I. Simplify.

a) (— 512 y3 — I =

a) x2+6x27 =

d) it2 +17x+1O =

n =

h) 1O+xx2 =

IPOLYNOMIALS REVEEV Date:

NIP\I 2D1

P. Ri’ A: Fill in the blank with the correct answer.)

b) (- 2x2y) =

c)— 30x5y’z =

45.’v5z

2. Expand and simplify.

a) (x+SXx—3) =

b) (2x+5X3x—4)=

c) (1÷2)2=

) d) (3x - 2y =

3. Factor fully.

—1” oR3%_j -

zx + 2x-jS

9x’- 12j÷ ffi

(x+ 9)(x-3)b) 9—4x2

c) 25x2y—Ssy=

2.

(criP)

- (x2-x-20)

tx-)(x÷ 4)

e) x(n —2) 1- 4(2 — ni) =

(S-2x)(32x)5xtj (Sx-’)

)

3)

(31z)(t5

can’+ -f.dtr(z_ jQ(g2g) ,4 —14a2 ÷33 =

_@x)(5-x) oR

XSxj )(a+)) 5 v(a + b)— (a ÷ h) =

_

(9PART B: Show all your work

I. Expand and simplify.-J

a) ix(2x + b) (x - 3X2 - 2x + 5) c) (3m + 2Xm -3)- (2in— iXttz + 3)

3xC%xt+xt2V :x3 2x 5x- 3+bx- j5 3m % - -(2+ 5rn-3’)I

I2c3*OtTh&X :x35x’*jlc-i5 3 ...%.-

d) 2(3x±l)2 ÷3(2x—lX2x+1) e) (2x—7X3x—2)—5C—4)2 +2(x2 +x—2)

r 2(9t.’-t+’) ÷3(t’’)+ 2 ÷i2 -3 _

2Sx. )_S.tfOL.3O4 il2x-

3’+2X— I

t) —4(5x+2X5x_2)—x2 —O—3x)2 +4x(1—2x) )(- Ioc3c*lc2x 14

‘-‘. ioytI5

2. Factor fully

a) ,z 15n2 ÷54 b) 20m2 —8m—l2 c) 18y’ +60y2 + SOy(29)(t) tt2rv3) 2

ii) (IX + ay + it + 3y e) 2w2—

3p — 6w + nip fT 2x3y — I 4x2y2 ÷ 4x’

:2rn2-rn-3p4mp

(x1j)Cat3)(m-X2mtp)

In

1-

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N1[’M 2DI SYSTEMS OF EQUATIONS — WORD PRO3LEfs Date:REVIEW

I. \VILIIOLII solving determine whether the following s)stenis have one solution 110 solutions or an

) iiiniiice number

t -a2x-Jy=3-- Ic,

- 1)4v-óy=ID q

-6jSort’ t..,...a.. ;Akr.’ Ic.

cor’ No stLtA,ar

Uthe following word problems only by using let statements and/or charts. DO NOT

SOCVE

a) The difference of two numbers is 29. Four times the first plus twice the second is 64. Find the

numbers. I i1

b) The sum of two numbers is 25. Five times the smaller is 3 more than double the larger. Find the

numbers. a’.A

C 2jy2S

Sx-2j=1c) A coin machine has 345.50 in dimes and quarters. There are 12 more dimes than quarters. How

7¼many of each are there? j d&frl1

tf5So

d) The total of two investments is 350 000. Part is invested at 2.5%; the remainder at 4%. The

interest on the investment was $425. How much was invested at each rate?

&,4 -J asaa.f ..utwIa& o*% 1A

Øt antot&4 JVt4tJ- PJ

cD So 000

@0.025X+ &oqj =

e) A chemist has an acid solution in two concentrations, 85% and 60%. He needs to make a 500 ml

solution which is 70% acid by volume. How much should he mix of each9

rid J.’c tk nsLft)4Qt.4,1L4 GO°, AoI’*M-. ,,i ixsA

Soc

®o.2÷ o.y o.’3(SbO)

0 GORP is a mixture of trail mix and smarties. Trail mix sells for $9.00/kg and smarties for

$14.50/kg. We would like 10 kg of a mixture that costs S 10.75/ku. How much of each should we

mix? a t Jt .tL 0L. s ..2t t+t

‘ t#s. Ic

9€ 4 i’.S5 =

?lPM 2D1 QUADRATIC FUNCTIONS - REVIEW Date:

I. a) State whether the Ibliowing are functions.b) State the domain and range.

I) {(—5—I), (—4,0), (—3,2), (—2,2)}

bz )Jj

j:

ZEL:— /t

ii) y=—2(t 5)2f4

‘) Verkv Ck)k)(-2)-c) 4

— corn prt)ScsL j,,j4utftr

‘QVer C-45+ckkj 4kcFor a12

— rt+IfC1,%, i, ‘4z-’

ii)3

3

iii)

