Co(ege Level Math Study Guidefor the $CC UPIACER (CPT)

Created by Aims Community College English Facultywww. a i m s. ed u/As s ess m e n tS i te/a cc u p I a ce r_i n fo rm a ti o n . htm

The following sample questions are similar to the format and content of questions on theAccuplacer College Level Math test. Reviewing these samples will give you a good idea of how the testworks and just what mathematical topics you may wish to review before taking the test itself. Our purposesin providing you with this information are to aid your memory and to help you do your best.

I. Factoring and expanding polynomialsFactor the following polynomials:

l. 1 5a tb'

- 45a'bt - 60a2b

2. 7x3y' + Zlx 'y ' - l0xty ' -30* 'y

3. 6xa yo - 6*ty ' + 8xy2 - 8

4. 2x2 -7xy + 6y'

5. yo +y'-6

5. 7x3 + 56y3

7. 81r4 - l6sa

8. (* * y) ' + 2(x+ y)+ 1

Expand the following:

s. (** tX"- tX*-3)ro. (Z*+ 3 y) 'lr. (",6.+.6)(.J6.-fr)12. (*' -2x* 3)t

13. (x + 1)t

14. (* - l)u

IL Simptification of Rational Algebraic ExpressionsSimplify the following. Assume all variables are larger than zero,

t . 32+5-J4+402. 9+3.5 8 ' -2+27

lsL3' r/r5.

IU. Solving EquationsA. Linear

t . 3-2(*-1) -x-10

z. x- I=l

B. Quadratic & Polynomial( 8\r ?)=o[v-;J['* ')2. 2x3 - 4x2 -30x - 0

6.

7.

8.3.4.

5.

27x3 - 1(x -:X" + 6) = 9x +22t2 +t+1-0

4. z$B -sJn +T^h6z

6x-18 lZx-16

3x2 *2x- 8 4x-12

3. V(y +2) = y ' -64. 2l*- (1 - l*I = 3(x + 1)

3x3 = 24(** l ) '+xt =25

5y'-Y=l

05129t0r l :22 3 CED3CE I -0954-425 8. doc

C. Rational

r . 1 + 2 -o

y-1 y+1

x-3 x+3l2

+--6-x x*3

t2-x" -9

5x

x'-3x-18

Absolute value

r . ls -2r l -1=82. l "*51 -7=-23. ls*- t l - -2

Exponential

l . 10* = 10002. 1g3x+5 = 100

3. 2x+L = I

8

F. Logarithmic

l . log, (* + 5) - log, (1 - 5*)

2. 2logr(* * 1) = log, (+*)

3. log, (* + 1)+ log, (* - 1) = J

4. ln x * ln (2"+ 1)- 0

G. Radicals

1. 4J2y 1-2- o

z. Jzx+l+5-83.

' , i -2.,fuA-0

11 _ 2 _x'-25 x-5 x+5I -6-=a a2 +5

-1 I xI

x'-3x x x-3

lnx + h(x +2) = h3o 2x ,,r x*lJ =+

J. l . . '+g*x*1=o\hx+z+4-6

{w'+? -2

3. 3(r + 2) - 0 > -2(*- 3)+ la

4. 2<3x-10<5

4.

5.

6.

2.

3.

D.

4.

5.

I r 3 l Ir -X--r =-

12 41 4

lv- l= lz*vl

4. 3.'(9. )= +; . 2*, (4r . )= *

E.

5.

6.

4.

5.

6.

IV. Solving InequalitiesSolve the following inequalities and express the answer graphically and using interval notation.

. Linear

7l. x+4<-2

5z. 3(r+3) >s("-1)

0sl29l0r 2:22 3 CED3 CE I -09 54-4258. doc

B. Absolute value: Solve and Graph.

1 l+"+{<62. l+*+31 +2>e

C. Quadratic or Rational

t . 3x2 - I Ix-4<0z. 6x2+5x>4

3 lx+sl=tl3 l

4. ls - z"l < t5

3.

