Review For the Final Exam Name:______

As part of your review, I would suggest that you:

• Write all the Formulas and Definitions used in the course• Outline the steps needed to complete certain questions• Complete the suggested review questions• Redo knowledge and application sections of all tests, quizzes and assignments• READ your lessons thoroughly

Unit 1 Review - Linear SystemsTopics: Checking point on a lineSolving linear systems (graphing, substitution, elimination)Intersecting/parallel/coincident systems word problems (numbers, money, investments, mixture, speed/distance/time, currents/headwinds/tailwinds)

y = -2x + 6 (D1. Solve by graphing: 3 _

v = —x + 5 Gy 2

m. -a- .2

t 6

W 3

c. par i5

2. Solve using substitution, and check your answer:2x + y = 6(p

from(£) ^ 5c4 io

3x + 2y = l0©

3 -5C- ^ xH z- i O

- ”2_- 50 _/2-€/20 ^ " — 4 +4

= "2.

2. =«--<■ C

'** C5 ^ ^4x-3y = 25 (DLS-f2S LS ■=<**

fcyy I x C^<3. Solve using elimination, and check your answer: " /I)6 J -3x + 8y = 10 ^

0*3

-E

^ J) ^I 2- i - -

a3^- M5

CD

jjJL2-3

5zio

. 3 (T *°/ *0

LJX—1°

-3Clo)(- 5 cD

IO

C'j

4. Sue invested $5800, part at 7% and the remainder at 9%. After one year, the total interest _earned was $454. How much did she invest at each rate? Led cc feprexseirot &-fnau-^k. ^

«co ro ^ ^ y 1 ^S?oo 0

0.-o^-ac<0

7oc-+ o.o?yj xoJ 3 <4 oo

(p*o.c>9j 0.0A-; I ^o2ht± °£ilH 7-Hoo

SS'Oo- 2^oo

C/u/<? jT<a.eL_

O.ZS0+

fr&AL(P

^ =4? y^ 5§roo—Z*4oo3^tcxj5. Nick was counting quarters and dimes. He had 124 coins in all, totalling $19.60. How many of

each coin did he have? t^Jc repose,ck ruxm-l^-r *.-f <sjLest J_ re-pt^s^^d ru.Lm-ber&f-

1 z-^j Aoaod = idCo <S> d- credo <d)

ll.GO

HSJ — I z-q -

= 76tJicL haJL 76 iim£5

CUldL d6 ^(.{j&rbers.o.2S« + o.loClZH'l)

V (<<]_= 7-Zo =0£l'6. Thomas has two part-time jobs delivering flyers. He earns $9/h at his weekend job and $12/h at his

weekday job. Last week, he worked 23 hours and earned a total of $231. How many hours did \ Thomas work at each job? LeJc ^ tdx Houi6 o^ork^oL /A_ Cis^te/id-/ ~

t^t 23 KcctfS coorkecL 41lz/^ C1^1^ ^7

^jbe-f I'Z-y Tc ^'3

(t, y-^

1 X - & . X, (SW« i.4_ W«W-■“U+274~ -/V w^t.-

' * Ct/uL £> ^37. Coffee that sells for $3.60/kg is blended with coffee that sells for $2.40/kg to make 2 kg of coffee

that sells for $2.70/kg. How much of each type of coffee was used?. n $ 5-JoD / joaLed dx/ rePQi^^Jc CLmou-rcL cCf- Cofk& d/iad y^CLs wT ~J

D) CD3-LoxJc 2.^o^

Suggested review from the textbook:

(T)k?. 4 3-Gooc'f

3-6oocT— 1.2

J 1-s-

Page 156 #lac, 2, 4, 5,6

(96" ^3 °■4

6o/Mj/ ^

ode

Unit 2 & 3: Analytic Geometry and Geometric Properties.Topics:

• Midpoint of a line segment• Length of a line segment• Equations of lines• Applying slope, midpoint, length ® Equation of a circle• Properties of triangles• Properties of quadrilaterals• Properties of circles

i)v-j

5C| +3^-2-

J- J ^1. The endpoints of a line segment are A(-4, 3) and B(5, -2). Calculate:

a. The length of AB b. The midpoint of AB-q-i-5 -3Ti

c. The slope of AB

—. "2 —-3VYL:

4^ + C-s)’2' r 1 i")V 2- ) 2- /

•5 - t- H')

-S'1

2. Find the equation of the line that passes through the points in question 1.b no cL AC-4,3)

A

-3Y3- -f 3 c\ 3E3 -

3 13. Determine the equation of the following circles:

a. Centre (0, 0) and radius 4Z. ‘2- ?

70i

+ X1

b. Centre (0, 0) and through (3, 4)O '2- T—

9< - r

3^ a- <«> 'L-4-1C - r

*2- —a.T rr zS

"2_"A IT 2.5

4. Determine whether the point (1, -9) is inside, outside, or on the circumference of the circle x2 + y2= 100.

. '2L s~p 7

- 1 -f 5 I

33 % 2 -

1? 2- ^

L $ L fl—5 L—

|O0/ POLA* Cl/'‘=|)>

-tk*- 2dtU.

