Summer Work for Students Entering Pre-­‐Calculus M570 Dear Student, • You are to complete all circled or boxed exercises in the attached packet by the first day of the 2014-­‐15 school year. • Number all problems and show all work on separate pieces of paper. • Please put your name on the first page of your work,, and securely staple all papers before submitting them to your teacher. • All answers to all problems are enclosed for your reference. ~
MIXED REVIEW 1
NAME
For use after Lesson 1-4
DATE
Simplify by performing the indicated operation.
1-1
1. 13 - ( - lS.2)
2. -8.1 + (-4.3)
3. S.8 - 17.7
4. --+-
s. ;-(-~)
6. 178 - (233)
7. 72 + (-41)
8. -4S - (-63)
9. -14.27+(-11.74)
1-2
2
2
3
7
10. -S3.2 - (13.2)
@-~+(-.~)
1~ - ~6 (-~)
@(-~)(-~)(-~)
14 -9.6
• 24
Evaluate each expression.
1-3
15. 3y + Sx for y = - 2, x = 3
@4x-yforx= -7,y= -9
17. -yfory=--
~la -
@9x - !xi for x = 4
~ 6c -
2
3
bl for a = 4, b = 7
3ldl for c = 4, d = -4
Simplify.
1-4
21. 27t(r - h)
22. 7x(6y - z + 8w)
23. Se(1f - 4g - h)
24. Sy - (3y + 6)
25. 4x - 3(y + 4x)
26. 14a + 3(x - a - 2)
27. 2(2x - 4y) - 3{x - Sy)
28. - 7(3m - 2y) - 3(7m + Sy)
Factor.
1-4
29. 9x + 9y
30. Sa - 1Sb - S
31. xy + Sx
32. 27x - 36
33. 4x - 20y - 36z
34. abc +a
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Algebra and Trigonometry
65
MIXED REVIEW 2
for use after Lesson 1-8
DATE------------
Determine whether the indicated number is a solution of the equation.
l. 4x
1-5
+7=
-5; -3 - - - - - - - -
3. 1x + 37 = -9; -4 _ _ _ _ _ __
2. 9y - 14 = -4; 2 - - - - - - 4. Sy- 15 = O; -3 _ _ _ _ _ __
Solve.
1-5
5. x+ 14=4 _ _ _ __
6. y-11 = -6 _ _ __
8. -7.4x = -44.4 _ __
9. 1x - 10 = 11 _ _ __
11. 3x - 1x = 28 - - - - - - - - 13. 4a
= 3a + 7 - - - - - - - - - -
15. 4x - 100 = 15x
+ 21 - - - - - -
7.
3
7Y = -12 - - - - -
10. 4y+ 15 = 35 _ __
12. 6x-x= -25 _ _ _ _ _ _ _ __
14. 6a - 4 = 4a
+ 4 _ _ _ _ _ _ __
16. 5y+y-10=3y+ 11 _ _ _ _ __
Multiply and simplify.
1-7
17. 5·5·5 · 5·5 _ _ _ _ _ _ __
1-8
19. 11
5
•
11
3
18. (3xy)(3xy)(3xy)
-----------
22. (4b4 c- 3 )(-3b- 3 c- 4 ) _ _ _ _ _ __
24• (x4y-4)(x3y2) _ _ _ _ _ _ _ __
Divide and simplify.
x'
25. "3-------------x
1-8
3
xs--------------
27. x
24x- 5 y- 6
26. - 6x -10 y - · - - - - - - - - - 5-•aBb-l
28. S4a-2b2
Simplify.
29. (3 7 )4 _ _ _ _ __
1-8
32. (-2x 4 y- 5 ) 2
30. (2- 6 ) 3 _ _ _ _ __
_ _ _ _ _ _ _ _ __
·-·-.
,
66
Algebra and Trigonometry
J" Adcllaon-Wesley Publishing Company. All rlgh!S reserved.
-
MIXED REVIEW 8
For use after Lesson 4-7
Solve.
