ll ane :

Revisions on Algehraic Fxfrressions and I inear Equations

I When 2 SAME signs meet, the product is positive.(+)1+; = 4(-X-) = +

2 When 2 DIFFERENT signs meet, the product is negative(+)(-) = -(-X+): -

3 Only like terms can be added or subtracted.

3ab + Zab =Sab 3ab -

2xb -- ab

4ab -

3ac = 4ab -3ac

4LikeandUnl iketermscanbemuIt ipI iedordiv ided.2a x 3b = 6ab, -XE x (-3y)= 6xy, m xtn -rn26ab + 3a=2b

5 Coefficient of an expressionThe coefficient of xy in

-3xy = -lThe coefficient of x in

-3xy = -Jy. The coefficient of y in -3xy = -3t

6 Number of Terms : 2 terms are separated by 6*' or ' - '

2a+3b -4c+ 4ad (4 terms)

3ag * 4adx -a -3-p (5 terms),

7 Every term, evcry number has a sign! No sign means positive !

8 When 2 signs are to be written together, use a bracket.Example : -2 (-3p)

g. Write y for ly, ab for lab.

"?t /

I -^t h^ ' )I 17{ I I ' I .J

L

1- 1{r*rr)=(!l --7x +21y, B -7x-2ly

C.-7x-1yD "7x-Zly

. . ' . " '

2. fu*canbeiidplif iedto

. A-,r+t |n I' (P 3n-2n

C 4.tn.+4nD.4n-6m

3' -+ $p-3q+ l )=+

-2P-q + ii

@ -to+q.: l r ' .l '

c zp+c_;r

D 2p-q+ l rJ1- Qp-2, i -@'d=ffinAtr; 3 y;?

I , . .

. S"' 1g.s,ri' ,r }rilr1 . 1.4617; 4r1r1 =' A !gh+6hk .'D

'4ch-6hIC l}zh'r'4hk@asn-oa*

' 6. Vg* * 36yi. ' (22w +36y2) =. m A 27w+27y2

'* B,27w+36yz '. C 72yz

Qn'u' '' ' , t . ,

f , 7p-a(p+9)= .A 3p*36

, B l lp+94 el rrp * so,-f tzp-to

*$-'Sl$ *1a P*t..

8. lenn*2q\-iomn'=.'

.[ -6q - t3mnt'.8) -6rt -trn

' :E -7mn-2q

'D, 4*n-3q

+

Revision :Algebraic Expressions /Equations Exercise 1

f . .,ligniilr -3(3 +.r) + 4r' 3'nm{a,l-tz +x C I2'x@T lz+x D _12*_r

rc. +x'-(t=!4)=o l4ry+x'?

J

i)r%=d",

_i4.xy-*:J

n ._!atNEa

1 t. + (49ah --Ztbc) + 2abc =$ 1ab+.3\c+?abc ,, , ,r ,r

,D tob -3uc + ubt

C -lab-3bc+futbc

. . l , .- iab+3bc-2abc .

e, 5(z '-3k4-4tk-6h)='.' i i i Mn-tgl.*ts" 34ft- tt&

c - l4h-19kD

-lah-l lk

t.7 !t+n + tnd - iQrt - 31il =

tg f,er * swt ..

B iQr-3ndc.l(2r + tsr at

,

"thffintllt0it

D *@e:-Ispc)

igcrii

? -q -

] ic+al f *f * t3 t l$

. The above figurc thoys a-Par:allclogggt, Th.g PPtirribter, in94n, of the Parallclogram is .fe ' ro ' C 3x+4y .A ar1'zy 'D Zi+y

/3f, e square piece of PlYw.oodhas a length of (4p + 3-q) m.

, The perjmeter of tho PlY'woodi. iri mctre.st is

' A I6p- tzq C rFP+9q,f i tep+lz4'D -16p-L2a

(l-.vlcm

, i6.

Iq' 6m 3cD1rJ02,

. ,,'E

Fj i t

-: l.

, l; i

t :

. ,

In the abovq figri're, P.rRSl is rsquare" Th9 qrca,.in.crh3, bfthe. whole figure is ,

' The-''above,':,figur0,' shovs a:fpctsngle PQX;1-r:A' ittadedporrion ii remove

How to solve Linear Equation

How to solve a linear equation ?

-.

1. Simplify, if nessary.

2. Collect the terms involving the unknown on one side, and the other terms on the other side.

(a) This can be done by the basic principle of equality that what you do on one side, youmust do the same to the other side.

r(b) To got rid of a term or the coefficien! you can take the "Opposite" action.

,

Leam the technique of solving equations by doing the following exercise.

Solve the following equations.)

l . 1y=243-Z\ =L4 x;t .

