9749346807 by unknowsharefun

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Designed and illustrated by Adam Constarkine

W ~ d Troy y

(Gddsmith s College, London)

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~%w&fies(Algebra) fi%wfla#u31u (Basic alge Sun?%(Equations) n%i%m i sl +%wfm i (Algebraic graphs Sunl%dl~si3~9 (Quadratic equations)

Su~15~~1~ (Simultaneous #¶4 equati

QSUM% (Inequalities)

79 80

fls6gu (Functions) 24 8m%ld?ubbar$mdau (Ratio adn propolrtion) 94 %Bv~~91nn%ld (Information from graphs) 27 ~ a u a r(Percentages) (Indices and standard form)

US@ II~:M& (Shape, Space rn&nsfiiiqm .96 4agw (Data) and Measures)

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~ s ~ i a f i(Geometry) m 32 ~u (Angles)

100

34 ~ ~ M B I U L M ~ U U (Polygons)

105 ~ l % h ~ S ~ i S o % 0(Representing 9?1 data)

ms&u (Solids)

d lL Q ~ U (Averages) 102 ni%%nl5n%r8iu(Measures of spread)

112 ~ ~ l ~ l ¶ . i l 9(Probability) rbfl~

42 SZJUIm3 (Symmetry)

116 %EIR?IN~~?~~~~u~I~LJU (money terms)

m%bbdas(Transformation) 45 ran~moj(vectors)

118

$ ~ ~ n 9 3 d r n ~ f l @ f (Maths f i ~ m fsymbols)

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47 m%S%"rn~wi~fim (Geometric constructions)

l a k l (Loci) . . 52 ~ l % 6 l M ~ B ~ (Drawing i ~ % l dto ~scale) ~ 55 i ~ m ~ u ~ d u a r $(Perimeter ud and area) 51

58 d%1(95 (Volume)

m%swftft (Trigonometry) 65 asnau (Circles) (Calculations involving circles) 66 nisdiuasw~i?uan'u~nau 70 ~ u ~ a l u ~ ~ (Angles ~ ~ uin ~a circle) ~ a a n ~ ~

72 ~ 3 % (Measurement) I

(Handling data)

Lani (Time)

(Index)

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d~od~don7~~IonT.iibIu ~~1a don " b ~ o m ~ (Contents u z ~ and Index) vilu~zw L ~ D ~ Ia5nldd U

~ 1 y n s d ~ a ~ ~ ' t . r ~ z ~ 3 a ~ ~ ~ ~ ~ 9 z ~ ~ ~ ~ a 4 ~ d ( ~ atiisl=i

I ~ w ~ (Numbers) n r

d 1 ~ 2 ~ ~ ( i l M " f i D ~ r r~du h q ~ -3, 6 -21.8. -40

hd'wqfirn~(Directed numbers) Q M ~ ~ ? ~ L ~ : ~ W " ~ W N R L L I (Number ~ ~ ~ Aline) ~ 8d2dRIC(~~d%~ddid ? ~ ~

d~iunii4iu?u3:~fianltr~ m : : i i ~ ~ ? i u ~ 1 ~ q ~ u n i d ~ : ~ i ~ ~ n i ~ ~ i ' b ~ ~ u n i ~ a ' m ~ i n q u 6

uafi~$?y?us:q$an?j uurJujiro?u?u

h i (Even number) <iu-~u~Wd~T(ilq dnidaiaer 2 LLQ~'~~LWGOLFII~

& w d (Odd number) ~ l ~ ~ b ~ RIC(~75bi7f.J ~ l ( i l27 L L ~ ? M ~ D L H W L h -1, 1, 3, 5

MM www.u&omicklink.mn

Internet links ~ W ~ I U ~ U

h m : :(Plime number) ~19dauAw1 i ~uatcA'aiiu~a~ ~~~ ~?ernii

#D&FY~M"R?~GAI

1 ~~Lfi¶d~l¶d?¶dLQWl~

2 L ~ l ~ ~ R I C ( L f i ¶ d ~ l l d ? ¶ dk~E~ lr~1 .b ~ ~ 9 ' 1 ~ 3 l d d

hmo7n'- (Cube number) < i u a u u a n ~ ~ ~ ~ ~ n ~ i n n i ~ ~ b u < i u a u ~huauu?&1flu~n~inni~~~<iuau~8u ~u

+ ~ W J I ~ (Square ~ B J number)

u d a : < i u a u i f u k u ~ ~ ~&od~u n i i ~fiunis 14iu

4x4

4 x

=16

7 x

=49

~ ~ u ~ ' ~ & E ~49DUCJM @ D J

udardiuauw"ubiau~a~u~o~~~f\~~w"~ ~~fia~bubiau & a ~ u ~ o ~ 5 n n f iGl ~~dYqu n i i d unisunt-h k m u "~~~~<iurnJu <iuapdfii~~aiui3u~a~~sn I&iuri 1 8 27 64 125 216 343 512 729 1000

Tnuuuu~a~fld~~kiu~4~~ ~~nUI7uf@7X7

&um@'wrvldw(Tiangular number) 4iuauuan&ijw~am~~<iuau~flu~Yw eion"u1d Ih

WQU%~'LU (pdirome)

Ad47Aq (SigniRcant figure) 4iuau~u?~ddadiuvin~1imailrkndiu L Q " ~ ~ ~ @ A ~ ~ ~ I U ~ ~ ~ I ~ ~ ~ H ~ ~ M

a#l u a ~ n r a mm n u m u ~ v m ~

+*Aas I*YnouAau~~tlTnm o, I.

i u ~ d a d~vi7Ju a L l l l d LY I m 4 1 U

4 LNTI:~ an~sii11'1uau~u~ftud~u~~a:~ ~ 6 u9 ~ftu~ml~n~ijw'iuinn"~Au~~~mu 9 ~Piau

~vii~u~a~~~uri?~~uw"udi6qn"u"oud~moa4iu . hummmtz (Rational number) ~~avinfiai?rmu'udiKqw'a~~~n (iiaii?ba"~~~"lldud~? +iuaub~q#aiuno~~uu~u$~awdau do n"Uuii~~uriT3~m~udiA"qdiau ~~vua:8ai7huaftu<iuau~iu ddtu8a4iuau 6i~lou~6iuaf~~~~nv:~~uu~daa~~u~do uan~~r4iuau~un1z~iv~ftun~Quu ~h 50.856 i?.~'iuauJ~o&~ftu(iia~~uii~q (sig. fig or s.f.) ~ ~ a r w ~ r i i u d d~th j v u0.i dam~dau~flu4iuau (iiaoliia~iu1 st, 2 sx or 3 s.f., Twuttaldm%ilm~~wij wsanu: (fi14ium~ufiounii5 apiin'y#omnnii 5 L%U

50.856 = lo00 0.3 = 3 = 1

V~~~RLHMI

w'?aeiiadu fii 328000 L%IU~I 2 s.f.. L~IA~~V: h a m (Irrational number) duu 3 aa a~a:KniIuh 2 ~a%v:qnfl~raw~?al.d bnr?uonnnur ao < i ~ ? u ~ ~ ~ m i s ' i ~ a ~ ~ ~hm'uafiu ~ 3 n u : 8 'Lnd lo wnn* 0 2 9:gnilw~Hw ;Sjlzjaiui~nduu~ftu~avdau~3onwiiuu di'L21~h330000 <7~auamsnurvru'~i~au'~rmii~~~9~~fiiu~~i~ 8 i'n&fi 10 wi~m'i,d~KiK7f i j 2 Onhrm m u (T)~hBiuauaessqnurI$i~~n' 3.141L ~ G ~ L . 9

h u & ( M I numbers) L ' I ~ ~ ~ ~ ~ I u ~ u R ~ ~ ~ ~ : L L ~ z ~ I w ~ u ~ ~ ~ ~ ~ ~ ~

1 .

(Sequences) 4iuauwaioq 4iuaud~o;~usiunis~3uan"u Sr~uu$rirwi::~3oq Gun41 h f (sequence) Gonuin::

4 i u a h h L i i rrw' (m) ~~iimn~~~aiunoh::'~11~i~in4iuauao~aiu4iuau~~snd0~

thah6-d (Fibonacci sequence)

~lhrs%& (Linear d sequence)

13 16 21

(2x1)- 1 = 1 (2x2)- 1 = 3

diKulmq idi~ir~~1un~d'i~::bQuiiK~l3Tudn

12 x 3) - 1 = 5 ... ~~ario'bfl

bdu 7, 10. 17.27 i i K u i P l u-uun ~p b2n ~ u I nLeonardo u

& h d i k ~ m(Quadraticsequence)

Fibonacci

~~u~fl;~diiiiK~lfs~u~d~us3su.11

kCddsau4iuauiibaoaQ~~~41 Z+1 b h 2, 5, 10, 17, 26

~uui9nsGng(rule) oie~ruams~wioubflu

$m (formula) diwa"'~1aui~n~bhuuuduan"u'11od

- -

47~7u~nuoenros$~aiu~niu~hani1~h 1 ue~iar~na~~uhuu~::adiu&artl~ .