4-J
@ A chemistry student needs 10 L of a 12%
acid solution. The laboratory has ample
amounts of 10% and 20% acid solutions.
How many liters of each solution should
the student mix?
2. A chemistry student needs lS L of a 32%
acid solution. The laboratory has ample
amounts of 30% and 40% acid solutions.
How many liters of each solution should
the student mix?
3. In triangle ABC, the measure of angle
C is 18° greater than three times the
measure of angle A. The measure of
angle B is S times the measure of angle
A. Find the angle measures.
4. The sum of three numbers is 270. The
second plus twice the firs.t is 36 more
than the third The first plus the third is
27 less than twice the second. Find the
numbers.
5. The Apollo missions used the Saturn V rocket.
The velocity at the end of the first stage was
approximately 637S m/h,
2~ minutes after launch. At
....
.
the end of the second stage, 9 minutes after launch,
the rocket's velocity was lS,lSO m/h.
a. Fit a linear function to the data points.
b. Use the function to predict the velocity 10 minutes
after launch.
c. Predict the velocity at the end of the third stage,
lS minutes after launch.
r
'
Graph. Find the coordinates of any vertices formed.
4-7
6. x
~
3-7
8. 2y + Sx < 23
4y < 3x + 7
3y+x~2 _ _ __
7. y < 0
0
2y + x < 6
y>x-3 _ _ _ __
2y S 3x + 6
lOy~
3x-18 _ __
Determine whether the graphs of each pair of equations are parallel, perpendicular, or neither.
3
9. y = x- 7
4
10. y = 4x - 10
11. y = 3x - S
2y-8x=S _ _ __
3y= -4x+8 _ __
Sy= 3x + 1 - - - -
+ 3x = 12
3y-4x=9 _ _ __
12. 4y
13. y = 2x + 6
3y=6x+ 18 _ _ __
14. Sy = 2x + 11
2y+Sx=S _ _ __
Determine whether the systems in Examples 9-14 are consistent or inconsistent.
15. - - -
16. - - -
17. - - -
18. - - -
19. - - -
20. - - -
Determine whether the systems in Examples 9-14 are dependent.
21. - - -
72
22. - - -
Algebra and Trigonomerr.v
23. - - -
24. - - -
25. - - -
26. - - -
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MIXED REVIEW 10
l'iA.\tlE
For use after Lesson ; ....
DATE
Factor.
5-5
@
2
:'
125y3
-
(!}x 3 + 8x 2 + 15x
4. 8t 3 + 1000s3
@
@
2
-11x+ 24
6." x 2 + lOx + 24
2
-lOx-24
8. x 2
9. 3x 4
5-7
2. x 3
+3x-10
48y4
-
11. 12x2
-
77x + 30
13. 12x2 + 40x
+ 25
2x - 24
-
10. 12x2
-
13x - 4
12. 12x2
-
25x + 12
@1sx2 + 39x + 20
15. m6
-
n6
16. x 2
+ 1x + 12
17. x 2
-
13x + 12
18. x 2
+ 4x -
12
19. Sa + Sc - 12a - 12c
20. ax - xb - ay + yb
21. S4w 3
22. 81m 3 + 37Sn 3
128z 3
-
@9c 2 -6cd + d2
25. x
2
27. w2
+ 12x -
24. a2
2
Sa
3
y + 36
+ 16 -
26. 2x + 6x
lOw - 9z 2 + 25
28. m5
2
(_
16x - 48
-
+ 2m 3 -
·~;
b2
7m 2
-
14
Solve.
@ Sx -
=x +1
29. 4(x - 2)
2-4
31. (3a - 4)(3a + 1) = 0
32. --y--y> 10
3
2
2-7
33. 13 ~ 3y + 4 < 18
34. l3x + 21 ~ 11
5-7
-
39. x 2
=4
x
= 12
43. 2(x + S) + 3(x + 5)
S)
1
@x 2 +20x=0
@-14x + 3x 2
40. 4x 2
41. 2x(x + S) + 3x(x + 5)
2-1
1
(~y2 = 22S
37. x 2
13
= 3(x -
2-1
=0
=0
-
4x
= 24
=3
42. 2x(x + 5) + 3(x + 5)
=0
Q(4x + 5) - 3(x - 4)
=-
13
_J
.r
74
Algebra and Trigonometry
!'
