algebra ii 6 six weeks - crhsalgebra2.pbworks.com hw... · algebra ii 6th six weeks 20 ... distance...

Algebra II

6th Six Weeks

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22 Chapter 9 Test 2 Review CW: Chapter 9 Test 2 Review Sheet

23 Chapter 9 Test 2 HW: Complete the Square, Midpoint, and Distance Formula Worksheet

24 In Class: Go Over Complete the Square, Midpoint, and Distance Formula Worksheet

27 Circles HW: PP 1-4 Circles WS EXTRA GRAPH PP37-38

28 Parabolas HW: PP 5-7 Parabolas WS 1

29 Parabolas Warm-Up PP 8 HW: PP 9-11 Parabolas WS 2

30 Circles & Parabolas Practice Day Warm-Up PP12-13 HW: PP 14-16 Parabolas & Circles Review

May 1 QUIZ Circles & Parabolas HW: PP 17 Spiral Rev WS 1

4 Ellipses

HW: PP 18-19 Ellipses WS 1

5 Ellipses HW: PP 20-21 Ellipses WS 2

6 US HISTORY EOC

7 Hyperbolas HW; PP 22-23 Hyperbolas WS 1

8 Hyperbolas HW: PP 24-25 Hyperbolas WS 2

11 Ellipses and Hyperbolas Practice Day HW: PP 26-27

12 QUIZ Ellipses & Hyperbolas HW: PP 28 Spiral Rev WS 2

13 Identify Conics HW: PP 29 Conic Sections Practice WS 1

14 Identify Conics HW: PP 30-31 Conics Sections Practice WS 2

15 Conics Review HW: PP 32 -35 Conics Review ODDS

18 Conics Review HW: PP 32-35 Conics Review EVENS

19 TEST Conics HW: PP 36 Spiral Rev WS 3

20 Graphing & Factoring Practice


22 Graphing & Factoring Quiz 1

25 Memorial Day


27 Cumulative Test

28 Graphing & Factoring Quiz 2

29 Review for Final Exam

1 FINALS Period 7 Exam

2 FINALS Periods 1, 6 Exams



Name___________________ Date__________ Period______

Circles WS

Write the equation of the circle in standard form

1

11.

2

Parabolas WS 1 Name____________________

Find the vertex, AOS, a value, p value, focus, and directrix. Graph the parabola.

1. 3)1(8

1 2 xy

Vertex___________

AOS_____________

a=______ p=______

Focus____________

Directrix_________

2. 4)2(4

1 2 xy

Vertex___________ AOS_____________ a=______ p=______ Focus____________ Directrix_________

3. 2)1(16

1 2 xy


5

4. 5)1(4

1 2 yx


5. 1)5(4

1 2 yx


6. 2)1(12

1 yx


6

Write equations for the following parabolas:

7. Focus (5, 4) and directrix: x = -3

8. Vertex (-7, 3) and Focus (-3, 3)

9. Vertex (-5, 1) and focus (-5, 2)

10. Write the equation for the graph below:

X

Y

Created with an unregistered version of Advanced Grapher - http:/ / www.serpik

7

Parabolas WS 2 Name____________________

Write in standard form (if necessary). Find the vertex, AOS, focus, and directrix. Graph the parabola.

1. 1)2(8

1 2 xy

Vertex___________

AOS_____________

Focus____________

Directrix_________

2. 21102 xxy

Vertex___________

AOS_____________

Focus____________

Directrix_________

3. 862 xxy

Vertex___________

AOS_____________

Focus____________

Directrix_________

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4. 42 yx

Vertex___________

AOS_____________

Focus____________

Directrix_________

5. 562 yyx

Vertex___________

AOS_____________

Focus____________

Directrix_________

6. 1282 xxy

Vertex___________

AOS_____________

Focus____________

Directrix_________

Write equations for the following parabolas in vertex form:

7. 09422 xyy

10

8. 017822 yxx

9. Focus (4, -4), directrix: y = -6

10. Directrix: x = 3 and vertex (4, -1)

11. Write the equation for the graph below:

X

Y

Created with an unregistered version of Advanced Grapher - http:/ / www.serpik.com/ agrapher/

11

Name_______________________________ Conics Warm-up

Graph each of the following parabolas. Label the axis of symmetry, the focus and the directrix on the graph.

