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Honors Geometry Summer Packet
This packet is to be completed by students entering into Honors
Geometry next school year.
Directions: Please complete the following packet before the start of
next school year. All odd problems in this packet are required, all even
numbered problems are optional. All work for this packet should be
completed on a separate piece of paper and saved to turn in with the
final packet. Answers should be transferred from your work to the
packet. If you have questions while completing the packet, use what
resources you have available to you (friends, family, the internet, last
year's online textbook if available). All work and the original packet
should be brought to class on the first day of school to be turned in. I
recommend using a folder of preferably a binder to hold and organize
the packet and the work.
In order to stay on top of the work, I recommend that you complete
about 3 pages per week. Don't leave it all for the last minute! This
packet is meant to review previously learned concepts that will be
essential to your success in Honors Geometry. Remember, you get out
of it what you put into it!
Good luck and have a great summer!
NAME CLASS DATE
12 6 SolviLig Proportions UNIT 4
0 JECTIVE: Solving a proportion for an unknown term
A proportion is an equality of two ratios. The four quantities in the proportion are called terms. If the ratios are equal, then the proportion is true.
Tell whether the proportion = is true or false. 9 3
Sohitwii 4 2
Since 4 X 3 9 X 2, you may conclude that
Therefore, the ratios are not equal. The proportion is false.
EXAMPLE 1
If a proportion involves an unknown, represented by a variable, you can find the number that makes the proportion true. To solve a proportion, find the cross products and set them equal to each other. Solve the equation that results.
If -a = ' -c
then ad = bc. b d
x 35 Solve -8 =
II Solution
To make the proportion true, the cross products must be equal. x _ 35 8 40
40x = 8 X 35 Set cross products equal. 8 '35
x = = 7 Divide each side by 40. 40
Therefore, x = 7.
Tell whether the given proportion is true or false.
15 45 ,.) 13 25 35 15 1.
6 18 - 7 143.9 - 4
Solve each proportion.
x 30 5 Y a 18 4. -6 =
= To- 6. = 3913
1 _ z 3 _ t 1 4
9. 1-3- = -a
7 5 9 18 10. 'I- = --3- 11. - i_ ----- 12. T -9- = -n-i c 5
128 Unit 4 Ratio, Proportion, and Percent Making Sense of Numbers
EXAMPLE 2
Copyrigh t
© by H
olt, R
i nehart an
d W
inst on
. All rights
reserved.
0 JECTIVE Using proportions to find unknown lengths of sides in similar geometric figures
Two geometric figures in the plane are similar if the ratios of the lengths of corresponding sides are equal.
Triangles A : C and XYZ shown at right are similar triangles. Find XY and. YZ.
6
9
NAME CLASS DATE
S Ins Involving Si
Ge4i1IC
Solution Triangle XYZ ---> XY _ 7.5 Triangle ABC 3.1 6.0
6(XY) = 3.1 X 7.56 XY = 3.875
So, XY= 3.875.
Triangle XYZ YZ _ 7.5 Triangle ABC --> 4.3 6.0
6(YZ) = 4.3 X 7.5 YZ = 5.375
So, YZ = 5.375.
Exercises 1-3: Figures LKMN and PQRS are similar.
1. Find PQ.
2. Find QR
3, Find RS.
Exercises 4-6: Figures CDEF and GHJK are similar.
4. Find DE.
5. Find ER 2.2
6. Find FC.
Exercises 7-9: Figures UVWX and MATH are similar.
7. Find VW.
8. Find TH.
9. Find UX.
130 Unit 4 Ratio, Proportion, and Percent Making Sense of Numbers
Copyright ©
by H
olt, Ri neh
art and W
i nston
. All rights
reserved.
UNIT 4.
5
A
V
2 3 3
X 4
NAME CLASS DATE
ig S--ares and I onaI Square Roots
0 JECTIVE Finding the square of a rational number and the square root of a perfect square
Recall that the expression a2 represents the product of a with itself, or a ° a.
Simplify. a. (—,\ 2
Soluti n
/ 5
)
2 _ 5\ /_5\ 25 a. =
— 7 \ \ 7/ 4-9
/ 1 \ 2 b. —2—
\ 3 /
b 7 1)2 --
/_7) (_7
)
= 49 _ 5 4 . —2j. =- 3 3 9 — 9
EXAMPLE 1
If there is a number, x, such that x2 = a, then x is called a square root of a. A rational number is a perfect square if its square roots are rational numbers.
49 Find all the square roots of each number. a. 144 b. 64 Solution
a. Since 12 X 12 = 144 and (-12) X (-12) = 144, the square roots of 144 are 12 and —12, denoted ±12.
EXAMPLE 2
49 7 b. Since 7 X 7 = 49 and 8 X 8 =--- 64, one square root of
. &Ti g.
7 The other square root is
Simplify.
1\ 2 2. (11\2 1.
2
4. /31 \ 2 1 \ 2 5. (-5-2 \ 3 /
3. (-0.3)2
6. (-1.3)2
9. 100
144 12. 25
225 15.