Addison-Wesley Publlahlng Company. All rights reserved.
MIXED REVIEW 12
For use after Lesson 6-9
DATE------------
Solve.
6-9
1. With pressure and volume constant, the number of
moles (n} of a gas varies inversely as its temperature
(T}. The temperature of a certain gas is 400 K when it
contains 5 moles. How many moles of the gas are
there when the temperature drops to 300 K?
6-7
2. The new RGH-5 microprocessor executes instructions
200,000,000 words/s faster than the ZP-13. While the
ZP-13 processes 8,000,000 words of data, the RGH-5
processes 10,000,000 words. Find the rate at which
each processes data.
5-8
3. Kim is installing a skylight to conserve energy. She
wants the width 50 cm less than the length and a
total area of 15,000 cm2 • What are the dimensions?
1-5
5-7
2-1
Solve.
4. 3x - 7 = 4 _ _ _ _ _ _ _ _ __
6. x 2
-
8x
{Y 2x(x -
+ 7 = o_________
3) = 5(3 - x) - - - - - -
(~ 3 2 = ~3 _ _ _ _ _ _ __
~ y+
l2. _s_+
y-3 3~-s
y -9 =-6y+3 _ _ _ _ __
Solve each formula for the given letter.
2-3
@E
=
~;
h___________
1
16. k = -lw 2 ,· ca2
2
---------1
2
2
; v
18. E = -mv
2
2 2
moc
2
20. m = c2 -
24. kv =
76
2
2;
c ---------
7. 36z2 = 121 _ _ _ _ _ _ _ __
Ci> m(m -
m+M
m
; m---------
Algebra and Trigonometry
+ 3) = o_____
f::)~- 32 = _16
x
3
x --------
x
2
13. ----x -2 = x 2 + 3x - 10 - x +S.
150 ~lw(a +
b); b - - - - - - -
17. E = 3 kT; T _ _ _ _ _ _ _ __
2
?,;). GM
19':.,.T
R ;.A1 ____________
2
21 • .A1 = _!!!__;
P-------r + ps
1
1
6)(2m
'!Y x + 7
Ti"+ I 2 =I; L - - - - - - - - - ~ m(x2 1
22.
l'
----------
1
5. 0.7(Sx + 10} = 14 - J (6x - 12) - - -
~-
\~Q
xi}+ Y1 = Y2; m - - - - - - -
= _r_s_; s ________________
s+t
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I
•.
MIXED REVIEW 13
!'SAME-----------
For use after Lesson 7·5
DATE-----------
Simplify.
7-1
1. J36z
2
2.
-----
~
7.3
7.5
VSXS-----7.~-10.
.J( -3a) 2 - - - - -
5. V54l 5 m4 n3
8.
Jc2oc 2 d) 3 _ _ __
3. V-12sx 3 _ _ _ __
_ _ __
fW
.y7------
11. <V10x2y)2 _ _ __
Write the radical expressions in Exercises 10-12 with rational exponents.
7-5
13. _ _ _ _ _ _ __
14. - - - - - - - -
15. - - - - - - - -
Multiply and simplify by factoring.
7-2
7-4
16.
JJJO ________
18.
f/x - y fJ(x -
20•
../3C5Jl2d
3
4
y)
-------
--------
<Ji+ Jf,)
24. if3<V9 + ViSa) _______
2
22.
--------
17.
iffOX vs;y _________
19.
J8.J36 _________
2
21. V4x y~---------
<JX + J"Y><JX + .j2) - - - - 25. <Jfi. + 3.j5)(2./3 + 2.J7) _ _ __
23.
Rationalize the denominator.
7-4
26.A------
2 ./5 _ _ _ __
27. 4./6
V4ii3
29. - - - - - - - - - - - - - -
ifW
28.