-Sc

4Go Nond’ Ct

b) b: LEft

gtjeR. -3j31,

a

b) D:2. Complete the followingtable. R:

b) Graph I) y÷6=1(x÷2)I

------____

*LL_I

Ir:;AEZEZ_Ltx

tWtLV (_, _i

yJt

2CxL)t_3

Verh’zt Ck3\c

z5t -3(x4l)t’

Vertsy (k)kiD ftr

-_3_ Qtz)’

3. i) Graph the following equations. Show all steps. (Complete the Square)ii) Determine the s—intercepts.

a) y=2x’—l6x+29

cZ4DEl

2 (c-43’’ -32429

(i)-3)

.:

o Z(x-9) -33

b) y=—3x1—12x—8

Oj: s(1+1x.) g

cit

a_

(

o

tth )L&Lapto

-2±1. :$..

4. Deterrrie the coordinates of the vertex for each of the following:

a) y=—2x2 —Rx—ll(4 :...2&2)t4(_2). I)‘-‘jt 4ilI,-l

at3- 2L

-

cVckSl )COAa(Qfnl —Zs’—2c jt —3Jlt :-2xXX4)

Vtr’k (-2,-f)

b) y 4r2 f40Xf982

- K-sY.’fo(-s)*9 i

q:$(4Io) Ci: iOO-2t9

r Xt10 -a

5. Setupthe following problems onlyiy the quaictnction.

a) The sum of2 numbers is 30. Find the numbers if the sum of their squLuts is to be a minimum.

c&t x St *L ,n.JnAo1 a-K SczkwZ AOAns

30

S 12+ 9o0-60X+X

S 211b) The difference of 2 numbers is 25. Find the numbers if their product is to be a minimum.

tt e4a- aunSa .Utha P

Px’.x2S+j

p(2Sj)Cj)?z a+2c

s_I 5itc) GO trains cony 5000 passengers per day from Milton to Toronto at $10.50 per ticket. A survey

shows that for every 50 cent increase in price there will be 100 less passengers. What ticket pricegives the maximum revenue?

x ,k at ccA &wna-

)(Pri’a L+) (14 a -LL% 4IJ)

g (io.co k o.Soy.)(Sooo -icoxj

R ,t4ihf5Ox1-5as()(

+t be. a_.’c

d) A faimer has 100 m of fencing, wishes to fence off an area along a river as shown in the diagram.No fencing is required along the river. What dimensions give the maximum area?

J-c frcpLtL

3

1146;o ioo‘1 i ,

At /ooc4xt

%

6. Ii JCV)=.C’ Hit 3 and g(r)=—Sx 5,tind:

a) J ( i)

(

b) go)

(

2

7. Deterniinc the equation of the following

a) vertex (—5,1) and y-interceptt of II

6c-kY4kut (xst* I

‘t’4u%iQd (O))

gi o(o+st-Hjjt c&(ZS)-ti

It2-S

ft

S

(3) -‘9

b) in the form y = a(x — 2)2 + k and passing through the points (3,5) and (0,9).

(SIC) a p tL

so(32j2+4

9= o(o—a -ticG1

2

&\o 4t@

GD

5:Q4Jj

)t 3q -$11‘-I

j

cek etJnC

&41<

(%AJ.R (o°)(ça pw tL

5-kz a

(9: ‘1(S-k)c)c Zo-4k-1-92ot_3t

Sabk:th3

-1, -3

cc\IPM 2D1 QUADRATIC EQUATIONS — REVIE\ Date:

Solve the tollowing quadratic CLIULILIOJIS using the method of your choice.

) a) 10v1:2U I,) (r-2=l2 c) r1

bC

cI) 2v -lvf-I=fl e) v =4v I) .v2—2.v+5=O

(2x-D&-DS

o( y..:

J: 2t-(U(s)ac 0

1

.. t’io rcd

) rootg) it2 ÷3x = t Ii) x1 +(x÷l) .=(x÷2)2

xt 2xt_,ttt2xt4 I-c

Xc -3±(i(2)(-i) x -tx- -

1(1)

X:-2tf9-

x

I) (v-IXx-2) x(x-I)= v-i

x1t2xx+z*xZ_xt x-i

t -

(2- %)a-1)

)2

j) v._.i—= 2

()k-)

t vt-I

(40(Y-)

)((+Q/q\ft4)

2x2

2-

‘-2x-2Ø123

2c Ø:Cxt3)(Y()x 2±JQ3 -3

— 2(l)

a

x1. Bill throws a baseball in the air. Its height, Ii metres, after t seconds is given by the formula:

h = I ÷ 20t 52

a) lithe ball was caught at the same height it was thrown, how long was it in the air?u1.- tzo

k=ilat_5tt .. 7fq itaJL ..coZot S±t- 6tQ44t)

b ) lithe bail was not caught, how long was it in the air?%Jr kto

5( L:-

X—-o.oS

LC5) UJJJJJC th• oS6’- 4O5cu-s

Ml’M 1D1 QUADRATIC EQUAT1OS — Word ProbIemsate:

I{EVIEV

I .L IIJ) le [allowing problems Dilly.

a) The sum of the squares of two consecutive odd integers is 290. Find the integers.

flZ4

(+2)= 29°x24x2-t-c ‘F 290

-

2..x- Z-c -

b) Find 2 integers whose sum is 96 and whose product is 1728.

j,c z<-

y

=j-9x+ i2

c) A rectangular nuclear-waste facility is 150 m long and 80(11 wide. A uniform strip, a safety zone,must be fenced around the facility. The area of the strip is twice the area of the facility.Determine Lhe width of the strip?