: :I

$iu~udu* tyrl~uwL~hwrnnrn:

r ~ r a o ~ d i u ~ ~iiu C l3o+~3 = ~ 6~ 1

~ ~ ~ ~ U L W ~ U U ~ T K!QU~LL?I%I! ~ ~ I ~ I ~ ~ G ~- U I T

L, A.H. .I300 ~

W -A

iw&mn&n~riiehaiafl3"~3 d4dL?.t4 Blake Pascal (R,fl. 1B23-62) ~ ~ p i l l t 0 d i l ,

; --ltlaaurri@M~~~aftPrm::%~p~ ihfi'1Bi

hu0111~d~~$aiu~n~up~1i~~u~~m ~ n y l i i s r ~ ,b u

ms@u(Multiples) ~agnrao~4iuau~iuau~d~~~u~1a~~~nis~m ~ I M ~ u & ~ ~ ~ ~ ~ I Uu~ M L W Lhd 3 X 2 = 6 3 X 4 =12 3 X 6 =18 ~afu 6.12 LLB: 18 ~ i ~ u n i s g m ~ i u a u ~ i u a u d ~ &El 3

hnnth~ (Common multiple)

~iuau4iuau~td~um~m"11odiuauk~~~oi 4.4-

am4iuaudoolinn41aodiuau hd WqgMlOilWO\r I6bri 2.4,6,8.10.12 wygm"uo;la?u 'LAasri 3, 6. 9, 12. 15 wvjqmia8~vos2 ua: 3 a; 6 ua: 12 %W4~m$dnlo~dqm~aa~ 2 &a: 3 % 6 rSun 6 -ii&liaqmim~u (a.s.u.1 and 2 2ua: 3

I%~~&NJ&JEI m e lowest or least common multiple (LCM)] a.3.u. ~1~~4iwu1~~4iuau~f ~uinn1i~a4iuau

dn~ou~qm~~~iim~innis~m"~~~~~iuau~~~w:tiuaudu ~~SI-

(Factors)

nis~~unKads:nou~o&iuau~mq E~O~~:LUAM~LI~S ~i3d~~l~g~'21~9&~d~:n~~db~~-3"i~~~lawi: L $ U12 B I, 2,3,4, 6, 12 ~fluKads:nau nisuun~ads:nou'210~12 ~::'Lhi~isd 12=2X2X3

hn-u (Common factpr) 4iuau~~nuwnms9'7uauK~u~01'aa~4iuau~3a ~innjiaa~4iuau udu rii?ds::namoi 15 I6ut-i 1.3.5. 15 Kadxnamod 40 16iuri I, 2,4,5,8.10,20,40 w'?ds:nou$amia\r 15 ua: 40~ku-i1 uua: 5

Fe highest common factor (HCF)] m.u,ao9~~uau~~9~luaunfouinnji 'Lsiuri knls:nrm~au~~in~qm'210~~iuaubnditd"u uhd t%MWhWm

$ads:nau$aumuin~gm"11~9 15 b~a: 40 5 q 9 2 f l ~H.7.U. 2 ' 109 15 bLl2 40

ZD 5

h n w r m r (Prime factor) w'?darnau~awi:\b6i~~ri$a~~::noud~~u4iuau~mi:: rhd 8ads:nomas di?da:nau~am:

12 InYuari 1,2,3,4, 6 u~a: 12 I6iuri 2,3 uwsi: 2,3 ~~u-3"iuau

Lami: (perfect nurnty) 4 i u a ~ ~ ~ s 4iumm~viirTu~auanmo~ r ~ ~ u r i Kads::nouYoah unb5uKa<u~os~ipu6 QKadsrnau L~IU 1.2.3.6 ~ipdaeda~~91~6 6I&iLLi 6 = 1 + 2 + 3 lntmet links tfo\l<llu?u'IdId4 www.usborne-quicklinks.com

---=+

- rn

IW (Set) J F

r~uu~~~nv~~~~wni 7~lrSyu"

--,.---------- ,--: notation)

d g d i ~ q$o@anvrii~~!o~~rnu?wni~ku st~iig~~eir~tdg~~dild"' r i u LTI~TJD~WS:: {a e, i, 0, U) %nisu"~?unii& g - d a (roster notation) r n ~ ~ ? u ~ h r i u d~i g o qf i u w a IUT%~DJ~IK~ r i u {a, e, i, o, u) OIVQ~L!UU {u, 0, a, e, i) W ? B L ~ U ~ ~ W iinn%&i U &bi41~9u ~ C(9z~ndL~uurln~4~ubBB9 01v9LLiJUULh (g3g..u n i ~ $ g n q v )n~duurhid"vrl4irdo L~ULI~R$M@I~

torn-a"

(universal set)

~~l&saur.anBu~ 8 d ~ u a~oeiismiuci?r%ol i fhlw un16oL Musi zg ~onnw&uw"nfir~~nu6aug~1n~su' % ~iu % = {rii?$n'i~q = (wu"wr)

bwm'hn'~(Finite set)

~~n&416~41um"uo~1u4nrii? LIlR A

L f h l l % ~ ~ ~ ~ l ~ 0? ~ d S ~ n h ~

A = {l, 3, 5) A ~fhd~~"116~ LYU~IZ~I

n (A) = 3 d o n r ~ u ~ i u a u ~ ~ a ~ n ~dld {~iuauvin1 1,000) ~ ~ w ~ dr!uu~~~u&auWu?O'n~sK~ri~a igy ~'~1maih6 (infinite set) rmiu A = {$iu?ud) ~"rr~~Ilj~i~~iuau~~o~au+n Iau~aIn~~~ld&~8nvs~~wi::~!uu~o~am ~h ~~mm~iuaud~9u~'11~mr"uA~wmr% z ~~nu~~maair4iuau~~u he mvvrua~u~~nmr"ufiau~Buu~A N rrnu~~n~o~1"7uauils5miii aa~mui~~~~nw Aauyarh ~urniu Q ~~wu~1ln~~oil9'7uau~ssnur B = (13.5, 7,...) B ~ h r ~ ~ l m R ~~nu~1leseogs"iu?uv3g d o n LLW~~I~?UIP~I~~O~ ~~muo$ufi (infinity) &3arriho~r%m(Element or member)

l d 8 ~ 8 n ~E d b~nunis~fiifu~ui~nuodb"~~n~ % h (Empty 9 set or null set) M 4 ~rnunisIljr~uaui$n~~o\~~~"iln ~1l~i1~~8~~1l~wd~ddlja ~41.4x = {?'U'~U&RI~G~ ~mhd 1 ~8uau1$rno;r~mrw r1lnii~duu~rnu6?u } N = { 1 , 2 , 3 , 4 , 5 ,...} v~duur~nuAai-ru x = { w3o x = 0 r!uu~gid" 1 E N -1 ~ljr~u1ui$n~~o9 N r%mLioda&~'~~m (Subset) ~ ~ n ~ ~ a ~ i ~ n ~ 8 u &?iaotii~~iu %o~dnb%n~~ h A = { w ~ ~ mLU: r ) B = {t, r, y} ndi?ii B ~9u&aqmo~~%n A 8 ~ 1 n ~ scu '

~ 8 uB c A L L c~ = {a, e, i} \M"I$~uLI~~~J & 8 ~ 1 n v qd! n u i u ~ ? i u i6%i i ~9u&~~~

v -

ng sets) 4ouinnii

a~s:8n'1~1~~huq~au~n%od~b6~:~~09~ba: 'jdiba09mdi8u~audn~auhw?o~d (Comp~emmtof a set) ~anl;auirin$~wurinuo~Tu~~(~~awi:b"~~m . H&I i a o e i i ~ ~ d61u A A3znou6au$iuau~aw1::

PIB~&I.PIW

A' s:e~s:nou~au$~uau$9~u~~u"Imi$iuau1awi: iiuo~duan"ad$s:ndial6ii A'=%-A d o % tls:nouc;i3u$iuauyn$iuau a ~ u w n " ~ u u h o s ~A~ c~%iuubfIu w A' ~ d f n d m d ~ w(Union m of

sets)

w~dn~oiranil~~09n4ouinniiaoil~~~uio~ &~uijidU L ~ ~ ~ ~ " U ~ ~ ~ % ( A L $ U ~ L L M u U~"~U~~~~'IJ~ ~oeildL&

A B AUB

= = =

(2, 4, 6) {1,3,5,6} {I, 2, 3, 4, 5, 6)

u (Intersection of~sets) m n~~mo~r.nrwdsingo~~uaoil~~109~4ouinnii

nowm ~u~mo~~~n~u~o~~~cw~$uu~b~luWau

iaundfl (Arithmetic)