'4-------
.J7-J10
. JS3..;3 - - - - - - - -
30 4
--·~----~~~------------------~~--~~
Use synthetic division to find the quotient and remainder.
6-5
31. (x 3
+ 4x2 -
32. (2x 3
33. (x 3
6-1
-
x - 4) + (x
+
l) _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ __
4x 2 + 3x + 1) + (x + 2) _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ __
+ 2x 2 -
6x
+ 3)-;- (x -
3) _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ __
Divide.
Sa - 20
a+ 3
34• a2 - 7a + 12..,.. a2 - 9 - - - - - - - - - - - - - - - - - - - - - 2
2
35. (16x 6
+ 28x4
36. (y 3
3y 2 + 4y - 5)-;- (y - 2) _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ __
-
-
32x
)
+ 4x
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--------------------
Algebra and Trigonometry
77
MIXED REVIEW 14
NAME-----------
For use after Lesson "' - JO
DATE----------I {
Add or subtract.
7-7
I. -3i + (5
+ 4i) _ _ _ _ _ _ __
2. (3 - 4i) + (7
+ 6i) _ _ _ _ _ __
3. (2 + Si) - (9 - 4i) - - - - - - -
4. 8i-(-3+9i) _ _ _ _ _ _ __
5. (11 - 6i) + (4
6. (4
+ 2i) _ _ _ _ _ _ _
+ i) -
(-7
+ i) _ _ _ _ _ __
'I ~
l
I
i
ifi. - sifi. + 4 ifi. ______ s. 6J6j - 2J28 + sJ? _____
4jh3 + .JUX - Jllii ______ 10. ifi4x4Y - 9 VJXY _______
1. 3
9.
11 • .J12y - 4 +
.J21y -
12. .Jx 3 + 3x2
9
Jl6x + 48 - - - - -
-
Multiply.
..r:::s ..J-15 - - -
7-7
13. J=6·3i _ _ __
14•
7-9
16. 2i. 3i - - - - - -
17. (5i)
19. (3 - 4i)
5-3
22. (3
2
-----
2
+ 4b) 2 - - - - - - - - - -
24. (3a
+ 4b)(3a -
26. (2 - 3w)(2
18. (3 - 4i)(5
------
+ 7i)(5 - 4i) - - -
20. (2
4b) - - - - - - -
+ 3w) - - - - - - -
.J=4 . .J-12 - -
15. -
21. (8 - i)(8
+ 6i) - - -
+ i) - - -
23. (2x + 7y)(5x - 4y) _ _ _ _ _ __
25. {2a
+ 7b)(2a -
7b) - - - - - - -
27. (Sx + y)(x + 6y) - - - - - - -
Divide.
7-9
28. 2-31
2 + 3~ _ _ _ _ __
6-4
31. (9a - 16b2 ) + (3a
33. (6x 3
-
1 lx 2
i
+ 4b) - - - - -
+ l lx -
30.
29. 1 + i - - - - - 32. (16b 2
J3
+ 3i _____
J3-3i
+ 24b + 9) +
(4b
+ 3) - - - -
1) + (2x - 3) _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ __
Solve.
7-6
34••.j4x
+1
= 3---------
4 _ _ _ _ _ _ _ __
37•
38. "' 3x - 4
39.
40.
= 2.Jx + 1 - - - - - v 4x + 9 - ,1x+6 = -1 _ _ _ __
.Jx + 5 = .J2x + 2 - - - - - JX+3 + .Jsx + 4 = 5_ _ _ __
41.
v12x + 6 =
t;sx 1
42. (2
+ 2i)x - i = 3i - - - - - - -
44. (1- i)x
78
+1=
4 = 2---------
36.
7-10
35. V9x
+ 3-4i = S + Sx _ _ __
Ah1ehra and Trigonometry
43. 3ix
+3-
45. (3 - 2i)x
t
..j4x
+
3i = (2
+3=
s-
1- - - - -
+ Si)x -
(4
i _ _ __
+ 3i)x -4i _ __
Addlson-Wealey Publishing Company All right& reserveel.
