient is (). 44. Divide a 9-meter-long rope into two sections, so that one section is shorter than the other, and the longer section is () meters long. Li Hua read a book. On the first day, he read the remaining 40% the next day. In two days, he read 144. This book has * * * () pages. 46. Multiply a number that is not 0 and subtract () times. 47. Mom deposited 20,000 yuan in the bank on June 1 994+1October1,with an annual interest rate of 5.82%. After the expiration, my mother got the after-tax interest of 2793.6 yuan, and she saved the deposit for () years. 48. A piece of wood was cut into five pieces in an hour. If each segment takes the same time, it will take () hours to cut into eight segments. 49. Xiaohong used to weigh 40 kilograms, but she lost weight due to illness 10%. Keep exercising after illness and gain 10%. His weight is higher than before (). 50. Li Shifu plans to ship a batch of goods within three days. Shipped 42 tons on the first day, accounting for the goods. The mass ratio of the second day and the third day was 4: 3, and () tons were shipped the next day. 5 1. The cigarette sales of a cigarette factory in March was100000 yuan, 20% less than that in March. If you pay taxes according to 45% of sales, you should pay () yuan in April. 52. Six. There are 40 people in Class One taking the math exam. There are 5 application questions in the test question * * *, and the test result is that the whole class made 25 mistakes, and the correct rate is (). 53. The number of sides of a triangle is ()% less than that of a square, and one angle of a rectangle is ()% more than that of an equilateral triangle. 54, a pile of coal, such as away, the remaining 60 tons, such as the remaining 80 tons, should be away. 55. Master Wang processed a batch of parts. On the first day, he dealt with 25%. The next day, he handled 36 more than the first day. In two days, he processed 57.5% of the goods and hired a * * * processing part (). 56. The diameter of a circle is equal to the side length of a square. Comparing their areas, the result is (). 57. Write two scores that are bigger than the small ratio. () () 58. When a number is divided by 12, the quotient is 8 and the remainder is a divisor. This number is (). The prime factor to decompose this number is (). 59. Xiaogang climbed the mountain. It took him six hours to climb it. When he went down the mountain, his speed accelerated, less than () hours. 60. The terms before and after the simplest integer ratio are () ①, coprime ②, prime ③, integer 6 1, and 0.89. The decimal unit is (), it has () such units, and it adds () such units to be 1. 62, 1.95656 ... is simply written as (), and two decimal places are about () and an integer is about (). 63. The degree ratio of the three internal angles of a triangle is 7: 5: 6, and the maximum angle of this triangle differs from the minimum angle by () degrees. 64. The minute hand walking on the clock face is (). 65, a batch of tasks, the master alone to do 10 hours to complete, apprentice 15 hours to complete, two people Qi Xin work together to complete the task, apprentice made 270 parts, for this batch of tasks * * * (). 66. Insert a bamboo pole into the bottom of the water. The bamboo pole is 40 cm wet, and then insert the bamboo pole into the bottom of the water upside down. At this time, the second wet part of the bamboo pole is 5 cm less than its length (). 67, cut a cube into two cuboids, the surface area increased by 32 square centimeters, the surface area of the original cube is (). 68. Two bags of rice weigh the same. Take out from A first, then take out 5 kilograms, take out 5 kilograms from B first, then take out the rest, and the remaining rice weighs (). 69. From A to B, the express train takes 6 hours and the local train 10 hours. Now, two trains leave from A and B relatively simultaneously. When they meet, the express train runs150km, and the distance between A and B is () km.
2004-2005 Second Term Physical Chemistry (II) Final Exam (Volume B) Who has the answer? If not, you can ask the teacher directly.
Today is the most precious and easily lost question in the final exam of senior one mathematics in Jiangsu Education Press. You can't find the answer online.
Spend more time thinking, copying the answers directly will make you lose valuable thinking time.
Satisfactory adoption
Ask for the final exam questions of physical chemistry in Chengdu University ~ Any year can be ~ urgent! The school photocopying club will definitely have it. Go and ask.
Kneel and beg for the final exam questions of ninth grade physical chemistry: jj 1.2 1JY. /czows 0o/nsoftmoved/20 10/09/28/2 1jy 20 109287050947 _ 2404033 ..
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:jj 1.2 1jy。 /czows 0o/NSoftMoved/20 10/ 1 1/28/20 10 128 1 1 1 1 1 1 186 _ 1750395 . rar
:nc.2 1jy。 /czows 0o/NSoftMoved/20 10/09/2 1/2 1jy 20 1092 19480 1 10 _ 24 1 1352 . rar
Please! 20 1 1 You'll know when you finish the final exam of the first volume of the ninth grade.
Ninth grade mathematics final examination questions, address. Ninth grade mathematics last semester final review training questions
(This training question is divided into three major questions, full score 120, training time *** 120 minutes. )
First, multiple-choice questions (this big question 10, ***30 points):
1. Known =, where a≥0, then the condition that B meets is ()
A.b<0 B.b≧0 C.b must be equal to zero D. Not sure.