)

wu~uu7n uur~~aj

fns"m ( W i t k n ) nisoi7riiunisnuwfimaia~uni~

m ~ ~ a ~ n u m m(Long m u multiplication)

nng'~hnim~:~iur~u3uianimd~"ll~ani~~m

r&+iuaudri1vnr~11~dia~.~'iu7u~n a n I a n ~3adiimm~rn~~mn9'7~70~d~~fiu9"iuau~~ DU

d ~ ~ i ~ t h *17U61~7fl

a+bmh 6 + 3 = 9

ni~uan~hnisn~:w"m"&n"unis~3~ d ngmu~wus:pa6

~iu?u~iu%.~ tta:~waurfiunuau ~h 143 = (I x 100) + (4 x 10) + (3 x I)

rw;tu (Subtraction)

megu (Multiplication)

a"awu7u

n~s~i~iiuniani~~riim~iam.Sifau'~ 4iu~aa~~iuauu74~nsrn'i~~~auKu

finlam*rn

~finh~~~m

UrJON

L ~ u 6 X 8 = 48

nruurrt$m

didu~i;o~~biumnda~au~n9'iuaunda 7"~~h w"1umr~uaflui~:gm~wau rrsnbi7~41uau~diu3au

fMnS

(Division)

n i s h ~ ~ u n i s n i g ~ d r n ~ i a f i 4 ~ri-mmm ~a (Long division) Tg6nt8dy7u wiaa~,6armnimis4iuauwd~~au n i m i s h ~ u ~ f i d i 1 f i n T m u h ~ d ~ ~~~' s' 1a1~ 6 m WiJuuLRJad ;fi6,,ia<iwuiin<iuamd~ ~JMIT 5996 ~ a 22 u WUIUIU~~:WI~L~Y~~~~LB~~: 4iuauhu 22 ~ ~ u ~ u q i n~ddiauu T u s ~ ~ w i ~ ~ 8 a d o n?mn?s bthd 40 i8 = 5 lig&ohJbi~#ju m m q : ~ 8 u u l u ~ d ~m~mm~a~i59'1ua~"bwJ~~m~da~d a ib udfia1~13~1~8wrlu~~ a/t~n3a (R"?adig~iu 40 wi.rdi?er 8 a i ~ ~ ~ ~ ~ ~ & w a i u ~ ~

ligi~h~ii

40 40 + 8 - 4018 - 8

1-WJFK&I

( b w s of arithmetic)

n g m u l d q (A!mciati"e

law)

~~niauanua:mre6u~~uI~mungd wimsau ru:nidli~i5u~drni~ngn~s~d~mw J t q m d m ~ m r n n (a b$U

b ) + c = a+(b+c)

(12+7)

+ 6 = 12 + (7 + 6)

q ~ ~ (Commutative i i d laws)

ngnisa~ud~9ung&~a~s~fi~~u4idi6u"~a~ <iuau~~a~~'d*~~a:8~~nw~~~Q~~o ~i~lhruada~aGw8 dM N & ~lQ b3% kt~& Âś% Jl fiiungfi q m ~ m r n m a n ndiadi a + b = b + a bipd

6+3=3+6

qm61&hgru ndia41 a x b = b x a

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1~~

m h r m (Mixed operations) niaA"iuaruir~ua~a~~~nia~i~iiun~uinnii !

~fiwkju(Fractions)

k d r m i i i s (Equivalent fractions)

~w'issjaud~~iKuaiui~o~iuam1~aun1~~6~n7o

Qouniirwwhu~Auda$unii m i ~ a a n d a or simplifying)

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$ 7 ~ 7 ~

d m h d m (Common or simple or vulgar

hdf&

(Reciprocal)

daun5u~'~lansii~r?uiiu?td~~~i5unimi~ 1 r~~d?td~~i+iuaurizJr9uiar~~~ra:Kadau~9u Aau4iuauQu

fraction)

~ ~ ~ d a u $ w u ~ ~ urdu dnuy

kohsrdu daun5innd 3 flu

rda~isf3un5u~'~laasra~dau 3~ni-iiiu$wx?i'u ~ ~ ~ ~ ~ ~ ~ ~ ~ M M M ~ ~ ~ ' ~ r~vdau ~ ~ U (n8uliarav~fluKahurra:nn"~1riiadau W ? ~ M " J I D ~ Q " I M ~ ~ b~u~a~damnsliau'u~as rfIuw"am+) liandisrdu daun5mns i n rdu -1 1 1 t 3 ~~-jq:jq 1 + 3 = 1x 4 = 4 3 4 2 4 1 4 1 3 3 -3 2 -7 SM*~

(complex fraction)

?&R~RJWN?~&UL~~~PIJ~I~~~N~~J

~nu7a7~~4i~mihun~11~a~~

I . I ,

M~~uu (Proper * fraction)

~hubra:5oua: r~~daud~li8w".lra~~nunjira"?dau~9u~~[~dau~rfi

' I

(Fractions and percentages)

b ~ b b (Improper * or top heavy fraction)

~wwdaudsidiaJinn%I LU:I~~ULB~M~~?U~~ iTara~zJinn-diKadawWunii r w u h u ~ i r ~ f i