-
(
ILPrncticeProblems
(~ fiL.L. o~ ~S~
•?
Simplify.
iZo g ~_H.S
,
.:JF/. ,_·~
-.,_,n" ·
-/
3. .:!\ 5 - 4\ 3 - 3\ 5
4. 7\11-5\13-4,13-3,11-,11
s, 7 -
6. f\ 35 - 16\ 5 -
s.
6, 21-
·h 5- \ 35
s, 63 - , 343- 1,TI
9. -3, 13 - 7\'75 - 6\ 8 - 3\ 12
10. 3, s -2, 12 -2"20-
9v3
11. \ 45 - 2, 3,... 2, 30
12.,~-.h:?o-s,a-,45-4, 3.?
13. 2\
s - s, 27 -
2, 50 - 3, 75 - 2, 13
14. 6" J 7 - 2, :rn -
16.
-s, -24- 3, -9 -
~,
7 s - , ..i.s - ::! , 60
·h -96- ·h -40
17. 7\ 1400 - 7\ 11 - ::!\ 13 - ::!\ 300
18. \ 45 - \ 490 - 2, 90 - 2,. 20
19. 3\ 144- - 3\ 34.,.. :!\Mo - 2\· 169
20. 3, 13 - 1, 5 - 1, 120 -
,·so
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25. 9 cis 90
26. 7 cis so·
27. 13 cis o
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28. 43cis O
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21.
23.
26.
29.
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i
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MIXED REVIEW 4
1. 2 <IC< 7
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20. 12
0
2nr - 27th
22. 42xy - 7xz + 56xw
35ef - 20eg - 5eh
24. 2y - 6
25. - Bx - 3y
118 + 3/C - 6
27. IC + 7y
28. -42m - y
9(x + y)
30, 5(a - 3b - 1)
31. x(y + 5)
9(3x - 4)
33. 4(x - 5y - 9z)
34. a(bc + 1)
:t
2
e
7
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2. -2 :S; IC S 1
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1.
13.
19.
24.
28,
3. No
4. No
5. -10
8. 11
-2s
8. 6
9. 3
10. 5
11. -7
12. -5
5
7
14. 4
15. -11
18. 7
17. 5
18. (3xy) 3
11 8
20. 7-z
21. y
22. -12bc- 7
23. 5 2 x 5 y 5
x1 y- 2
25. x 2
28. -4x 5y- 2
27. x- 2
5-HalOb-!
29, 328
30. 2-ll
31. 7 12
33. (-3)-3a11b-12
32. 1-212x1y-10
35.
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21
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28. 26
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44. t < -3
120
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0
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3
10 • -4..,.
.::. IC.,..~
;:::, 3
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45. IC
I
-3
I
I
9. x ~ 3 or x s; -3
43. y > 7
•I
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t
I
0
8. -4 <IC< 4
~
I
I 41 . .
7. IC= 1 orx= -1
!..
35
42. IC> -5
-5
39.
JC>
2P-w
33. -3.6
8
-I 0
< -3 or
13. 2
12. 1
18.
25. -14
30. -3
35. -16
11 .
2
Q
(a+b+c)
~
24.
.-2-
10. 2
JC
8. -12
5. 12
18. -5, -6
20.
(a +b)
29. 0
8.
4. -9
eta:• tee I•
I .. I * I
-3
3. -14
e
4
-3orJC> -1
•• •a
MIXED REVIEW 3
1. -9
2. 37
I
13. 6
I
I
I
I
0
14. 151C - 10y
4
15. 2ab -
,ac
2
'
16. -a+ 2b
MIXED REVIEW 7
1. 1
2.
~2
3. 129
8. 6x2
7. 9x - 20
9. y
2
-
12. y
15. Not linear
18. (2. -2)
4. -5
= - 21 x -
= -~x
- ~
3
3
16. Linear
2
5.
4x+ 2
9.
12.
11.
18.
21.
24.
5
2
MIXED REVIEW I
6• ~
2
3
10. y =
1
4
3
13. --
14.