1. 3 1 2. 2 6 8

3. Graph the circle: (x + 3) 2 + (y - 4) 2 = 9. 4. Graph the circle: 2 2 34 0

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_________________________________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.

6. ________________________________ 7. ______________________________

8. When graphed, which way does the parabola open? ______________________A. 3 4 8 ________________________B. 3 4 8

9. Find the center and the radius of the circle: 1 8 16 .

Center______________________ Radius________________________

X

Y


X

Y

13

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.

1. 21( 2) 6

8x y 2. 2 8 10y x x

Vertex____________ Vertex______________

AOS______________ AOS________________

Focus_____________ Focus_______________

Directrix__________ Directrix_____________

3. y2 – 8y + 8x = -16 4. (x + 3)2 + (y - 5)2 = 36

Vertex____________ Center______________

AOS______________ Radius______________

Focus_____________

Directrix__________ 14

5. Write the equation for a parabola given the focus (5,10) and the equation for the directrix: y = -4.

6. Find the center and radius of the circle (x + 4) 2 + (y + 5) 2 = 16. Graph it. Center________________

Radius________________

7. Write the equation in standard form of the circle: x 2 + y 2 + 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 (-2,5) and passes through the point (11,15).

9. Write the equation of the circle with endpoints of the diameter at (2, 2) and (0, 6).

10. Write the equation of a parabola given the vertex (-2, 5) and the directrix: x = 6.

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11. Write the equation of the parabola with focus (3, 5) and directrix: y = 1.

12. Write the equation of the parabola with focus at (-2,0) 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.

X

Y


16

Name_______________________ Date________________ Period__________

Spiral Review Worksheet 1

Show all work on your own paper.

Simplify:

1. 125 4 5

36 2 2 5 2. 2 6 3. √2 √7

4. 5√2 √2 √8 √2 5. √

√ 6. √

√

Solve. Check for extraneous solutions.

7. 2 1 3 4 8. √5 2 5 9. √ 7 1

10. log 5 4 log 1 3 11. log 4 1 2 12. 5 17

Simplify:

13.

14.

15.

16. 17.

18. ∙

Solve:

19. Sarah invests some money at 6% compounded continuously for 20 years. How much was her initial investment if she has $500,000 at the end of 20 years?

20. Chase buys an antique clock for $2500. Assuming that the clock will appreciate 2.25% per year, what will the

clock be worth after 15 years? t0A A 1 r

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ELLIPSES WS 1 Name________________________

Graph the following ellipses. Include the foci on your graph.

1. 1 2. 1

Center:____________ Center:______________

Vertices:___________ Vertices:_____________

Co-vertices:_________ Co-Vertices:___________

Foci:_______________ Foci:_________________

3. 1 4. 1

Center:____________ Center:______________

Vertices:___________ Vertices:_____________

Co-vertices:_________ Co-Vertices:___________

Foci:_______________ Foci:_________________

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5. 2 2( 2)

136 49

x y 6.

2 2( 4) ( 4)1

16 4

x y

Center:_____________ Center:______________

Vertices:____________ Vertices:_____________

Co-Vertices:__________ Co-Vertices:___________

Foci:________________ Foci:_________________

7. 2 2( 3)

19 49

x y 8.

2 2( 1) ( 3)1

81 36

x y

Center:_____________ Center:______________

Vertices:____________ Vertices:_____________

Co-Vertices:__________ Co-Vertices:___________

Foci:________________ Foci:_________________

19

Ellipses WS 2 Name______________________

Write the equation for each ellipse shown in standard form.

1. _____________________ 2. _________________________

3. Write the equation of the ellipse whose foci are (12, 0) and (-12, 0) and whose co-vertices are (0, 5) and (0, -5) 4. Write the equation of the ellipse whose vertices are (-9, 2) and (5, 2). The co-vertices are (-2, 5) and (-2, -1). 5. Write the equation of the ellipse whose vertices are (2, 12) and (2, -4). The co-vertices are (4, 4) and (0, 4). 6. Write the equation of an ellipse whose major axis length is 20 and minor axis length is 6. The major axis is parallel to the y-axis. The center is at (4, 2).