hwwmt ( ~ i e number) d

d i k & ~ ~ ~ # (Mthmetic b u

~~~~~

with fractions) n m n b h (To add a fracth)

&fiarq~fiau#a~av~r~~i#ad~uq6u&*ae Kadau

(To ~

U Wa fra&on) Y

~1~~1vd?td~bEQia:sj7U~'14~8adau~aa~Ku~~a: du 2 x 1 = 3 4 2 4 x 2

iihhqmu~7uandi1~~~4i~au&

$+6

- $ + : = Z -6

1 61

ni-icolh-

dmdu~dbiuu$iua

~hdrnbi~4dur-i~~

rn%m&&u (To suwract a fraction) dir~l3Qia~uda:4iuau'1~liad7~4aa~Kur~~: + ~ f l l t ( ~1 ~8 9 d l h ~ ~ ~ l h r 2 8 2

Irh 34

3 8

(To d i i a fraction)

I 1X 8

3 - m = 5 m 1 % =

- 1 ~ 9 - s . B 3

ni'lWmaan I~(LW~?U~LY~I~U); (#7d?u 17; BU I ?ULWU 6; ~ ? d - ~ u d i i ~ i i o i i17 A q(~flnd?ud~ri78u); ~ dididqm~vii 17 (L~%B~?u~L~I~u); n17qru 11; &LRY 17: $OUR~Z.27: WIfI 66; ~ a a u n h k21

nflUau (Decimals)

h u M m & u (Decimal place) gm&u (Decimal point) d i ~ ~ ~ i ~ ~ o ~ d i u a u 4 i u a u d ~ ~ d n ig~B~'Idun.J'iuau~Wumiamin.J'iurU~i~~ndau~ ~"~ai~o~ n&u~~~nriuunn~do~nimamodgn~fl~er~~~u ~:aidgma~.a:ndi~.J'iuauoi7ilq ( ~ d u1.2) YIJ~SELWR ~ ~ Q ~ U ~ I L L ~ J A ~ J L L ~ E ~ I L L M ~ ~ PI+,i~~~ornu. ~ ~ ~ ~ L ~ ~unugn M H G( LU~NUI, 2 ) donbindu~rnr ~ I L L M ~ ~ ~ ~ w o s uI d ~ ~ : ~ ~ ~W~n"~~&L~~%Lh8~~~d~d

n & u w (Intinii w non-terminating n&d'briri7wu(iloi7u~mdw~a~na&m diuaubq Siaundi 1 WIUI~~LLWRJ~A&~?U n&u K a o d i ~ ~ i0.375 U ~9~~~1'13daun~fler~ n & u G i u w : w d i

u-r

(Decimal fraction)

&LLEJB~AK~

3+ o + -10

7 100

5 +-1000

M H ~ ~ ~ U ~ ~ ~ ~ U W N ~ I ~ ~ ~ ~ ~ ~ L ~ Iri$in'pr ~ a o d i d ~ dMW~~UUYDS~IU u ( 7 ~&L$OJ(R"U ) L W M ~ ~ ~ W ~ Q U U U I J R ~ G ~ ~ ~ U ~ ~ & ~ L ~ 3.1 U 41592653...

w & u m (Mixed decimal) ~iu?u~iua~s~dddd~:nau(iiauii~d?u~i~~~a: n d (Retuning decimal) d n m d u h~o d i d ~ j o d15.76 L ~ W ~ ~ ~ N W ~~ Jw U ~ j d i ~ ~ a ~ ~ m T . n m "" f &ua~~l~~m hshom~lo~orihWin"&aIri&~n

... w "n & d ~ ~ i u a u " ~ ~ ~ ~ f i u ~ ~ MWQ~N$I ~ ~ i~~:' %L~~DJMNI u ~ uU r,

LiU

(Finite decimal 1 = 0.5 2

l7 = 0.0272 625

terminating decimal)

0.125125125

.~ufi~rn~i~ioll~

si7~cnri?~~snua:iia~mfiimo~~~~u~ddinisdi Kaodi.jhs6u9:duu~Bi~~u

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qsuherw&or

(Arithmetic with

decimals)

nram~~eifm&a(To add or subtract a decimal)

(To multiply by a decimal)

'brjfi~d6i~$$g?mmwiiuu l~g6uLnjjaun"u~1uauQu

~biSa9'g'IdmmnwQu~lmu4iuauAbbslraiswwQuu~iiCu

b~unia\riiud~ruanw~a@unwQuuTmuni~~~uu &uaumuuuak &ksmn~iiuu0ila~~u

- -. '

I nduun7uw'7uMiJ

-, auiliui~u~n'uni~au9'iu~uiBfu rfu#u Q ? ~ W I ~ ~ $ . ~ ~ ~ $ D

nmhm&or

(TO

IrjdlriJEgqnnnQuu

divide by a decimal) ld41u2uLdu(fioJuilq.jl

~ (To round a a decimal)

~da~i~"~~~~ifuanu~lwwQuuui~~f~fi9" ~a~~diin~sruini[muni~m~w&w4a~~ di~du~zua r-~uniai~m~w~4iuau~iu ~~e~'il~~w~iu~u'1ntidqm~ 33 iIu 3au i" bmrDi~qI d nYSmuo~n"Yiifia~n7s di~~~~~u~~~~~~hm~udiA'

nohdLdu 63.5378 alQQrflmLFIB~~Walu~~ ~~~+gwi4iuaumiiZ ~a"~r~i5u~PiPd~~ua~unimia u 63.538 (WH~UUHIU~ILL~~~~~)

4 i u a u h q L~;$u6audiuauLiuan"u~rmhunhk nwQuuAaun~[Quu

bPiPd

3 2 + 0.4

63.54 64

(n~[Quuaa~di~~WPiS) ( 8 a ~ a " l l u i A '2 IRua)

M S ~ ] A ~ ~ ~ A Y Y $ I (Rounding A error)

aa1u~~n~m~unia67ua~dn7~n~~ 8aaeii~~du th 0.69473 i j m ~ ~ ~ 0.69 , f h nia Id

$nuid 8 (~IU~U~I~~EJIU): n~ciiuu.humciinrriluu,gmndiiuu 19: ~rinhu17: 41u?udu 6; h u n b 18: n?$hflw 16; WY')~rn!hdiA'q 9: ~ L V ~ U U ~8 % (biu?ufi?&~od): ~$N ~ ~ J u ~ Y u I w s ~ ?23~

(INDICES AND STANDARD FORM)

smmw (Index (plural is indices) or exponent)

raaun~* (Power)

4 i ~ ~ ~ d d w o ~ u ~ t l 0 ~ 4 i i m ~ i " 1divm4lu?u41uaud~~~nu&&aumm 1~~~n~i~a~d~ Y O ..

(Fmcthal index or fractiond

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l o "

ty~l~uu'n'lk (Laws of indices) t

6.msundi$ma~1mundi&~Mi~miailxn~~, ( a n ) m ,a n x m

do a, n wr m ~~m.&u2dslq

ng~~:G.iuil.iiria"td~a"u~nia~~~unii "rylae~ 3. m m n a w~ 4 % tun41 "ypmrsrauni~k'~ U

b b (5213 = 52 3 =

brn51~j7( 5 9 3 = 52 X 52 X 5 2 = 52+2+2 ~s~.llunn'7adwuqiudu2n"u1fiJi~a"u~diGd = 56

+ a -

uinudnn"u I

7. ni%unniad'p10dm~uwa~ bupniagt-ub~unniadI "u09~~66~~ 41~2~

a n x am = a m ~ d aa, n uar m ~~wu4iuaurLhq

42 x 44 = 42* (a x b)"= a n x b n = 46 bUda a b, n ~r~lu4iuaulfiq b w j i ~ ' f i 4 ~ ~ 4 ~ = ( 4 ~ 4 ) ~ ( h4( ~5 x4 3~) 24 =~ 542 X 3 2 = 46 anrii (5 x 3 ) 2 = 1 5 =~225 %,?Becu~mpn h$diqiuvii~n"u'Lri~fl LLa: 52 x 3 2 = 25 x 9 =225

bit4

2. n i ~ m n a " u u n ~ i ~ ~ i i ~ i u ~ ~ u ~ ~ u ' 1n fl iri n ~ ~m~Bm~~i % ~ ~~~~l ~ u ~ n ~ 5 W I l ' b ~ ~ p n

uiatlnuM

"uairumar4iuau

a"+#'=

a"-"' rn ~~wu4iuaulslq

LBOa b ua::

= 34 LWTIZ~I

(b)%

~ d aa , n: : IL i,%u 36 i 32 = 36-2

m uwu4iuaulslq

(BY-

3 6 i 3 2 = ( 3 ~ 3 ~ ~33 ~~ 33 ) + ( 3 ~ 3 ) = 34

~~h~~a"uunh&di~iu61iln"u1i~1

2 33

~wn:ii

4 x 7 x 7

LLEJ::

S3 -

27 a

= 22 64

43 = 3. ~iuaulslqdundi~gm~~w~&w.~~::~hfitl4iu?uu"u ar = a 9. ~ m u n i i 1 d ~ i ? ~ a ~ d d i $ 9 ~ ~ u ~ ~ ~ d 2 u 6 5 i u i

~ d aa ~~wu41wulm7

niarnilb~.dsndu~n"u~~l~m~din'~du~ 1 1 b.dsn 6T x 67 = 6 ~ + =$ 61

4. <IU~U 1 Uftfil~d~slq DI(I~"w~'L&~ 1 LHNO 1" = 1 ~ d an ~rnu9"1~13u'Im7

. v - l u - r w b m - ~U I I ~ IIM V ~ U U [UI

~ V I I I I U I UIYTIII

~ u n inpnnsnfiskgud i (zero index rule)

a i ~ n ~ i ? ~ b6; i l X~ 6i = 6 ~4.62 6: b f h ,b ~ J J ~ L ~

Lh3

- . .

@nUUSgw (Standard form) ~uuuuim~~i~~SuiBni'~nu*~Iuni~ ~?i~~Iiuau~ ~ L I a x 10" do a u l n n i m i o d i h I u~gaurrj~ 10 (1 5 a c 10 ) L ~ 63,000 J = 6.3 x104 r ~ s l i ~ ~ ~ i u o i ~ ~ ~ n ~ d ~

&a @ m r i ' u + a u n M n 3 ~ ~ ~ 1 ' %BMwlnf (index notation, exponential notation or notatii)

r n ~ ~ ~ ~ u ~ i u a u d . i u a 1~ ~ ' I u ~ 1 ) ~ ~ ~

mnqi~hbsawg~m~[iuu5ai1sUa~m u " u r i i ~ ~ i a ~ r . z n ~ ~ ~ z ~ a ~ d u d( i ~ ~ ~ a d 1 5 1 ~ a

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huau

&IS"&UiIFd/nd3U (Ratio and Proportion)1

Bm~iau~8uni~ad~w wfiuuln~~uis~wo~d~8]is~"1uo"u&ubawi: i (particular order) l n h ei?odi-j~du fiiilr7~tin~~@daiu~u~~az~in@iu u~ARuov"~~$oo & "Dm~ i~s ~l S l t i ? ~ ~ ~ d d n ~ i u d o 8~ d~~3n ~ ' ~ 1 ~ ~ 8 u ~ n h u ~ i i u u & i ? u ~ f: l~~Jn¶d~n&~W ~~ I8A do~3 duudu 8 : 3 1 - .. %~niw:dtlu'lu~d bfl~sdr~b~¶.l 75nndJ = 5 :4

s)ambmm . . (Simpling ratios)

iikrxhyk&(unitary d o ) 6 m m h u i d ~ n 1b I,&1 : 3 bbaz 8 : 1

gmh&~&

msv:i16mdau'b~6fiu8~1~1dauou'ia9iu~ufi

~ow'i~$&~dm~~b~~$i~a~ddo~

(Ratios

m m

b~~~~~d?~fi~lib~13'l~~~bi6i~~

dauc&au~iuw~Juah&:w"i~ps"d7"11oa6fi~idau~u ~19~5~ ~~~d53nid~iuuwvd~flunr~flw~~iu<iuau~$~u~7 ~dodau$~~~o~.lroa6msidauadidou1a~siiA'~t ~~u~~lkir~a:iiuau~n~i~uibu$iuaudu t7un bdu a : b , b : c b ~ t a : c $ ~ ~ T I I ~ U ~ ~ I L S U L L Y Y ~(simplest " ~ I U ~ ~form) ~

terms) i%-~idauBdmd4u~ bw'uu 3 wvd

than two

idad a :b :c

kd~w'ik (E~UM ratios or equal ratios) $mmdauw~d$m"w%7da'lddo~~inhi ~hibvhfiu jiaBei7dbdu 4 : 8 b w 8 : 12 ~ ~ u $ m 3 i d a u i b h h

~ 6 ~ % 7 6 j m o ~ a p d ~ ~ u ~(TO ~~eii&tl simplify a whole number ratio)

5141 ~~ud~:w"i8m~idr~"tps"~~6msidauoii~ ~mz#aao~8mhu~ua1~11~sm"i~hoddi~~A 2 :3 &u wglw"~iu'vi?dauoiii~~ m~$m~idauoeiauwdau d~dRs~d%~b~~n"pdw"~I~fi~%>4l ad* duafiu il~nsi?u~~mfiu$~31dauo~ld91~~~u da'~d"~n~6mishudhu~~r~b~ua~u(~%n~iii~8a) , ~ , ; d a o ~ u ~ a n l ~ ~ a u ~ ~ ~ B J l n ~ q A (n.3u.) I,&~m~idau~~siin"u~~5;9"iuau~~~ 2 :4 (highest m m o n factor) I : 2 n=idaiu 2 Aodid~h 4 : 8 ip(a/au 2 b~a9i76midau40; MI : 2 #aIud %"Sjfiuoiiahu 40 uifl : 2 &'bud = 40 uiq : 120 u i g (2 ialud = nrsnF3au~3auBmhpd(TOcompare ratios) 120 UI~) 40 : 120 rr~~md6m~idau~u$~fidau6audadau~a~~uan"u = I : 3 (m~~d1tGiuau6iau 40) u&?bd4w~Guv fi& 40 uifl : 2 & h a d i f i $ o & d i u $ u 1 : 3 si?~E!'IiIb~u 'JdI,fl~YI,~tl~% 3 :4 nio 5 :6 n " l ~ l U a u ~ d a o ~ o y ~ u ~ ~ 8~sidau~nud~iuinnii (common factor) ~ d 7u : 9 8msida~dfioylupl