4.

x*2>03-x(x + t)(x -:) < o

2x +7

V. Lines & Regions

1. Find the x and y-intocepts, the slope, and graph 6x + 5y = 39.2. Find the x and y-intercepts, the slope, and graph x = 3.3. Find the x and y-intercepts, the slope, and graphy = -4.4. Write in slope-intercept form the line that passes through the points (4, 6) and (-4,2).5. Write in slope-intercept form the line perpendicular to the graph of 4x - y = -l and containing the

point (2, 3).6. Graph the solution set of .x - y 22

7. Graph the solution set of -.r +3y < -6 .

Vl. Graphing Relations, Domain & RangeFor each relation, state if it is a function, state the domain & range, and graph it.

r . y-Jx+22' Y = J-. -2

3. y- x- lx+2

4. f (*)=-1"+11 +3

s r(*)=X

VII. Exponents and RadicalsSimplify. Assume all variables are >0.

r f f i r

6. x- y '+2

7. y-x2 +8x-6

8. y=J=

9' ! =3*

roh(*)=#

Rationalize the denominators when needed.

Ji -J,

6,

7.

8,

4 [F)'

9.

( s+u-6b') 'I - I

t 9a -'b* )2. s-rh47 - 4J 48

3 Js(".ffi--6)

W>"

1yn

zazb22

0512910r 3:22

f r+3

3 CED3CE I -09 54-425 8. doc

VUI. Complex NumbersPerform the indicated operation and simpliff.

1. "h6-aJaz. J{6.J4

J16

IX. Exponential Functions and Logarithms

Graph: f (*)=3* +1

Graph' g(x) = )x-l

Express 8-2 - ! - in logarithmic form.64

Express log ,25 - 2 in exponential form.

Solve: logrx=4

X. Systems of Equations & Matrices

2x*3y -7l. Solve the svstem:

6x-!=1x+2y +22 -3

2. Solve the system: 2x +3y + 6z - 2

'x+y+z=0

(+ -:i)(+ + 3i)(+<i) 'i "3 -2i

4+5i

Solve: log *9 - 2

Graph, h(x)= log, xUse the properties of logarithms to expand as

much as possible: log o t

vHow long will it take $850 to be worth $1,000if it is invested at 12% interest compoundedquarterly?

4. Multiply:

4.

5.

6.aJ.

7.

3.

6.

7.

8.

t .

2.

9.4.

5.

3. Perform the indicated operation:-,[j, l] .,[i a1.

2.

5.

6.

Find the determinant: ll

Find the Inverse: t 1

L-1

ilt lil_?l

:)

1 -1

02-2 I

Story Problems

Sam made $10 more than twice what Pete eamed in one month. Iftogether they earned $760, howmuch did each eam that month?A woman burns up three times as many calories running as she does when walking the samedistance. If she runs 2 miles and walks 5 miles to bum up a total of 770 calories, how manycalories does she burn up while running I mile?

3. A pole is standing in a small lake. If one-sixthof the length of the pole is in the sand at thebottom of the lake, 25 ft are in the water, andtwo-thirds of the total length is in the air abovethe water, what is the length of the pole?

0sl29l0r 4:22 3 CED3CE 1 -09 5 4-4258. doc

7. Fxpand the following: i f i)xk y4-kv fid[k,

;

Xtr. Conic Sections

l. Graph the following and find the center, foci, 2. Identiff the conic section and put into standardand asymptotes if possible. form.

a) (*-2) '*y '=16 a) x ' -4x-12+!2 =0

(x + t)' , (y - 2)' b) 9xz +l8x +16y2 - 64y = 11b)

T*7=' c) 9xz +rgx-t6yz +64y=r99

c) +-(v -z) ' - , d) x '+v-Ax=o

d) (*-2) '*y=4

XIII. Sequence & Series

l. Write out the first four terms of the sequence whose general term is dn = 3n-2 .

