Algebra II. 6 th Six Weeks

Transcription

1 Algebra II 6 th Six Weeks 0 1 Chapter 9 Test Review 7 Circles HW: PP 1-4 Circles WS EXTRA GRAPH PP Ellipses 8 Parabolas HW: PP 5-7 Parabolas WS 1 5 Ellipses CW: Chapter 9 Test Review Sheet 9 Parabolas Warm-Up PP 8 HW: PP 9-11 Parabolas WS 6 US HISTORY EOC 3 Chapter 9 Test HW: Complete the Square, Midpoint, and Distance Formula Worksheet 30 Circles & Parabolas Practice Day Warm-Up PP1-13 HW: PP Parabolas & Circles Review 7 Hyperbolas 4 In Class: Go Over Complete the Square, Midpoint, and Distance Formula Worksheet May 1 QUIZ Circles & Parabolas HW: PP 17 Spiral Rev WS 1 8 Hyperbolas HW: PP Ellipses WS 1 HW: PP 0-1 Ellipses WS HW; PP -3 Hyperbolas WS 1 HW: PP 4-5 Hyperbolas WS 11 Ellipses and Hyperbolas Practice Day HW: PP QUIZ Ellipses & Hyperbolas HW: PP 8 Spiral Rev WS 13 Identify Conics HW: PP 9 Conic Sections Practice WS 1 14 Identify Conics HW: PP Conics Sections Practice WS 15 Conics Review HW: PP 3-35 Conics Review ODDS 18 Conics Review HW: PP 3-35 Conics Review EVENS 19 TEST Conics HW: PP 36 Spiral Rev WS 3 0 Graphing & Factoring Practice 1 Graphing & Factoring Practice Graphing & Factoring Quiz 1 5 Memorial Day 6 Graphing & Factoring Practice 7 Cumulative Test 8 Graphing & Factoring Quiz 9 Review for Final Exam 1 FINALS FINALS 3 FINALS 4 FINALS Period 7 Exam Periods 1, 6 Exams Periods, 3 Exams Periods 4, 5 Exams

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3 Name Date Period Circles WS Write the equation of the circle in standard form 1

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7 Parabolas WS 1 Name Find the vertex, AOS, a value, p value, focus, and directrix. Graph the parabola. 1. y 1 ( x 1) 3 8 Vertex AOS a= p= Focus Directrix. y 1 ( x ) 4 4 Vertex AOS a= p= Focus Directrix 3. y 1 ( x 1) 16 Vertex AOS a= p= Focus Directrix 5

8 4. x 1 ( y 1) 5 4 Vertex AOS a= p= Focus Directrix x ( y 5) 1 Vertex AOS a= p= Focus Directrix 6. 1 x ( y 1) 1 Vertex AOS a= p= Focus Directrix 6

9 Write equations for the following parabolas: 7. Focus (5, 4) and directrix: x = Vertex (-7, 3) and Focus (-3, 3) 9. Vertex (-5, 1) and focus (-5, ) 10. Write the equation for the graph below: Y X Created with an unregistered version of Advanced Grapher - / 7

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11 Parabolas WS Name Write in standard form (if necessary). Find the vertex, AOS, focus, and directrix. Graph the parabola. 1. y 1 ( x ) 1 8 Vertex AOS Focus Directrix. y x 10x 1 Vertex AOS Focus Directrix 3. y x 6x 8 Vertex AOS Focus Directrix 9

12 4. x y 4 Vertex AOS Focus Directrix 5. x y 6y 5 Vertex AOS Focus Directrix 6. y x 8x 1 Vertex AOS Focus Directrix Write equations for the following parabolas in vertex form: 7. y y 4x

13 8. x x 8y Focus (4, -4), directrix: y = Directrix: x = 3 and vertex (4, -1) 11. Write the equation for the graph below: Y X Created with an unregistered version of Advanced Grapher - / 11

14 Name Conics Warm-up Graph each of the following parabolas. Label the axis of symmetry, the focus and the directrix on the graph Graph the circle: (x + 3) + (y - 4) = Graph the circle: 340 1

15 5. Write the equation for a circle that has endpoints of the diameter at (6, 8) and (10, 8). Write the equation of the graphs below in standard form Y Y X X Created with an unregistered version of Advanced Grapher - / 8. When graphed, which way does the parabola open? A B Find the center and the radius of the circle: Center Radius 13

16 Parabolas and Circles Review Name Graph each of the following equations. Include the focus and directrix on the graph. Find the vertex, AOS, focus, and directrix ( ) y 6 x. 8 y x x 8 10 Vertex AOS Focus Directrix Vertex AOS Focus Directrix 3. y 8y + 8x = (x + 3) + (y - 5) = 36 Vertex AOS Center Radius Focus Directrix 14