~ ~ l

a~~~rmduu6ms~hu~u~eI1,a~dau~~1a~~erod OMIBUaa ~w~d~u~ulu~lhfi~daud~8adau~isw8a.iauddd1

hfgm

d~6~~$q?~~pj7&m~bfi9~&

3:4=3= 9

(To simplify a ratio that includes a fraction)

k W :

5 : 6 = 5 = 70

~I$IL~U w ~ ~ I , L P ~ ~ v ~ ; o P ~ ~ I # ~ : J B o \ ~ binisinmy'luwdautltnhu ulaarutfi~dau&mii a 12 > 12 9 &$u 5 : 6 r i i i u l n n i i 3 : 4 ~,flu~iu?~~iiu ~~azg~dau~u~rmlsidauhau sj?uau~Juan"u 5i&arn~i?~oa6mmll?u~~wuwpdauni~a'fi a i oa li d lu l9di ~~~y"lu~o aaiuena 6m~~u~vii~fiu~au~4u?n"uImudn4 ~Pdnid p?ruBau2 hwmdiuau $&:~ddadaii~~7nh~fiu~adWhd~unh 1 x 2 =I na: 2 x 2 = 4 2 du 1 1uw7: 47 ~mirsla3= 100 ~"11ufi~ufi3 : 47 kzu : 2 ~ , i l m ~ u ~ d o i i d i 1u :~4h ~.au4wm= l 0 0 : 4 7 * " m d a a w: heiau, rnsttm 76 rnmiimwtum w:nm* dun"" "m.3" 1 ~';nou=i;");

li]

;

~ami.rAfi61ddtp 17 (rmdaudrri~h).wwgru I4 [niqru): n.n~daun&uM

&&u (Proportion)

(Inverse proportion)

h ~ d a n m d i e r t d l ~ ~ r t d d ~ fdi a i ~ l I ~ r w d i ~ f i i m d &ddmm 19q 9.94 riu L?flfl~5dd~d~od"'tkil$Ad3u M%lbgu8lildasl &bNme~ulm&mzWRM1u~ml~aw ~~h hfi~awz8u $~~sw'k~wwms~h1~dau1d oc imm&a~~dddu16udaammB&imd9

0 1 1 2 3 4 5 b . l'JEJI(T8.) (a)

- --

'.id.

--F.

.-.

-3

m 0

r n s l ~ l h - ~ u

l l i i r n l d

(Solving proportion problems) (Solving ratio problems) n n ~ 1 ~ 1 ~ ~ ~ ~ 5 i~+fi 7 ~ (unitary A ~method) m t d (To divide a quantity in a given ratio) ?3%flasnis~~fi~~~d~nlfuim~d~~SPdb~md I. ~ a & w a u ~ i iid~udu6mmdau ~q W ? ~ ? U ? ~ O J ~nd$uiw~d~munimidwo3ddwsdam~~nl~ui~ daudidq #mumiaozls %naz~imga$a~idi%oddiuau~o~wsdaudidq 2. m~uim~au~iuauM'd~~mo~daudidq dam dbsnls hddd3u Kaohadub~flu$~~m~&~aiuisnw'uw"b6 7. ~m~~d~iaz47td?u~uo"mmd?~4~udmmwl~~ddau mIi yn 5 u i i ~sd~iu&:i~uw~6~~fii~u~awi 3 $mpi~mrrgiwztiau QaTus rhadwrh 61 qyu a b ~ ~ a r cq %ad@@innduu u 1. mj2~mifdlau 1 u i i b 5 u i i q:flua6 da"wndau~9u 4 : 3 : 5 q u r r d n z q u h i ~ ~ s i i ~ s 200 dl 11-41 u i i q:iuw%6 200 AI 4iu?un"9wma~~8maid?~6 4 + 3 + 5 = 12 Ts~flugqrw"u4640 ~ f i$0i 1 H I J Y ? ~ ~ ~ ~ ~ I U ' I ~ ~ ' J M180' ~ ~ ~ ~ 2,E n Jl-IjlnIlJ L3M ~ UL$Ui U fuLi~ ~ U m ~ m m y ~ ~ d a u r33 17 $, u: 3. 1 QaIus = 60 ~d74 qu a %itdlR 4x 15 = :. 3 $aTud = 180 u i i q8l. b jjflw~3x15 = 45. lu I80 u i i (3 3aTus) Tss~udi~ufih" yu c huim 5x15 = 75' 180 x 4 0 = 7,200 dl /

zii

dhDJb&mO1o i~~~ ( ~ a t i omemad)

?3ni5~~iiil~ifi#g~da~T(il~~~~l~? ~ 7 u ' P I o J L & ~ ~ ~ ~ l ~ ~ J i n L L ~ j B O n n l u ~6m~idaudi?uduaaJ'1~liiuu~ud~~['1~dau~$aKa~~['1 MM~~ DDJLR'~J?U ( x ) ~$u~a'y~%=nuii h a d x m m u u n n m i u l n d a u d d i ~ u 6~ 1l ~3 ~P ed s z ~ i i d ?A ~LLB: ?R B ~ u r & u d ~ ~ d a u ? ~ M ' a o d ~~~ums~011~['1~daun"~~~~~~iaudiuaub~ au . s r m h u ~ a ~ r ~ uAB m s~nutidniu~udiumu~n'Iu ~ h o i i s ~ d ~ssfiuvu'r~i~d~uw'~u'il~o~A u 200 M ~ I AP uwzdiuau$ao~3~b~muiau PB sl"~si~j7ur~mtdr3i3u 514 ~sdfluvu'qdu&~i~~u*i6i~d~a11 (3 + 2) d7u d7~3w~ihfl7g A / P 3% (To divide a line in a given ratio)

~e gn"uj"7uSir h7d7l.l 3 :2

-+.

4iuauwu"i"11o~nisfiuu 3 $ a h rfIu~(ildau bum.jsn"119' i uauwu"idirm"Iu 5 uifi 6i?m P o ~ d a u d d a o o n l k l o ~ d ? ~ d " ~ ~ a d b ~ m ~ d 180 U I ~ (3 &) AB (do AB BA) n l ~ ~ ~ d L ~ u ~ L ~ u n ~ l ~ Ifi a uX~~tu<iuaum~iC(iluWau a3 rflums~~n~deisniuuon bi7dau~~srno~6msidauuin 1L = 2 0 0 niid?uflam 9~ P f ti 9~ B u i n n i i 9~ A ~ s z 180 5 9R P V ~ ~ ~ U U ~ ~ U % O JAB L &dd000nIi UAN 1

a h -

j . 8 6 ~ A ,= 1 8 0 ~

3 dm d~u~wrhw ABs gnu& ~ drnusnvmgm57dy 3 :2 u?nnd7 &uu vuuonr&$m~7rJ'?u3 :2 p P i'nIjp B 1hd?~ddamo~6imd?~dmmn~(il Ph Bpm A mnn ' il B rurahdapd~m~8pdmsd BA d?oaan\i

d P

180x

=36000 5

o rile,%

- 3 dm

7,200

m"~ Ta~Cu~aiuis~fiu&A h 7,200 di .(u /

3 &aTsw

d3tl%#6&#~ AB gnuhuu~ni'u$~md3u2 :3

loon

17 (rfl~si?ud~vhtYu):Y I ~ I Q U ?anfliluu U. 19; ~VIS~-JUAW 25: LW ( ~ ~ ~ ~ u d t17; i vh~nr k ) Wnrlflumrr 25: h w h u 24

17:

~IB~~~~RL~~I~~cLBU'LJ~B~

(Percentages)

%"oua::~$lu3ddd"11osn75~~amd~~a133dau~!ower~u~~d~9~ dau"~~oir%"au ~daj~"11u6 WBSIU~~IBS~I"%u~~iat5ou" Kaodid b"lj 10 ~E]D'%.%u~ (10%)

fraction or decimal to a percentage)

express one quantity as a pemmtage of another)

!m~w~dauw3owwQuudiau100 rdu 3 = ( 3 XlOO)%

wid3uimd~~aud3~i~dn~j5~1mwd~uargm wa8ridAau loo

%era:

300% = 75% 4

A x 100% =*ad B

m (To find an original

q 1-

m~el3uim~wsi~6au50ua:: M (I 1 % nod ~ a ~ i d b b h %r ~) B ~ m f i a100 e (mdhmi'wua) percentage to a fraction) duur9prwwQuu%hid wi$ouarhau 1 00 ~~Bav?i~w'1~daulGdu mnl5uim~~si~fiau3ouar ~w~-sjauoeii~pigi~~i~v::~~~~d~A ~i;liiidunii%wsxi%m& (reverse percentages) b d d d a s a t h m (To change a

~du60%

snldmWasa:h&u

(To change a percentage to a decimal)

~1430uarAau 100 1 4 ~60% = 0.6 5.2% =0.052

r (TOfind n a b

percentage of a known qwntity)

ii3ouarlGrfiu~wwirn(i&d ua:gonhuJhnol rd~m3ouadrran~1a"rhwwQuur~a::~m6aufiuim

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int-J4

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Lib

=- 1

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Xl&x

P Lhl5orhJ R ~h8maon~d (i8~h3oua::) u T ~ h ~ a (imrhg) rn

m~~uaw& Ij,sw = p+

d m d 1 Lh72aJLbw 5QO x 1.05 L l d (cjuoiu x Qnl)

P X R X T 100

krohariu qfifia@daaqu m i l a d l h ~ o n ~ 8 u f l eronrd~~jiruma::il~hrh 20 dau6

4% f

Lrn::jl

CTo-canpould-(Lorrg~l

Id&a~nnn~&ufi s d m o n ~ f i u r & m

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r5uswrh

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fmku'w

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kqaiu9i$ali~awuianiun5ii1u s l r ~ a i ~ m i mdm (Parallel) ? ~ n i d d ~ ~ ~ h i ~ ~ i ~ % ~ ' Pw% I~L&~~~~didq

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I-

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fin'daBplpd

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p~~?~~ihmra~'uBaijaiuu'i

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'ru (Angles) I

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i ~ ~ ~ i(Null l f langle l or zero angle)

nysn~~l (Whole turn, MI turn, round angk

quImq b i i n n d n n i i yuain (90') r~d~vuimdn niiyussad (180째)

angle)

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ha pain Iiui% 90' quinaowu~fIq~~:nou &quain hmuAnuin!&gws~uiiirl~ we

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$mLwdumuerm ~riibiUBi7uyu~da::@ m1n60e

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pmcave quadrilateral) d

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m m w 7 d (Poiyhedron) v

5 X d~

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(Platonic solids)

Aurvi?

n3aWmdhhn6 (Semi-regular palvhedronl

(Dihedral angle)

yud&znoumulunu w a l m w lL b j ; ~ ~ ~ € l ~ M u ' l ~ l

v r m m d r ) i 7 (Concave

bwnJih(Plan) d d r ~ ~ ~ ~ I ~ I ~ w \ ~ w ~ ~ ~ ~ ~ I u L ' Yaatiiguwid"am I ~ u B ~ L L ~ : ~ . I ~ u ~h$mu~duubsnwdua(9 (apex)Bma&:i~ WS~~~U&U~~I~~UDPI $ ~ C ~ m a 5 3 ~ % m i 3 : i & ~ 3 ~ ~ ~uuh @ b~lrn4 mub~f nwh q h~3:ddu~h%:ililr~nrii (regular p m i d ) i &u'~p L y w u (Elevation) ilU6NtJUU a a ~ 9 h r n n ~ a i u # ~ u e ~ ( ~ ~ (ap4u min&7~di 67uM61) da6iu%i4(qu~~ubi?u%i~) &iuwU'i~flu

M F I (Pyramid)