5. Line segment AB has endpoints A(3, -7) and B(-9, -5). Determine the equation of the perpendicular bisector of AB. ^ = ^ -J|- > _ <-3,-0

'Z- )

0<3y-=O™-AC>

A ^

v

^ -'-Z ^-(-2_"i-3

no. dpc— ^0 l(^^-t C ^ Q=x:A ^ — £

0^-9'^ »4^ Td&ijcUL

+ "h3 -S5 :xl -V"

^5

7. Verify that the quadrilateral with vertices K(-l, 0), L(l, -2), M(4, 1) and N(2, 3) is a rectangle.- -7-^ ^

^L C 1+1)2^-

= 4 C2^yzt C3 "O 06

cl^ ^ 4 cA'Oy vTilT

A L u =■ 4 ('2+07L C3-43— J"*l?

Y7V'H|v/ ' 3

nrv_^ 3"Ua 3

- 2.

TV

2=- —•2.

33

l

Off&l 'te-

$icUj af£^j■eQULGJt' CLfU?-~-

^ u, Lf&ffr ^ ^(nt--l is _L— -/o m= A

Suggested review from the textbook: Page 156# 7, 9, uac, 15 & Page 439 # 12 9v6?5

y im 5Topics:

• Multiplying polynomials ® Special products• Common factors• Factoring trinomials• Factoring difference of squares• Factoring perfect square trinomials

1. Expand and simplify each: a. (2x + 5)(3x - 2)

^ Cxx?'— 15^" 1°

ss Qtsc?' -f- l ( t O

2. Factor completely:a. -4x2 - 28x CQc f3

b. 3(x + 3)(x + 2) - (x - 2)2 = 3 Z.tx.-*') 1

= 3 [ O-***“3

... lg- ' ^

b. x2 -7x + 12 ^ SLmf Cd

^ A~) toC-=0

L£l

i

c. 4x2 -28x + 40 CT£\C|^3

^ q ( X^-"?oe-Ho)

e. 10x2 + x-3 rCo/rLjptc^'l 2_

|c>rc -t-Ccc-'Sre-' 3

— ( •Zrae - l 3)

g. 4x2 -1 lx + 6 H GcM^LX-'S

F- 4z 3^-F £=■

( 4^3) toc-^)

Suggested review: Page 320# 8, 9, 11,12

d. 36x2 -49 tltos]

c

f. 3x2 -2x-8 Ccomf^^

— 3->£ Gx~ 2 )

■=- C C'OC.-'^)

K,. 2 3^ -2f9ac 4- q

- £ 5oc^ ^2 p<frf-^<^

Sq

4^JL

Topics:

a(x - r)(x - s)

Transformations of quadratics Graph y = a(x - h)2 + k Quadratic relations in the form y Maxima and Minima Solving quadratic equations Solving quadratics using x-intercepts The quadratic formulaSolve problems using the quadratic equations

1. For each parabola, state the following and graph:

y = -—x2 +12 y = 3(x + 7)2 — 3

a. direction of openingr\_ o-p

b. the vertex Coy f)

c. step pattern■2 v > ' ' 1J -Z ' 2 , a. / 2-

d. the axis of symmetry ~XL ~ o

e. the max or min value ivkxx <3 'f d- frybru - 3

f. the transformations o Verdin Ihj ccioop^ £2-3jdv c fv>r- -yd

' O/L "*.c;irXlScv 3

. Koriion^A 5^^ ^ Uft^1 Vig rft<xJL sV-^k.

2. Determine if each forms a linear or quadratic relationship or neither. 6W_ fust 'a.

X y0 71 92 153 25

b.

. &

X y2 -53 -114 -175 -23

-6

•£.

1k.C$ L5> Q— Uiszxk4cu\i~c~

reiaAco^

S^CO^LecjtuxJL^

TPUl$ L5 <£?_- [xd^car

'CeXvA'ofi- sc/l^c. 'fPuc

fcrsdr coe'

G& AS -VcXA^tx

g 4° £—

3. Determine the equation of the parabola with vertex at (-8, 1) passing through the point (-1, -48).y-1 — Cpcs~ )0 2\- U- o^ — a, C ^c_+s’)% \ sob sc=-\ 7j

-MB ■= ^ Cr t +S^\ |

■—Mg — 4 ^ cl -h |

~ 47 P ——

a= -14. Solve by factoring:

a. x2 + 4x = 0

^cGc+m}- O

<=>r

:5 O+SO +1

3C' 7

b. x2 -36 = 0

(oc- G^ CxM G 4 — °

£ G

li-Ci

c. x2+4x-12 = 0

( OC-hG) £x-p)~ O

DC——G or ^C—

d. 12x +17x = 52_| 2dc -g |7^C— 5"-—O jv\

1 2.;3c4 + ZOoc — 3^C-Si=0 - GD

4x (3x+5> 1(3^5)

bc~l) C3DLhS>= 0

^ I M

»7 \¥2d-3

o

X=+1 c.r'3- 5+4. 'f 3

5. Solve using the quadratic formula. Round to 2 decimal places if necessary.

6. Determine the vertex by completing the square, a. y- 3x2-6x-8

~ 3 %

3C — 0) — S>

— 3

- 3 CxL-£f'-'!X

b. y =-x2 - 6x + 1 ■S- — L -+- J_

*— *3>C-

- r^3)^hlP

7. Determine the vertex by factoring/averaging the zeros, a. y = - 2x2+14x + 36 b.rr — 2_ Cocl2'-

rr —3 C=C— *4^)