100
Find all the square roots of each number.
7. 25 8.1
49 81
10. 11. 100
400 9 13. 14.16
192 Unit 6 Rational and Irrational Numbers Making Sense of Numbers
Copyright ©
by Holt, R
i nehart and Wi nston. A
ll r ights reserved .
UNIT
NAME CLASS DATE
Approximating irrational Square Roots
OBJECTIVE: Finding a decimal approximation to a square root that is not rational
If a rational number is not a perfect square, then its square roots are irrational numbers. You can approximate the roots by finding rational number approximations.
Two integers are consecutive if they differ by 1. The integers 7 and 8 are consecutive. The integers 7 and 9 are not.
Find two consecutive integers between which V52 lies.
S.
Note Note that 72 = 49 and 82 = 64. Since 49 < 52 < 64, V52 is between 7 and 8.
Using trial and error, you can find a decimal approximation to a square root.
Approximate V52 to the nearest tenth.
Soitation
Since V32-, is closer to 7 than it is to 8, test 7.2 and 7.3. 7.22 = 51.84 7.32 = 53.29
So, V52 is between 7.2 and 7.3.
Since V52 is closer to 7.2 than it is to 7.3, test 7.21 and 7.22. 7.212 = 51.9841 7.222 = 52.1284
Since 7.212 is closer to 52 than 7.222 is, V52 is closer to 7.21 than it is to 7.22.
To the nearest tenth, V52 is about 7.2.
Approximate each square root to the nearest tenth. First find two consecutive integers between which the square root lies, as in Example 1, and then calculate an approximation, as in Example 2.
1. V-2- 2. -V-- 3. V7 4. V11
5. V10 6. V15 7. V30 8. V83
9. V120 10. V163 11. V269 12. V399
Making Sense of Numbers Unit 6 Rational and Irrational Numbers 193
EXAMPLE
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t, R
ineh
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Name Class Date
Practice 7-2 Solving Systems Using Substitution
Solve each system using substitution. Write no solution or infinitely many solutions where appropriate.
1. y = x 2y = —2x + 4
2. y =- x + 8 y = 5x
3. y = 3x — 9 y = 2x — 4
4, y = x — 7 3x + y = 9
5. y = 2x — 5 6. 4x — 2y = —2x + y = —5 x+ y = —6
7. 4x + y = 12 y = —4x + 5
9. 2x + 4y = —8 10. 6x + 2y = 10 —3x + y = 2 -\ y = —3x + 5
y 2x + 7 y = 5x + 4
11. 4x — 2y = 8
y = 2x + 9
12. 5x + 1y = 10 1 —5-y = 2 — x
C,
13. 2x + y = —1 0_
x + y = —2
1 14. y = —7tx + 5
x + 4y = —8
a
15. y = + 1
0 2x + 6y =-- 6
-0
0 cu • 17. 3x — y = —9 a_
x + 1 = —y
16. 3x + 6y = —7
5x + y = —10
18. y = 4x + 5
x = 3y + 9
19. At a concession stand, popcorn costs $1.10 and nachos cost $2.35. One day, the receipts for a total of 172 popcorn and nachos were $294.20. How many popcorns were sold?
El Practice Algebra 1 Lesson 7-2 315
Name Class Date
Practice 7-3
Solving Systems Using Elimination
Solve by elimination. Show your work.
1. 2x + y = 16
2. x + y = 0 3x — y = 4 x — y = 4
3. 5x + 3y = —4 4. —3x + 2y = —6
x+ y = —4 —2x+ y= 6
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ed
. 5. 4x + 3y = —3 2x + y = —1
6. x + 2y = 1 x — y = —5
7, 3x — y = 10 2x — y 5
8. x — y = 3 3x + y = 25
9. 3x + 5y = 10 x — 5y = —10
10. —2x+ y = —9 x — 3y = 3
11. 4x — 3y = 11 12. 2x— y =- 8
3x — 5y = —11 3x — 2y = 0
a)
13. 2x — y = 7 14. x + 2y = 2 3x + 4y = 22
a) a.
cr)
15. 10x — 4y = 6 16. 4x — 7y = —15 10x + 3y = —4x — 3y = —15
0 3 17. x + y = —34 18. —2x + y = 7
u.1
—2x — y = —20 —5x + y = 4 0
a_
19. Andrea buys four shirts and three pairs of pants for $85.50. She returns the next day and buys three shirts and five pairs of pants for $115.00. What is the price of each shirt and each pair of pants? •
EJ Practice Algebra 1 Lesson 7-3
0
Name Class Date
rke 7-4 A.plicatons of Linear Systems OOOOOOOOOOOOOOOOOOOOOOOO ••••••••••••••••••••0•0000•0••••••••••••••••••• OOOOOOOOO 0
Use a system of linear equations to solve each problem.
1. Your science test is worth 100 points and contains 38 questions. There are two-point and five-point questions on the test. How many of each type of question are on the test?