2. The analytical formula of a given parabola is y= -(x-3)2+ 1, and its fixed-point coordinate is ().
A.(3， 1) B.(-3， 1) C.(3，- 1) D.( 1，3)
3. Among the following traffic signs, the one with both axial symmetry and central symmetry is ().
4. Given (1-x)2+=0, the value of x+y is ().
A. 1
5. In the school sports meeting, Xiao Ming's shot put made a hole with a diameter of 10cm and a depth of 2cm, and the diameter of the shot put was about ().
A.10cm B.14.5cm C.19.5cm D.20cm.
6. At the New Year's party, the class committee of Class 9 (1) designed a game to give winners A and B one of two different prizes. Now the names of the prizes are written on the same cards, with the back arranged neatly, as shown in the figure. If the card with the second prize written on it is placed in the shadow, the probability that the winner Xiaogang will win the second prize is ().
A.B. C. D。
By the end of 2007, a city had afforested 300 hectares. After two years of afforestation, the afforestation area has increased year by year, reaching 363 hectares by the end of 2009. Let the average annual growth rate of afforestation area be x, and the listed equation is correct ().
a . 300( 1+x)= 363 b . 300( 1+x)2 = 363
c . 300( 1+2x)= 363d . 300( 1-x)2 = 363
8. It is known that the unary quadratic equation x2 +mx+4=0 about x has two positive integer roots, so the possible value of m is ().
Morning & gt0b.m > 4 c-4，-5 D.4，5
9. As shown in the figure, in order to save the handling effort, Xiao Ming rolled a cubic wooden box with a side length of 1m on the ground along the straight line L from the initial position without sliding. After rolling for one week, the curved surface ABCD, which was originally in contact with the ground, falls back to the ground, so the length of the path taken by point A 1 is ().
A.()m B
C. Doctor of Medicine
10. As shown in the figure, it is known that the straight line BC cuts ⊙O at point C, PD is the diameter of ⊙O, the extension line of BP and CD intersects at point A, ∠ A = 28, ∠ B = 26, then ∠PDC is equal to ().
34 BC to 36 BC
II. Fill in the blanks (this big topic is 6 small questions, *** 18 points):
1 1. Known = 1.45438+04, then (keep two significant figures).
12. If the radii of two circles are two in the equation x2-3x+2=0, and two
If two circles intersect, the range of the distance d between the two circles is.
13. If the function y=ax2+3x+ 1 has only one intersection with the X axis, the value of a is.
14. As shown in the figure, it is known that the large semicircle O 1 is inscribed with the small semicircle O2 at point B, and the chord MN of the large semicircle is tangent to the small semicircle at point D. If MN∑AB, when MN=4, the area of the shaded part in this figure is.
15. In order to encourage consumers to ask for invoices from merchants, the state has formulated certain incentives. Among them, there are four kinds of invoices for 100 yuan (the appearance is the same, and the reward amount is sealed with a sealed label): 5 yuan, 50 yuan and thank you. Now a merchant has 1000 100. The reward of this 1000 invoice is shown in the following table. If a consumer spends 100 yuan and asks the merchant for an invoice, the winning probability of 10 yuan is.
5 yuan150 yuan, 0 yuan Thank you for asking.
Quantity: 50, 20, 10, and the rest.
16. As shown in the figure, AB is the diameter ⊙O, CD is the chord, and CD⊥AB is in E. If CD=6 and OE=4, the length of AC is.
Three. Solution (8 questions in this big question, ***72 points):
17.(6 points) Calculation:.
18.(6 points) Solve the equation: x2-6x+9=(5-2x)2.
19.(8 points) Simplify before evaluating:
Where a is the solution of equation 2x2-x-3=0.
20.(8 points) As shown in the figure, it is known that there are three concentric circles, and the three vertices of the equilateral triangle ABC are on three circles respectively. Please rotate this triangle clockwise around point O 120 and draw △A/B/C/. Draw with a ruler, don't draw, leave a mark.
2 1.( 10) There are only two different colors of red balls and yellow balls in the sealed pocket. If you randomly take a ball out of your pocket, the probability is.
(1) Find the functional relationship between y and x;
(2) If you take six red balls out of your pocket, and the probability that one of them is a red ball is zero, how many red balls and yellow balls are there in your pocket?
22.( 10) In order to measure the accuracy of a circular part, two right-angle triangular rulers with the same size and an angle of 30 degrees were designed on the processing line, and the measurement was carried out according to the schematic diagram.
(1) If ⊙O is tangent to AE and AF at points B and C respectively,
Where the edges of DA and GA are on the same straight line. Verification:
oa⊥dg；
(2) In the case of (1), if AC= AF, and
AF=3, find the length BC of the arc.