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7. Write the equation of the ellipse whose major axis length is 12 and minor axis length is 6. The major axis is parallel to the x-axis. The center is at (-2, 6). Write the following in standard form. State the center, the direction, and the lengths of the major and minor axes. 8. 0362444 22 yxyx 9. 0115032254 22 yxyx For each of the following: A) Write in standard form B) Center C) Vertices D) Co-vertices E) Foci G) Graph 9. 0122432416 22 yxyx 10. 0144722494 22 yxyx

A)___________________ A)_____________________ B)___________________ B)_____________________ C____________________ C)_____________________

D)___________________ D)_____________________ E)___________________ E)_____________________

21

Hyperbolas WS 1 Name______________________

Put the following in standard form and graph.

Find: a) center b) vertices c) foci d) slopes of asymptotes

1. 2 2

149 36

x y 2. 2 24 36 144y x

Standard Form:___________________ Standard Form:_________________________

a) __________________ a) _____________________

b) __________________ b) _____________________

c) __________________ c) _____________________

d) __________________ d) _____________________

3. 2 216 64x y 4. 2 2 16y x


a) __________________ a) _____________________

b) __________________ b) _____________________

c) __________________ c) _____________________

d) __________________ d) _____________________

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5. 2 2( 2) ( 1)

14 9

x y 6.

2 2( 3)1

9 4

x y


a) __________________ a) _____________________

b) __________________ b) _____________________

c) __________________ c) _____________________

d) __________________ d) _____________________

7. 2 2( 1) ( 1)

116 25

x y 8. 2 216 4 16x y


a) __________________ a) _____________________

b) __________________ b) _____________________

c) __________________ c) _____________________

d) __________________ d) _____________________

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Name_______________________ Date______________ Period______

Hyperbolas WS 2

For each of the following, find:

A) Center B) Vertices C) Foci D) Slopes of the asymptotes

24

Write the equations of the hyperbolas graphed below.

9.___________________________ 10.______________________________

Write the equation for the hyperbolas described below.

25

Name_________________________ Ellipses and Hyperbolas Practice

1. Graph the ellipse: 2 2( 1) ( 2)

19 16

x y . 2. Graph the ellipse:

2 2( 3) ( 6)1

4 25

x y .

Include vertices and foci. Include vertices and foci.

3. Graph the hyperbola: 2 2( 2) ( 1)

14 9

x y . 4. Graph the hyperbola:

2 2( 4) ( 2)1

16 4

x y .

Include asymptotes, vertices and foci. Include asymptotes, vertices and foci.

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4. Put the following equation for an ellipse in standard form and graph. 2 24 4 24 36 0x y x y

Standard Form:__________________________________

5. Put the following equation for a hyperbola in standard form and graph. 2 29 018 6 9x y x y

Standard Form:___________________________________

_______________________________6. A vertical ellipse with center at (4, -2) whose major axis length is 20 and minor axis length is 8.

______________________________7. Write the equation for the ellipse with vertices at (2, 12) and (2, -4) and co-vertices at (4, 4) and (0, 4).

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Name_______________________ Date________________ Period__________



Simplify:

1. 5 4√3 9 8√12 2. √

√ 3.

√

√

4.82 3632 4

6

5. 6.

Solve. Check for extraneous solutions. 7. log 5 log 11 2 8. log log 27 2 9. log 3 3

10. log 3 8 log 5 24 11. log log 6 2 12. 8 9 27

13. 14. 1 15. 4 2 4 2 18

Write each exponential equation in logarithmic notation.