2. Suppose you are starting a cleaning service. You have spent $315 on supplies. To clean a house, you use $4 worth of supplies. You charge $25 per house. How many houses must you clean to break even?
3. The baseball team and the softball team had fundraisers to buy supplies for their trip to the championship game. The baseball team spent $135 buying six cases of juice and one case of bottled water. The softball team spent $110 buying four cases of juice and two cases of bottled water. How much did a case of juice cost? How much did a case of bottled water cost?
4. Rachelle spends 330 min/wk exercising. Her ratio of time spent on aerobics to time spent on weight training is 6 to 5. How many minutes per week does she spend on aerobics? How many minutes per week does she spend on weight training?
5. Suppose you invest $1530 in equipment to put your school logo on T-shirts. You buy each T-shirt for $3. After you have placed the logo on a shirt, you sell the shirt for $20. How many T-shirts must you sell to
0 break even?
a_
co
6. Suppose you bought supplies for a party. Three rolls of streamers and :a 15 balloons cost $30. Later, you bought 2 rolls of streamers and -
4 balloons for $11. How much did each roll of streamers cost? How much did each balloon cost'?
.2 co z
-c, LJJ
0
co
Practice Algebra 1 Lesson 7-4 319
1. 4y3 — 4y2 +3 — y 2. x2 + x4 — 6 3. x + 2
4. n2 — 5n 5. 6 + 7x2 6. 3a2 + a3 — 4a + 3
7.
Simplify.
10.
2 + 4x2 — x3 8. 4x3 — 2x2 9. y2 7 _ 3y
Write each answer in standard form.
(3x2 — 5x) — (x2 + 4x + 3) 11. (2x3 — 4x2 +3) + (x3 — 3x + 1)
12. (x2 — 6) + (5x2 + x — 3) 13. (5n2 — 7) — (2n2 + — 3)
14. (3x + x2 — x3) (x3 + 2x2 + 5x) 15. (d2 + 8 — 5d) — (5d2 + d — 2d3 + 3)
16. (4x2 + 13x + 9) + (12x2 + x + 6) 17. (2x — 13x2 + 3) — (2x2 + 8x)
18. (3x2 — 2x + 9) — (x2 — x + 7) 19. (2x2 — 6x + 3) — (2x + 4x2 + 2)
20. (x3 + 3x) — (x2 + 6 — 4x) 21. (7s2 + 4s + 2) + (3s + 2 — s2)
22. (x2 + 15x + 13) + (3x2 — 15x + 7) 23. (7 — 8x2) + (x3 — x + 5)
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Name Class Date
Pre:7:tice 9-1 Adding and Subtracting Polynomials OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO •9••••••••••••0000903909009990 0 0 9•9900000•9 00900
Write each polynomial in standard form. Then name each polynomial based on its de ee and number of terms.
171 Practice lryninrm / I e,ccrse, 0_1
Name Class Date
Practice 9-2 uitiplying and Factoring OOOOOOO •• • OOOOOOO • • 0. 0 • • 0 e • • • • • • 0 • • • El • al • • 11,0 0 GI • • e • • 0 0 •00
Simplify each product.
1. 4(a — 3) 2. —5(x — 2)
3. —3x2(x2 + 3x) 4. —x(-2 + 3x — 2)
5. 4d2(d2 — 3d — . 7) 6. 5rn3(m + 6)
Find the GCF of the terms of each polynomial.
7. 8x — 4 8. 15x + 45x2
.ta(2
:ft 9 x2 + 3x 10. 14x3 + 7x2
11. 8x3 — 12x 12. 9 — 27x3
13. 8d3 + 4d2 + 12d 14. 6x2 + 12x — 21
15. 8g2 + 16g — 8 a>
a_ Factor each polynomial.
16. 8x + 10 17. 12n3 — 0_
Cu'
18. 14d — 2
19. a
_ 5x2
2 20. 8x3 — 12x2 + 4x
-0
22. 2w3 + 6w2 — 4w a.
21. 7x3 + 21x4
23. 12c3 — 30c2
24, 2x2 + 8x — 14 25. 18c4 — 9c2 + 7c
26. 6y4 + 9y3 — 27y2 27. 6c2 -- 3c
El Practice Algebra 1 Lesson 9-2 359
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.
1. (x + 3)(2x — 5)
3. (3w + 4)(2w — 1)
5. (5x — 3)(4x + 2)
7. (x — 2)(x + 4x + 8. (2r + 1)(3r — 1)
2. (x2 + x — 1)(x + 1)
4. (x + 6)(x2 — 4x +3)
6. (3y + 7)(4y + 5)
Name Class Date
Practice 9-3 Muitipiying momials 000000 00000000000000000000 000000000 ote•oe eolooseem Goo 000000 aoacteacteti'e•e'ooes
Simplify each product. Write in standard form.
