PreCalc AMC Practice worksheets

240 Pages·2007·7.93 MB·English

Merrill
AdvancedMahematicalConcepts
GLENCOE
McGraw-Hill
New York, New York
Columbus, Ohio
Woodland Hills, California
Peoria, Illinois
1 1
Copyright© byGlencoe/McGraw-Hill.
All rightsreserved.Permissionisgrantedtoreproducethematerialcontainedhereinonthe
conditionthatsuchmaterialbereproducedonlyforclassroomuse;be providedtostudents,
teachers,andfamilieswithoutch.arge;andbe usedsolelyinconjunctionwithMerrillAdvanced
MathematicalConcepts.Any otherreproduction,foruseorsale, isprohibitedwithoutprior
writtenpermissionofthepublisher.
Sendallinquiriesto:
Glencoe/McGraw-Hill
936EastwindDrive
Westerville,OH43081
ISBN:0-02-824292-0
PrintedintheUnitedStatesofAmerica.
6789101112131415 009 0302 01009998
CONTENTS
Lesson Title Page Lesson Title Page
1-1 Relationsand Functions..................1 5-8 AreaofTriangles...........................35
1-2 Composition andInverses of
Functions....................................2
1-3 Linear Functionsand 6-1 GraphsoftheTrigonometric
Inequalities..................................3 Functions..................................36
1-4 Distanceand Slope.........................4 6-2 Amplitude,Period,and
1-5 FormsofLinear Equations..............5 PhaseShift...............................37
1-6 Paralleland Perpendicular 6-3 Graphing'Trigonometric
Lines ...........................................6 Functions..................................38
6-4 Inverse"l'rigonometric
Functions..................................39
2-1 SolvingSystemsofEquations.........7 6-5 PrincipalValues ofthe
2-2 Introduction to Matrices...................8 InverseTrigonometric
2-3 Determinantsand Multiplicative Functions..................................40
InversesofMatrices....................9 6-6 GraphingInversesof
2-4 SolvingSystemsofEquations TrigonometricFunctions...........41
byUsingMatrices .....................10 6-7 SimpleHarmonicMotion...............42
2-5 SolvingSystemsof Inequalities....11
2-6 LinearProgramming......................12
7-1 BasicTrigonometric
Identities ...................................43
3-1 Symmetry......................................13 7-2 VerifyingTrigonometric
3-2 FamiliesofGraphs........................14 Identities ...................................44
3-3 Inverse Functionsand 7-3 Sumand Difference
Relations...................................1.5 Identities ...................................45
3-4 Rational Functionsand 7-4 Double-Angleand Half-Angle
Asymptotes...............................16 Identities ...................................46
3-5 Graphsof Inequalities...................17 7-5 SolvingTrigonometric
3-6 Tangenttoa Curve .......................18 Equations.........................".........47
3-7 Graphsand CriticalPointsof 7-6 Normal Formofa Linear
Polynomial Functions................19 Equation....................................48
3-8 ContinuityandEndBehavior..........20 7-7 Distancefroma Pointtoa
Line ...........................................49
4-1 PolynomialFunctions....................21
4-2 QuadraticEquationsand 8-1 GeometricVectors ...................._..5.0
Inequalities................................22
4-3 The Remainderand Factor 8-2 AlgebraicVectors ..........................51
Theorems..................................23 8-3 Vectors inThree-Dimensional
4-4 The RationalRootTheorem..........24 Space........................................52
8-4 PerpendicularVectors ...................53
4-5 Locatingthe Zerosofa
Function....................................25 8-5 Applications withVectors ..............54
4-6 RationalEquationsand 8-6 Vectors and Parametric
PartialFractions........................26 Equations ..................................55
4-7 RadicalEquationsand 8-7 UsingParametricEquations
Inequalities................................27 to ModelMotion........................56
5-1 Angles andTheir Measure............28 9-1 PolarCoordinates .........................57
5-2 CentralAngles andArcs ...............29 9-2 Graphsof PolarEquations............58
5-3 CircularFunctions....'.....................30 9-3 Polarand Rectangular
5-4 Trigonometric Functionsof Coordinates ..............................59
SpecialAngles ..........................31 9-4 PolarFormofaLinear
