12
City of Brockton BROCKTON PUBLIC SCHOOLS Matthew H. Malone, Ph,D. + Superintendent of Schools Robert Perkins Mathematics Department Head Brockton High School Phone (508) 580·7410 [email protected] June 6,2012 Dear StudentlParent, The attached Math Packet is intended for students taking a Pre-Calculus or Trigonometry Class in the fall. The packet contains problems emphasizing necessary skills for the student beginning this course. While completion of these problems is optional, it is important to note that if you complete this packet successfully you will be eligible for up to 5 points extra credit on your Term I average. You may seek help on the problems. It is hoped that you will do whatever is necessary to complete all of the problems successfully. You must submit the answer sheet (which details the problems that must be done) and your work on separate sheets of paper. The answer sheet and work should be stapled together and submitted to your teacher on or before Monday, September 10, 2012. If you are in a second semester math class please return the completed packet to the Green Math Office by September 10,2012. Late packets will not be accepted. Once again, it is worth your effort to complete all of the problems in the packet successfully. You may seek help from family and friends, from Internet sites, books or any other available source. You must however show the work for each problem on paper separate from the answer sheet. It is important that you follow the directions in order to obtain the maximum 5 points. Good luck in completing this work. Remember while it is optional, it is an opportunity for all students to take a step in improving their term I grade and to review some important math skills at the same time. If you have any problems with the math packets you may e-mail me at [email protected]. I check my e-mail frequently during the summer and I will get back to you as soon as possible. Thanks, Bob Perkins Brockton High School. 470 Forest Avenue +BI·ockton. Massachusetts 02301 www.brocktonpublicschoofs.com Brockton. Education. Industry. Progress.

City of Brockton BROCKTON PUBLIC SCHOOLS · Refer to the indicated lesson in the Geometry textbook for help . with the following problems. Skills ~actice . Distance and Midpoints

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Page 1: City of Brockton BROCKTON PUBLIC SCHOOLS · Refer to the indicated lesson in the Geometry textbook for help . with the following problems. Skills ~actice . Distance and Midpoints

City of Brockton BROCKTON PUBLIC SCHOOLS Matthew H Malone PhD + Superintendent of Schools

Robert Perkins Mathematics Department Head

Brockton High School Phone (508) 580middot7410

robertoperkinsbpsmaorg

June 62012

Dear StudentlParent

The attached Math Packet is intended for students taking a Pre-Calculus or Trigonometry Class in the fall The packet contains problems emphasizing necessary skills for the student beginning this course While completion of these problems is optional it is important to note that if you complete this packet successfully you will be eligible for up to 5 points extra credit on your Term I average

You may seek help on the problems It is hoped that you will do whatever is necessary to complete all of the problems successfully You must submit the answer sheet (which details the problems that must be done) and your work on separate sheets ofpaper The answer sheet and work should be stapled together and submitted to your teacher on or before Monday September 10 2012 Ifyou are in a second semester math class please return the completed packet to the Green Math Office by September 102012 Late packets will not be accepted

Once again it is worth your effort to complete all of the problems in the packet successfully You may seek help from family and friends from Internet sites books or any other available source You must however show the work for each problem on paper separate from the answer sheet It is important that you follow the directions in order to obtain the maximum 5 points

Good luck in completing this work Remember while it is optional it is an opportunity for all students to take a step in improving their term I grade and to review some important math skills at the same time If you have any problems with the math packets you may e-mail me at robertoperkinsbpsmaorg I check my e-mail frequently during the summer and I will get back to you as soon as possible

Thanks

Bob Perkins

Brockton High School 470 Forest Avenue +BImiddotockton Massachusetts 02301

wwwbrocktonpublicschoofscom

Brockton Education Industry Progress

Refer to the indicated lesson in the Algebra 1 textbook for help with the following problems

Skills Practice Multiplying Rational

Expressions

Find each product

s4(n + 2) n(n - 2) n + 2

8 ( - 2)( + 2) bull 2(ax + 3) x(ax + 3) x - 2

Skills Practice Rational Expressions with

Unlike Denominators Find the LCM for each pair of

expressions

3 2r - 1 r + 4

5 x2 - 2x - 3 (x - 3)2

Find each sum

7bull y 1 +y2

9 ~+~bull 2m m

b 2 11 b-f + b=4

ax + 15 + x 13 2 _ 25 X+5

Find each difference

5 2 15~ - r2

x 4 17X+2 - x1

a 2 19 2a - 1 - a + 3

6 b 21 b2 - 1 - b+1

Skills Practice Dividing Rational Expressions

Find each quotient

x-56 X+3 + (x - 5)

Skills Practice Mixed Expressions

and Complex Fractions Write each mixed expression as a

rational expression

416 + Ii

34b+E c

Simplify each expression

4 a 2 122

11middot s 5 44 5

Refer to the indicated lesson in the Geometry textbook for help with the following problems

Skills ~actice Distance and Midpoints

Use the Pythagorean Theorem to find the distance between each pair of points

5

7 K(2 3) F(4 4)

F

y

G V

(CI x

Use the Distance Formula to find the distance between each pair of points

9 Y(2 0) P(2 6) 1lA(-7 -3B(5 2)

Find the coordinates of the midpoint of a segment having the given endpoints

17 1(3 I) U(5 3) 18 J( -4 2) F(5 -2)

Find the coordinates of the missing endpoint given that P is the midpoint ofNQ

19 N(2 0) P(5 2) 21 Q(3 9 P(-1 5)

Find x andy

Sldlls Practice Special Right Triangles

1 ~24 2 x1 3 x~12 x~ ~32 ~

y y y

~ 4~R 5

16 Y

60 x

bull ID

Refer to the indicated lesson in the Geometry textbook for help with the following problems

Sldlls Practice Special Right Triangles

For Exercises 7-9 use the figure at the right B 60

7 Ifa = 11 find b and c

A 30 c ~~ b

8 If b == 15 find a and c

9 Ifc = 9 find a and b

For Exercises 10 and 11 use the figure at the right Al1B 10 The perimeter of the square is 30 inches Find the length of BC

D~C 11 Find the length of the diagonal BD

12 The perimeter of the equilateral triangle is 60 meters Find the length of an altitude

Skills Practice Trigonometry

Use MST to find sin RJ cos R tan R sin SJ cos Sf and tan S Express each ratio as a fraction and as a decimal to the nearest hundredth

1 r = 16 s = 30 t = 34 2 r = 10 s = 24 t = 26

Use the figure to find each trigonometric ratio Express answers as a fraction and as a decimal rounded to the nearest ten-thousandth

9 tan C 10 sin A 11 cos C

Find x Round to the nearest tenth

18 271~ 19~ AL-----dB A 27 B

Refer to the indicated lesson in the Geometry textbook for help with the following problems

Sldlls Practice Skills Practice The Law of Sines The Law of Cosines2 Find x to the nearest tenth

For Questions 1 and 2 find x to the nearest tenth 1 ~ ~ 2~

32 18

8 Solve MBT Round your answers toS Solve MBC Round your answers to Rthe nearest degree

the nearest tenth

TU76 S

A~ C4r

Refer to the indicated lesson in the Algebra 2 textbook for help with the following problems ac Ice Pr t

e

RelatIons and Functions Determine whether each relation is a function Write yes or no

2 0 R 4 y

Graph each relation or equation and find the domain and range Then determine whether the relation or equation is a function

5 (-4 -1) (4 0) (03) (2 on 6y = 2x - 1

c

y

x

J J

J I

Find each value if f(x) - Z 2 and g~) - -k + 3

7 f(3) 8 (-4)

10 (-2) 11g(-6) 12(m - 2)

Refer to the indicated lesson in the Algebra 2 textbook for help with the following problems

Skills Practice Writing Linear Equations

State the slope and y-intercept of the graph of each equation

32y = -sx + 3 43x+4y=4 8 2) = 6 - 5x63x-2y+6=0

Write an equation in slope-intercept form for each graph

9 1141 II n1 2)