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h d % ~ l ( 9

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6zrSL.7

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(Plane

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reflective symmetry or line s y r n m ) ~ 3

f6rder of roZation (al)

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nlsauulas WU U I?~ ~ n ~ . b 1 4 9 ~ 0 oon~~uao~dau'b@u~&wd~~&w'rosmi~l ~i:da'~dq~q+~dum~:$~T~~y%:91 -,,/

s j m w ~ n i u h n i m y u s m360' W"j7d

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~ R ~ ~ ~ ~ ~ D ~ ~ ~ u bdhr ~ , " P ~

3 : : ~ d l ~ l ~ ~ ~ ~ 4 s ~ 1 % ~ ~ ~ ~ l ~ ~ l ~ Tflr) ~ ~ d(object) ~ ~ ~ 1 LLa~flaS(~fiR$~fiUrrj1 3 b b f l f l 9 b " %mw ~~~1 (image) nrn~dw~fluWd~<nn"pd~bI~mn13ddio (mapping) ~ l & d d \ d ~ b l ~ ~ ~l@hq d ~ u uu ~ i ~ d & ~ D s ~ 7 % 5 1 3 ~ 9 , "$~iao~19bh ~ 3 7 ~ 1 ' b 6daod"p~fNb~~fl39 A B d4&~d$9 A'B'

m'mp m1~ ~ U r ~ & " ~ ~ ~ ~ w l i f d M ~ ~ l ~

mwd~ARihrfi~9~m~~~u~~u~n~mw~fimM (mtre of rotation) &L&U (axis of rotation) Ifd

b~n'~la'~q~~~ua::unmim~iufi~ui~b~a::qu

~ o ~ n l ~ I ~ f i ~ ~ b ~ l n ' ~ ~ l ~ ~ ~ d ~

ii?rh~mo~i~~~~dpiw~u~~at:quhriir

f l l m 5 h (R4eclion) mnud~~~m~~91'a::~mgnd~~du"qrnAnu~uKd sru::vhd~hn'uuarn'iqu 90' C'~4ua::fiou ( m i m line) 6ia'wqbisusrui~~~uans::~m::b~u~Bu 6ia'nq

~isuns~rnufi3 ~~u?nszsnsr~hsruimuim~~arqu

q~a'm~~~un~lqmmmmyu (angle of rotation) h q m o i l n i a w ~ ~ ~ ~ m u ~4m1Rrnnhi7

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~ ~ r n w d (Glide r n reflection)

mmer (Enlargement)

mn~daa~~uldmi~~'api~eldm$iim~ r n ~ ~ ~ d a ~ ~ p l q d u d a ~ d d u u ~ ~ ~ ~ d i u n i

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Image

@&her(Similar figures)

~@~iw~iimh~~~iw~~Cpln~kk Q~i,w~ia~w'a~nunimuiu

OA' = 3 OB' = 3 03 = 3 OD' = 3 OE' = 3

x OA x OB x OC x OD x OE

A'B' B'C' C'D' D'E' E'A'

= 3 x AB =

3 x BC

= 3 x CD =

3 x DE

= 3 x EA

o ~8u?rnguu'nam~~n7mu7u J

pkymrn (Conguent figures)

5~pl~fi~iiaua~nri~~~uan'usa&~~~

6ibBuKad~rnoummidauaf1 (negative scale factor) 3afufina79"11~9~

~uiwro~~rdia?"Cplq~~arrnw

nsrsn ni~wrflounis~~awuiub~azmm~~sdw'il째~i

onf=-2

XOA OBI=-2x06 m'=-2xoc

'i%q ABC YO?UMT%$ &dsznwmm7dau

o ri7upnguu'nm~

r/,,

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L ~ E N L3 ~flnu~ws B

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1x1

= Ixl =

J2-X

JGF J9+18

& 5

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Internet links

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IH,

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pan&mC

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vectors)

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~ ~ (Geometry aui~~~n~~l

' ~ I / ~ N ~ M S B ~ W M S Y ? ~ U ~ Z ~ ~ ~ S ~ ~ ~ R ~ ~ ~ ~ n7mn (Comm&&e and ascciafhfe laws of a d d h ) a+b=b+a

.d u~lwniopnusrpm~inr (cornpasse. or a pair ~ p l n s t n s ~ m n a o 1 ~ u a (To s ~ draw 3 ~ an arc -.

of ~ p a s s e s )

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bYwsuuwmd

(rnctor)

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n3::mi~Tmmln~~u"L~~~mn~84o~'3::~~.b~'In~~a::rrvu r i f i u f i ~ ~ a ~ n a m ' r o ~ ~ n a ~ u o n odaiu ~wi'b~~ou~ ~ d b i m ~ ~ u l u " L w s u m ~::(R'o~oiunrna n~~o4 .. 6~6uwngJ~nuo

(rlrJ?rluniw)

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Internet links rjo~suuin'lrr~~n15utlad 'td111dw.usbomequicWinks.com

h r i k J d u w 1 7(Useful ~ ~ construction terms)

dauambhmq

1.5 mi. P 1.5 mi.

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rmthhgu (Basic constructions)

~ W & W (TO comet ~ aL perpendiwlar bisector)

* ddmld

(To constmct a perpendicular line

a~idr4u~b~~~~au:W"~iain~udauao~b4u~1~ through a wlhdar point) &L~FI&J~I~ 1.

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niiras~%uu?~iaiiu~%~mm~aiuuimo~dau bthmsd AB &~~t4(il~1ild7il aod~Bums%mua7~?mflaiuaoda~b?up1&m A

I . ms?mnlaiur~wam.lrain~~?enr#pm P a7ndaubhfim

* yu 3n:dnilt 47 (L~uu~?u'~~/J); u v u m q u 32 (Ju~uiu):~ 5 u 47: u yuniu'lu 37 (yu'lu3daiu~nduu);~ ? U % O J L ~ ~ U30: ~ I Jbin, ga 30; lu'lw1unsnrma5 47; yuain 32: geuom 34 (pinriurnduu)

(Constnrcting triangles)

szlqkmJLd+k w n u m b u h

B &

10 m.

10 far.

JQ W,

rh?Bopiiiw%au' 4. a7nr&rhu Z MU'E ~ ~ f ? r i i r a n u mr v~i ?~fdi f i 7 w m & d (ti71~hs'/~~urvd~1~&?~6 ~ m u ~ ? w ' ~ ~ ~ ~ ~ d aniwldti)~NS~uuh~mr uT~mr i'w'nmiuuu~~nuu~?rvi~ xnnu xnnuhd7uThr~n&ff c AB)

I. mnn'?umutluw5~~&wr7'~ 2 ?I7 A rfiu?npu'nn~~s'flu"3.717 B

laXu"anq310 m. i7mn @+mr

* dd~~aii1m~~fl~i;uan"'i~$a1ub~duudd~xi~~~9~~i9~w"1~fl1~1d$a1ub~duu61(19~d~~0d Dl9~aD96l.lwo'iJ #d~Undln%&m~ai(ambiguous case)

6aaoei.I~a519~1Iaiurwduolii AB = 7.5 "Ha. AC =" 5 "1IU.

Lrazyu ABC = 50

\ r25 Sm

A I

5 -"' ,--

vu.

(To consauct a regular polygon)

liaaimi-u a ~ ~ ~ ~ d u ~ n f i u ~ i m m a r p (l54l.0~')~ ~ f ~ l s l ~ ~ l u ~ u ~ ~ u ~ ~ ~ ~ us:lWqumqto~yrruria:yr $ ~ I I , ' Y I (I ~08'u) ~

Id%L ~ A I W M ~ % ~Q~QY~SJIU% J ~ Q b?USrn~d?flsihl~ fh a n m ~ s i o ~ i ~ u d ou~hoiq~ihnwiu utu Aofibaawd" Q

Ia~mhnl~i~a~~~~w~~iu~m~~nw~i~rngl~t~&mquu'nm~ ~osadna~~bar~flhmadn6385~tuia~iifidadb~"U.uu rhuna&~u' 10 ms ur~,ru1r&gwprli,fl?~ (Compound loci)

from a fbred point)

'bea*~

.' P

(Locus from d d

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,.a â&#x20AC;&#x2DC;

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~%m~lr~m~d4aona~o~~]inn~iwi;"9dou1'~ ~domnIa1~s:nm: 1. ainIfi4&id~vi7~~m~i~:~]m~1a'a~huii~~:1~ 2. 1 d ~ e l w : ~ ~ ~ 3 " u u a f i ~ w i w q l i l ~ i u ahw~hw"6'1dimt-13 3. L ~ ~ u u ~ ~ I LL ~~I ~U L ~~ ~U FU I ~ ~ W ~ ~ E ] O ~ ~

%m~su~aarhu~vi7h:vii'b 4. a:mu~sisdau~a~~w~~~~a~wfi1mK'i~dm~"

@ ~dih91ngelmaoqlil+o du k i n u a r h ~ 9 a ~ & h n ~ 8 a $a ~ 7UU~~PXAP:~" %u,*??w P ~ : M a o d u

rrflqw Q tn'in'u

h (bcw from ~ a line) T a k a a o ~ s m ~ ~ d 9 i ~ : u : hd4iilhn n d u

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~JMX]~U~:YP~I~~~~'ULLI~JE~~

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d ri'

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(I.ocus

from Memeding Ii)

b6a~yqd~&o~~minsd7~1'uo~bhma~ ao~~lhrfi~fiu bhT:u3l% LV~~KUSJ:: L ~ L ~ ~ ! u U ~ A ~ ~

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$'w7 w ~ a g r n : f i : ~ i h & f w ( ? u M ~ ~ 5 ~ & , Wwsin 6A UE dB riir-dqm nm&dw'wn"uuwm,rkznd intem~trtnb

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(Drawing to Scale)

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%h&~r;f~~ds81a& (Area of a rectangle) nii~%rn$~~n&uiod~i Pd"pl~?o~~.J"i~aun~au"11o~maiuuia ~~a:gmJaiau ~iuau~tiamplro~maiuna"~~

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Llslncls (volume)

I dhfUM

(Trigonometry) (Finding unknown sides)

[Sine ratio (sin)] . .@IS

sine 0 =

suol~o~ipab4d ~ ~ a1= 69 x sin 48' nIIIiju "sinn u'ldb~"sm~nrmrd~m~w~il sin 48' rurufiaunis a = 9 x 0.74314482 a = 6.69 "11a.J. (IIf3fiusl 2 ~ 1 L b ~ d ) & w V I % ~ ~ U ~ U48' fna 6.69 69'ijldhJfl3-(IJfii

ilbivrds)

knwrJrurrfusnn [(Hypoten-

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d ~ ~ b ; u ~ ~ r n ~ i 7 u W s ~ s l y ~~)'~Imi'T~Idunz6~m~BUPj in~~ rnI~v~n~~)&Rwim

b ~ h ~ ~ O ~ h O J $ d b ~ b ; ~ u S ' ~ ~ ~Tw&11/~Butl i ' sin, ms ua: tan ~ d m 3 s l r r n ~ ~ "$ sIosine a cosine wz tangent I h l u ~ 2 o f ~ & w d w(Wdduslm) ~fi LL~MIJ & ~ h r h m n a @"shrd o Ymn riou

hznouyslain