2. Write out the first four terms of the sequence whose general term is dn = y12 -1 .

3. Write out the first four terms of the sequence whose general term is dn = 2" +I.

4. Find the general term for the following sequence: 2,5,8, ll,14, 17, . . .

5. Find the general term for the following sequence: 4,2,1,+,+,..

o

6. Findther"* ' l2k-1k=0

XIV. X'unctions

Let f(x) = 2x-r9 ana g(x) = l6 - xt. Fi.rdthe following.

r. r(-:)+g(z) 5. (e.rX-z)z. r(s)-e(+) 6. r(ek))3. r(-t) 's(-z) 7. f- '(2)

^ r(s)/.. 8, r(r-'(3))+' '/e6

XV. Fundamental Counting Ruleo Factorials, Permutations, & Combinations

_8!l. Evaluate:

3!(8 - 3 )!2. A particular;; model is available with five choices of color, three choices oftransmission, four

types of interior, and two types of engines. How many different variations of this model care arepossible?

3. In a horse race, how many different finishes among the first three places are possible for a ten-horserace?

4. How many ways can a three-person subcommittee be selected from a committee of seven people?How many ways can a president, vice president and secretary be chosen from a committee of sevenpeople.

0sl29l0l 5:22 3 CED3CE 1 -095 4-4258. doc

1.

2.3.

XVL Trigonometry

Graph the following through one paiod: f (x)= 561

Graph the following through one puiod: g(t) = cos(Zx)A man whose eye level is 6 feet above the ground sgnds 40 feet from a building. The angle of

elevation from eye level to the top of the building is 72o. How tall is the building.

4. 4. A man standing at the top of a 65m lighthouse observes two boats. Using the data givbn in thepicture, determine the distance between the two boats.

EEEEEEEE

6ft t

05t2910t 6:22 3 CED3CE I -095 4-425 8. doc

Answers:

1. lla'U(uU -3b2 - 4)

z. 7x3y' + 2lx 'y ' - loxty ' - 3o* 'y

* 'y(7xy' +Zly , l0xy - 30) . ,*iv[*y' +2lv)+ (- loxy -30)Jx' ylt v("y + 3) - t o(*y + 3)J*'y(ty - to)(xy + 3)

3. zb*'y'* 4X"v' - 1)4. (z* -3yX" - zv)5. yo + y ' -6

u'+u-6(u-2Xu+3) \(v ' - i \ r '+ l )

Answers

I. Factoring and Expanding Polynomials

When factoring, there are three steps to keep in mind.l. Always factor out the Greatest Common Factor2. Factor what is left3. If there are four terms, consider factoring by grouping.

7. (gr - zs)(3r + 2i(9r' +ar')

8. (**y+1) ' Hint :Letu:x*y

9. x ' -3x2-x+310. 4x2 + l2xy + 9y'

1r. 3Jix2 -3Jt12. xo - 4x3 +10x2 - l2x+9

13. xt + 5xa + l0x ' + 10x' + 5x + It4. xu -6x5 +15x4 -20x' ,+15x2 -6x+1

When a problem looks slightly odd, we can make it appear morenatural to us by using substitution (a procedure needed for

calculus). Let u - y' ,'Factor'the expression with u's. Then,

substitute the yz backin place of the u's. If you can factor more,

proceed. Otherwise, you are done.

Formula for factoring the sum of two cubes:

a3 +b3 =(a+bXu'-ab*bt)The difference of two cubes is:

a'-b ' - (a-b)(r '+ab+bt)

Since there are 4 terms, we consider factoring by grouping.First, take out the Greatest Common Factor.

When you factor by grouping, be careful of the minussigr between the two middle terms.

When doing problems 13 and 14, you may want touse Pascal' s Triangle.

I11

12113 3l

l4 6 4l

6. 7(" +2il(*' -2xy + ay')

0sl29l0r 7:22 3 CED3CE I -095 4-425 8. doc

II.