II ICl

II 1(-1 -4)

1 j

I I

x

11

++++(4 -1)

~y I

03) 1

(J x i

(3 -3)~ Ll L~

Write an equation in slope-intercept form for the line that satisfies each set of conditions

12 slope 3 passes through (1 -3)

16 passes through (-1 -2) and (-a 1)

14 slope -2 passes through (0 -5)

Skills Practice Radical Expressions

Simplify

1 Y24 7 4-id2f5 13 (4vi2)(aV20) 19 (1 - V5)(1 + V5)

3ru 9 -f 10 vi2 - 2v3 + Vi08

O 4V50x5 liZ11 j5z 17 2WB - I7s - vi2

-- - ---shy

Refer to the indicated lesson in the Algebra 2 textbook for help with the following problems

Skills Practice Solving Quadratic Equations by Factoring

Solve each equation by factoring

14 x2 + 18x = -812x2 - 100 0

16 2x2 + 5x - 3 == 04x2-4x+3=0

18 3x2 - l3x - 10 == 06x2 - ax - 10 =0

Study Guide and Intervention Completing the Square

Complete the Square To complete the square for a quadratic expression of the form x2 + bx follow these steps

1 Find -+ 2 Square -+ S Add ( Yto x2 + bx

poundxample 1 Find the value of c that makes x2 + 22x + c a perfect square trinomial Then write the trinomial as the square of a binomial

Step 1 b == 22 = 11

Step 2 112 = 121 Step 3 c = 121

The trinomial is x2 + 22x + 121 which can be written as (x + 11)2

example 2 Solve 2x2 - ax - 24 = 0 by completing the square

2x2 - ax - 24 0 Original equation

2x2 - ax - 24 02 = 2 DIvide each side by 2

x2 - 4x - 12 0 il- 4x - 12 is not a perfect square

x2 - 4x = 12 Add 12 to each side

2x - 4x + 4 = 12 + 4 Since (-tt =4add4Ioeachslde

(x - 2)2 16 Factor the square X - 2 = plusmn4 Square Root Property

x = 6 or x = - 2 Solve each equation

The solution set is 6 -2

Find the value of c that makes each trinomial a perfect square Then write the trinomial as a perfect square

25 2 11 x2 - lOx + c 3 x - ax + c bull x + 2x + c

Solve each equation by completingthe square

102x2 - ax + 1 = 0 12 25x2 + 40x - 9 = 0

--_bull _ _ -

This page is for students entering Precalculus Honors Refer to the indicated lesson in the Algebra 2 textbook for help

Practice Skills Practice Monomials Rational Exponents

Simplify Assume that no variable equals G Write each expression in radical form 1

136

Write each radical using rational exponents 12m8y 6

9 -9my 5 V5i -278(-7)

11 160 7 Vi53 18 -(4w-3z-5)(8w)2

Evaluate each expression15 (fd2f4)4(-fd5f)8 (3x-2y3X5xy-8)

17 (x-3)4y-2 Simplify each expression 12 s

17c6 c6

s IS 162

1 5 15 21i 278

JY 2

28-1 ji

Study Guide and Intervention Radical Equations and Inequalities

SOlve each equation

13 + 2xv3 5 2 2vSx + 4 + 1 = 15 S8+Vx+l=2

9 vx2 + 7x = v7x - 9 IG4V2x + 11- 2 = 10

Name ____________-Precalculus Summer Work Answer Sheet

Write the answer to each specified problem on the indicated line on this answer sheet The work supporting these answers must be done neatly on separate paper and included along with this answer sheet and the downloaded worksheets as part of the complete packet Submit the packet to your Precalculus teacher by September 72010 If your Precalculus class is scheduled for second semester you must submit the packet to Mr Perkins or Mr Corbett in the Green Math office by September 72010 Packets will not be accepted after this date

Please note that the last page is part ofthe packet for Honors level only

Algebra 1

Lesson 12-3

2 ____

4 ____

6 ____

8 ____

Lesson 12-4

2 ____

4 ____

6 ____

8 ____

Lesson 12-7

1 ____

3 ____

5 ____

7 ____

9 ____

11 ____

13 ____

15 ____

17 ____

19 ____

21 ____

Lesson 12-8

1 ____

3 ____

11 ____

12 ____

Geometry

Lesson 1-3

5

7

9

11

17

18

19

21

Lesson 7-3

1 ____

2 ____

3 ____

4 ____

5

6

7

8

9

10

lL

12

Lesson 7-4

1

2 ___

9

10

11 ___

18 ___

19 ____

20 ____

Lesson 7-6

2

3

Lesson 7-7

1

2

3

Algebra 1

Lesson 2-1

2 ____

4 ____

5 J

10 x

6

7

8

9

10

11

12

Lesson 2-4 17

2 19

4 21

5 23

6 Lesson 6-3

8 2

9 4

10 6

11 14

12 16

14 18

16

Lesson 5-6 Lesson 6-4

1 1

3 3

5 5

7 8

9 10

11 12

13

15

The following problems are for Honors level only

Lesson 5-1

3

5

7

9

11

13

15

17

Lesson 5p7

1

3

5

7

9

11

13

15

17

19

21

23

Lesson 5-8

1

2

3

9

10

Page 2: City of Brockton BROCKTON PUBLIC SCHOOLS · Refer to the indicated lesson in the Geometry textbook for help . with the following problems. Skills ~actice . Distance and Midpoints

Refer to the indicated lesson in the Algebra 1 textbook for help with the following problems

Skills Practice Multiplying Rational

Expressions

Find each product

s4(n + 2) n(n - 2) n + 2

8 ( - 2)( + 2) bull 2(ax + 3) x(ax + 3) x - 2

Skills Practice Rational Expressions with

Unlike Denominators Find the LCM for each pair of

expressions

3 2r - 1 r + 4

5 x2 - 2x - 3 (x - 3)2

Find each sum

7bull y 1 +y2

9 ~+~bull 2m m

b 2 11 b-f + b=4

ax + 15 + x 13 2 _ 25 X+5

Find each difference

5 2 15~ - r2

x 4 17X+2 - x1

a 2 19 2a - 1 - a + 3

6 b 21 b2 - 1 - b+1

Skills Practice Dividing Rational Expressions

Find each quotient

x-56 X+3 + (x - 5)

Skills Practice Mixed Expressions

and Complex Fractions Write each mixed expression as a

rational expression

416 + Ii

34b+E c

Simplify each expression

4 a 2 122

11middot s 5 44 5

Refer to the indicated lesson in the Geometry textbook for help with the following problems

Skills ~actice Distance and Midpoints

Use the Pythagorean Theorem to find the distance between each pair of points

5

7 K(2 3) F(4 4)

F

y

G V

(CI x

Use the Distance Formula to find the distance between each pair of points

9 Y(2 0) P(2 6) 1lA(-7 -3B(5 2)

Find the coordinates of the midpoint of a segment having the given endpoints

17 1(3 I) U(5 3) 18 J( -4 2) F(5 -2)

Find the coordinates of the missing endpoint given that P is the midpoint ofNQ

19 N(2 0) P(5 2) 21 Q(3 9 P(-1 5)

Find x andy

Sldlls Practice Special Right Triangles

1 ~24 2 x1 3 x~12 x~ ~32 ~

y y y

~ 4~R 5

16 Y

60 x

bull ID

Refer to the indicated lesson in the Geometry textbook for help with the following problems

Sldlls Practice Special Right Triangles

For Exercises 7-9 use the figure at the right B 60

7 Ifa = 11 find b and c

A 30 c ~~ b

8 If b == 15 find a and c

9 Ifc = 9 find a and b

For Exercises 10 and 11 use the figure at the right Al1B 10 The perimeter of the square is 30 inches Find the length of BC