5-5 RightTriangles..............................32 Function....................................60
5-6 TheLawofSines ..........................33 9-5 SimplifyingComplex
5-7 TheLawofCosines ......................34 Numbers ...................................61
=I=ImI
GlencoDeivisionM,acmillan/McGraw-Hill
CONTENTS
Lesson Title Page Lesson Title Page
9-6 PolarFormofComplex 13-6 The MandelbrotSet.......................93
Numbers ...................................62
9-7 ProductsandQuotientsof 14-1 Permutations.................................94
ComplexNumbersin
14-2 Permutationswith Repetitions
PolarForm................................63
andCircularPermutations.........95
9-8 Powersand Rootsof
14-3 Combinations................................96
ComplexNumbers ....................64 14-4 Probabilityand Odds.-....................97
14-5 Probabilitiesof Independent
10-1 The Circle......................................65 and DependentEvents .............98
10-2 The Parabola.................................66 14-6 ProbabilitiesofMutuallyExclusive
10-3 The Ellipse....................................67 or InclusiveEvents....................99
10-4 The Hyperbola...............................68 14-7 ConditionalProbability ................100
10-5 ConicSections ..............................69 14-8 The BinomialTheoremand
10-6 TransformationsofConics ............70 Probability...............................101
10-7 SystemsofSecond-Degree
EquationsandInequalities.........71
10-8 Tangents and Normalsto 15-1 The FrequencyDistribution.........102
the Conic Sections....................72 15-2 MeasuresofCentral
Tendency .........................'.......103
11-1 Rational Exponents.......................73 .15-3 MeasuresofVariability................104
15-4 The NormalDistribution..............105
11-2 ExponentialFunctions...................74
11-3 The Numbere ...............................75 15-5 Sample Setsof Data...................106
15-6 Scatter Plots................................107
11-4 LogarithmicFunctions...................76
11-5 Common Logarithms.....................77
11-6 Exponentialand Logarithmic 16-1 Graphs ........................................108
Equations..................................78 " 16-2 Walksand Paths.........................109
11-7 NaturalLogarithms........................79 16-3 .EulerPathsand Circuits..............110
16-4 ShortestPathsand Minimal
Distances ................................111
12-1 ArithmeticSequencesand 16-5 Trees ...........................................112
Series........................................80
16-6 Graphsand Matrices...................113
12-2 GeometricSequencesand
Series................................._......81
12-3 InfiniteSequencesand 17-1 Limits............................................114
Series........................................82 17-2 Derivativesand
12-4 Convergentand Divergent DifferentiationTechniques.......115
Series................................i.......83 17-3 AreaUndera Curve....................116
12-5 SigmaNotationandthe nth 17-4 Integration...................................117
Term .........................................84 17-5 The FundamentalTheorem
12-6 The BinomialTheorem..................85 ofCalculus ..............................118
12-7 Special Sequencesand
Series........................................86
12-8 Mathematical Induction.................87 .
13-1 IteratingFunctionswith Real
Numbers ...................._..............88
13-2 Graphical Iterationof Linear
Functions ..................................89
13-3 Graphical Iterationofthe
Logistic Function.......................90
13-4 ComplexNumbersand
Iteration.....................................91
13-5 EscapePoints, Prisoner
Points,andJulia Sets...............92
iv
GlencoDeivisionM,acmillan/McGraw-Hill
NAME DATE
1-1 Practice Worksheet
Relations and Functions
State the domain and range of each relation. Then state whether the relation is a
function. Write yes or no.
1. {(-1, 2), (3, 10), (-2, 20), (3, 11)} 2. {(0, 2), (13, 6), (2, 2), (3, 1)
3. {(1,4), (2, 8), (3, 24)} 4. {(-1,--2), (3, 54), (-2,-16), (3, 81)}
Given that x is an integer, state the relation representing each of the following by
fisting a set of ordered pairs. Then state whether the relation is a function. Write yes
or no.