1. 132. 38

93.

X-

Simptification of Rational Algebraic Expressions

4. 4gJ'

If you have J 4, you can write 4 asa product of primes (2'2). Insquare roots, it takes two of the same thing on the inside to get one

thing on the outside, J-a = J Z a - 2 .

3. v - -3 4. x:1

Solving quadratics or Polynomials:l. Try to factor2. If factoring is not possible, use the quadratic formula

-q+Jb'4ac , ) ,x= where ax" *bx+c-0.

5.

III.

x+2

Solving EquationsA. Linear

l . x:5

Quadratic & Polynomials

82l . ! -

3'32. X: 0, -3, 5

1 .1* i" ,63. ' [=

3'64. x:10,-4

-1t i . ,65. t -

14 ^42.55

B.

Note: i = GT and thnt J 12 = iJD -'iJ 2.2.3 - ZiJs

r= 2,-1 t i \6x:3, -4

IT JLI8. y-

C. Rational

6.

7.

10

v+Dh=Q

1. I + 2 =Q

y-l y+1

(v-rXv.t)[+.+1-Ly- l y+l l

(v - rXv * r)+ + (v - rXY-r

(y * 1)+ z(v:1) - o3y-1 =0

I\ r =-J3

-o(y-tXv+1)

2. Working the problem, we get x = 3. However, 3 causes tle denominators to be zero in theoriginal equation. Hence, this problem has no solution.

Solving Rational Equations:1. Find the lowest common denominator for

all fractions in the equation2. Multiply both sides of the equation by the

lowest common denominator3. Simpliff and solve for the given variable4. Check answers to make sure that they do

not cause zero to occur in thedenominators of the original equation

05129101 8:22 3 CED3 CE I -09 5 4-425 8. doc

3.x

4.5.6.

_ _ 15

4x:2d: -1, -5x- '2r l

D, Absolute Value

r . [s - 2t l -1 = 8

ls-2zl-e5-22-9 or 5-22--9-22- 4 or -22= - I4z=-2 or z-7

2. x:0or-103. No solution ! An absolute value

can not equal a negative number.4. x:2or 1

s. lv- t |= lz*vly- l=7+y or y- t=-(7+y)

0=8 or 2y--6No Solution or y = -3Hence,Y = - 3 is the onlY solution.

E. Exponential

l . 10* = 1000

10* = 103. ' .X -3

2. x: - l3. x: -44. x--1,-15. x--1,-3

F. Logarithms

l . log, (" + 5) = log ,( l - 5")x*J=1-5x

6x--4

x- -?3

2. 2logr(* * 1) = logr (+")

1og, (* +I)' - 1og, (+*)(x+l) '=4x

x' - 2x+1 :0

3. x : 3 is the o,,iy:"h1,"" since -3cause the argument of a logarithm tobe negative.

Solving Absolute Value Equations: 'l. Isolate the Absolute value on one side of the

equation and everything else on the other side.

2. Remember that l"l = Z means that the object

inside the absolute value has a distance of 2away from zero. The only numbers with adistance of 2 away from zero are 2 and -2.Hence, x: 2 or x - -2. Use the same thoughtprocess for solving other absolute valueequations.

Note: An absolute value can not equal a negative

value. l"l - -Z does not make any sense.

Note: Always check your answers!!

." .il

i,

Some properties you will need to be familiar with.

I f at =at, thenr:s.

I f at = bt , then a: b.

Properties of logarithms to be familiar with.

m exponential form as bY - x .

. ( tvt) l

of logarithms can not be negative.

0sl29l0l 9:22 3 CED3 CE I -095 4-4258. doc

I2

-1

4.

5.

6.

J

is the only solution since -l causes the argument of a logarithm to be negative.

is the only solution since -3 causes the argument of a logarithm to be negative.