16. 7 49 17. 25 125 18. 4 64

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. kt

0N N e

20. Sharon received $1200 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? ntrA P 1

n

28

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. 2 29 4 36x y 11. 2 2( 3) ( 4)

14 16

x y

2. 2 2 36x y 12. 2 2( 6)

125 16

y x

3. 2 2 36x y 13. 2 2( 4)

125 16

x y

4. 2 2( 4)

14 9

y x 14. 2 3x y

5. 2 22 4y y x 15. 2 2( 2) ( 3) 16x y

6. 2 236 4x y 16. 2 2 62 6 14x y x y

7. 21

6x y 17. 2 4 4 16 0y x y

8. 2 23 3 9x y 18. 2 216 40 4 164x y y

9. 2 225 5x y 19. 2 29 4 36 8 4x y x y

10. 2 25 25y x 20. 22 16 31y y x

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Name:____________________________ Date:________________ Period:____________

Conic Section Practice WS 2

Identify each of the following conic sections. Write in standard form (if not already in standard form).

1. 2 8 8 16y y x 2. 22

3x y

3. 2 216 9 64 18 71 0x y x y 4. 2 26 6 36x y

5. 2 24( 2) 16( 5) 64x y 6. 2 2( 4)

116 25

x y

7. 2 2 16 8 10x y x y 8. 2 2( 8) ( 7) 25x y

9. 2 24 4 16x y 10. 2 2( 6)

125 16

y x

11. 2 216 4x y 12. 2 6x y

13. 229 4 16 54 29 0x y y x 14. 017822 yxx

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15. 2 28 10y y x 16. 2 2 36x y

17. 2 26 36x y 18. 2 29 4( 5) 36x y

19. 2 22 4y x 20. 2 24 9 36x y

Identify the conic section from the graph.

21. _________________ 22. _________________

2 4–2–4 x

2

4

–2

–4

y

2 4–2–4 x

2

4

–2

–4

y

23. ____________________ 24. __________________

8–8 x

8

–8

y

X

Y

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Name___________________________ Date________________ Period____________

Conics Review

Identify each of the following conic sections. Write in standard form.

1. 𝑥2 − 𝑦2 = 49 2. 2 4 4 16 0x y x

3. 2 24 4 16x y 4. 2 24 9 36 8 4x y y x

5. 2 24 36 144y x 6. 0122432416 22 yxyx

Graph the following conics. Fill in the blanks.

7. 𝑥 =1

4(𝑦 − 1)2 − 6 8. 2 2 54 6 14x y x y

Vertex________________ Center________________

AOS__________________ Radius_________________

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9. 2 2( 6)

125 16

y x 10.

2 2( 4)1

4 9

y x

Center_________________ Center_________________

Vertices_______________ Vertices________________

Co-Vertices____________ Slopes of Asymptotes_________

Lines of Symmetry_____________ Domain_____________ Range___________

11. Write the equation of a circle whose center is (-1, 9) that goes through (2, 5).

12. Write the equation of a circle whose diameter has endpoints (6, 8) and (4, -2).

13. Write the equation of an ellipse whose vertices are (2, 12) and (2, -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 12 and a minor

axis length of 8. The major axis is parallel to the x-axis.

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15. Write the equation of a circle with center (-2, -5) and diameter 12.

16. Write the equation of the following parabola in vertex form. Which direction does it open?

2𝑦2 − 16𝑦 + 𝑥 = −31

Write the equation for the following conics.

17. ____________________ 18. ____________________

19. _____________________ 20. ______________________

X

Y

X

Y

X

Y

X

Y

35

Name_______________________ Date________________ Period__________



Simplify:

1. 102

36

)1(4

6612 2

x

x

x

xx 2.

4

563

2

2

y

yy 3.

33

11

y

yxx

Write in expanded form Write as a single log

4. log 5. 3log 5 log 5 log 6. log 8 3 log 2 log

Solve. Check for extraneous solutions.

7. log 5 4 log 1 3 8. log 5 10 4 9. log 4 2 3

10. log 8 36 log 5 12 11. log log 16 12. 4 6 27

13. 5 4 3 14. √3 4 √3 8 15. 3y 5

42 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 1620 miles in the same amount of time it takes a corporate jet to travel 1260 miles. The rate of the commercial jet is 120 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

before the land is worth $1000 per acre? Use the formula t0A A 1 r

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

account be worth when the child turns 18? ntrA P 1

n

20. Write the equation of the circle with the center at (3,1) and passes through the point (6,7).

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algebra ii 6 six weeks - crhsalgebra2.pbworks.com hw... · algebra ii 6th six weeks 20 ... distance...

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