~~~odm~m~anunm'~7~'Iu~~on"m~~'Ldi 6d"'Iii rru'I9-i?~Aidslmo~'Iuwn-n:: 'DEG" ~oliirmlioram

Iju n - I liuLR;mhmlflw~l sh xo

h ~ a ~ 4 m l m i ~ i ~ a 4 ' . j ~ar'iunn

h@oqm"thdd c = 5 x tan 50' nmqu w u u d m f i ~ m ~ ~ m d m tanm9' wufimrns c = 1.19175359 x 5 c = 5.96 tiU. ~ W 2 il~h) J u3.p asD l 1 5.96 r r n f i m (nrisuod 2 diu~43)

gkl'uh%1~1-

(Non-

right-angled triangles)

~"~IIBJ~H~U~~~'IBJ'I~~IBJ~M~UBJ~BJQ~~LL~ 8m'wairj?u~oilldlflldunr b r ~ u ~ w w ' ~ a i n a ~ i s d i u i

bZ=$+$-28bcos~

~hn'qrnrn ~mhuuar~~* 67!& I al.oli 4 a brLwrriw lu@nu~mublu A C w i u ~ r n h u r ~ a r a~A~ .lo B &IUAIW lngamlalml

a 1 2 a64278780

0.996194@

a=1 2x 0.64278760

I & nu.

uflaun~s

ww'ma~A

mmBJâ&#x201A;ŹrtmWhl'lda r 15 na. a2 = d + c 2 - & c o s ~ a2 =102+152-(2x l o x 1 5 x m 5 0 '

- (300 x 0.64278761) 9325 - 192836283 5 = 132.163717 a 11.5 h d a Ula 115 Lm8b01015 3

= 100 + 225

m t h l m k (The ambiguous case)

d hs u q W m h (Area of a triangle) X d aa

~m~~awunamWiuam~iu"~~~mu~wduu rfio'Idrnz~sydnmmmmos~tlaiurwduu r ~ z q w ~ I h o ~ ~ x ~ 7 u d a m p m u s l u u mu7snh3alaliluld1ms ddii7(~d~hIdA 2 dimou &rhnsFii~Wm~wd&

Y J

mm = $ absinc

I r i j 8 o y a ~ ~ m o d e n ~ m r w d u (aimso dn1~ 4.9) a3qdmumwduun"idin~u2 diwou Ih&i

rimufilM"o~s::Miii~fiiu a rra:: b

A 12 41

ri7~~dm~1aiumrn~~17uao~6iur~a::, yamudd~u~u~m$alur~au~ 9 V#.

