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
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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
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-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?
__
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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
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8.9
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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
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(
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
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6. Determine the area of triangle DEF where e = 18cm, d = 18cm, and angle B = 65°
I-a tQt
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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:
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do
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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
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a,’ -Th
Iota- IC
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p* o’%tI&)n2
c) an equation for FG, the right bisector
11tj
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1
)
1°2.
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)
(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.!
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C -))
a
2-
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mz4MM Ar
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a
b) MN is half the length of BC
‘-7--
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MNJ
I.
2
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3(:2f
s
(es)*fl
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