9. (k + 4)(3k — 4)
11. (3x + 4)(3x — 4)
a_
co a_ 13. (n — 7)(n + 4)
10. (2x + 1)(4x + 3)
12. (6x — 5)(3x + 1)
14.(3x — 1)(2x + 1)
5
s
15. (d + 9)(d — 11) 16. (2x2 + 5x — 4)(2x + 7)
0
-0
0
17. + 6x + 11)(3x + 5) 18. (5x + 7)(7x+ 3)
19. (4x — 7)(2x — 5) 20. (x — 9)(3x + 5)
Practice Algebra 1 Lesson 9-3
• 21. (29)(31) 22. (19)(42)
is; (2x + 1)(2x — 1) '16. (5x — 2)(5x + 2)
17. (6x + 1)(6x— 1) 18. (2x — 4)(2x- 4)
19. 182
20. (64)2
-0
O Find the area.
24.
3x — 2
3x + 2
-CD CD 23. 0
2x + 1
2x + 1
El Practice Algebra 1 Lesson 9-4
Name Class Date
Practice 9-4
Multiplying Special Cases 61000000•••••••••••••••500000•0•090•0 00 0 0000000 W 000000000 •••ea aaaaaaell•-• ••••••••
Final-each product.
1. (w — 2)2 2. (y + 4)2
3. (4 + 2)2 4. (w — 9)2
5. (3x.+ 7)2 6. (3x — 7)2
7. (2x — 9)2 8. — 12)2
a 0, 7. =• a 9. (6x + 1)2 10. (4x — 7)2
11. + 8)(x — 8) 12. x — 11)(x + 11)
13. (x — 12)(x + 12) 14. (y + w)(y — w)
publis
hin
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ears
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all.
0
Name Class Date
Practice 9-5
Factoring Trinomials of the Type x2 + bx + c eeeeeeeeeeeeeeeeeeeeeeeeeeeeee ••••••••••••••••••••eamoseeeeeep000••••••••••••••
Factor each expression.
1. x2 + 8x + 16 2. y2 + 6y + 8
3. x2 — 9x + 20 4. a2 + 3a + 2
5. x + 5x — 14 6. x2 + 14x + 45
All
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serv
ecl.
7.
9.
11.
13.
x2 — 8x + 12
x2 — 6x — 27
x2 — 5x — 24
x2-+ 9x + 20
15.
17.
19.
21.
23.
25.
27.
— n — 6
b2 + 4b — 12
a2 ±2a — 35
x2 + 2x — 63
x2 — 8x + 15
y2 — 16y + 64
a2 + 7a + 6
8. n2 — 7n + 10
10. x2 + 7x + 10
12. x2 — 3x — 18
14. x2 — 8x + 16
16. x2 + 7x + 12
18. x2 + x — 20
20. x2 + 3x — 10
22. x2 — 11x — 60
24. c2 + 3c — 10
. 26. r2 — 14r — 51
28. x2 — llx + 28
0 Practice Algebra 1 Lesson 9-5
3. 3x2 — — 4
4. 5x2 — 2x — 7
8. 7/12, + 9n 2 6. 3x2 + 8x + 4
7. 3y2 — 16y — 12 8. ,5x2 + 2x — 3
07
9. 7 -- 10x + 3 10. 3x2 + 8x + 5
11: 5x2 — 7x + 2 12. 5x2 — 22x + 8
13. 5x2 — 33x — 14 14. 3x2 — 2x — 8
8 15. 4y2 — lly — 3 16. 5y2 — 3y — 2
a.
a_ 17. 7y2 + 19y + 10 18. 3x2 ± 17x± 10
19. 2x2 + 5)c — 3 20. 3x2 + 10x + 3
-0 21. 2x2 — x — 21 22. 3x2 T 7X — 6
0
23. 2x2 — 5x — 12 24. 4x2 + 7x + 3
•
Name Class Date
Practice 9-6
Factoring Trin miais of the Type ax2 + bx+ c
Factor each expression.
1. 2x2 + 3x + 1 2. 2n + n — 6
0 Practice Algebra I Lesson 9-6
Name Class Date
Practice0-3 Solving Quadratic E uati ns OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO OOOOOOOOOOOOOOO •••••••••••••••••••61055050
Solve each equation by finding square roots. If the equation has no real solution, write no solution. If necessary, round to the nearest tenth.
1. x2 = 16
4. x2 + 16 = 0
7. x2 + 8 = -10
10. .x2 = 80
13. x2 = 300
All r
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ts res
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.