32* - 4x+r

2xln3-(** t ) tn+2xln3-xln4-In4*(21n3 - ln 4)=ln4

ln4

G.2ln3 -In4

Radicals

r . 4J2y 1-2- o Solving Equations with radicals:1. Isolate the radical on one side of the equation

and everything else on the other side.2. If it is a square root, then square both sides.

If it is a cube root, then cube both sides, etc. . .3. Solve for the given variable and check your

answer.

Note: A radical with an even index such as

t - ' - en rr^f hq.ra1.1 , V ,\l e... c&11 not have a negative

argument ( The square root can but you must

..use corpplex numbers).

When solving linear inequalities, you use the samesteps as solving an equation. The difference is whenyou multiply or divide both sides by anegativenumber, you must change the direction of theinequality.For example:

5>3- 1(s). -t(r)

-5<-3

X-

2v -r

I

21

45

45

8

2y

2. x:4

3. ./flT -zJx+I - 0

fv.

2v -r

(.. Tf =QJ.*r)'5x - I - 4(x+ 1)

x-5

4. No solution. x : 4 does not work in the original equation.5. x:26, \ry: 3, -3

Solving Inequalities

A. Linear

3l. x +4<-z

53ix <-65

I ( -10

0s129101

Interval Notation: (- "",- I 0]

l0:22 3 CED3 CE I -09 5 4-4258. doc

544

f 7 s lInterval: | --"- |

L 4'4)

z. x>lor x<-t2

Interval: "")

3. x(-20 or x)10

Interval: (- ".,-201u [t 0, *)

4. -5 < x < 10

Interval: (- S,t O)

Think of the inequality sign as an alligator. If thealligator is facing away from the absolute value sign such

l l -

os, l*l < 5 , then one can remove the absolute value and

write -5 < x < 5. Thisexpressionindicatesthatxcannot be farther than 5 units away from zero.

If the alligator faces the absolute value such ur, l*l > 5 ,

then one can remove the absolute value and write

x > 5 or x < -5 . These expressions express that xcan not be less than 5 units away from zero,

For more information, see page 132 in the CollegeAlgebra tbxt. '

- l I)

<oo>

Interval Notation: (- *r7l

Interval Notation: (+, "")

Interval Notation: [+,S]4.

2. x{7

3. x>4

Absolute Value

1. l+"+{ <6

-6<4x+1<6-7<4x<5

-Z(;14

7

4

4<x<5 < F F >

45

[ - "" ' - )u(1 '

-5 l0

05129101 lI:22 3 CED3CE 1 -095 4-4258. doc

3 everywhere in the first region.Likewise, x-4 will be negativethroughout the l*role first region. If xis a number in the first region, then

a_,.- ( r,) H1,ff:ilxlH,Ti#';#:i::"Answer: | --.+ |I f ' 'J positive, x in the first region is not a

i l solution. Continue with step 5 until

., ( __ _1.l , , I r _) ilufl,ffi*rion tlat satisnes the

z, | -€.-- l \ . , , 1 - .6 |

[ ' Z )- lZ' ) 7 ' Especially with rational expression,

^ t aa\ checkthatyourendpointsdonot3' F z,J ) make the original inequality

( l \ r rundef ined.4. l -* , -* luf t , l l

\ z ) Page 145 of the College Algebra textdiscusses this topic in detail.

V. Lines and Regions

For details on how to solve these problems, see page 263 of theCollege Algebra text.

l. x - intercept: (5, 0)y - intercept: (0, 6)

6slope: -

5

2. x - intercept: (3, 0)y - intercept: Noneslope: None

C. Quadratic or Rational Steps to solving quadratic or rationalinequalities.

l. 3x2 -11x - 4 < 0 < 1' Zero should be on one side oftheinequality while every thing else is on

(3x + 1)(x - a). 0 +-----__ the other side.I ----2. Factor

x = -i and x : 4 make the abOve <-3. Set the factors equal to zero and solve.3 - 4. Draw a chart. You should have afactors zero.