^ercs '■ ^ , "2-

C| +<oz)3.S’

y = -4x2 + 20x - - C^c-

2£yoi> '■ <D or

OCv~ of5 <2.-^2_

2L'5LA-

\j(y>5^O.L)

B- The height of a golf ball after being hit is described by h = -512 + 201, where h metres is the height. t seconds after the ball has been hit.

a. Is this ball being hit from the ground ot on a tee? How do you know?On- Jh^qmjuL C imfial h~o)

b. What is the maximum height of the ball? o( av€ °*(T

t^rvS\ o or H

1V-

2■2-

k^jk^-

ux&s. 'XOfa^,

sC^^'ZoC^) ^ 2o

c. How many seconds after impact is the maximum height reached?2- S£co/lJ~5>

d. When does the ball hit the grouiy}? , C /, ^ 9IM^ra5tk k^o Sdtft w V L T&x** f

- W 'Zo-t - O

— S4r ( 4:^ 9)~o

b 4

, A^r H ziotds,-#*- go if MC^5 'jUgrcw^

e. For how long is the ball over a height of 10 m? Round to one decimal place.-t- -H-Jr xT^^KOC^)-5^’2> ,2o't —

"2ort '

H't'F'Z - O

Ibe-s rt^-4 -ft^r £

o '2 <2 0

- _ 4i2-e»32_-

4-

"2_

a- - 4-2-a3_ 0.5^

jjy^ haJld locls Wzf cc hei^^Jc of fc)/a "fi>r 2-^3 ^c-

Suggested review: Page 320 #2, 3bc, 15,16,17ac, I9ad, 20, 21

(O

9. The revenue, R, from concert ticket sales at a local venue is calculated as (number of tickets sold) x (price of ticket). The current price of a ticket is $20, and the venue typically sells 100 tickets. For each $1 decrease in ticket price, 10 more tickets are sold.

a. Write an equation to model the Revenue.

(<20' loo +lo-xf)

IM o repXXxL ru-^r^r- -f

b. What is selling price that will maximize the Revenue? Determine the maximum Revenue.

J) (rjpctfuL <XrdL UimfUJjL. Square.

.r

— C 2o —-•=£ ") C j oo -+ I °

pX S 33C — 2? O

, (v5% 15°)'oi_o -s) CluC5 '' ^

oiT £ ~ ”2x300 h-: IcoX to:

i 2_ , | 0<50C + '2.000I <3 X ~F 1^ '2— 'Jh'2'°cc^__ t<3 C DO - 1 '

_ __ t o( X^ 1°^^ 2250

-lop X. " 51 v ^

- ffl^X K - ^ <tr

>5) >oG

c. Find the selling price of each ticket if the Revenue was $2,090.Pn ce 0~.o -"5 ' - 15

R - Zo^o

o*— j o X T 100 -’o'f '2- O’SO 2° 10

_ t O aPp- — O

( fofo 'ipo

Lc» ( X ^

o r

o

CSX"

ppce— 2o-'/ fC&

M

cpr-for fiance- r)o b ^ ^

$\\ or ^ H

Suggested review from the textbook: Page 320 #2, 3bc, 15,16,17ac, lgad, 20, 21

Topics:® Similar triangles• The Tangent, Sine and cosine ratios• Solving problems using two right triangles• The sine law• The cosine law

1. Determine the length of the indicated side to the nearest tenth and the angle to the nearest degree.

’S'3) ->1

\p -' | ^ S irt,3 )

1 o- L\ crx.

B

• a__ —-

5 “\a 5^^

^ C ^5 i r\ t>

f. H

Ct>SQ' ^ 0 ' ‘Bcf | r 10= cos'1 Coins')

\ o^ cjVa.st-

7^. ^5“

-t-

^ 6, (o c m_

2. Use the measurements given in the diagram to find the height of the building.

w

c.i.rv 5 2"

pC-

15^StA^Q

15° 6sLn,sy) jy jay. %

S'‘rv'7'c>

L

Suggested review from the textbook:

w=

_U 113-3

i^u -f * ^J23 ■ ^ /yx—

Page 434#2, 3a, 4, 5, 7, 8, 9,10,11,12,14,15

4-tru 9 'O

6i3C&/^

FINAL COURSE REVIEWPage 438# 3a, 4d, 5, 9, n, 14,19b, 20, 24, 25a, 36c, 37,42acdf, 44acf,

45bef, 46,48abc, 49ade, 53b, ssbd, s6abc, 6oac, 66, 68, 69, 75, 77, 80