AB CALCULUS ALGEBRA REVIEW - Bergen
10
AB CALCULUS ALGEBRA REVIEW MULTIPLY THE FOLLOWING POLYNOMIALS 1. ) 1 2 2 )( 2 3 ( 2 + − + s s s 2. ) 4 2 )( 2 3 ( 2 + − − z z z 3. 2 ) 3 2 ( + x SOLVE FOR x 4. ) 3 )( 1 ( ) 5 )( 2 ( − − = − + x x x x 5. 0 ) 1 ( 2 ) 4 )( 5 2 ( = − + − − x x x x FACTOR 6. 2 2 15 9 6 b ab a − − 7. 3 8 18 x x − 8. 2 2 3 20 20 15 rs s r r − + 9. b a b a ab 3 2 15 9 6 − + 10. 2 2 5 10 5 b ab a + + 11. 2 2 12 18 6 d cd c + + 12. 3 2 27 3 x xy − 13. ab a b a a 6 3 2 2 2 3 − + − 14. 4 4 b a − 15. 3 2 2 3 2 4 8 b ab b a a − − + 16. ) 3 ( 8 ) 3 )( 2 ( − − − + a a a a SIMPLIFY 17. x x 4 5 2 1 2 − 18. y x y y x x − + + 19. 2 2 3 1 2 2 + − − + d d d
Transcript of AB CALCULUS ALGEBRA REVIEW - Bergen
ABCALCULUSALGEBRAREVIEWMULTIPLYTHEFOLLOWINGPOLYNOMIALS
1. )122)(23( 2 +−+ sss
2. )42)(23( 2 +−− zzz
3. 2)32( +x SOLVEFORx4. )3)(1()5)(2( −−=−+ xxxx 5. 0)1(2)4)(52( =−+−− xxxx FACTOR
6. 22 1596 baba −− 7. 3818 xx −
8. 223 202015 rssrr −+ 9. babaab 32 1596 −+
10. 22 5105 baba ++ 11. 22 12186 dcdc ++
12. 32 273 xxy − 13. ababaa 632 223 −+−
14. 44 ba − 15. 3223 248 babbaa −−+ 16. )3(8)3)(2( −−−+ aaaa SIMPLIFY
17.xx 45
212 − 18.
yxy
yxx
−+
+
19.22
312
2 +−
−
+
ddd
WRITEASAFRACTIONINSIMPLESTFORM
20.2132
+
+−yyy 21. 1
231
+−
−−
bbb
22. ⎟⎠
⎞⎜⎝
⎛ +÷⎟⎠
⎞⎜⎝
⎛ −nmm
nnm 11
23. 111+
+
−+zzz
24.42
24
++
−++
vv
vv
25.baba
ba+
−−
+ 1322
DIVIDEUSINGLONGDIVISIONORSYNTHETICDIVISION
26.4122
−
−−
xxx
27.1319 2
−
+
yy
28.2
22 23
+
++−
nnnn
29.216
2
4
+
+
zz
SIMPLIFYTHEFOLLOWINGRADICALS,RATIONALIZINGTHEDENOMINATORIFNECESSARY.
30. ( )( )( )2738223 − 31. ⎟⎠⎞⎜
⎝⎛⎟
⎠⎞⎜
⎝⎛ 5
3332 yy
32.52 33.
157
34. 127811 −− 35.313 −
SIMPLIFY.EXPRESSANSWERSWITHPOSITIVEEXPONENTSONLY.
36. 47 93 −⋅ 37. ( ) 132−−
38.( )
1
123
242−
−− ⋅ 39.
42
32
−−
⎟⎟⎠
⎞⎜⎜⎝
⎛
nn
40. ( ) 122 33−− ⋅ xx 41. 5
3
−
−
dd
EXPRESSINEXPONENTIALFORM
42. 7 5 43. ( )54 3 SIMPLIFY
44. 3127 45. 4
381 46. 34125
SOLVETHEFOLLOWINGQUADRATICEQUATIONS
47. 1582 −=+ nn 48. 805 2 =r
49. 02032 2 =−+ xx 50. yyy 1130120445 2 +−=+− SOLVEUSINGAQUADRATICEQUATION51. Thewidthofarectangularparkis5mshorterthanitslength.Iftheareaoftheparkis300m2,findthelengthandthewidth.52. Ifthesidesofasquareareincreasedby3cm,itsareabecomes100cm2.Findthelengthofthesidesoftheoriginalsquare.53. Hollyhasarectangulargardenthatmeasures12mby14m.Shewantstoincreasetheareato255m2byincreasingthewidthandlengthbythesameamount.Whatwillbethedimensionsofthenewgarden?