,/ number line and lines dividing regionson the numbers that make the factorszero. Write the factors in on the side.

x- 4substitute it in for x in each factor.

| | 6. In our example, 3x+l is negative in*re first region when we substitute a

I I number such as -2 in for x.

- -:- 4 Moreover, 3x+1 will be negative

05t29t0r 12:22 3 CED3 CE I -09 54-425 8. doc

3. x - intercept: Noney - intercept: (0, -4)slope: 0

4.

5.

IV- X+4J2

I . r lv- x+i-142

6. -y>2

7. -x+3y <-6

05129101 13:22 3 CED3CE 1 -095 4-4258. doc

Graphing Relations

For details on how to solve these problems, see Chapter 2 of the College Algebra text.

1. y-^ l x{2Domain: [- Z, "")Range: [0, *)

z. y - J-* -2Domain: h,*)Range: 1.2,*)

x-13. y-' x+2

f (*)=. lx+11 +3Domain: (-

-, -)Range: (-

-,3]

Domain: All Real Numbers except -2

Range: (- -,1)

u (t,"")

4.

0sl29l0r l4:22 3 CED3 CE 1 -09 5 4-425 8. doc

s f (*1-2\-sx'-9

Domain: All Real Numbers except t 3Range: All Real Numbers.

6. x=y'+zDomain: 2,*)Range: (- t-,

"")

7. y-x '+8x-6

Domain: (- -,

*)

Range: l-22,*1

8. y -"1 - .Domain: (- *,0]

Range: [0, "")

0sl29l0l 15:22 3 CED3 CE I -09 5 4-425 8. doc

6. x : 3; -3 is not a solution because bases are not allowed to be negative

7. n(*)= log, x

*sf dN+{$4{s$!r{'di$'}drf

iFt'$tstws$tr$'*!t$d'F

{sr{rs{c*'n$'ts

E

8. log o1= log 43 -logo yv

s A- r( t* l l "\ n)

f A-mdney.ndrOwithII P - Principle started withI

where J r-yearlyinterestrateI

I n = number of compounds per year\ . I

L t = humber of years

lo

lo l

4

)- '

2 )o ':)

o=7o)7)) ) _7)

log

-osl

l720\nt20)i)

lo

I loe

000'

20n

(zor l' \.tz(zo'\ . 17.

l

4lo

-(3[,

, I24

r \at'_ lI/. l

I

+-

t2

85

(

\.

=

8i

=

,(- \

al1

+)t

g

05129101 18:22 3 CED3CE I -095 4-4258. doc

7. ! =3*

Domain: (-*,*)

Range: (0, "")

8.fr(*) =#

Domain: All Real Numbers except - ],fJ

Range: (2,*)u (- "",0]

VII. Exponents and Radicals .). For details on how to solve these problems, see page 29 and36l of the College Algebratext.

1. 4-x

2.

3.

4.

5.

6.

5..,6-trx7

7

_ uubt '

36

3a' . i .@ 3a'Jffi 3'J4ab7.

8.

9.

..F +Jj{z*te {m 2ab 2b

3 CED3 CE I -095 4-425 8. doc

s$47 -4J4s - 3s..6 -L6J: -rs$

2xJ5x

v'

2a2bz

0512910r l6:22

1.

2.

3.

Complex Numbers

Jn -4.,1 4 =4i-rzi=-8i

"h6..1 4 =(+iXl i ) =tz iz -- t2

h6 4i 4i 3i r2i2 -n 4-=-=-.-=-=-=-J-g 3i 3 i 3 i g iz -9 3

(+ -: i)(+ + 3i) = t 6 -9i2 -16 +9 = 25

(+ 3i)' - (4- 3i)(+ - 3i) = 16 - 24i + eiz - 16 - z4i - e - 7 - z4i

iz ' = i , i2a - i ( i ' ) t ' - i ( - t )" - i

3 - 2 i .4 - 5. i _ 12 * 23i +10i2 _12 - 23i -10 _L23i

4.