16. x2 + 8 = 72
19. 5x2 + 20 = 30
22. 2 -- 7 = 74
25. 9x2 = 1
28. x2 = 9
2. x2 - 144 = 0 3. 3x2 - 27 = 0
5. x2 = 12 6. x2 = 49
8. 3x2 = 300 9. 2x2 - 6 = 26
11. 81x2 - 10 = 15 12. 2x2 = 90
14. 4x2 + 9 = 41 15. 2x2 + 8 = 4
17. 4x2 + 6 = 7 18. x2 = 121
20. x2 + 6 = 17 21. 3x2 + 1 = 54
23. + 1 = 0 24. 4x2 - 8 = -20
26. x2 + 4 = 4 27. 3x2 = 1875
29. x - 10 = 100 30. 4x2 - 2 = 1
,D, Practice Algebra 1 Lesson 10-3 iga
Ca
a_ 19. 2t2 + 8t — 64 = 0
Ca
3 C- C.)
22. 2a2 — a --21 = 0
7.4
25. 2n2 — 5n = 12
@
28. 6m2 = 13m + 28
20. 3a2 — 36a + 81 = 0 21. 5x2 — 45 = 0
23. 3n2 11n + 10 = 0 24. 2x2 — 7x — 9 = 0
26. 3m2 — 5m --- —2 27. 5 — 17s = —
29. '4a2 — 4a = 15 30. 4r2 = r + 3
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Name Class Date
Practice 0-4
Factoring to Solve Quadratic Equations
2. (x — 2)(x + 9) = 0 3. (b — 12)(b + 12) = 0
0 5. (x + 7)(4x — 5) = 0 6. (2x + 7)(2x — 7) = 0
0 8. (8y — 3)(4y + 1) = 0 9. (5x + 6)(4x + 5)* = 0
11. b2 — 7b — 18 = 0 12. c;•2 —4 = 0
Use the Zero-Product Property to solve each equation.
1. (x + 5)(x — 3) = 0
4. (2n-+ 3)(n — 4) =
7, (3x — 7)(2x + 1) =
Solve by factoring.
10. x2 + 5x + 6 = 0
13. x2 + 8x — 20 = 0
16. x2 + 7x = 8
14. y2 + 14y + 13 = 0 15. s2 — 3s — 10 = 0
17. x2 = 25 18. h2 + 10h = —21
Practice Algebra 1 Lesson 10-4
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2 0
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Name Class Date
Practice 1O6 Using the Quadratic Formula ••••••• OOOOOOO OOOOOOOOOOOO 009990•00 Geeee••••••••609.0999•099000500•••••••95500990
Use the quadratic formula to solve each equation. If the equation has no real solutions, write no real solutions. If necessary, round to the nearest hundredth.
1. x2 + 8x + 5 = 0 2. x2 - 36 = 0 3. d2 - 4d - 96 = 0
4. x2 + 12x - 40 = 0 5. 4n2 - 81 = 0 6. x2 + 13x + 30 = 0
7. 6w2 - 23w + 7 = 0 8. 4x2 + 33x = 27 9. 7s2 - 7 = 0
10. x2 + 5x - 90 = 0 11. 5b2 - 20 = 0 12. 4x2 - 3x --F 6 = 0
13. 5y2 =17y + 12 14. g2 - 15g =54 15. 27f2 = 12
16. x2 + 36x + 60 = 0 17. x2 + 10x + 40 = 0 18. t2 - 10t = 39
19. 4x2 + 7x - 9 = 0 20. 8x2 + 25x + 19 = 0 21. 36w2 - 289 = 0
22. 3x2 - 19x + 40 = 0 23. 14x2 =56 24. 32x2 - 18 = 0
25. SaL 9a + 5 = 0 26. x2 = 9x + 120 27. 8h2 - 38h + 9 = 0
28. x2 + 3x -F 8 = 0 29. 6m2 - 13m = 19 30. 9x2 - 81 = 0
9 Practice Algebra 1 Lesson 10-6 391
6. V80 7. V27 8. 8 5. 2 "\16 V77
0 0_
cn 33. V300
-0
0 41. V12 • V27
0_0
. 45. V-8- • Vi
V120 31. 5 32. V75 30. V10
7 34. V125 35. V28x4 36.
V60 3 39. 40. (2V-3-)2
V12 "\13
42. (TO)2 43. Vir:4 • V-8 44. (5V)2
46. V3x • V5x 47. 2-0- • 2V-5" 48. 4-Vi • 2-1/2
Name Class Date
Practice 11-1 Sim !Hying Ra Icais OOOOOOOOOOOOOOOOOOOOOO •••••••••••••seoeseee••••••••seseseeeeeeceeeeeeeeeeeeeeesee
Simplify each rascal expression.
1. V32 2. V2-2" • Vi 3. Vi /
V 17 144
9. V12x4 10. V200 11. V15 • V6 12, V120
cg en 13.
'
4 2 m Viii ..., = m .c
V65 15. , V13
14. V250 16. V48s3
17. 3.1/24 18. V160 6 V180 19. 20. r- V 3 V9
• Virg • \/8 23. V50 24. V48
13 81 25. V-2-0- ... 26. V-8- 27. V25x2 28.
Practice Algebra 1 Lesson 11-1 405
1.
4.
7.
3[7 + 5-\/77 2.
5.
8.