1
17. Not linear
11. (3, 2)
20. (1. 3)
21. (2,4)
22. (0, 1)
1.
1.
1.
11.
13.
11.
11.
21.
24.
%1.
30.
32.
35.
37.
31.
Perpendicular
Perpendicular
Consistent
18.
Consistent
11.
Not dependent
Not dependent
-48 - 24b
2. 10x -1B
3• .:..36
4. 66b - 30
1B
8. -66
1. 38
8. -10
-3x3 - 4r + Bx+ 2
10. 1a2 - 3ab - 4b 2 - 10
-5x4 - 7x3 - 2x3 + 4x - 4
12. 3x4 + 4x3 - 6x 2 - 4x - 9
- r + 6x + 10
14. 6x5 v'
11. x-Jys
18. 1oa'b- 2 c•
3- 3 a- 6 b 12c- 3
18. 128.f - 1oa2 b + &ab 2 - 3b3
-4x3 + 11x1 + Bx - 15
20. 2x3 + 10x1 - S4x - 42
x3 22. aaJ + 19ab + 11b2
23. 12x2 + x - 8
~ - 12st + 411
21. 49r + 28xy + 4r
28. 4r - 38
98 2 - 25b 2
21. b(x - y + z)
21. 4w(3x - 2y + 4z)
(Sy+ X + 3)(3y - JC - 3)
31. yl(&y + z)(5y- Z)
r(JC - B)(JC + B)
33. (JC - 3)(yl - 5)
34. JC(2x + 3) 2
(a + c)(b + d)
38. 3(3a - 5) 2
3(a 1 + 4b1 )(a + 2b)(a - 2b)
38. 2(b - 3c + 3d)(b - 3c - 3d)
(XJ + 4)(JC + 6)
r
<;;o
23. (3. 2)
24. (2, 2)
25. (2. -1)
27A
. on y - - 1 x + s
• ny point
2
29. (5, -2)
30. (2, 1, 4)
33. (-1, -2. -3)
2
28. (3,3)
28. No solution
31. (3, -2, 0)
32. (2, 2, 2)
REVIEW
+
8. (4, 1). (0, 3), (0, -3)
3. 1B0 , so•. 12°
4. 36. 99, 135
b. 18,500 c. 23,250
7. (-2. 0), (6, 0), (-4. -3)
W)
1. (JC - 2)(x + 5)
2. (x - 5y)(x1 + 5xy + 25y2 )
3. x(x + 3)(x + 5)
4. B(t + 5s)(t1 - 5st + 25s 2 )
I. (X - B)(x - 3)
8. (X + 6)(X + 4)
7. (JC - 12)(X + 2)
8. (x - 6)(x + 4)
•• 3(x1 + 4yl)(x + 2y)(x - 2y)
10. (3x - 4)(4x + 1)
11. (12x - 5)(x - 6)
12. (4JC - 3)(3x - 4)
13. (Bx + 5)(2x + 5)
14. (Sx + 5)(3x + 4)
15. (m + n)(m - n)(m 2 + mn + n 1 )(m1 - mn + n 2 )
11. (x + 4)(x + 3)
17. (x - 12)(x - 1)
18. (x + S)(x - 2)
11. - 7(a + c)
20. (x - y)(a - b)
21. 2(3w - 4z)(9wl + 12wz + 1Br)
22. 3(3m + 5n)(9m 2 - 15mn + 25n 2 )
23. (3c - d) 2
24. (a + b - 4)(a - b - 4)
25. (x + y + S)(x - y + 6)
21. 2(r - B)(x + 3)
27. (w + 3z - 5)(w - 3z - 5)
21. (m 3
~t::::1::f::::j1WP-'2:"112 L. 3 L
5. a. v(t) = 1350t 3000
10. Parallel
11. Neither
13. Parallel
14. Perpendicular
Inconsistent
17. Consistent
Consistent
20. Consistent
22. Not dependent
23. Not dependent
25. Dependent
21. Not dependent
7)(m 2
-
+ 2)
34. x 2: 3 or x ~ -
32. y < -12
311. 15, -15
38.
o. -20
1 3
31. 2, -2
40.
