Third grade general courseware teaching plan exercises summary Chinese mathematics English physical chemistry 20. (Full score of this question 10)? As shown in figure 1, in Delta OAB, ∠ OAB = 90? ，∠AOB=30？ ，OB = 8。 Take OB as one side, make an equilateral triangle OBC outside △OAB, D is the midpoint of OB, connect AD, and extend the intersection OC to E? (1) Find the coordinates of point B; ? (2) Verification: quadrilateral ABCE is a parallelogram; ? (3) As shown in Figure 2, fold the quadrilateral ABCO in Figure 1 so that point C coincides with point A, and the crease is FG. Find the length of OG. 2 1. (full mark of this question 10)? (1) background: In the figure 1, the line segments AB and CD are known. Where the points are e and f respectively. (1) If A(- 1, 0) and B (3,0), the coordinates of point E are _ _ _ _ _ _ _ _ _; C(-2) If c (-2,2) and D(-2,-1), the coordinate of point F is _ _ _ _ _ _ _ _; ② Exploration:? In fig. 2, the endpoint coordinates A (a, b) and B (c, d) of the line segment AB are known, and the coordinates of point D in the figure AB (expressed by an algebraic expression containing A, B, C and D) are obtained, and the solution process is given. ? Induction:? No matter where the line segment AB is located in the rectangular coordinate system, when its endpoint coordinates are A (A, B), B (C, D) and the midpoint of AB is D(x, Y), X = _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ (without proof). Application: In Figure 3, the linear function y=x-2 and the inverse proportional function x y3? The intersection of images is a and b, ① find the coordinates of intersection a and b; ? ② If the quadrilateral with vertices A, O, B and P is a parallelogram, please use the above conclusion to find the coordinates of vertex P ... Answer? O B x？ Washington, DC? y？ ●? ●? Answer? b？ O x？ y？ 64 2 24 68 5 5 10 15 A？ b？ y？ o？ x？ X y3 Y=x-2 figure 1 figure 2 figure 3 2 1 title map? Twenty questions? 22. (Full score of this question 10)? As shown in fig. 22, the rectangular OABC is placed in a rectangular coordinate system with O as the coordinate origin. Point a is on the positive semi-axis of the x axis. Point E is the moving point on the AB side (not coincident with points A and N), and the inverse proportional function (0)k yxx intersects BC side at point F through the image of point E? (1) If the products of △OAE and △OCF are S 1 and S2 respectively, and S 1+S2 = 2, find the value of k:? (2) If OA = 2.0C = 4. When point E moves to what position, what is the maximum area of quadrilateral OAEF? 23. (Full score of this question 12)? As shown in fig. 23, it is known that the parabola 249 yxbxc intersects the X axis at points A and B, and its symmetry axis is a straight line 2x? , intersects the x axis at point d, ao = 1. (1) Fill in the blanks: b = _ _ _ _ _ _. C=_______, and the coordinate of point B is (_ _ _ _ _): (2) If the perpendicular line EF of line BC intersects with point E and the X axis intersects with point F, find the length of FC; ? (3) Inquiry: Is there a point p on the parabola axis of symmetry that makes ⊙P tangent to the X axis and the straight line BC? If it exists, request the coordinates of point P; If it does not exist, please explain why. ? 22 questions? 23 reference answers 1. Multiple choice questions (3 points for each question. * * * 24 points. )? Question number 1 2 3 4 5 6 7 8 Answer? c？ b？ c？ c？ b？ d？ d？ d？ Fill in the blanks (4 points for each question, * * 32 points. ) 9.？ 1 10.2 1 ? 1 1.？ 15 12.？ 1? 13. 1, 12 14.33? 15.3 1 16.？ 3 1 1, 1 1? Third, write the necessary text description, proof process or calculus steps when solving problems? 17. (The full mark of this question is 6) Solution: The frequency of (1)C option is 69.23%-60-36-45 = 90 (person), and the bar graph is completed accordingly: m% = So m=20. 2 points (2) The number of people who support option B is about 5000×23%= 1 150. ? 4 points (3) The probability of Xiao Li being selected is: p =1002115023? . 6 points: 18. (this question is full of 8 points)? Solution: (1) As shown in the figure, △ABC is the demand. ? Let the analytical formula of the straight line where AC is located be 0ykxbk? ∵A 12C29,, ∴229kbkb solution 75kb? ，∴75yx？ . 4 points (2) As shown in the figure, △A 1B 1C 1 is what you want. According to Pythagorean Theorem, AC52? . ? As shown in the figure, ABC111s722716222 △12acc905225S3602 sector ∴△ The area swept by ABC during the above rotation is/kloc. △ fan. 8 points 19. Solution: (1) Connect oc, CD and O at ∴OC⊥cd. c? And ∴OC∥AD ∴ CD ∴ OCA = ∠ DAC. ∵OC=OA,∴∠OCA=∠OAC。 ? ∴∠OAC=∠DAC。 Ac split ∠DAB. ? The intersection o of 3 points (2) is the perpendicular OE of line segment AC, as shown in the figure: 4 points? (3) In Rt△ACD, CD = 4, AC = 45, ∴ AD = AC2-Cd2 = (45) 2-42 = 8. ? ∵OE⊥AC,∴AE= 1 2AC=25 .？ ∠∠oae =∠CAD,∠aeo=∠adc,∴△aeo∽△adc。 ? ∴OECD=AEAD。 ∴OE=AEAD×CD=258×4=5。 That is, the length of the vertical line segment OE is 5. Eight points? 20. (The full mark of this question is 10) Solution: (1)∵ In △OAB, ∠ OAB = 90? ，∠AOB=30？ ，OB=8，？ ∴OA=43,AB=4。 ∴ The coordinate of point B is (43,4). ? 2 points ②≈∠OAB = 90? ∴ab∥ec. ∴ab⊥x axis and ∵△OBC is an equilateral triangle, ∴ OC = OB = 8. ? And ∵D is the midpoint of OB, that is, AD is the midline on the hypotenuse of Rt△OAB. ∴AD=OD,∴∠OAD=∠AOD=30？ ,∴OE=4。 ∴EC=OC-OE=4。 ∴AB=EC。 A quadrilateral is a parallelogram. Six points? (3) Let OG = x, then we can get GA = GC = 8-x from the property of folding symmetry. In Rt△OAG, we can get 222gaoog from Pythagorean theorem, that is, 22843xx? ,? Solution, 1x? . ∴ The length of og is 1. 10 point 2 1. (Full score of this question 10)? (1) background: ①( 1, 0), ②? 2 1 22 points? (2) Inquiry: When point A and point B are perpendicular to the X-axis and Y-axis respectively, it is easy to get the coordinates of point D in AB as 2,2 2dbca by using the trapezoid midline theorem. Induction: 2,2 2dbca gets A(- 1, -3) and B(3, 1)② from the meaning of the question? P(2,-2) when AB is diagonal; When AO is diagonal, P(-4,-4); P(4,-4) when BO is diagonal; ∴s 1= 1 1 122kkxx？ ，S2=22 122kkxx？ . ∵S 1+S2=2,∴ 222 kk .∴2k？ . Four points? (2)∵ Quadrilateral OABC is a rectangle, OA=2, OC=4, ∴ Let E(2k, 2) and F(4, 4k). ∴BE=4-2 k，BF=2 -4 k .∴S△BEF=？ 2 1 1424224 16 kkkk？ ，S△OCF= 14242 kk？ , s rectangle OABC=2×4=8, ∴S quadrilateral OAEF=S rectangle oabc-s △ bef-s △ OCF = 8-(21416kk)-214160. =2 145 16k？ . ? ∴ When k=4, the S quadrilateral OAEF=5. ∴AE=2。 ? ∴ When point E moves to the midpoint of AB, the area of quadrilateral OAEF is the largest, with the maximum value of 5. ? 10? 23. (The full mark of this question is 12) Solution: (1)169,209,5,0. ? 2 points (2) The analytical formula of parabola from (1) is 24162099yxx, and the vertex is 2 4249 yx. ? ∴C(2,4)。 ? ∫E is the midpoint of BC. From the midpoint coordinate formula, the coordinate of E is (3.5,2). .. three points? Let the BC line expression be ykxb, then 5024kbkb? , the solution is 43 203kb. ? ∴ The expression of line BC is 4 2033 yx? . ? Five points? Let the expression of straight line EF be ymxn,? EF is the middle vertical line of ∴ef⊥bc. BC Province ∴: Can you get 34m from similarity? That is, the expression of the straight line EF is 3 4 yxn. Substitute E (3.5,2) to get 3 E(3.5 n? The solution is 58 n. The expression of straight line EF is 35 48 yx. Seven points? In 3548yx, let y=0 and get 35048x and 5 6x? . ∴F(56，0 .∴FC=FB=5-52566？ . A: The length of FC is 25 6. ? Eight points? (3) existence. If the bisector of ∠OBC intersects DC at point P, then P satisfies the condition. Let P(2, p), then the distance from p to X axis is equal to the distance from p to straight line BC, both of which are |p|. ∫c point coordinates are (2,4), B point coordinates are (5,0), ∴CD=4, DB = 5-2 = 3. ∴BC= 2222CDDB4+35？ . ∴sin∠BCD= PEBD3 CPCB5. 10 point When point P is above the X axis, you get 345pp, and the solution is 32p? . The coordinate of point P is (2,3 2). When the point p is below the x axis, you get 3 45 pp? The solution is 6p. The coordinate of point P is (2, -6). There is a point p on the axis of symmetry of the parabola, which makes it tangent to the X axis and the straight line BC. The coordinates of point P are (2,32) and (2,6). ? 12 point

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