D~C 11 Find the length of the diagonal BD

12 The perimeter of the equilateral triangle is 60 meters Find the length of an altitude

Skills Practice Trigonometry

Use MST to find sin RJ cos R tan R sin SJ cos Sf and tan S Express each ratio as a fraction and as a decimal to the nearest hundredth

1 r = 16 s = 30 t = 34 2 r = 10 s = 24 t = 26

Use the figure to find each trigonometric ratio Express answers as a fraction and as a decimal rounded to the nearest ten-thousandth

9 tan C 10 sin A 11 cos C

Find x Round to the nearest tenth

18 271~ 19~ AL-----dB A 27 B

Refer to the indicated lesson in the Geometry textbook for help with the following problems

Sldlls Practice Skills Practice The Law of Sines The Law of Cosines2 Find x to the nearest tenth

For Questions 1 and 2 find x to the nearest tenth 1 ~ ~ 2~

32 18

8 Solve MBT Round your answers toS Solve MBC Round your answers to Rthe nearest degree

the nearest tenth

TU76 S

A~ C4r

Refer to the indicated lesson in the Algebra 2 textbook for help with the following problems ac Ice Pr t

e

RelatIons and Functions Determine whether each relation is a function Write yes or no

2 0 R 4 y

Graph each relation or equation and find the domain and range Then determine whether the relation or equation is a function

5 (-4 -1) (4 0) (03) (2 on 6y = 2x - 1

c

y

x

J J

J I

Find each value if f(x) - Z 2 and g~) - -k + 3

7 f(3) 8 (-4)

10 (-2) 11g(-6) 12(m - 2)

Refer to the indicated lesson in the Algebra 2 textbook for help with the following problems

Skills Practice Writing Linear Equations

State the slope and y-intercept of the graph of each equation

32y = -sx + 3 43x+4y=4 8 2) = 6 - 5x63x-2y+6=0

Write an equation in slope-intercept form for each graph

9 1141 II n1 2)

II ICl

II 1(-1 -4)

1 j

I I

x

11

++++(4 -1)

~y I

03) 1

(J x i

(3 -3)~ Ll L~

Write an equation in slope-intercept form for the line that satisfies each set of conditions

12 slope 3 passes through (1 -3)

16 passes through (-1 -2) and (-a 1)

14 slope -2 passes through (0 -5)

Skills Practice Radical Expressions

Simplify

1 Y24 7 4-id2f5 13 (4vi2)(aV20) 19 (1 - V5)(1 + V5)

3ru 9 -f 10 vi2 - 2v3 + Vi08

O 4V50x5 liZ11 j5z 17 2WB - I7s - vi2

-- - ---shy

Refer to the indicated lesson in the Algebra 2 textbook for help with the following problems

Skills Practice Solving Quadratic Equations by Factoring

Solve each equation by factoring

14 x2 + 18x = -812x2 - 100 0

16 2x2 + 5x - 3 == 04x2-4x+3=0

18 3x2 - l3x - 10 == 06x2 - ax - 10 =0

Study Guide and Intervention Completing the Square

Complete the Square To complete the square for a quadratic expression of the form x2 + bx follow these steps

1 Find -+ 2 Square -+ S Add ( Yto x2 + bx

poundxample 1 Find the value of c that makes x2 + 22x + c a perfect square trinomial Then write the trinomial as the square of a binomial

Step 1 b == 22 = 11

Step 2 112 = 121 Step 3 c = 121

The trinomial is x2 + 22x + 121 which can be written as (x + 11)2

example 2 Solve 2x2 - ax - 24 = 0 by completing the square

2x2 - ax - 24 0 Original equation

2x2 - ax - 24 02 = 2 DIvide each side by 2

x2 - 4x - 12 0 il- 4x - 12 is not a perfect square

x2 - 4x = 12 Add 12 to each side

2x - 4x + 4 = 12 + 4 Since (-tt =4add4Ioeachslde

(x - 2)2 16 Factor the square X - 2 = plusmn4 Square Root Property

x = 6 or x = - 2 Solve each equation

The solution set is 6 -2

Find the value of c that makes each trinomial a perfect square Then write the trinomial as a perfect square

25 2 11 x2 - lOx + c 3 x - ax + c bull x + 2x + c

Solve each equation by completingthe square

102x2 - ax + 1 = 0 12 25x2 + 40x - 9 = 0

--_bull _ _ -

This page is for students entering Precalculus Honors Refer to the indicated lesson in the Algebra 2 textbook for help

Practice Skills Practice Monomials Rational Exponents

Simplify Assume that no variable equals G Write each expression in radical form 1

136

Write each radical using rational exponents 12m8y 6

9 -9my 5 V5i -278(-7)

11 160 7 Vi53 18 -(4w-3z-5)(8w)2

Evaluate each expression15 (fd2f4)4(-fd5f)8 (3x-2y3X5xy-8)

17 (x-3)4y-2 Simplify each expression 12 s

17c6 c6

s IS 162

1 5 15 21i 278

JY 2

28-1 ji

Study Guide and Intervention Radical Equations and Inequalities

SOlve each equation

13 + 2xv3 5 2 2vSx + 4 + 1 = 15 S8+Vx+l=2

9 vx2 + 7x = v7x - 9 IG4V2x + 11- 2 = 10

Name ____________-Precalculus Summer Work Answer Sheet

Write the answer to each specified problem on the indicated line on this answer sheet The work supporting these answers must be done neatly on separate paper and included along with this answer sheet and the downloaded worksheets as part of the complete packet Submit the packet to your Precalculus teacher by September 72010 If your Precalculus class is scheduled for second semester you must submit the packet to Mr Perkins or Mr Corbett in the Green Math office by September 72010 Packets will not be accepted after this date

Please note that the last page is part ofthe packet for Honors level only

Algebra 1

Lesson 12-3

2 ____

4 ____

6 ____

8 ____

Lesson 12-4

2 ____

4 ____

6 ____

8 ____

Lesson 12-7

1 ____

3 ____

5 ____

7 ____

9 ____

11 ____

13 ____

15 ____

17 ____

19 ____

21 ____

Lesson 12-8

1 ____

3 ____

11 ____

12 ____

Geometry

Lesson 1-3

5

7

9

11

17

18

19

21

Lesson 7-3

1 ____

2 ____

3 ____

4 ____

5

6

7

8

9

10

lL

12

Lesson 7-4

1

2 ___

9

10

11 ___

18 ___

19 ____

20 ____

Lesson 7-6

2

3

Lesson 7-7

1

2

3

Algebra 1

Lesson 2-1

2 ____

4 ____

5 J

10 x

6

7

8

9

10

11

12

Lesson 2-4 17

2 19

4 21

5 23

6 Lesson 6-3

8 2

9 4

10 6

11 14

12 16

14 18

16

Lesson 5-6 Lesson 6-4

1 1

3 3

5 5

7 8

9 10

11 12

13

15

The following problems are for Honors level only

Lesson 5-1

3

5

7

9

11

13

15

17

Lesson 5p7

1

3

5

7

9

11

13

15

17

19

21

23

Lesson 5-8

1

2

3

9

10

Page 3: City of Brockton BROCKTON PUBLIC SCHOOLS · Refer to the indicated lesson in the Geometry textbook for help . with the following problems. Skills ~actice . Distance and Midpoints

Refer to the indicated lesson in the Geometry textbook for help with the following problems

Skills ~actice Distance and Midpoints

Use the Pythagorean Theorem to find the distance between each pair of points

5

7 K(2 3) F(4 4)

F

y

G V

(CI x

Use the Distance Formula to find the distance between each pair of points

9 Y(2 0) P(2 6) 1lA(-7 -3B(5 2)

Find the coordinates of the midpoint of a segment having the given endpoints

17 1(3 I) U(5 3) 18 J( -4 2) F(5 -2)

Find the coordinates of the missing endpoint given that P is the midpoint ofNQ

19 N(2 0) P(5 2) 21 Q(3 9 P(-1 5)

Find x andy

Sldlls Practice Special Right Triangles

1 ~24 2 x1 3 x~12 x~ ~32 ~

y y y

~ 4~R 5

16 Y

60 x

bull ID

Refer to the indicated lesson in the Geometry textbook for help with the following problems