ABCALCULUSPRECALCREVIEWWRITETHEEQUATIONFORTHESPECIFIEDLINE
54. Through(-3,6)and(1,-2)
55. Through(3,3)and(-2,5)
56. Thehorizontallinethrough(2,-3)
57. Theverticallinethrough(2,-3)
58. Through(3,1)andparallelto2x–y=-2
59. Through(4,-12)andparallelto4x+3y=12
60. Through(-2,-3)andperpendicularto3x–5y=1
61. Through(1,4)andperpendiculartoy=-x+2
DRAWTHEGRAPHOFTHEFOLLOWINGFUNCTIONS
62. 23 +−−= xy 63. 142 +−= xy
64.
⎪⎪⎩
⎪⎪⎨
⎧
<
≤−=
xx
xxxf
1,2
1,3)( 65.
⎪⎪⎩
⎪⎪⎨
⎧
≤
<=
xx
xxf
0,
0,1)(
66. ⎪⎩
⎪⎨
⎧
<−
≤≤
<
=
xxxxxx
xf2,1220,0,
)( 3
2
WRITEAPIECEWISEFORMULAFORTHEGIVENFUNCTION
67. . 68.
FOREACHPAIROFFUNCTIONSFIND: ( )xgf ! ( )4gf ! ( )xfg ! ( )4fg !
( )xgg ! ( )4gg !
69. ( ) 5+= xxf 3)( 2 −= xxg
70. ( ) 1+= xxf 1)( −= xxg
71. ( ) 21 xxf −= xxg =)(
Algebraically,findtheintersectionofthefollowing
72. 3x–5y=9 x+y=3
73. y=x2–16 y=x–1
74. 2x+y=10 y=9–x2REWRITETHEEXPONENTIALEXPRESSIONTOHAVETHEINDICATEDBASE
75. y=92x base3 76. y=163x base2
77. y=(1/8)2x base2 78. y=(1/64)x base4
SOLVEFORx.79.1600=e5x 80. ln(3x)=10
81.10ex-5=125 82. -ln(2x)= 21
83.(1.5)x=2 84. 5(3x)=1 85.-2log(7x)=2 86.log2(x)+log2(x-1)=1
FINDTHEINVERSEFUNCTION 1−f FORTHEFOLLOWING
87.f(x)=2x+3 88. f(x)=x3–1
89.f(x)= 32x ,x≥ 0 90. f(x)=x2+2x+1,x≥ 1
91.Given θ = cos−1(3 / 7) find sinθ, tanθ,& cscθ
TRIGFUNCTIONSFORCOMMONANGLES
Youareexpectedtomemorizethetrigfunctionvalues(sin,cos,tan)forthecommonangleslistedbelow.Allanglesareinradians.
92.FillinthefollowingchartWITHOUTacalculator!!EXACTanswersONLY!
FindthevalueWITHOUTacalculator!Exactanswersonly!
93. sin 2π3
!
"#
$
%& 94. tan 5π
3!
"#
$
%& 95. cos 3π
4!
"#
$
%&
96. sin 7π6
!
"#
$
%& 97. csc 7π
4!
"#
$
%& 98. sec 5π
6!
"#
$
%&
θ 0 π6 π
4 π
3 π
2
π 3π2
2π
Sinθ
Cosθ
Tanθ
99.Solveeachequationfor0 ≤θ < 2π withouttheuseofyourgraphingcalculator.
a)cscθ=2 b)tanθ +4 = 5 c) 2cosθ = -1
100.Sketchthegraphsthefollowingfunctionswithoutacalculator!Youwillbeexpectedtoknowthesegraphswithouttheuseofyourgraphingcalculator!
a) y=sinx b) y=cosxc) y=tanxd) y=1/xe) y=1/x2f) y=x2g) y=x3h) y= x i) y= x3 j) y=x3/2k) y=x2/3