23.( 12 point) As shown in the figure, the intersection of parabola y=-x2+bx+c and X axis is A, and the intersection with Y axis is B, OA and OB (OA
(1) Find the coordinates of point A and point B;
(2) Find the analytical expression of this parabola and the coordinates of vertex d;
(3) Find the coordinates of another intersection point c between this parabola and the X axis;
(4) Is there a point P on the straight line BC, which makes the quadrilateral PDCO trapezoid? If it exists, find the coordinates of point P; If it does not exist, explain why.
24.( 12 minutes) As shown in the figure, in the Cartesian coordinate system xoy, point A (2,0) and point B are in the first quadrant, and △OAB is an equilateral triangle. The positive semi-axis of the circumscribed circle of △OAB intersects with the Y axis at point C, and the tangent of the circle passing through point C intersects with the X axis at point D. 。
(1) Determine whether point C is the midpoint of arc OB? And explain the reasons;
(2) Find the coordinates of point B and point C;
(3) Find the analytical expression of the function of the straight line CD;
(4) Point P is on the line segment OB, and the quadrilateral OPCD is equal.
Waist trapezoid, find the coordinates of point p.
Reference answer:
First, multiple-choice questions: BADCB, BBCCB.
Second, fill in the blanks:
1 1.0. 17; 12. 1 & lt； d & lt3; 13.a= or 0;
14.2 ; 15.； 16.3 .
Third, answer questions:
17. solution: the original formula =1-(2-1)+2 =1-1+2-=+2.
18. Solution: x2-6x+9=(5-2x)2, (x-3)2=(5-2x)2,
[(x-3)+(5-2x)][(x-3)-(5-2x)]=0
∴x 1=2,x2=。
19. solution: original formula =()(a+ 1)= 1
= ,
From the equation 2x2-x-3=0: x 1=, x2=- 1,
But when a=x2=- 1, the score is meaningless; When a=x 1=, the original formula =2.
20. Omit.
2 1.( 1) from the meaning of the question:, arranged as: y =；;
(2) Judging from the meaning of the question, the solution: x= 12, y=9, a: omitted.
22. solution: (1) proof: connect OB, oc, ∵AE, AF is the tangent of ⊙O, BC is the tangent point,
∴∠ oba =∠ OCA = 90, which is easy to prove ∠ bao =∠ cao;
∠EAD=∠FAG，∴∠dao=∠gao； ;
∠ Dag = 180, ∴∠ Dao = 90, ∴OA⊥DG.
(2) Because ∠ OCA = ∠ OBA = 90 and ∠ EAD = ∠ FAG = 30, ∠ BAC =120;
And AC= AF= 1, ∠ OAC = 60, so OC=, the length of the arc BC is.
23. Solution: (1)∵x2-6x+5=0, and the two real roots are OA and OB (OA
∴oa= 1,ob=5,∴a( 1,0),b(0,5).
(2) ∵ parabola y=-x2+bx+c, the intersection with the x axis is a, and the intersection with the y axis is b,
The solution is,
∴ The analytic formula of quadratic function is y=-x2-4x+5,
Vertex coordinates are: d (-2,9).
(3) The coordinate (-5,0) of another intersection point c of this parabola and the X axis.
(4) The analytical formula of linear CD is y=3x+ 15,
The analytical formula of BC line is: y = x+5;
① If CD is taken as the cardinal number, the analytical formula of OP∑CD and straight line OP is y=3x.
So there is,
Solution:
The coordinate of point p is (5/2, 15/2).
② If OC is the cardinal number, DP∨CO,
The analytical formula of straight line DP is: y=9,
So there is,
Solution:
∴ The coordinate of point P is (4,9),
There is a point p on the straight line BC,
The quadrilateral PDCO is made into a trapezoid,
And the coordinates of point p are (5/2, 15/2) or (4,9).
24. solution: (1)C is the midpoint of arc OB, connecting AC,
∴ac ∵oc⊥oa is the diameter of a circle,
∴∠abc=90；
△ OAB is an equilateral triangle,
∴∠ABO=∠AOB=∠BAO=60，
∠∠ACB =∠AOB = 60，
∴∠COB=∠OBC=30，
∴ arc OC= arc BC,
That is, c is the midpoint of arc OB.
(2) Let B BE⊥OA be at point E, ∫ A (2,0), ∴OA=2, OE= 1, BE=,
∴ The coordinate of point B is (1,);
∫C is the midpoint of the arc OB, CD is the tangent of the circle, and AC is the diameter of the circle.
∴AC⊥CD,AC⊥OB,∴∠CAO=∠OCD=30，
∴OC= ,∴C(0)。
(3) In △COD, ∠ COD = 90, OC=,
∴OD=, ∴D (,0), ∴ The analytical formula of linear CD is: y= x+.
(4)∵ Quadrilateral OPCD is an isosceles trapezoid,
∴∠CDO=∠DCP=60，
∴∠OCP=∠COB=30 ,∴PC=PO.
The crossing point p is PF⊥OC in f,
And then ∴PF=
The coordinates of point P are: (,).