10V4 - V-4
V45 + 12V11 + 7V11
V28 + \/63 3\ 8'¼ 8V6
10. V18 - V50 11. 4V2-. + 2V-8-
13. 3(81/2 -7) 14. 8(2V5- +
16. \16-(7 + 3V--3) 17. ,8(4 - 31/2)
19. 19V3- + V12 20. 8V26 + 10V26
22. 9-1/2 - V50 23. 10V13 - 7V13
25. 5\/5 + V28 26. 8V13 - 12VT3
28. 29. 12V29 - 15V29
31. 8V3- _.\/75 32. 17V35 + 2V35
34. 12V9- - 4V-9- 35. Vi(Vi. - 7)
37. 38. (V6 - _ V5 + 5
40. 12
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12. 13V15 - 11V15
15. 17V-21 - 12V21
18. 2V12 + 6V27
21. V10(3 - 2V-6)
24. 12V-6 - 4V24
27. 13V40 + 6V10
30. 10V-6 - 2 \/6
33. V19 + 4V19
36. 1
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39. (3V-- + -6)2
Name Class Date
Practice 11-2 Operations With Radical Expressions OOOOOOOOOOOOOOOOOOOOOOO .0•00•48000 ,200••6•0061•000G•0000••••••••••••••••••••••• 0 61 000
Simplify each expression.
Practice Algebra 1 Lesson 11-2
14. 13. 39 75.
Name Class Date
Practice 1-5 Trigonometric Ratios OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO • OOOOOOOO •••000000000000.00•••••06)00000•006)•••
Use LA C at the right. Find the value of each expression. A
1. sin A 2. cos A
4. sin B
6. tan B
41 9
40
3. tan A
5. cos B
All
rig
hts
re
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ed
. Find the value of each expression. Round to the nearest ten-thousandth.
7. tan 59°
9. sin 8° 10. cos i3°
11. sin 32° 12. tan 67°
Find the value of x to the nearest tenth.
8. sin 75°
30
15. 16:
36
17. 18.
19. A 12-ft-long guy wire is attached to a telephone pole 10.5 ft from the top of the pole. If the wire forms a 52° angle with the ground, how high is the telephone pole?
Practice Algebra 1 Lesson 11-5 413
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Name Class Date
Practice 1-6 Angles of Elevation and epression OOOOOOOOOOOOOOOOOOOO O• 00a a ea a S S I a •• S Stall aaa a. OOOOOOOOOOOOOOOOOOOOOOOOOOO f/a a a Oa.
1. A tree casts a shadow that is 20 ft long. The angle of elevation of the sun is 29°. How tall is the tree?
2. Suppose your angle of elevation to the top of a water tower is 78°. If the water tower is 145 ft tall, how far are you standing from the water tower?
3. The angle of elevation from the control toWer to an airplane is 49°. The airplane is flying at 5000 ft. How far away from the control tower is the plane?
4. A boy scout on top of a 1700-ft-tall mountain spots a campsite. If he measures the angle of depression at 35°, how far is the campsite from the foot of the mountain?
5. A 100-foot kite string makes a 35° angle of elevation to the ground. How high is the kite?
Practice Algebra 1 Lesson 11-6 n
Honors Geometry Summer Packet: Answer Key
Directions: After completing each page in your summer packet. Use this
answer key to check your answers to verify that you are finding the
correct solutions.
Be smart! If you find that you have answered most of the questions
correct on a page, move on. However, if you find that you have solved
many of the problems incorrectly on a given page, look for resources on
the internet to help you master this topic. Then, go back and complete
the even numbered problems on that page to verify that you have
corrected the mistakes you were making originally.
Good luck!
1. true
2. false
3. false
4. x = 15
5. y = 25
6. a = 54
1 7. z =
n 27 ,3 o.
9. a = 52
5 1 10. c =I, or 21
63 3 11.
12. m -= 38
1. 2.4
2. 3.6
3. 4.56
4. 4
5. 2
6. 6
1 7,
8. 41 2
2 9. 2-
3
.
2.
3.
71
9 Ti
0.09
100
13. _-3-, or -±61
14. +3 -4
3 1 15. -..t, or -±1-i
1.
2.
3.
4.
5.
6.
1.4
1.7
2.6
3.3
3.2
3.9 4' 9 7. 5.5
5.
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9.
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6. 1.69 10. 12.8
11. 16.4 7. ±- 5 12. 20.0
8. 1-1
9. -±10
10. -+-7 -8
11. -H 9 -10
12. or -±2-2
Practice 7-3
11 1. (4,8)' 2. (2, -2) 3. (4, -8) 4. 8, -30) 5.