Sldlls Practice Special Right Triangles

For Exercises 7-9 use the figure at the right B 60

7 Ifa = 11 find b and c

A 30 c ~~ b

8 If b == 15 find a and c

9 Ifc = 9 find a and b

For Exercises 10 and 11 use the figure at the right Al1B 10 The perimeter of the square is 30 inches Find the length of BC

D~C 11 Find the length of the diagonal BD

12 The perimeter of the equilateral triangle is 60 meters Find the length of an altitude

Skills Practice Trigonometry

Use MST to find sin RJ cos R tan R sin SJ cos Sf and tan S Express each ratio as a fraction and as a decimal to the nearest hundredth

1 r = 16 s = 30 t = 34 2 r = 10 s = 24 t = 26

Use the figure to find each trigonometric ratio Express answers as a fraction and as a decimal rounded to the nearest ten-thousandth

9 tan C 10 sin A 11 cos C

Find x Round to the nearest tenth

18 271~ 19~ AL-----dB A 27 B

Refer to the indicated lesson in the Geometry textbook for help with the following problems

Sldlls Practice Skills Practice The Law of Sines The Law of Cosines2 Find x to the nearest tenth

For Questions 1 and 2 find x to the nearest tenth 1 ~ ~ 2~

32 18

8 Solve MBT Round your answers toS Solve MBC Round your answers to Rthe nearest degree

the nearest tenth

TU76 S

A~ C4r

Refer to the indicated lesson in the Algebra 2 textbook for help with the following problems ac Ice Pr t

e

RelatIons and Functions Determine whether each relation is a function Write yes or no

2 0 R 4 y

Graph each relation or equation and find the domain and range Then determine whether the relation or equation is a function

5 (-4 -1) (4 0) (03) (2 on 6y = 2x - 1

c

y

x

J J

J I

Find each value if f(x) - Z 2 and g~) - -k + 3

7 f(3) 8 (-4)

10 (-2) 11g(-6) 12(m - 2)

Refer to the indicated lesson in the Algebra 2 textbook for help with the following problems

Skills Practice Writing Linear Equations

State the slope and y-intercept of the graph of each equation

32y = -sx + 3 43x+4y=4 8 2) = 6 - 5x63x-2y+6=0

Write an equation in slope-intercept form for each graph

9 1141 II n1 2)

II ICl

II 1(-1 -4)

1 j

I I

x

11

++++(4 -1)

~y I

03) 1

(J x i

(3 -3)~ Ll L~

Write an equation in slope-intercept form for the line that satisfies each set of conditions

12 slope 3 passes through (1 -3)

16 passes through (-1 -2) and (-a 1)

14 slope -2 passes through (0 -5)

Skills Practice Radical Expressions

Simplify

1 Y24 7 4-id2f5 13 (4vi2)(aV20) 19 (1 - V5)(1 + V5)

3ru 9 -f 10 vi2 - 2v3 + Vi08

O 4V50x5 liZ11 j5z 17 2WB - I7s - vi2

-- - ---shy

Refer to the indicated lesson in the Algebra 2 textbook for help with the following problems

Skills Practice Solving Quadratic Equations by Factoring

Solve each equation by factoring

14 x2 + 18x = -812x2 - 100 0

16 2x2 + 5x - 3 == 04x2-4x+3=0

18 3x2 - l3x - 10 == 06x2 - ax - 10 =0

Study Guide and Intervention Completing the Square

Complete the Square To complete the square for a quadratic expression of the form x2 + bx follow these steps

1 Find -+ 2 Square -+ S Add ( Yto x2 + bx

poundxample 1 Find the value of c that makes x2 + 22x + c a perfect square trinomial Then write the trinomial as the square of a binomial

Step 1 b == 22 = 11

Step 2 112 = 121 Step 3 c = 121

The trinomial is x2 + 22x + 121 which can be written as (x + 11)2

example 2 Solve 2x2 - ax - 24 = 0 by completing the square

2x2 - ax - 24 0 Original equation

2x2 - ax - 24 02 = 2 DIvide each side by 2

x2 - 4x - 12 0 il- 4x - 12 is not a perfect square

x2 - 4x = 12 Add 12 to each side

2x - 4x + 4 = 12 + 4 Since (-tt =4add4Ioeachslde

(x - 2)2 16 Factor the square X - 2 = plusmn4 Square Root Property

x = 6 or x = - 2 Solve each equation

The solution set is 6 -2

Find the value of c that makes each trinomial a perfect square Then write the trinomial as a perfect square

25 2 11 x2 - lOx + c 3 x - ax + c bull x + 2x + c

Solve each equation by completingthe square

102x2 - ax + 1 = 0 12 25x2 + 40x - 9 = 0

--_bull _ _ -

This page is for students entering Precalculus Honors Refer to the indicated lesson in the Algebra 2 textbook for help

Practice Skills Practice Monomials Rational Exponents

Simplify Assume that no variable equals G Write each expression in radical form 1

136

Write each radical using rational exponents 12m8y 6

9 -9my 5 V5i -278(-7)

11 160 7 Vi53 18 -(4w-3z-5)(8w)2

Evaluate each expression15 (fd2f4)4(-fd5f)8 (3x-2y3X5xy-8)

17 (x-3)4y-2 Simplify each expression 12 s

17c6 c6

s IS 162

1 5 15 21i 278

JY 2

28-1 ji

Study Guide and Intervention Radical Equations and Inequalities

SOlve each equation

13 + 2xv3 5 2 2vSx + 4 + 1 = 15 S8+Vx+l=2

9 vx2 + 7x = v7x - 9 IG4V2x + 11- 2 = 10

Name ____________-Precalculus Summer Work Answer Sheet

Write the answer to each specified problem on the indicated line on this answer sheet The work supporting these answers must be done neatly on separate paper and included along with this answer sheet and the downloaded worksheets as part of the complete packet Submit the packet to your Precalculus teacher by September 72010 If your Precalculus class is scheduled for second semester you must submit the packet to Mr Perkins or Mr Corbett in the Green Math office by September 72010 Packets will not be accepted after this date

Please note that the last page is part ofthe packet for Honors level only

Algebra 1

Lesson 12-3

2 ____

4 ____

6 ____

8 ____

Lesson 12-4

2 ____

4 ____

6 ____

8 ____

Lesson 12-7

1 ____

3 ____

5 ____

7 ____

9 ____

11 ____

13 ____

15 ____

17 ____

19 ____

21 ____

Lesson 12-8

1 ____

3 ____

11 ____

12 ____

Geometry

Lesson 1-3

5

7

9

11

17

18

19

21

Lesson 7-3

1 ____

2 ____

3 ____

4 ____

5

6

7

8

9

10

lL

12

Lesson 7-4

1

2 ___

9

10

11 ___

18 ___

19 ____

20 ____

Lesson 7-6

2

3

Lesson 7-7

1

2

3

Algebra 1

Lesson 2-1

2 ____

4 ____

5 J

10 x

6

7

8

9

10

11

12

Lesson 2-4 17

2 19

4 21

5 23

6 Lesson 6-3

8 2

9 4

10 6

11 14

12 16

14 18

16

Lesson 5-6 Lesson 6-4

1 1

3 3

5 5

7 8

9 10

11 12

13

15

The following problems are for Honors level only

Lesson 5-1

3

5

7

9

11

13

15

17

Lesson 5p7

1

3

5

7

9

11

13

15

17

19

21

23

Lesson 5-8

1

2

3

9

10

Page 4: City of Brockton BROCKTON PUBLIC SCHOOLS · Refer to the indicated lesson in the Geometry textbook for help . with the following problems. Skills ~actice . Distance and Midpoints

Refer to the indicated lesson in the Geometry textbook for help with the following problems