5. y = 3x2 - 5 and 0 < x < 5 6. y2 = 3x2and x = -3
7. 13y+41 =xandO<x<3 8. lyi = Ixl andO<x<2
The symbol [x] means the greatest integer not greater than x. If f(x) = [2x] • 3x, find
,each value.
9. f(o) 10. f(o.5) 11./(-3.5) 12. f(x- 1)
Given f(x) = 13x- 41+ 5, find each value.
13. f(l/ 14. f(0.5) 15. f(-0.5) 16. f(5d)
\°]
Name all values of x that are not in the domain of the given function.
1
17. f_(x) - xx+- 24 18. f(x) =:_2x+ 51
19. f(x) = k/_x2-25 20. f(x) - x - 10
_16
21', f(x) -- xx22_+2255 22. f(x) - _x---17
1
Glencoe Division, Macmillan/McGraw-Hill
NAME DATE
1-1 Practice Worksheet
RelationsandFunctions
State the domain and range of each relation. Then state whether the relation is a
function. Write yes or no.
1. {(-1, 2), (3, 10), (-2, 20), (3, 11)} 2. {(0,2), (13, 6), (2, 2), (3, 1)
{-2, -1, 3}, {2, 10, 11, 20}; no {0, 2, 3, 13}, {1, 2, 6}; yes
3. {(1,4), (2, 8), (3, 24)} 4. {(-1,-2), (3, 54), (-2,-16), (3, 81)}
{1, 2, 3}, {4, 8, 24}; yes {-2,-13}, {-16,-2, 54, 81};
no
Given that x is an integer, state the relation representing each of the following by
listing a set of ordered pairs. Then state whether the relation is a function. Write yes
or no.
5. y = 3x2 - 5 and 0 < x < 5 6. y2 = 3x 2and x = -3
{(1,-1), (2, 7), (3,22), (4,43)};yes {(-3, 3_/3-3,-3Vr3); no
7. 13y+41 =xandO<x<3 8. lyl = Ixl andO<x<2
5 2
{(1,-1),(1,- _),(2,-_),(2, =2)}; {(1, 1),(1,-1)}; no
no
The symbol [x] means the greatest integer not greater than x. If f(x) =[2x] - 3x, find
each value.
9. f(O) 10. f(0.5) 11. f(-3.5) 12. f(x - 1)
0 -0.5 3.5 [2x]-3x+l
Given f(x) =13x- 41+5,find each value.
/ \
13. f(1) 14. f(0.5) 15. f(-0.5) 16. f(5d)
8 7.5 10.5 115d-41+5
Name all values of x that are not in the domain of the given function.
17. f(x)- x_+-42 18. f(x) - 12x1+5J
-4 _5
2
19. f(x) = _- 25 20. f(x) - x - lO
-5< x< 5 -4 _<x _<4
21. f(x) - x2+25 22. f(x) - x - 7
x2- 25 _ : ]
___5 ___1-
T1
, GlencoeDivisionM,acmillan/McGraw-Hill
NAME DATE
1-2 Practice Worksheet
Composition and Inverses of Functions
Given f(x) - x2+4 and g(x) = x2- 2, find each function.
1.(f+g)(x) 2.(f-g)(x) 3.(f'g)(x) 4. (f/(x)
\_/
Find If og](x) and [g of](x).
5. f(x)= _1x + 5 6. f(x)= 2x3-3x 2+1
g(x) = x - 3 g(x) = 3x
7. f(x)=2x 2 5x+1 8. f(x)=3x 2-2x+5
g(x) = 2x - 3 g(x) = 2x - 1
Determine if the given functions are inverses of each other. Write yes or no. Show
your work.
9. f(x) = 3x - 5 10. f(x) = x - 10 11. f(x) - 2x-5 3
g(x) - x +3 5 g(x) = x + 10 g(x) - 3x-3 5
12. f(x) = 2x 13. f(x) = 3x - 7 14. f(x) = 4(x + 2)
1 x_2
g(x) - 2x g(x) = _ x+ 7 g(x) = 4
Find the inverse of each function. Then state whether the inverse is a function.
