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
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-
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
!'
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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. 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
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