6. 2) (-3, 7. (5, 5) 8. (7, 4) 9. (0, 2) 10. (4.8,6) 11. (8,7) 12. (16,24) 13. (13,19) 14. (18, -8) 15. (1,1) 16. (1.5,3) 17. (54, -88) 18. (1,9) 19. shirts: $7.50; pants: $18.50
Practice 7-2 1.(1,1) 2. (2, 10) 3. (5, 6) 4. (4, -3) 5. infinitely many solutions 6. (-2, -4) 7. no solution 8. (1, 9)
9. 7 -1 10. infinitely many solutions
11. no solution 12. infinitely many solutions 13. (1, -3) 14. no solution 15. infinitely many solutions
16. (-1-2-6 --5 ) 17 27' 27 •
19. 88 popcorns
Practice 9-3 1.212 + x - 15 2. x3 + 2x2 - 1 3. 6w2 + 5w - 4
4. x3 + 2x2 - 21x + 18 5. 20x2 - 2x - 6
6. 12y2 + 43y + 35 7. x3 + 2x2 - 4x - 8 8. 6r2 + r - 1
9. 3k2 + 8k - 16 10. 8x2 + 10x + 3 11. 9x2 - 16
1 2. 18x2 - 9x - 5 13. n2 - 3n - 28 14. 6x2 + x - 1
1 5. d2 - 2d -99 16.4x3 + 24x2 + 27x -28
17.3x3 + 23x2 + 63x + 55 1 8. 35x2 + 64x + 21
19.8x2 - 34x + 35 20.3x2 - 22x -45 5 3\
18. no solution Li
Practice 9-4 1. w2 - 4w + 4 2. y2 + 8y + 16 3. 16w2 + 16w + 4 4. w2 - 18w + 81 5. 9x2 + 42x + 49 6. 9x2 - 42x + 49
(0, -1) 7. 4x2 - 36x + 81 8. x2 - 24x + 144 9. 36x2 + 12x + 1 1 0. 16x2 - 56x + 49 11.x2 -64 12. x2 -121 13.x2 - 144 14. y2 - w2 ' 15. 4x2 - 1 16. 25x2 - 4 1 7. 36x2 - 1 18.4x2 - 16 19.324 20.4096 2 1. 899 22. 798 23. 4x2 + 4x + 1 24. 9x2 - 4
Practice 7-4 1. 30 2-pt; 8 5-pt 2. 15 houses 3. $20; $15 4. 180 min/wk; 150 min/wk 5.90 T-shirts 6. $2.50; $1.50
Practice 9-1 1. 4y3 - 4y2 - y + 3; cubic polynomial with four terms
2. x4 + x2 - 6; fourth degree trinomial 3. x + 2; linear
binomial 4. n2 - 5n; quadratic binomial
5. 7x2 + 6; quadratic binomial 6. a3 + 3a2 - 4a + 3;
cubic polynomial 7. -x3 + 4x2 + 2; cubic trinomial
8. 4x3 - 2x2; cubic binomial 9. y2 - 3y - 7; quadratic
trinomial 10. 2x2 - 9x - 3 11. 3x3 - 7x2 + 4
12. 6x2 + x - 9 1 3. 3n2 - n - 4
1 5. 2d3 - 4d2 - 6d + 5 1 6. 16x2 + 14x + 15
17. -15x2 - 6x + 3 1 8. 2x2 - x + 2
19.-2x2 - 8x + 1 20. x3 - x2 + 7x - 6
21, 6s2 + 7s + 4 2 2. 4x2 + 20 23.x3 - 8x2 - x + 12
Practice 9-5 1. + 4xx + 4) 2. (y + 4)(y + 2)
3. (x - 4)(x - 5) 4. (a + 2)(a + 1)
5. (x + 7)(x - 2) 6. (x + 9)(x + 5)
7. (x - 6)(x - 2) 8. (n - 5)(n - 2)
9. (x - 9)(x + 3) 1 O. (x + 5)(x + 2)
11. (x - 8)(x + 3) 1 2:(f::- 6)(x + 3)
13. (x + 4)(x + 5) 14.(x - 4)(x -4)
15. (n - 3)(n + 2) 16. (x + 4)(x + 3)
17. (b + 6)(b - 2) 18. (x + 5)(x - 4)
19. (a - 5)(a + 7) 20. (x + 5)(x - 2)
21. (x + 9)(x - 7) 22. (x - 15)(x + 4)
23. (x - 5)(x -'3) 24. (c + 5)(c - 2)
25. (y - 8)(y - 8) 26. (r - 17)(r + 3)
27. (a + 6)(a + 1) 28.(X - 7)(x -4)
Practice 9-2 1. 4a - 12 2. -5x + 10 3. -3x4 - 9x3 4. 2x4 - 3x3 + 2x2 5. 4d4 - 12d3 - 28d2 6.5m4 + 30m3 7.4 8.15x 9. 10.7x2 11.4x 12.9 13.4d 14.3 15.8 16.2(4x + 5) 17. 4n(3n2 -2) 18. 2(7d - 1) 19. x2(x - 5) 20. 4x(2x2 - 3x + 1) 21. 7x3(3x + 1) 22. 2w(m)2 + 3w - 2) 23. 6c2(2c - 5) 24. 2(x2 + 4x - 7) 25. c(18c3 - 9c + 7) 26. 3y2(2y2 + 3y - 9) 27. 3c(2c - 1)
Practice 9-6 1. (x + 1)(2x + 1) 2. (n + 2)(2n - 3) 3. (x + 1)(3x - 4) 4. (x + 1)(5x - 7) 5. (n + 1)(7n + 2) 6. (x + 2)(3x + 2) 7. (y - 6)(3y + 2) 8. (x + 1)(5x - 3) 9. (x - 1)(7x - 3) 10. (x + 1)(3x + 5) 11. (x - 1)(5x - 2) 12. (x - 4)(5x - 2) 13. (x - 7)(5x + 2) 14. (x - 2)(3x + 4) 15. (y - 3)(4y + 1) 16. (y - 1)(5y + 2) 17. (y + 2)(7y + 5) 18. (x + 5)(3x + 2) 19. (2x - 1)(x + 3) 20. (3x + 1)(x + 3) 21. (2x - 7)(x + 3) 22. (x - 3)(3x + 2) 23. (2x + 3)(x - 4) 24. (4x + 3)(x + 1)
Practice 10-3 1. ±4 2. ±12 3. ±3 4. No solution 5. ±3.5 6. +7
7. No solution 8. ±10 9. ±4 10. ±8.9 11. 4 12. +6.7
13. ±17.3 14. ±2.8 15. No solution 16. ±8 17. +1 -2 18. ±11 19. ±1.4 20. ±3.3 21. ±4.2 22. ±6.4 2E. No solution 24. No solution 25. ±1 26. 0 27. +25 Z8. ±3 29. ±10.49 30. +0.87
Practice 10-4 1. -5,3 2.2, -9 3.12, -12 4. -1.5,4 5.