= zL

3. x+L=Zol5

Nll / IEx iX=3DOlbn =zDo 6 ,

x = Z9o = i82=16'J )' lh u'

. -L*=4oL.2ff\ = - 40 xe i)

:BO

3k2, - - -=Q+.53

ti

\zk2E3

Z /Tl< = 2*5'QK = tu,

,14 =9 ="1* W;!, ,--*,g= ltZ .7

5. 4(2x - 5) =3(2x+8)?t -)o= 6rc"+l+8x-6x =24'+)o

2cL = Vtl .-y_=y=)2l l

7. -(3y+6)- 3Qy-1)=20

z G9+q - : 0 3 -+) = i :uQg+tG -+9+f, = () t ' ' ,

59 = izo-)b9 =y = t iL,

l lg 3G*-))=:(x+3)

,6a*-4 = Z bc+a)r-q '= zY+1*,* - lx- = 9+4

) f =LZy =t7 ^7

---= /'r

ott t5 +?n - is=+0

2 rr = 4o+19) t \ = 55

n = EI =rfzTY

n ' ' - - (x -2)= 12o.g1,9 r 1x_ -s ix -:) = t 7vS

1t ' ' -5' t +tb =' /b-s( = Q6' ia-X =,9u

: ($x-2)=;(x+3)J (rrr l "= )+O(+\.)

111 \:: = 6+')s

]L =te- l = $5

- ln= 2-7=21;-?

X\: I

*1,

ff

X r.= -8010

XK,1't]lc - l+ '= ly2c*( 7i7.* -ltlc = L:r *rE

q' / - = lL 'x =* =,)*

xProblems Involving Algebraic Expressions and Equations

l .

= 23+5q ,= 96 = l4i l>

2. At a party, there were l0 more boys than girls. The boys paid RM4 each and the girls paidRM3 each. If the total amount collected was RM I24.find how manv bovs were there in theno*.,e t9+ +t\u-o- tive.{Q b botlt l"(' tl, qids = U-iC

There are 5 more girls than boys in a form 3 class. If there xe 23 students in the class- find

how many girls are there in the class? 124 ?twnz ar< 3 o, ,irls , N'' i t'7: = g - 5

+ f t - , :23)+ = 23(J \Ckrs ' t4- 3 i r lsg+

narrv ? t-o--t "ttrru-a ,ve.rQ b bil{t pu tl, q (rt5 = b -t U'";'i,I

,{:t;':?A )4 t "r=!,H +,ns' z 2 Lo6>7k = n4+)r \ I' =, Z)

3. Jimmy is 5 years old and his father is 30 years older than him. In many years time will JimmyI

be 3 of his father's age?

5+X.2\

3 L5+ rSr t+ ? x2K**

t^e+ i1 brLL.\

- +; '3c r x )3!

: BI ' t X2

't\' -L YJV' | 'v

: 7c *15

t tirt L \)et{; tt rqe

2y = (5y =i* '_=7SYrS,A tsr | ,

r)._

t ,T

t l-'. r

-

| .\\. 7. < Jqt; -l''44< .l rn9- Jr l / i tsv I > l - ' -

Madam Nicole is 32 years old and her daughtea Lily is 3 years old. In many years time will

Lily be half as old as hermother? b-l i+ h' 'Y Y6rf 5 |

3+L -*(z2rY) | x=21' t

D (l-r r) = z2-+Y I Aut, irt ) b ja/r$' l^ne6+>*=??*X, I ""J-t^N =22'b I

A man is 4 times as old as his son. In 4 years'time he will be 3 times as old as his son, Whatare theiragesnow? tt+ *{a eet 4 y le^ts , a-rA fa+l'o* 4l

Lty)+tr =](q++) ^

.

L+Y1 4-+ =Zl+.(2 ' , A+s' {at t=9\Yt

4s-*:*-- (aH"eY=3)Jrs '

The sum of 3 consecutive odd numbers is 69. Find the largest of the 3 numbers.Le+ 1{* 3 rLrs La- a, T*), x+4

X+ 7+) +x-*4 =.6- iZcc' t 6 =91

Zt- = 67-b

' t r =62

E =F -r l.5

TL,p- V iLt iS r t r - l ) i t )3 i2.5J-cryys*

-

>5

The sum of 3 consecutive even numbers is 66. Find the smallest of the 3 numbers.

f;;t J'fo 3 r\$ I'a- Y. ,tlot, 4 +-4

g t Y'..a; ytq ,"7 UL !h" 3 ^as Gti )D' ) zt )4

3 1 -l- o _= rl,l_ ( (,(-; (rr.a|,tr,.{ -- ) C- zy =, '^ ' ' -u-

.g: y=u,

The perimeter of a rectangle is 56 crn. If one of the two adjacent sides is 8 cm longer thanthe other, what are the lengths of the pides ?. , i

La-'+ +t* *"'-o'tw'[39-il" t!- & ctr^ ' lfc u' tl's

[.- ,1' , -,..Ttt) ,^t rf]\) ?, t" TnB @'gtts 0[ +1',o ? c, + 2( a+ri,. = | | irpt ap t0A1

' , -a+ >4"+LL = 5b,+q : s6-{6 aLf 'L l fa^+c\ : /+0

c4 = 49=IOcn4+

5