15. f(x) = 3x + 7 16. f(x) = x5 17. f(x)= x2 + 4
GlencoeDivision,Macmillan/McGraw-Hill
NAME DATE
1-2 Practice Worksheet
Composition and Inverses of Functions
Given f(x) -_ x 2+Z4_and g(x) = x2- 2, find each function.
1.(f+g)(x) 2.(f-g)(x) 3.(f'g)(x) 4. (f/(x)
\s/
x3+4x2-2x-6 -x3-g'_2+2x+ 10 2x2-4 2
X+4 _ _'+_ ' X+4 _ (x+4)(X2-2) '
x _ -4 _ ¢ =4 x_¢ -4 x_i-4, _+V_
Find [f og](x) and [g of](x).
5. f (x) = 1
-_x + 5 6. f(x) = 2x3- 3x2 + 1
g(x) = x - 3 g(x) = 3x
X +4, 54X3-27X2+ 1,
1
-_X + 2 6X3-gX2+3
7. f(x) = 2x2- 5x + 1 8. f(x) = 3x2- 2x + 5
g(x)= 2x- 3 g(x) = 2x- 1
8xz. 34x+ 34, 12xz- 16x+ 1O,
4x2-10x-1 6x2-4x+9
Determine if the given functions are inverses of each other. Write yes or no. Show
your work.
9. f(x) = 3x - 5 10. f(x) = x - 10 11. f(x) = 2x5- 3
g(x) - x +5
3 g(x) = x + 10 g(x) = 3x-5
3
yes yes no
12. f(x) 2x 13. f(x) = 3x - 7 14. f(x) = 4(x + 2)
=2_ 1 x -2
g(x) x g(x) = -_x + 7 .g(x) = 4
no no yes
Find the inverse of each function. Then state whether the inverse is a function.
15. f(x) = 3x + 7 16. f(x) = x5 17. f(x) = x2 + 4
f_l(x) 1 s.
=_x-_, yes f-l(x)=ffx, yes f-l(x)=_+_v/x-4;
no
T2
GlencoeDivision,Macmillan/McGraw-Hil
Find the zero of each function.
4. f(x) = 0.2x + 10 5. f(x) = 11.5x 6. f(x) = 13x - 9
7. f(x) = -3 8. f(x) = -5x + 6 9. f(x) = 0.3x + 0.2
Graph each equation or inequality.
10. y = 3x-2 11. 1- y = 2x 12. x->-2
.-...-....._. y _ _- _ _--- y ...... _'=_ ._
*- c x _ x 5
i '
13. y= 12x+41 14.-y>2x+2 15. -4-<x-2y-<6
__ __d _ ...... y.... :...... y&--
....... -.---- __ ...........
*" -- 0 __x_ _ x ..... (:.....
............. i
I i I ' ,
3
Glencoe Division, Macmillan/McGraw-Hill \
NAME DATE
1-3 F'l"acticeWorkstl 2c_t
Linear Functions and Inequalities
Write an inequafity that describes each graph.
1. 2. 3.
_- _ ...............
__- ___ _._ ......
.... ___ ............ ....
.-...-.... -_-_--_ ._............ ........ E, __
y-> -2x-4 -2 -<y_< 4 _-3-< Y-< -5_-_+4
Findthezeroof eachfunction.
4. f(x) = 0.2x + 10 5. f(x) = 11.5x 6. f(x) = 13x - 9
9
-50 0 _3
7. f(x) = -3 8. f(x) = -5x + 6 9. f(x) = 0.3x + 0.2
6 2
none
5 3
Grapheachequationor inequality.
10. y = 3x-2 11. 1-y = 2x 12. x ->-2
.... L_L__...... ___z L__ _ _y __
.... _- _ ........ _- __.__ _ __ _--
._... _-t..... T _,3-7 _--....._ ........ . --
_ ____/-:--- ..... _.... ; -........ _
_ _ x__ _ _ x
-_ _-_--- .............
_ __-/ ............... _ ...... _ __
__ • x .'_-:2
T3
Glencoe Division, Macmillan/McGraw-Hill