17 5. Write the equation for a parabola given the focus (5,10) and the equation for the directrix: y = Find the center and radius of the circle (x + 4) + (y + 5) = 16. Graph it. Center Radius 7. Write the equation in standard form of the circle: x + y + 8x + 10y = -16. Find the center and the radius. Graph it. Standard form Center Radius 8. Write the equation of the circle with the center at (-,5) and passes through the point (11,15). 9. Write the equation of the circle with endpoints of the diameter at (, ) and (0, 6). 10. Write the equation of a parabola given the vertex (-, 5) and the directrix: x = 6. 15

18 11. Write the equation of the parabola with focus (3, 5) and directrix: y = Write the equation of the parabola with focus at (-,0) and vertex at the origin. 13. Write the equation of a circle with a center shifted 3 to the left and 5 down from the origin and goes through the point (1,0). 14. Write the equation of the circle below. State the center and the radius. Y X Created with an unregistered version of Advanced Grapher - / 16

19 Name Date Period Spiral Review Worksheet 1 Show all work on your own paper. Simplify: Solve. Check for extraneous solutions log 5 4 log log Simplify: Solve: 19. Sarah invests some money at 6% compounded continuously for 0 years. How much was her initial investment if she has $500,000 at the end of 0 years? 0. Chase buys an antique clock for $500. Assuming that the clock will appreciate.5% per year, what will the A A 1 r clock be worth after 15 years? t 0 17

20 ELLIPSES WS 1 Name Graph the following ellipses. Include the foci on your graph Center: Vertices: Co-vertices: Foci: Center: Vertices: Co-Vertices: Foci: Center: Vertices: Co-vertices: Foci: Center: Vertices: Co-Vertices: Foci: 18

21 5. x ( y ) ( x4) ( y4) Center: Vertices: Co-Vertices: Foci: Center: Vertices: Co-Vertices: Foci: 7. ( x 3) y ( x1) ( y3) Center: Vertices: Co-Vertices: Foci: Center: Vertices: Co-Vertices: Foci: 19

22 Ellipses WS Name Write the equation for each ellipse shown in standard form Write the equation of the ellipse whose foci are (1, 0) and (-1, 0) and whose co-vertices are (0, 5) and (0, -5) 4. Write the equation of the ellipse whose vertices are (-9, ) and (5, ). The co-vertices are (-, 5) and (-, -1). 5. Write the equation of the ellipse whose vertices are (, 1) and (, -4). The co-vertices are (4, 4) and (0, 4). 6. Write the equation of an ellipse whose major axis length is 0 and minor axis length is 6. The major axis is parallel to the y-axis. The center is at (4, ). 0

23 7. Write the equation of the ellipse whose major axis length is 1 and minor axis length is 6. The major axis is parallel to the x-axis. The center is at (-, 6). Write the following in standard form. State the center, the direction, and the lengths of the major and minor axes x y x y x 5y 3x 50y 11 0 For each of the following: A) Write in standard form B) Center C) Vertices D) Co-vertices E) Foci G) Graph 9. 16x 4y 3x 4y x 9y 4x 7y A) B) C D) E) A) B) C) D) E) 1

24 Hyperbolas WS 1 Name Put the following in standard form and graph. Find: a) center b) vertices c) foci d) slopes of asymptotes 1. x y y 36x 144 Standard Form: Standard Form: a) a) b) b) c) c) d) d) 3. 16x y y x 16 Standard Form: Standard Form: a) a) b) b) c) c) d) d)

25 5. ( x) ( y1) ( x 3) y Standard Form: Standard Form: a) a) b) b) c) c) d) d) 7. ( x1) ( y1) x 4y 16 Standard Form: Standard Form: a) a) b) b) c) c) d) d) 3

26 Name Date Period Hyperbolas WS For each of the following, find: A) Center B) Vertices C) Foci D) Slopes of the asymptotes 4

27 Write the equations of the hyperbolas graphed below Write the equation for the hyperbolas described below. 5

28 Name Ellipses and Hyperbolas Practice ( x1) ( y) ( x3) ( y6) 1. Graph the ellipse: 1.. Graph the ellipse: Include vertices and foci. Include vertices and foci. ( x) ( y1) 3. Graph the hyperbola: Graph the hyperbola: 4 9 ( x4) ( y) Include asymptotes, vertices and foci. Include asymptotes, vertices and foci. 6

