mac 1147- section 11017 exam1 8february 2010

MAC 1147 - Section 11017 Exam 1 8 February 2010

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IPART I - Basic Skills I

Each question is worth 2 points. Write your answer in the space provided after eachquestion. No partial credit is awarded.

1. Evaluate the following for x = -3 and y = 2: Ixl- 21ylxy

\-1\-2\'2)~

--1,2

.1-Answer: 6 .

2. Factor and simplify: (x - 2)2 _ y2

l(X-?. )-j) (1.,-2}+J )

- (X-j-t.)(y,:~J--1.)

:3. Simplify and write with positive exponents:

t .(-t6)" rl(.,(- '1)('1.fl ,r-11 . 'f...b Answer:

4. Solve by using square-root method: (x + 3)2 + 1 = 17

'1-(X-+1) ::l6X1'.1 z: =FL( .> X -; - i'/..---~TL, ~ X -;. -t'

Answer:

1

5. Factor by grouping: 3x2 + 6x - x - 2

'1~(~i'l) ~ ('tt'l)

( ~X --I , (11"1 )

6. Rationalize the denominator:1

Answer:

7. Write in the standard form a + bi:I" I "l ::I

1

,.. f r:- -L - I ,.. -l- - .-r'L- -

I -lAnswer:

r-l

8. Solve and express your answer using interval notation: -3(x - 1) < 12

lX-') ') -(./'/.. ')-~ Answer: .. .(.--:3.1. .cf.:?J. ....

9. Find x and y intercepts for 5x + 2y = 10. Write them as ordered pairs.

)(~o ."..., J~;' ~ 7J ( C), 'S ) X'-IAt; (1-(0 )

j':..':) -, '/.-:. 1....- ->J (2(~) Answer: .j.-:-)rd ... :.-.,(~/~ )

2

IPART II - Problem Solving skills I

Each problem is worth 10 points. You must show your work to get full credit.Answers without the relevant steps will not get credit even if the answer is correct.

1. (10 points) Perform the operation and simplify:

((

x1---

x+lx-I

2---x

)~ ()<').(X-ti)

') .(1-~)(Xt'J

£-<: xA-1.. ~

1)(-t'l1<-~+'

rt.l X -+ X ') - i..-X

2. (10 points) Solve for x:

3x 1 4 - 7x-x -+-2 + -x ---1 = ---"'X2~+-x---2

~ y .(1C-r~ J i~1" 1.\ _ Lt-'lxC)(+1..)(~-\) ()(.-n(~1l) (~-L) bc-t\)

~)(lX-I) -+ ('1.i1) - Li--1x (9~i-- 1-,< + X f 1.., -=- ~ -1)(

'1.. ;f}')~x ;-~"'-'2 ~O&(1~ -\)(x+2.) -:.,:)

Sy.-l '":-J o-t, 'l'11-=- .:J

(f) )('=-1 oIL x~, - L

bv+ X - -2... i) r-o+it\ t\.e. 6 /V'Ct"l v-f f\..L

p"'Oh\O~ .

CD 71 ~\t'l. is

3

:3. (10 points) Solve for x in the complex number system:

X1/2

- 3X1/4

- 4 = 0

L \12-=-1 VI -=- x,be.(.~)

1...u -~u-Lz=-~

(v,.-L1) (\A-H)=-O

L/X =- L{

. 'liAU :-L[" X '-:;:-) -=- L/• i~\.1-- -I ~ X 't I ~

~- -, ~~(-I) -:..J -==1. C~clc:

~\,-f\Ci'\.. h --6;Lt!)4. (10 points) Consider the following equation: 2x2 - 3x + 5 = 0

r f) a) Find the discriminant. .0::. l) 6-::.-~I c, :::.)~ .1.. l ('L

b - (0 c:.. .-~) - '-t. 1... . <; -:. 4 - i-/G -

.....,

~b) Determine the number and type of solutions.l!;:J l't " I() -~ oc. <- 0 => 2.../\:Y\ --t'e.c.r') C~~lMc ~d,,~,

~c) Find the solution(s) by using the quadratic formula.

(?) '/..~ -6 +- J oJ-lt 0 c 1'2..Q

~-'1( 1 ~:;:w r- (-'S) 1- l 1 .- 6\ r:- - -- - l-- '1--'2.1- ~ L-{ l-(

4

5. (9 points) Solve for x: 1. 1( X)=(Svix \

"-"/) :x ~ bLtX~'LX - Gl, X ~:J

X ( X - 6l-. I -:0 c9

C iAec Ie.: (j)x:-;:::J -'-) 0 c: ~~£; \,./'""

)( ~ b L.. "'j 6L, :. 3. 101,. V-

S\r\ ~ (Ot b~)

6. (10 points) For z = i and w = 2 - 5i, write the following in standard form:

a) z, i», Z15

-::.-I

- 4+-£'\

~C)Z-W

--(~-lIv )

. -.•.. --- '\- 2 -~\ - -L~L,~

5

7. (9 points) Solve and express your answer using interval notation:

-12x -112": -3--( -(

lL}(-I\ L 3-~ .c...1.I<-1 <-~

-L L 't. ~ u~-- J(-l s- t. ~i [-I t L J'~-..--.~-.-----.---.---~------

8. (9 points) A flash of lightning is seen, and the resulting thunderclap is heard3 seconds later. If the speed of sound averages 1100 feet per second, how faraway is the storm?

d::: (',t.I

9. (9 points) Find all points on the x-axis that are 5 units from the point (4, -3).

P~\"\-~ ~~ \\.L '1..- P1C\) ', Ci.P).-=") D~')~ue- ~ fU'..€.1\ ( '1-.1 ~ l CAO

. ,s:: i('x-~)L + L 0 -i -~))L

I 'L ")~ --:- 'i ()( -,",) 1- 4

''L?s -: (X -" ') -f 4

'L(X~~' c, \6'(_~ 7- :;: L/

6

-:;:-) X:.. L/ 1- Ll

.......,.1\ -; ~~ 'Jr'