Sldlls Practice Special Right Triangles

For Exercises 7-9 use the figure at the right B 60

7 Ifa = 11 find b and c

A 30 c ~~ b

8 If b == 15 find a and c

9 Ifc = 9 find a and b

For Exercises 10 and 11 use the figure at the right Al1B 10 The perimeter of the square is 30 inches Find the length of BC

D~C 11 Find the length of the diagonal BD

12 The perimeter of the equilateral triangle is 60 meters Find the length of an altitude

Skills Practice Trigonometry

Use MST to find sin RJ cos R tan R sin SJ cos Sf and tan S Express each ratio as a fraction and as a decimal to the nearest hundredth

1 r = 16 s = 30 t = 34 2 r = 10 s = 24 t = 26

Use the figure to find each trigonometric ratio Express answers as a fraction and as a decimal rounded to the nearest ten-thousandth

9 tan C 10 sin A 11 cos C

Find x Round to the nearest tenth

18 271~ 19~ AL-----dB A 27 B

Refer to the indicated lesson in the Geometry textbook for help with the following problems

Sldlls Practice Skills Practice The Law of Sines The Law of Cosines2 Find x to the nearest tenth

For Questions 1 and 2 find x to the nearest tenth 1 ~ ~ 2~

32 18

8 Solve MBT Round your answers toS Solve MBC Round your answers to Rthe nearest degree

the nearest tenth

TU76 S

A~ C4r

Refer to the indicated lesson in the Algebra 2 textbook for help with the following problems ac Ice Pr t

e

RelatIons and Functions Determine whether each relation is a function Write yes or no

2 0 R 4 y

Graph each relation or equation and find the domain and range Then determine whether the relation or equation is a function

5 (-4 -1) (4 0) (03) (2 on 6y = 2x - 1

c

y

x

J J

J I

Find each value if f(x) - Z 2 and g~) - -k + 3

7 f(3) 8 (-4)

10 (-2) 11g(-6) 12(m - 2)

Refer to the indicated lesson in the Algebra 2 textbook for help with the following problems

Skills Practice Writing Linear Equations

State the slope and y-intercept of the graph of each equation

32y = -sx + 3 43x+4y=4 8 2) = 6 - 5x63x-2y+6=0

Write an equation in slope-intercept form for each graph

9 1141 II n1 2)

II ICl

II 1(-1 -4)

1 j

I I

x

11

++++(4 -1)

~y I

03) 1

(J x i

(3 -3)~ Ll L~

Write an equation in slope-intercept form for the line that satisfies each set of conditions

12 slope 3 passes through (1 -3)

16 passes through (-1 -2) and (-a 1)

14 slope -2 passes through (0 -5)

Skills Practice Radical Expressions

Simplify

1 Y24 7 4-id2f5 13 (4vi2)(aV20) 19 (1 - V5)(1 + V5)

3ru 9 -f 10 vi2 - 2v3 + Vi08

O 4V50x5 liZ11 j5z 17 2WB - I7s - vi2

-- - ---shy

Refer to the indicated lesson in the Algebra 2 textbook for help with the following problems

Skills Practice Solving Quadratic Equations by Factoring

Solve each equation by factoring

14 x2 + 18x = -812x2 - 100 0

16 2x2 + 5x - 3 == 04x2-4x+3=0

18 3x2 - l3x - 10 == 06x2 - ax - 10 =0

Study Guide and Intervention Completing the Square

Complete the Square To complete the square for a quadratic expression of the form x2 + bx follow these steps

1 Find -+ 2 Square -+ S Add ( Yto x2 + bx

poundxample 1 Find the value of c that makes x2 + 22x + c a perfect square trinomial Then write the trinomial as the square of a binomial

Step 1 b == 22 = 11

Step 2 112 = 121 Step 3 c = 121

The trinomial is x2 + 22x + 121 which can be written as (x + 11)2

example 2 Solve 2x2 - ax - 24 = 0 by completing the square

2x2 - ax - 24 0 Original equation

2x2 - ax - 24 02 = 2 DIvide each side by 2

x2 - 4x - 12 0 il- 4x - 12 is not a perfect square

x2 - 4x = 12 Add 12 to each side

2x - 4x + 4 = 12 + 4 Since (-tt =4add4Ioeachslde

(x - 2)2 16 Factor the square X - 2 = plusmn4 Square Root Property

x = 6 or x = - 2 Solve each equation

The solution set is 6 -2

Find the value of c that makes each trinomial a perfect square Then write the trinomial as a perfect square

25 2 11 x2 - lOx + c 3 x - ax + c bull x + 2x + c

Solve each equation by completingthe square

102x2 - ax + 1 = 0 12 25x2 + 40x - 9 = 0

--_bull _ _ -

This page is for students entering Precalculus Honors Refer to the indicated lesson in the Algebra 2 textbook for help

Practice Skills Practice Monomials Rational Exponents

Simplify Assume that no variable equals G Write each expression in radical form 1

136

Write each radical using rational exponents 12m8y 6

9 -9my 5 V5i -278(-7)

11 160 7 Vi53 18 -(4w-3z-5)(8w)2

Evaluate each expression15 (fd2f4)4(-fd5f)8 (3x-2y3X5xy-8)

17 (x-3)4y-2 Simplify each expression 12 s

17c6 c6

s IS 162

1 5 15 21i 278

JY 2

28-1 ji

Study Guide and Intervention Radical Equations and Inequalities

SOlve each equation

13 + 2xv3 5 2 2vSx + 4 + 1 = 15 S8+Vx+l=2

9 vx2 + 7x = v7x - 9 IG4V2x + 11- 2 = 10

Name ____________-Precalculus Summer Work Answer Sheet

Write the answer to each specified problem on the indicated line on this answer sheet The work supporting these answers must be done neatly on separate paper and included along with this answer sheet and the downloaded worksheets as part of the complete packet Submit the packet to your Precalculus teacher by September 72010 If your Precalculus class is scheduled for second semester you must submit the packet to Mr Perkins or Mr Corbett in the Green Math office by September 72010 Packets will not be accepted after this date

Please note that the last page is part ofthe packet for Honors level only

Algebra 1

Lesson 12-3

2 ____

4 ____

6 ____

8 ____

Lesson 12-4

2 ____

4 ____

6 ____

8 ____

Lesson 12-7

1 ____

3 ____

5 ____

7 ____

9 ____

11 ____

13 ____

15 ____

17 ____

19 ____

21 ____

Lesson 12-8

1 ____

3 ____

11 ____

12 ____

Geometry

Lesson 1-3

5

7

9

11

17

18

19

21

Lesson 7-3

1 ____

2 ____

3 ____

4 ____

5

6

7

8

9

10

lL

12

Lesson 7-4

1

2 ___

9

10

11 ___

18 ___

19 ____

20 ____

Lesson 7-6

2

3

Lesson 7-7

1

2

3

Algebra 1

Lesson 2-1

2 ____

4 ____

5 J

10 x

6

7

8

9

10

11

12

Lesson 2-4 17

2 19

4 21

5 23

6 Lesson 6-3

8 2

9 4

10 6

11 14

12 16

14 18

16

Lesson 5-6 Lesson 6-4

1 1

3 3

5 5

7 8

9 10

11 12

13

15

The following problems are for Honors level only

Lesson 5-1

3

5

7

9

11

13

15

17

Lesson 5p7

1

3

5

7

9

11

13

15

17

19

21

23

Lesson 5-8

1

2

3

9

10

Page 5: City of Brockton BROCKTON PUBLIC SCHOOLS · Refer to the indicated lesson in the Geometry textbook for help . with the following problems. Skills ~actice . Distance and Midpoints

Refer to the indicated lesson in the Geometry textbook for help with the following problems

Sldlls Practice Skills Practice The Law of Sines The Law of Cosines2 Find x to the nearest tenth