29 4. Put the following equation for an ellipse in standard form and graph. x y x y Standard Form: 5. Put the following equation for a hyperbola in standard form and graph. 9x y 18x6y 9 0 Standard Form: 6. A vertical ellipse with center at (4, -) whose major axis length is 0 and minor axis length is Write the equation for the ellipse with vertices at (, 1) and (, -4) and co-vertices at (4, 4) and (0, 4). 7

30 Name Date Period Spiral Review Worksheet Show all work on your own paper. Simplify: Solve. Check for extraneous solutions. 7. log 5log log log 7 9. log log 3 8 log log log Write each exponential equation in logarithmic notation Solve: 19. In 5 years, radioactivity reduces the mass of a 100-gram sample of an element to 75 grams. For this element, find the approximate value of the constant k. N N e 0 kt 0. Sharon received $100 for her tenth birthday. She wants to use it for college, so she deposited it into a certificate of deposit that earns 4.75% interest compounded monthly. How much money will she have when she is 18? r A P 1 n nt 8

31 Name: Date: Period: Conic Section Practice WS 1 Identify each of the following conic sections. Write in standard form (if not already in standard form). 1. 9x 4y ( x3) ( y4) x y ( y 6) x x y x ( y 4) y ( x 4) x 3 y 5. y yx ( x ) ( y3) x 36 4y 16. x y 6 6x 14y 7. x 1 6 y 17. y x y x 3y x 40y 4y x 5 5y 19. 9x 4y 36x8y y 5x 5 0. y 16yx 31 9

32 Name: Date: Period: Conic Section Practice WS Identify each of the following conic sections. Write in standard form (if not already in standard form). 1. y y x x 3 y 3. 16x 9y 64x18y x 6y ( x ) 16( y 5) x ( y 4) x y 16 8x 10y 8. ( x8) ( y7) x 4y ( y 6) x x 16 4y 1. x y x 4y 16y 54x x x 8y

33 15. y 8yx x y x 36 y 18. 9x 4( y5) y x x 9y 36 Identify the conic section from the graph. 1.. y y x x y 8 Y 8 8 x 8 X 31

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35 Name Date Period Conics Review Identify each of the following conic sections. Write in standard form. 1. x y = 49. x y x x 4y x 9y 36y 8x y 36x x 4y 3x 4y 1 0 Graph the following conics. Fill in the blanks. 7. x = 1 4 (y 1) 6 8. x y 54 6x 14y Vertex AOS Center Radius 33

36 9. ( y 6) x y ( x 4) Center Vertices Co-Vertices Lines of Symmetry Center Vertices Slopes of Asymptotes Domain Range 11. Write the equation of a circle whose center is (-1, 9) that goes through (, 5). 1. Write the equation of a circle whose diameter has endpoints (6, 8) and (4, -). 13. Write the equation of an ellipse whose vertices are (, 1) and (, -4) and co-vertices are (-3, 4) and (7, 4) 14. Write the equation of an ellipse whose center is (-1, -4) with a major axis length of 1 and a minor axis length of 8. The major axis is parallel to the x-axis. 34

37 15. Write the equation of a circle with center (-, -5) and diameter Write the equation of the following parabola in vertex form. Which direction does it open? y 16y + x = 31 Write the equation for the following conics Y Y X X Y Y X X 35

38 Name Date Period Spiral Review Worksheet 3 Show all work on your own paper. Simplify: 1. 1 x 6x 6 6x 3 4( x 1) x 10. 3y 6 5y y 4 3. x x 3 1 y y 3 1 Write in expanded form Write as a single log 4. log 5. 3log 5 log 5log 6. log 8 3 log log Solve. Check for extraneous solutions. 7. log 5 4 log log log log 8 36 log log log y 5 4 y 7 Solve: 16. David can do a job in 4 hours. Amanda can do the same job in 3 hours. How many hours will it take the two of them to do the job if they work together? 17. A commercial jet travels 160 miles in the same amount of time it takes a corporate jet to travel 160 miles. The rate of the commercial jet is 10 mph greater than the rate of the corporate jet. Find the rate of each jet. 18. The Browns buy some land for $800 per acre. If the land s value appreciates 3% per year, how long will it be A A 1r before the land is worth $1000 per acre? Use the formula t 19. Jim and Pam just had a baby boy. They decide to invest $10,000 for the child s college fund. If this money is deposited into a money market account with an interest rate of 4.5% compounded monthly, how much will the r account be worth when the child turns 18? A P 1 n 0. Write the equation of the circle with the center at (3,1) and passes through the point (6,7). nt 0 36

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