__

- -‘ t&I)Iso I /

-->i ç

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lS0*ltc*tI.vs

J(U

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S.

2. Find the lengLh of the indicated side or the indicated angle in each of the following.

5.6

Sin F5.6

F

F

______

ci) S

12:5t*rt_25r (coST)St 2.

(2.7) +Qz.Z) 2

a) A rB

9.3

b)

C

D 10.4F

16.3

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ss1g__

Z:

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9:

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c) D

8.9

530

T8.7

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3.°sin F

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4. From a pouit 20 in train the base of a building, lie angle of elevation to the top of the building is 72°,Determine the height of the buildi .

fl

1a3 fEE

20

x (0L

5Cn C-ffl% VP

2o’-.i— — . .1 —

%.tLa cLA

eot Sin

3: J1 tksL

S 2o C

(

Determine the height of the cliff

A

5. From the top of a cliff the angle of depression to 2 boats is 25° and 400. The boats are 125 itt apart.

-í

)

(Vt.

JV% /bC

Sn snAAC

Ac 125

Ac2 2Ssn2S°

Ac 20± i

->--

4ta

k

B C 12cr?’

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0

6. Determine the area of triangle DEF where e = 18cm, d = 18cm, and angle B = 65°

I-a tQt

-f . Iz’l’---z(L%XrSCci2

ft jZ

At (2)(1G.3)

A j23.2 cm

7. Two buildings are 125 rn apart. From the top of the taller building, the angles of depression to thetop and bottom of the shorter building are 51° and 36° respectively. Determine the height of

i) the taller building

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NIPM 291 ANALYTIC GEOMETRY - REVIEW Date:

Given the points P(—3,4) and Q(J,—2), determine:

a) the slope of the line segment PQ

mt1a =jtj’ADC

mt

my’ —

fri

2. State the equation of the circle centered at (0,0) with the given radius.

4

X1-f1tt (SfE’X14j’a 250-)

the diagonals of the kite areerpendiculas{provt +ka+ m -I. rm,T)

m: -

:5-I7-S

— I ck”.&Z

t6L<_ipn.cak. tku4Jiaon/s if i-k kele

b) he length of the line segment PQ

Jt )2(4)t

ci) the equation of the line through P and Q

—c) the midpoint of the line segment PQ

)

1 H:

*L(

do

z /-2 )-)

it #5c.1nc (o)la

r..1)10

3. The vertices of a kite

a) Graph the kite

c,jii) 5Ji

are G(2Sj

1. -14(5,1), 1(8,2) and J(7,5).

b) VeH& that

rfl :_t3

3

&w *L thp

r,

D

_____

D 7z4(— 6

-, 0-(’3)q)

mAD: 453-4

Slave ->b) an equatio4 for CE,

nack p+ :

a lit

— 1-2.

-S

cr ?Cxj) 6.-

e)7-

4. AABC has vertices A(2, IL B(8,3) and C(4,7). Determine.

a) ih equatic for BD, the median from B to AC

ree pt 0.d stoj”e

)3

f(x)

12x.

the attitude from C to AB.

rflce

ICt’ ipraC

I5

onOAj

a,’ -Th

Iota- IC

Sc

V

p* o’%tI&)n2

c) an equation for FG, the right bisector

11tj

-1

1

)

1°2.

ii2 ) 1-• ‘V

)

(fl)5. fhe vertices of a triangle are A(—4,S), B(2,—4) and C(6,2). If M is (he midpoint of AS and N is the

midpoini ofAC, verify (hat;

Jt

a) MN is parallel to BC 4 neet 40

A

tko-tMt.!

NJ(,S )

Sc

C -))

a

2-

ç2

L})

j

ND (I)s)Mt C-\ )2)

mz4MM Ar

I-fl:3

• mMZ

cC

a

b) MN is half the length of BC

‘-7--

‘I’‘2Ii

MNJ

I.

2

\W(&)‘ 3C

3(:2f

s

(es)*fl

ii’

ici-s)4..Jt-+1f(xi-)

(zs)

0

CtC

2

S(i-I)+X

Zt—

99-h9÷cc)(Qzh

QfU3I

‘(b’S)nu5

ct

T),oitr’ta

10

aV.9

s*n.ph3cV

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