For Questions 1 and 2 find x to the nearest tenth 1 ~ ~ 2~

32 18

8 Solve MBT Round your answers toS Solve MBC Round your answers to Rthe nearest degree

the nearest tenth

TU76 S

A~ C4r

Refer to the indicated lesson in the Algebra 2 textbook for help with the following problems ac Ice Pr t

e

RelatIons and Functions Determine whether each relation is a function Write yes or no

2 0 R 4 y

Graph each relation or equation and find the domain and range Then determine whether the relation or equation is a function

5 (-4 -1) (4 0) (03) (2 on 6y = 2x - 1

c

y

x

J J

J I

Find each value if f(x) - Z 2 and g~) - -k + 3

7 f(3) 8 (-4)

10 (-2) 11g(-6) 12(m - 2)

Refer to the indicated lesson in the Algebra 2 textbook for help with the following problems

Skills Practice Writing Linear Equations

State the slope and y-intercept of the graph of each equation

32y = -sx + 3 43x+4y=4 8 2) = 6 - 5x63x-2y+6=0

Write an equation in slope-intercept form for each graph

9 1141 II n1 2)

II ICl

II 1(-1 -4)

1 j

I I

x

11

++++(4 -1)

~y I

03) 1

(J x i

(3 -3)~ Ll L~

Write an equation in slope-intercept form for the line that satisfies each set of conditions

12 slope 3 passes through (1 -3)

16 passes through (-1 -2) and (-a 1)

14 slope -2 passes through (0 -5)

Skills Practice Radical Expressions

Simplify

1 Y24 7 4-id2f5 13 (4vi2)(aV20) 19 (1 - V5)(1 + V5)

3ru 9 -f 10 vi2 - 2v3 + Vi08

O 4V50x5 liZ11 j5z 17 2WB - I7s - vi2

-- - ---shy

Refer to the indicated lesson in the Algebra 2 textbook for help with the following problems

Skills Practice Solving Quadratic Equations by Factoring

Solve each equation by factoring

14 x2 + 18x = -812x2 - 100 0

16 2x2 + 5x - 3 == 04x2-4x+3=0

18 3x2 - l3x - 10 == 06x2 - ax - 10 =0

Study Guide and Intervention Completing the Square

Complete the Square To complete the square for a quadratic expression of the form x2 + bx follow these steps

1 Find -+ 2 Square -+ S Add ( Yto x2 + bx

poundxample 1 Find the value of c that makes x2 + 22x + c a perfect square trinomial Then write the trinomial as the square of a binomial

Step 1 b == 22 = 11

Step 2 112 = 121 Step 3 c = 121

The trinomial is x2 + 22x + 121 which can be written as (x + 11)2

example 2 Solve 2x2 - ax - 24 = 0 by completing the square

2x2 - ax - 24 0 Original equation

2x2 - ax - 24 02 = 2 DIvide each side by 2

x2 - 4x - 12 0 il- 4x - 12 is not a perfect square

x2 - 4x = 12 Add 12 to each side

2x - 4x + 4 = 12 + 4 Since (-tt =4add4Ioeachslde

(x - 2)2 16 Factor the square X - 2 = plusmn4 Square Root Property

x = 6 or x = - 2 Solve each equation

The solution set is 6 -2

Find the value of c that makes each trinomial a perfect square Then write the trinomial as a perfect square

25 2 11 x2 - lOx + c 3 x - ax + c bull x + 2x + c

Solve each equation by completingthe square

102x2 - ax + 1 = 0 12 25x2 + 40x - 9 = 0

--_bull _ _ -

This page is for students entering Precalculus Honors Refer to the indicated lesson in the Algebra 2 textbook for help

Practice Skills Practice Monomials Rational Exponents

Simplify Assume that no variable equals G Write each expression in radical form 1

136

Write each radical using rational exponents 12m8y 6

9 -9my 5 V5i -278(-7)

11 160 7 Vi53 18 -(4w-3z-5)(8w)2

Evaluate each expression15 (fd2f4)4(-fd5f)8 (3x-2y3X5xy-8)

17 (x-3)4y-2 Simplify each expression 12 s

17c6 c6

s IS 162

1 5 15 21i 278

JY 2

28-1 ji

Study Guide and Intervention Radical Equations and Inequalities

SOlve each equation

13 + 2xv3 5 2 2vSx + 4 + 1 = 15 S8+Vx+l=2

9 vx2 + 7x = v7x - 9 IG4V2x + 11- 2 = 10

Name ____________-Precalculus Summer Work Answer Sheet

Write the answer to each specified problem on the indicated line on this answer sheet The work supporting these answers must be done neatly on separate paper and included along with this answer sheet and the downloaded worksheets as part of the complete packet Submit the packet to your Precalculus teacher by September 72010 If your Precalculus class is scheduled for second semester you must submit the packet to Mr Perkins or Mr Corbett in the Green Math office by September 72010 Packets will not be accepted after this date

Please note that the last page is part ofthe packet for Honors level only

Algebra 1

Lesson 12-3

2 ____

4 ____

6 ____

8 ____

Lesson 12-4

2 ____

4 ____

6 ____

8 ____

Lesson 12-7

1 ____

3 ____

5 ____

7 ____

9 ____

11 ____

13 ____

15 ____

17 ____

19 ____

21 ____

Lesson 12-8

1 ____

3 ____

11 ____

12 ____

Geometry

Lesson 1-3

5

7

9

11

17

18

19

21

Lesson 7-3

1 ____

2 ____

3 ____

4 ____

5

6

7

8

9

10

lL

12

Lesson 7-4

1

2 ___

9

10

11 ___

18 ___

19 ____

20 ____

Lesson 7-6

2

3

Lesson 7-7

1

2

3

Algebra 1

Lesson 2-1

2 ____

4 ____

5 J

10 x

6

7

8

9

10

11

12

Lesson 2-4 17

2 19

4 21

5 23

6 Lesson 6-3

8 2

9 4

10 6

11 14

12 16

14 18

16

Lesson 5-6 Lesson 6-4

1 1

3 3

5 5

7 8

9 10

11 12

13

15

The following problems are for Honors level only

Lesson 5-1

3

5

7

9

11

13

15

17

Lesson 5p7

1

3

5

7

9

11

13

15

17

19

21

23

Lesson 5-8

1

2

3

9

10

Page 6: City of Brockton BROCKTON PUBLIC SCHOOLS · Refer to the indicated lesson in the Geometry textbook for help . with the following problems. Skills ~actice . Distance and Midpoints

Refer to the indicated lesson in the Algebra 2 textbook for help with the following problems

Skills Practice Writing Linear Equations

State the slope and y-intercept of the graph of each equation

32y = -sx + 3 43x+4y=4 8 2) = 6 - 5x63x-2y+6=0

Write an equation in slope-intercept form for each graph

9 1141 II n1 2)

II ICl

II 1(-1 -4)

1 j

I I

x

11

++++(4 -1)

~y I

03) 1

(J x i

(3 -3)~ Ll L~

Write an equation in slope-intercept form for the line that satisfies each set of conditions

12 slope 3 passes through (1 -3)

16 passes through (-1 -2) and (-a 1)

14 slope -2 passes through (0 -5)

Skills Practice Radical Expressions

Simplify

1 Y24 7 4-id2f5 13 (4vi2)(aV20) 19 (1 - V5)(1 + V5)

3ru 9 -f 10 vi2 - 2v3 + Vi08

O 4V50x5 liZ11 j5z 17 2WB - I7s - vi2

-- - ---shy

Refer to the indicated lesson in the Algebra 2 textbook for help with the following problems

Skills Practice Solving Quadratic Equations by Factoring

Solve each equation by factoring

14 x2 + 18x = -812x2 - 100 0

16 2x2 + 5x - 3 == 04x2-4x+3=0

18 3x2 - l3x - 10 == 06x2 - ax - 10 =0

Study Guide and Intervention Completing the Square

Complete the Square To complete the square for a quadratic expression of the form x2 + bx follow these steps