43. -5
31 • ~3. _!_3
30. -1
29. 3
37. 4, -3
41.
-2·2
o. -5
38. 6,
42. -5•
13
3
-34
_!2
44. -7
MIXED REVIEW 11
1. -12Jt11+SJy«•+•1
8. (-1.1),(3,4),(5, -1)
4. 4s" - 3614
5. (y + ll)(y - 3)
y(y + 2)
12. (y - 4llY + 31
13. 6b + 1
y
111. y
3
21. x1
\
122
Answers
\
-
-
23.
3x2 -
•
2(x'
21
(x
x-4
11. 1 + x y
11. a - 3 - __!!_
a-3
Bxy
+ By2
12y2 -
+ 11)
+ S)(x -
4)
5
22. 4x 2
24. s
a-b
17. x + 6
x"y
-
20. y - 7
-
+t
28.~
7 a+3
· 2
14. ~
1 3
3yl - 4y
3. 12a 2 -14ab-10b 2
l.x+6
r-4
b+ll
+3
18. y
\
2. -6a 11 b- 2
3x + 3y
+ 2xy + 3
.!!
26 _,_
25 •
)'
29.
• JI'+ 3
4(8- 3)
(s - 4)(• + 3)
(
\
1::;;D
Rm;.;)
23. 0,
1. ~
3
2. RGH-5: 1,000,000,000 words/s: ZP·13: 800,000,000 words/a
1
4• .!..
3
3. 100 cm by 150 cm
-i
8. 3,
13. _,!!
4
...!J!L.
/1
G
!.!.=..!'.!.
18. ~
2. 3 l l l 3. -5.r
1.
r- Q
21. x'y
.,
V4KY
25.
J2X + ..;;y + Ji;
12 + 5Jj5 + 4$1 + e.J35
21. ./ii
7
21. ~
27 JiO
• 12
__,,
33. Q: r + S.r + 9, R: 30
1.a
-.. - a
ef2
30. -
1
1,/3
2+ T
31. 3a - 4b
+ 4 + 2ll ~ 3
38. No solution
43•
21. -13 +13 1
1
33. 3r - •
•
17
31.. 4
35. 1
34. 2
39. 1
J2
! ± lv1
37•
3. y- II
7• .JrJ-a3 -b3
11 •
I
4.
II
./PR
12.
11.
..!!..
1
1125'
~
L
-m ± ,,j,,,J
211
V
Pt
5.
14.
±":' ±../3
11. 1, 12
23. 2real
11.
9. r2F
Gm
+ lb
13•
12
20.
11. -~
8. 8
±!.4
24. 2 complex
27. 1 double real
Y•;r
±!.5
21. 2 complex
28. 2 real
32. y=2.rz
40. -2
0.18
·Y=7
33.y-~
z
MIXED REVIEW 17
2. None
1• .r-axls, y-axis, origin
5. x-axis, y-axis, origin
I. None
8. Origin
I. y-axis
10. None
12. Origin
13. 150 cm/a, 200 cm/a
11.
11.
17.
11.
11.
20.
.!.
25
5 1
17.
21. -1, -8
21
iii
i'i
22. -8, -7
21. 2 real
30.
Y-~
34.y .. ~
w
3. Origin
4. y-axis
7. x-axis, y-axis, origin
11. x-axis
14. 4.12 aim, 49.4 atm
.!.+.!.1
2 2
21•
32. 4b + 3
44 -~-~,
.!._!1
4
4
12
5
S.r3 + 31.ry + 6y3
31.. 3 ± 2
2
34.!-~
3' 3
3303
• •
2
MIXED REVIEW 11
A
2. mx, + Y2 - Ya
1. "1'+it
31.