5,

6.

7.4+5i 4-5i 16-25i2

Exponential Functions and Logarithms

1. f (*) =3'+1

2. S(t) = )x- l

16 +25 4l

3. log,I - - /64

4.

5.

52 -25

log ,x = 4

24=[16=x

0st29tjr 17:22 3 CED3 CE I -095 4-4258. doc

X. Systems of equations

Please see chapter 5 ofthe College Algebratext for an explanation of solving linear systems andmanipulating matrices.

2.I (: '2'-;)

3 [ , ' i l ]

5.5

Story Problems

1. Let x - the money Pete earns

2x*10:the money Sam earns

2. x - burned calories walking

3x - burned calories running

3. x : length of pole

Conic Sections

(z*+lo)** =760

}Qx) +5x =770x: 70

2 ' I-X + 2J +-X = X36

t

forke Naturalnumbers

{{Pete earns 5250

Sam earns $510

Answer: 2I0 Calories

Answer: 150 feet

3, 2K+-

558, 2

k+-55

k

4.

6.

For an explanation of the theory behind the following problems, see chapter 7 of the CollegeAlgebra text.

1. a) (x-2) '+y '=16

Center: (2, 0)Radius: 4

- l o 2l2 4 ol1 -2 -5J

I 1 l5 - t lI 1 l44J

asngrcl 19:22 3 CED3 CE I -095 4-4258. doc

, \ (x+1) ' , (y-2) ' _1b)

\ / * ,n

, _r'169

Center, (- I,2)I r - \

Foci ' ( -1tJ7,2)

c)(x+1) ' _(y-2) '_1

t69

Center' (- I,2)

Foci' (- 6,2),(+,2)

!= 3* -2Asymptotes:

r O, O,

Y-- 4**A

(x- 2) ' + y - 4

vertex , (2,+)/ ,5)

Foci : | 2, t ' - |\ '4)

Directrix: y -Y-4

2. a) Circle

b) Ellipse

c) Hyperbola

d) Parabola

(x - 2) ' +y ' -16

(x + r) ' * (y - z) ' - ,169

(x + 1) ' _$ -z) ' _t169

y--(x -2) '*+

05129101 20:22 3 CED3CE I -0954-425 8. doc

XII. Sequence and Series

For an explanation of Sequences and Series, see Chaper 8 in the College Algebra text.

l . l , 4, '1, l0

2. 0, 3, 8, 15

3. 3, 5,9, l7

4. 4o =3n-1

XfV. Functions

For an explanation of function notation, see page 176 in the College Algebra text.

r . f ( -3)+ s(2)-3+r2=15

z. f (s)-s( =t9 0=19

3. f ( - l ) . g(- 2) = 7 .12 = 84

16]l Le reA =-=--

s(s) -e e

s. (s . f)(- 2) = s(f (- z)) =s(s) = -s

5 an - 4 [;)

n-' =(z1a-a

6

6. I Qtt- l ) =-1+1+3+5 +7 +9+11=35k--0

7. i f i lxky4-k - y o +4xy'+ 6xzy' +4x3y+xof i [k /JJJ. ]

6. f(s|)) = f(6 - * ')- -2(6 - * ')+e - -2x2 + 4r

0sl29l0r 2l:22 3 CED3CE I -0954-4258. doc

XV. Fundamental Counting Ruleo Permutations, & Combinations

See chapter 8 for assistance with the counting rules.

l . 56

2. 120

3. 720

4, Committee 35Elected 210

XVI. Trigonometry

For assistance, see the text, Frmdamentals of Triqonometv on reserve in the Aims CommunityCollege's library.

l . f (x)= s in 1

2. g(x)= tos(2x)

$

v*.4

$'?

3. x=6+40tan72=I29.I4. Distance between the boats = 65tan42 - 65tan35" 50'= 1 l.59meters

0st29/0r 22:22 3 CED3CE 1 -09 54-4258. doc