1 Find -+ 2 Square -+ S Add ( Yto x2 + bx

poundxample 1 Find the value of c that makes x2 + 22x + c a perfect square trinomial Then write the trinomial as the square of a binomial

Step 1 b == 22 = 11

Step 2 112 = 121 Step 3 c = 121

The trinomial is x2 + 22x + 121 which can be written as (x + 11)2

example 2 Solve 2x2 - ax - 24 = 0 by completing the square

2x2 - ax - 24 0 Original equation

2x2 - ax - 24 02 = 2 DIvide each side by 2

x2 - 4x - 12 0 il- 4x - 12 is not a perfect square

x2 - 4x = 12 Add 12 to each side

2x - 4x + 4 = 12 + 4 Since (-tt =4add4Ioeachslde

(x - 2)2 16 Factor the square X - 2 = plusmn4 Square Root Property

x = 6 or x = - 2 Solve each equation

The solution set is 6 -2

Find the value of c that makes each trinomial a perfect square Then write the trinomial as a perfect square

25 2 11 x2 - lOx + c 3 x - ax + c bull x + 2x + c

Solve each equation by completingthe square

102x2 - ax + 1 = 0 12 25x2 + 40x - 9 = 0

--_bull _ _ -

This page is for students entering Precalculus Honors Refer to the indicated lesson in the Algebra 2 textbook for help

Practice Skills Practice Monomials Rational Exponents

Simplify Assume that no variable equals G Write each expression in radical form 1

136

Write each radical using rational exponents 12m8y 6

9 -9my 5 V5i -278(-7)

11 160 7 Vi53 18 -(4w-3z-5)(8w)2

Evaluate each expression15 (fd2f4)4(-fd5f)8 (3x-2y3X5xy-8)

17 (x-3)4y-2 Simplify each expression 12 s

17c6 c6

s IS 162

1 5 15 21i 278

JY 2

28-1 ji

Study Guide and Intervention Radical Equations and Inequalities

SOlve each equation

13 + 2xv3 5 2 2vSx + 4 + 1 = 15 S8+Vx+l=2

9 vx2 + 7x = v7x - 9 IG4V2x + 11- 2 = 10

Name ____________-Precalculus Summer Work Answer Sheet

Write the answer to each specified problem on the indicated line on this answer sheet The work supporting these answers must be done neatly on separate paper and included along with this answer sheet and the downloaded worksheets as part of the complete packet Submit the packet to your Precalculus teacher by September 72010 If your Precalculus class is scheduled for second semester you must submit the packet to Mr Perkins or Mr Corbett in the Green Math office by September 72010 Packets will not be accepted after this date

Please note that the last page is part ofthe packet for Honors level only

Algebra 1

Lesson 12-3

2 ____

4 ____

6 ____

8 ____

Lesson 12-4

2 ____

4 ____

6 ____

8 ____

Lesson 12-7

1 ____

3 ____

5 ____

7 ____

9 ____

11 ____

13 ____

15 ____

17 ____

19 ____

21 ____

Lesson 12-8

1 ____

3 ____

11 ____

12 ____

Geometry

Lesson 1-3

5

7

9

11

17

18

19

21

Lesson 7-3

1 ____

2 ____

3 ____

4 ____

5

6

7

8

9

10

lL

12

Lesson 7-4

1

2 ___

9

10

11 ___

18 ___

19 ____

20 ____

Lesson 7-6

2

3

Lesson 7-7

1

2

3

Algebra 1

Lesson 2-1

2 ____

4 ____

5 J

10 x

6

7

8

9

10

11

12

Lesson 2-4 17

2 19

4 21

5 23

6 Lesson 6-3

8 2

9 4

10 6

11 14

12 16

14 18

16

Lesson 5-6 Lesson 6-4

1 1

3 3

5 5

7 8

9 10

11 12

13

15

The following problems are for Honors level only

Lesson 5-1

3

5

7

9

11

13

15

17

Lesson 5p7

1

3

5

7

9

11

13

15

17

19

21

23

Lesson 5-8

1

2

3

9

10

Page 7: City of Brockton BROCKTON PUBLIC SCHOOLS · Refer to the indicated lesson in the Geometry textbook for help . with the following problems. Skills ~actice . Distance and Midpoints

-- - ---shy

Refer to the indicated lesson in the Algebra 2 textbook for help with the following problems

Skills Practice Solving Quadratic Equations by Factoring

Solve each equation by factoring

14 x2 + 18x = -812x2 - 100 0

16 2x2 + 5x - 3 == 04x2-4x+3=0

18 3x2 - l3x - 10 == 06x2 - ax - 10 =0

Study Guide and Intervention Completing the Square

Complete the Square To complete the square for a quadratic expression of the form x2 + bx follow these steps

1 Find -+ 2 Square -+ S Add ( Yto x2 + bx

poundxample 1 Find the value of c that makes x2 + 22x + c a perfect square trinomial Then write the trinomial as the square of a binomial

Step 1 b == 22 = 11

Step 2 112 = 121 Step 3 c = 121

The trinomial is x2 + 22x + 121 which can be written as (x + 11)2

example 2 Solve 2x2 - ax - 24 = 0 by completing the square

2x2 - ax - 24 0 Original equation

2x2 - ax - 24 02 = 2 DIvide each side by 2

x2 - 4x - 12 0 il- 4x - 12 is not a perfect square

x2 - 4x = 12 Add 12 to each side

2x - 4x + 4 = 12 + 4 Since (-tt =4add4Ioeachslde

(x - 2)2 16 Factor the square X - 2 = plusmn4 Square Root Property

x = 6 or x = - 2 Solve each equation

The solution set is 6 -2

Find the value of c that makes each trinomial a perfect square Then write the trinomial as a perfect square

25 2 11 x2 - lOx + c 3 x - ax + c bull x + 2x + c

Solve each equation by completingthe square

102x2 - ax + 1 = 0 12 25x2 + 40x - 9 = 0

--_bull _ _ -

This page is for students entering Precalculus Honors Refer to the indicated lesson in the Algebra 2 textbook for help

Practice Skills Practice Monomials Rational Exponents

Simplify Assume that no variable equals G Write each expression in radical form 1

136

Write each radical using rational exponents 12m8y 6

9 -9my 5 V5i -278(-7)

11 160 7 Vi53 18 -(4w-3z-5)(8w)2

Evaluate each expression15 (fd2f4)4(-fd5f)8 (3x-2y3X5xy-8)

17 (x-3)4y-2 Simplify each expression 12 s

17c6 c6

s IS 162

1 5 15 21i 278

JY 2

28-1 ji

Study Guide and Intervention Radical Equations and Inequalities

SOlve each equation

13 + 2xv3 5 2 2vSx + 4 + 1 = 15 S8+Vx+l=2

9 vx2 + 7x = v7x - 9 IG4V2x + 11- 2 = 10

Name ____________-Precalculus Summer Work Answer Sheet

Write the answer to each specified problem on the indicated line on this answer sheet The work supporting these answers must be done neatly on separate paper and included along with this answer sheet and the downloaded worksheets as part of the complete packet Submit the packet to your Precalculus teacher by September 72010 If your Precalculus class is scheduled for second semester you must submit the packet to Mr Perkins or Mr Corbett in the Green Math office by September 72010 Packets will not be accepted after this date

