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MPM1D7: Unit Five & Eiqht Test: Analvtic Geometrv

Name: (h ui:fiil,.a*

Date;

Answer all questions as completely as possible, showin your work. ication: \'1/16 ro Y

-K+

Total: :)l-l50

Think

1-

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1.

6 {V -- ^T-1, /l-z:-t-iTt ,\

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Communication: \y'10

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Determine the range in proper notation for the relation is {-2, -t , 0,-1 ,2}. Show your work. (4 marks) i. ,.?

! = x2 + 2 when the domain

{,aupi'' 3'2't'z'3'b i

:

(i

\.-'

,- \ C " @hrovide 4 ordered oarrs that satisfy the equatio nZx+y = within the domain -g, v'i-:<"<:].(+mart<s)

\\ \l

f lV -

,-

\-/

--T-

\i

I

I I

.

A line passes through ilre

lineis-2.(3marks)

point\#8) and (-

',,

a.1-.' ze \+9* ,7 : c r ) f-vtSo'c --.,' _-:_c ;*L>-61

{{= -fo

\

V

8,

4).

,,J*fl. d)

tt' -tr|,,, -1; Y.*-1t _,/_\t-

rl_Li_-=

Y ',,n*r-^

value of r if the stope of the

\C

-i

D i-_. *i\r '"1-- -!(),

Zx+li +\7- ? 'v

i_-

"ffiequationinstandardformforthe|inethatpqssesthrough(.7,-3)andhasthe

,

,,. / .-'/) f- -r

slope

5 -i.fs e marks)

r /.

.2

-0'1

I;x--r-e-d-=!-2_F

5. A line passes

/

-d L\+ -)tt Y+ 5 ? (il \3=f,-h.,3si '-'4x *q' Y(j q L"*r3i = - \.y, ^ 35 -.----4;HL:L= --Qx -sd

...,,/

o

through the point (1 1, - 9 ). State the coordinates of onA other point on the ' line so that the slope of the line is: (2

!

a.undefined

b.

o

\

f-*

marks)

+q--OU-tt/ )*o.-= -,o

i\

\1

(O,'Q)

tl

6.

-)

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#

Zx *() * 5

3y,-6 6

u^- Z ){t'lr: +3-/

ZJ\

mar*s) O 3V-\ga- b= '

Find the stope and the x-intercept of the line 3x -1gy = 5. (2

,, pagel ,/

- -..

-F -- '-E FA=

-AX

*--fr

- .------i-,e-,^ lt\=t-b: JUNEO9B t -l

Li' ],0:7 -

e)

",,: rr;;<;*.*

1. Each large square is rnade with shaded border squares and white interior squares,

ffiffi FTi,$fE

1.-

ffi l'< o\-

/'>{

5-o,^a*

Side length of Large

'),

_aI

2. Graph the lines x- y = -2 and 2x+ y = 5 n tn" point of intersection. (5 marks) .ZU ::_tt

l_-1

l

l'l 2J

L\ t/

Ce>*re-llna*rAs; c:+ in.<-r
Ui-

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./l',"t-f i'{

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(2,3,2 marks) 3. Determine an equation in standard form for each of the following lines'

f:

--;;--% ^3y+1=0

Li

""

Ff

--'2

-z

V.t.=:

\ w.,=\€ 'o

/1

/^ /+^Yi: -' \

*)

andhasthesamey-interceptastheline

a) AiineperpendicularloZx -

b) A line passes through point

\-

(\l'*22-)

_r

(1

:-\.-4O,

t€4i? -

\: , ,,,-3)

-t L^^

L /ru'*Ju.

3y=x-3-.-;' ( o,?-r

s

_\

q-3= ZLx^

.

'

-l

\

/\

d

Lx V?* 3K ___jr-J} = Lr4 -Z'3:: €-10:! the same i- intercept as a1;211', -:)

tL^

.,

.9 in{'arnan+ -* ac

,^r_^

.4 y-

(-

,/X =!{.1)

Yi"'r

!-______I___

-; = -E

determine whether the lines are 1. lf you are given 2 equations of a line, explain how you would parailei perpindicutar or intersecti.ng Giyg an example. (4 marks) L(to- 3: c''
.

', I '\-/

|

/g

(;*

,?-9.r-tr,.,,- .

'ru ; o,- Ii-'- -'1-i I / 7''e'v-G.i-i'1| €-i;..:i' Uj = 3X t3 , ct;,_e). g51 4*r ""sJ-'&4_- ::v,- 4- *)-,n- vt,j,;

"-tfl::].*]i;;';;;i, \ qzcrQ-g6di.Ctr\"r., ;- n *-." s',t-:-1.*-:t=,- *:.*;*'',l*--6"€(*o J*:'o. -l- 'do-

',

t;o-

|tQ-

=,aJtr'Q"

: ,-l:t,.:,-r{

-

-a.L,r,,4 L= -, \ i-('L{i-r'i'', ' '-7'* ' *J-''ti . '' -iO,,:.3 v 2-v v'3,, ',u-':;onsX \'oo+ i^.-"?*,,.*. .^?' =!tpg clg*.--;..1-4r,r.r- ;^;l*---'at (i marks) "r-t-"isr "-fr=

t;,,";*u.,o.

a' ) j'

t

i)t:

r'i' i*'tr

={s:ilf*

-..,c "*t oI and contrast tlffgraphs 2. compare

ni^^*Ar3-=t,*

it ,;;;

, Jr"'"*

x=5

ptf;ptr;ff

and

)

\

t-H%?+

= 5.

{y';-":fi=r*i*'';;:")7*r't q' '#-'u'J t2.' 5 !''i 4r' T= r3l'*'po:--it

'-1f

V='3.:,i?r-, 't'ctl ,.,1,t ,':'!,t:r'-'

tfOvltCregi'' C-t-'^',r*L'-':r'-** ir-,.-n- \ -:oi<]'-'-; i'5 \"'orii::t''Li'f {4..-a- \i-'e .'*-5, ,-t,,""ei€i-:Lr^.-iiJI; '=\'oo

6 +-*

Tff il

-:';;'+l*{,'1

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JUNE oe B

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3. Describe a practical situation that could be represented by the following graph. Be sure to use approprjate measures to support your description. [3 marks]

i-i-,*:i.'1fa

sS

tt--- !.'s

of 2 medians in triangle AqC. (4 marks) -\ =- ,-zrv-2)equations : :1.i , .t,'.:" t),gl vt-.t h'q|fi""a, ?t. .tt:'.';'' 1,',9' 6,,2,i',,t3,;/5.ru;r s -:3*1t -' slu\-

./-',\--'rJt

-i"l-

d-r-r"'

., UP

fr

r-'';rI"'i

l'

c 40 i[-t]-iffi o r

\x-Y\ Y-'j-l-' Xr-Y'

i Determine algebraically the centroid of this triangle. (2

2

n*rd J'-'

(2 5,3)

marks)

,-.; "\t& 1-.{ - 3} '

-P-.r 61-q*-i \

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JUNE 09 B

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