~~DRmEW14 _)
1. 5+1
~
3. -7+91
4. 3-1
5. 15-41
a. 11 1. 2
a. 19Ji 1. (• + 2)$
10. (2.r- 9)~
11. 5.J3y-1
11. (.r - 4).J.r + 3
14. -5.Ji
15, 4.Ji
11. -e
11. -25
13. -3Ji
11. 39 - 21
19. - 7 - 241
20. 38 + 271
21. 65
21. 9 + 24b + 18b3
23. 10.a + 21.ry- 28,a
24. 9a3 - 18b3
21. 4a 2 - 49b3
21. 4 - 9r
27.
5
32.-1±"
± lvi
30. 1
2
31. Q: r + 3.r - 4, R: 0
32. Q: 2.r3 - 8.r + 19, R: -37
35. 4.r' +
29. 1 ± .j1ii
2
31. -7 ± .J157
4
4
8
31. r+38-o
40. r-6.r+10-o
41. r-2../2x+3
42. r-4.r+a-o
43. r-38=0
44. r-6.r+a=o
45. .a - 2 .. o
41. .a + 31fJf - 1or = o
Sb
so - 4.,/ii - 12./21
30• s../i + 3../30.
22
34. 5
23. • +
21. a ~10011
2
-
3
22. 2 + 2 $ + b
24. · 3 + 3 ~
•
Ji
-1 ±2
10. 2fi
40ct11df.J5d 11 • .r~10 ..r 12. 7a bifib
13. 20lc3ctl
14. 1~.Jyl
11. 49la 3 bi
11. J39
11. Vso.r3,
11. t./<• - Y>'
11. 12J2
20. Sct1ld!.Jcd
10.
21 1 + lv2
2
m
~f
1.
3
31.
± v1o
31mn~213m
s.
4. 2.r
a. M
i
21. _.!M_
q-Ma
21. ~
Irv - 1
~IXEDR~p
a. rlvzW20xrz
I
mJvJ
27. -1
21. -3 ± .Jti
21. -3 ± " ::;
24. 0, 7
31. -2 ± ..j8
12. -14
m2-mi
24. .....!!__
X2 - 111
1. 6j~
11. 8
20.
7• .!!
_,!!
8.
8
1, 7
/w
19. g~
23.
+ /2
10. 7
/w
11. 2E
m
3k
a.
2
15. sv - a (or) sv - a/w
14. El
c
17. ~
22.
-i
9. o. 6,
s.
i
37. 3
42. 1 +I
41. 5
41 ~-.!!/
17
• 28
28
MIXED REVIEW 15
1.
)
-i
2. ;
3.
s.
All real numbers
9.
-~.
s -~3
2 1
13.
5' 3
18.
±~
10.
~e'
7
~
4. No solution
8. - 7
-4
-2
11. 9, -4
2' -1
15. 3,
19. ±41
20.
14.
7. 6,
-29
±f,
9
18.
21.
8. 4
12. -6, 4
3
±2
±'./21
3
17. 0
22.
o. 52
Answers
123
"
-lo
IV. Answer Key
l. ~h 2
:it)- ~
Je.19-l> I eA-/-.S
S"Hli...E- T
1
(h'+fc..J. ~, Pr.t1..dit!L- J>ro!l4!M.S.
2. -3, 5
... 4\ 3 - , 5
.).
4. 9,·13
5. 2\ 6 - 6\ 5 - 3\ 3
6. 6, 35- 20, s-a, 7
7. 4\ 5 -
s, 3 -
-
6, 2
.-
8. 32, 3- 36, 7
-
-
9. -21, 2 - .31\' 3
10.
-4', 5
11. 3\'5- 4,2- 6\•10
12. 7\ 3- 7\ 5
13.0
14. s, 3 - 7, 5
-
4\ 15
15. -, 11- 6\ 2- l·h 3
16. 54\ 6- \ 10
17. 70v 14· - 12v·3
18. 7,s-, 10
19. 36 - 4-\ 35
20. 9\ 2 - 14\ 30 - 3" 5
t'5':5':~~~Ja~.'"!'lniee~kMwpliJ¥.l;J~oadiie&ll:s-eeftiire-ieeinpa•iBt--theTctdicend!r.
6
.~~-41 '1s:Pf'
'!'4\ £3
~s ,
13
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