Please note that the last page is part ofthe packet for Honors level only

Algebra 1

Lesson 12-3

2 ____

4 ____

6 ____

8 ____

Lesson 12-4

2 ____

4 ____

6 ____

8 ____

Lesson 12-7

1 ____

3 ____

5 ____

7 ____

9 ____

11 ____

13 ____

15 ____

17 ____

19 ____

21 ____

Lesson 12-8

1 ____

3 ____

11 ____

12 ____

Geometry

Lesson 1-3

5

7

9

11

17

18

19

21

Lesson 7-3

1 ____

2 ____

3 ____

4 ____

5

6

7

8

9

10

lL

12

Lesson 7-4

1

2 ___

9

10

11 ___

18 ___

19 ____

20 ____

Lesson 7-6

2

3

Lesson 7-7

1

2

3

Algebra 1

Lesson 2-1

2 ____

4 ____

5 J

10 x

6

7

8

9

10

11

12

Lesson 2-4 17

2 19

4 21

5 23

6 Lesson 6-3

8 2

9 4

10 6

11 14

12 16

14 18

16

Lesson 5-6 Lesson 6-4

1 1

3 3

5 5

7 8

9 10

11 12

13

15

The following problems are for Honors level only

Lesson 5-1

3

5

7

9

11

13

15

17

Lesson 5p7

1

3

5

7

9

11

13

15

17

19

21

23

Lesson 5-8

1

2

3

9

10

Page 8: City of Brockton BROCKTON PUBLIC SCHOOLS · Refer to the indicated lesson in the Geometry textbook for help . with the following problems. Skills ~actice . Distance and Midpoints

--_bull _ _ -

This page is for students entering Precalculus Honors Refer to the indicated lesson in the Algebra 2 textbook for help

Practice Skills Practice Monomials Rational Exponents

Simplify Assume that no variable equals G Write each expression in radical form 1

136

Write each radical using rational exponents 12m8y 6

9 -9my 5 V5i -278(-7)

11 160 7 Vi53 18 -(4w-3z-5)(8w)2

Evaluate each expression15 (fd2f4)4(-fd5f)8 (3x-2y3X5xy-8)

17 (x-3)4y-2 Simplify each expression 12 s

17c6 c6

s IS 162

1 5 15 21i 278

JY 2

28-1 ji

Study Guide and Intervention Radical Equations and Inequalities

SOlve each equation

13 + 2xv3 5 2 2vSx + 4 + 1 = 15 S8+Vx+l=2

9 vx2 + 7x = v7x - 9 IG4V2x + 11- 2 = 10

Name ____________-Precalculus Summer Work Answer Sheet

Write the answer to each specified problem on the indicated line on this answer sheet The work supporting these answers must be done neatly on separate paper and included along with this answer sheet and the downloaded worksheets as part of the complete packet Submit the packet to your Precalculus teacher by September 72010 If your Precalculus class is scheduled for second semester you must submit the packet to Mr Perkins or Mr Corbett in the Green Math office by September 72010 Packets will not be accepted after this date

Please note that the last page is part ofthe packet for Honors level only

Algebra 1

Lesson 12-3

2 ____

4 ____

6 ____

8 ____

Lesson 12-4

2 ____

4 ____

6 ____

8 ____

Lesson 12-7

1 ____

3 ____

5 ____

7 ____

9 ____

11 ____

13 ____

15 ____

17 ____

19 ____

21 ____

Lesson 12-8

1 ____

3 ____

11 ____

12 ____

Geometry

Lesson 1-3

5

7

9

11

17

18

19

21

Lesson 7-3

1 ____

2 ____

3 ____

4 ____

5

6

7

8

9

10

lL

12

Lesson 7-4

1

2 ___

9

10

11 ___

18 ___

19 ____

20 ____

Lesson 7-6

2

3

Lesson 7-7

1

2

3

Algebra 1

Lesson 2-1

2 ____

4 ____

5 J

10 x

6

7

8

9

10

11

12

Lesson 2-4 17

2 19

4 21

5 23

6 Lesson 6-3

8 2

9 4

10 6

11 14

12 16

14 18

16

Lesson 5-6 Lesson 6-4

1 1

3 3

5 5

7 8

9 10

11 12

13

15

The following problems are for Honors level only

Lesson 5-1

3

5

7

9

11

13

15

17

Lesson 5p7

1

3

5

7

9

11

13

15

17

19

21

23

Lesson 5-8

1

2

3

9

10

Page 9: City of Brockton BROCKTON PUBLIC SCHOOLS · Refer to the indicated lesson in the Geometry textbook for help . with the following problems. Skills ~actice . Distance and Midpoints

Name ____________-Precalculus Summer Work Answer Sheet

Write the answer to each specified problem on the indicated line on this answer sheet The work supporting these answers must be done neatly on separate paper and included along with this answer sheet and the downloaded worksheets as part of the complete packet Submit the packet to your Precalculus teacher by September 72010 If your Precalculus class is scheduled for second semester you must submit the packet to Mr Perkins or Mr Corbett in the Green Math office by September 72010 Packets will not be accepted after this date

Please note that the last page is part ofthe packet for Honors level only

Algebra 1

Lesson 12-3

2 ____

4 ____

6 ____

8 ____

Lesson 12-4

2 ____

4 ____

6 ____

8 ____

Lesson 12-7

1 ____

3 ____

5 ____

7 ____

9 ____

11 ____

13 ____

15 ____

17 ____

19 ____

21 ____

Lesson 12-8

1 ____

3 ____

11 ____

12 ____

Geometry

Lesson 1-3

5

7

9

11

17

18

19

21

Lesson 7-3

1 ____

2 ____

3 ____

4 ____

5

6

7

8

9

10

lL

12

Lesson 7-4

1

2 ___

9

10

11 ___

18 ___

19 ____

20 ____

Lesson 7-6

2

3

Lesson 7-7

1

2

3

Algebra 1

Lesson 2-1

2 ____

4 ____

5 J

10 x

6

7

8

9

10

11

12

Lesson 2-4 17

2 19

4 21

5 23

6 Lesson 6-3

8 2

9 4

10 6

11 14

12 16

14 18

16

Lesson 5-6 Lesson 6-4

1 1

3 3

5 5

7 8

9 10

11 12

13

15

The following problems are for Honors level only

Lesson 5-1

3

5

7

9

11

13

15

17

Lesson 5p7

1

3

5

7

9

11

13

15

17

19

21

23

Lesson 5-8

1

2

3

9

10

Page 10: City of Brockton BROCKTON PUBLIC SCHOOLS · Refer to the indicated lesson in the Geometry textbook for help . with the following problems. Skills ~actice . Distance and Midpoints

5

6

7

8

9

10

lL

12

Lesson 7-4

1

2 ___

9

10

11 ___

18 ___

19 ____

20 ____

Lesson 7-6

2

3

Lesson 7-7

1

2

3

Algebra 1

Lesson 2-1

2 ____

4 ____

5 J

10 x

6

7

8

9

10

11

12

Lesson 2-4 17

2 19

4 21

5 23

6 Lesson 6-3

8 2

9 4

10 6

11 14

12 16

14 18

16

Lesson 5-6 Lesson 6-4

1 1

3 3

5 5

7 8

9 10

11 12

13

15

The following problems are for Honors level only

Lesson 5-1

3

5

7

9

11

13

15

17

Lesson 5p7

1

3

5

7

9

11

13

15

17

19

21

23

Lesson 5-8

1

2

3

9

10

Page 11: City of Brockton BROCKTON PUBLIC SCHOOLS · Refer to the indicated lesson in the Geometry textbook for help . with the following problems. Skills ~actice . Distance and Midpoints

5 J

10 x

6

7

8

9

10

11

12

Lesson 2-4 17

2 19

4 21

5 23

6 Lesson 6-3

8 2

9 4

10 6

11 14

12 16

14 18

16

Lesson 5-6 Lesson 6-4

1 1

3 3

5 5

7 8

9 10

11 12

13

15

The following problems are for Honors level only

Lesson 5-1

3

5

7

9

11

13

15

17

Lesson 5p7

1

3

5

7

9

11

13

15

17

19

21

23

Lesson 5-8

1

2

3

9

10

Page 12: City of Brockton BROCKTON PUBLIC SCHOOLS · Refer to the indicated lesson in the Geometry textbook for help . with the following problems. Skills ~actice . Distance and Midpoints

The following problems are for Honors level only

Lesson 5-1

3

5

7

9

11

13

15

17

Lesson 5p7

1

3

5

7

9

11

13

15

17

19

21

23

Lesson 5-8

1

2

3

9

10