6. -3.5,3.5 7. 13--7, -0.5 8. -0.25 9. -1.2, -1.2510. -3, -2 11.9, -2 12. -2,2 13. -10,2 14. -13, -1 15.5, -2 16. -8,1 17. 5, -5 18. -7, -3 19.4, -8 20. 3, 9 21. -3,3 22.3.5, -3 23. 2, 24. 4.5, -1 25.4, -1.5
26. 1, 27, 3,0.4 28. 3.5, --34- 29. 2.5, -1.5 30. 1, -0.75
Practice 11-2 1. 817-7 2. 18 3. 8-1/2 + 8-\A 4. 5V-5- 5. 19V11 6. 2"\4 - 8 7.S\/ 8. 9. 31/2- - 6 10. -2V-2- 11.8V'i 12.2\i5 13. 24-6 - 21 14. 16-V + 40Vi 15.51/21 16.71/6 + 91/i 17.32 - 24-1/2 18. 221/5 19. 211/5 20. 18-1/26 21. 3V10 - 4V15 22. 41/2,- 23. 3V13 24. 41/6 25. 7-\/-i 26. -4V13 27. 321/10 28. -9-1/2 - 9 29. -3V29 30. 8-\/6- 31. 31/5 32. 19V35 33. 51/19 34. 24 35. 4 - 14V-2- 36. -1/5 -
+ 15 or -3(V5- - 5) 20 20 33. 15 - 6V-6 39. 80
40. 4(V6 + 3)
Practice 11-5 1 0 2 -9 3 4-0 4 2- ' ' ' 5. 0 6 -9 7 1 6643
° 41 • 41 ' 40 8.0.9659 9.0.1392 10. 0.9744 11.0.5299 12. 2.3559
13. 10.1 14. 12.7 15. 25.4 16. 22.5 17. 3.8 18. 40.2 19. 20 ft
Practice 10-6 kt -7.32, -0.68 2. -6,6 3. -8,12 4. -14.72,2.72 If 5.4.5, -4.5 6. -10, -3 7. 0.33, 3.5 8. -9,0.75
9. -1,1 10. -12.31,7.31 11. -2,2 12. No real solutions
13.4, -0.6 14. -3,18 15. -0.67,0.67 16. -1.75, -34.25 17. No real solutions 18. -3,13 19. -2.61,0.86 20. -1.82 -1.30 21. 2.83, -2.83 22. No real solutions
- 23. -2,2 24. -0.75, 0.73-23. No real solutions 26. 16.34, -7.34 27. 4.5,0.25 28. No real solutions 29. 3.17, -1 30. -3,3
Practice 11-1 1. 4-1/2- 2. 41/11 3. 71/5 4. -1-7 . 3 6. 41/-
7. 31/5 8. 8-,\P 9. 2x21/5 10. 10-1/2 11. 31/1-6
12.2V30 13. 2 Va2a 14.5V10 15.1/5 16. 4s1/Ts
17.6V 18.4V10 19.2V 20.2V' 21.12
22. V17 23. 5-1/2, 24. 41/5 25. 21/5- 26. 2-1/2 8
27. 5x 28. V13 29. -116- 30. 2-6 31. 5\-2I 32.5/. 9 2
33. 10Vi 34. 51/- 35. 2x21/77 36. 7\13- 37. -VP
38.1/5- 39.1/5 40. 12 41. 18 42.245 43. 4-Vi 44. 125 45. 21/14 46. x1/1-5- 47. 20 48. 81/6
Practice 11-6 t 11.1 ft 2. 30.8 ft 3. 6625 ft 4. 2428 ft 5. 57.4 ft 6.33.69° 7.57 ft