1 x 9 x 12 x sin 60' m i s i i l r m R ~ ~ m

sin A = 0.91925333

& & q ~ ~ n u a l u u1 x 12 x 15 x sin 49.4!j839813 2

Internet links ~%\lfl'iln~fi8Ifildd www.usborneauicklinks.com

i (TrigommMc or circular graphs)

~'Hmd~r)nrhhni

(Sine graph

nsMo&& or sine cum) ~Guunsi&m1m?p1umjw~a~1~dm 8d

~z~~daulM5uni.i fidwojI.au" LL~U@[N sl?ulh&iKu4nl m0 bdunsiauld~dii fiimm 360' mdaiu7sn1hiirno~sin x do x ~i3wya~Inq sin 90' ~viifiu1

mTAl-hiTAld

y = sh x

I I I

Crwm graph or tmmt -1 d~n57.hehl~L~LW.d~~~pI~~~h0~

isoo%dun41 nnhzu~un~infiud~& tan 8 ~ v i 7 ~ r ~ d i ~ ' L(m z jsoo d u& ~h ~ i ~ # ulmnmdw1~1nr~4m~til~~)aouuunuvl~j?u* u%~#ddur~j7&jfla~dw (discontinuities) midaimn~kdmm tan x do x dwplfll hoti7~~du da x = 45'. y = 1 %&dm99 tan 45* ~vhfiu1

8 dddo~$o~qzdifiuynt

F I ~ O 180' J

(Circles)

(Parts of a circle)

"uosa~nau

(Arc)

ihld~91mhm~d ?~nau(i7~hsoummasnau

h& iwrdmul "

me&6

(Seniarcular arc ) hhddenabh&d~0d

h k m e & i (Quadrant =I

h&uia~vi~iiir~~d dauihm~o~asnau

LmmC(sector) dau~masnaddsrnou 6auh'uarMnm~&u dm~dnniiqosasnauSun %L~&PI ~bazdmd bidnii~?unii

(Quadrant)

nm6a~aod~1udkainriid (90) ~ r n r h h h * J

m'm (Chord) lm"~~os~du~%sdmnah~

(Radius ypW9dad radii)

Internet links ~ O J $ ~ J ~ R 'Lfi1lli U www.usbornequicklinks.corn

3:.

h (Calculations InvolvingCimles) mmmhhmngi , 5,. wsb~u~nsihu"11~9bh3mmmailnauh (To find the length of an arc) ,;;,L ,;A

vvlcl (IT) (Pi)

~ ~ ~ ~ P ~ I ~ ~ ~ ~ ~ ~ & D S Z U Z M W nnrl?u~o9bho9~mi~~elaiuw"9~~ir~lmdatd~ T D ~ O W I Q ~ ~ ~ ~ ~ ~ ~

b~w~iuu~Y7Zu~mi~mn~1P11614ufin8i9 Lh41uruOms nu~wWI~61~luaEU9/npil~~L~u n~4uuMduinnii~iua~hu 6iu 6iu ~ I L L ~ J ~~oidmosmdsui 3.142 (~nQuu 3 di~~hil) $a 2 $QtTnwdfld~9u~n~~n~n n ~iuisn 7 * d. I.ihmos n Iuni%~11iAuhma9nau W P ~ M LWL~~ Z Gui~moil~~~nau mfiln~ruonnsau

&'LnJ~jgslquJnahmmxn~u~~afimimm~~uA~~li #u daniaugo~mu~aa~datdTA~csi~aaiuui?"um ~hsaummajnau sr~hii~&nai& 41fl"IIos qufi~gubnai960360' (mimo~~moy~~ufinm aagajnau) Pj;-u30 I x c --360 L

(To find the circumference of a c k k )

~~~aiu~am~hgj7uqu6n~i9iimiu (n) ~n~lumavn~8usmair~l~sa9n1u A"a - = ~ d h 2 n r do r bhRa7uui?%mH

120

= 360 x 27Cr

Lx2xn:x6 3 = 12.6 %u. kcid mummdau'bhAB ~ranm 12.6 ~miwm

w db ~ ~ a I U ~ i ~ 2 1 ~ b ~ ~

'gj7~~6nmirPlmxmu

- 360'"

..nT

aai~uimm~tu~oux &~~9asnwubhn"fl (Areaofacirde) 2 x n x 5 adnauasmdu5nu ( r )

. U " U

= 2 x 3.142 x 5 = 31.42 bm~ruess.

8uRnsunaoJbgu30flmm

L ~ ~ Z A ? I ~ U I ? " ~ ~ ~ ~ ~ ~ S D ~ ~ ~

rmssa~na8(2nr) fililbbd~ a9ma~~nb9udau~ i1dpdho9

' ZSY

$~iuluwbuuiai~iorhrs~~h$db~duuiuhidud/ d l i i n " i ~ ~ ~ m a i o l u i ~ m ~ ~ ~ s ~ ~ m WmB JnW a~ Wunr x r 9. ~ i a n s n h i 1 ~ a n s w l ~ a i 0 ~ ~ ~ ~

1dhrldPj1u~u6na?~tlm~na~Tnuld~~adold YO.",

#O"IY

w.. 2

0 1 1-

.' . Ir

ifaii~ldi~~nkd ~9widuhm mman & A h v a o n

15 %S

= 2 x n x 6 x 15

II II

= 565 m319blll~ld~;1~'~93 (To findthetotal surface area ofa cylhmder) 105 = -x n x $ 360

g xnx,

~~?kurnrnnsarn~dIfi~~mrn &h~1~wbu~&&A~~"~109msn~::uon) w&mmp4n1~84aow (9dBwa iXd = m2

1hrn&*me3~)

(To find the toCel s u b area .ofa m)

r ~hT~h'aa~q7un Ir sh~~~~urnojdrn~~to'u Jr "

Y d-

&a'aa&i7~~4iusimmunw~~i~u~~mnsaud hdij~~ubiijrm~dns?u~vi~n'u~ x 4 x 10 1 '

= 125.66 ~ ~ ~ L ' ~ I U ~ L U W S

h ~ n w ~ m h

==+; --

- - - -- - -

-,<K . , 8

Om,

r-=w,==---

. ..

- .. .-

. ...

- -

.-..'(

-- -

F-7A T. I.; I(

- - . -- .- -

nwnnuim~ 4,

(To find the swface

(To find the volume

=4 -7w . I

iau"um~~umdmns~ln~~$udnb~i9'bel~~ ~o~lwiu~~uaarnu~on dun41 A $ ~ & ~ O S L L ~ ~ on (semi-major axis ) dau"uo~~8uws~Aain ing~~~~na1~1nl~mo~1wiu~~uar~nu'6~ dun n wism9"11os~mPd%w ( semi-minor axis) fh ~:Iflun~%~~iiuamrnw"uho~~

uufia1uuuius~3~nau (Angles in a Circle) a

@a~rn~ilriji+rr nU'14~il~1ufiw~3~3 ~dn6u~~"Ipdsjaudw~ ~~o~adna~

imkhwq WUVFJ (Properties of angles)

AGE, A& w"Jadm huTkJ~n~\ra~w~di~n"ud~u

~$8,

T$$OU A! W~"DR,D% AB APE = AQB = ARB

I. rrau?m~sofurnu'1uAo~~4~iu1hiifi 180'

~ ~ d ~ f i ~ ~ b ~ ~ B ~ n @ ~ ~ ~ ~ ~ 0 9 b ~ i 7

~dhr~mud~o~%kurlauTiid~Wuan"~(~u~m I pdnaia 70) qlnptil9sil~a~"~uiI+ ~u&w19&ulfi2a

Laa: 2b

Za :.a

+ Zb = 360" + b = 180'

~ i n ~ " i ~ u u ~ :OA ~ h~ d id ~&C fd n'1a4 0% = OAC 2.yuniuuom:~d.lhyuniu~u~o~mdiu y x rhh 180' - a LM~I:~%IUU~M€I~ m r i ~ ~ i i n ' u ~ u d ~ ~ ~ ~ ~ a d ~ o ~ d1ho4whriirsauriir~hn"u m~~mdiu 180" 4s

3. ofu~~nmu~in~&~uw'a~~w::~03~ ~ma~lw'mrn

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(Measurement)

~S I&I

MWI

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614

20 ~~n~fJpa5ou

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( M e system)

~ ~ & B ~ z ~ w Q ~ u ~ ~ ~ ~ ~ ' Y I I I u dz~wmTaTan W J I J W S ~ ~ & ~ ~ M ~ &

~BEIQI L K ~ Z * w'~~fin1~6~~1ua~ldm~'bnlrn~w1 ht4rusls

I mm*urn WW3

miamwane

rrilkir w. (rnm) m. (cm) u. (m) nu (km) kh (mg) n. (g) fin. (kg)

0) ihfh

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loo L

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1.000W W ~

~i7h1

loo ialn% 1,000n$u 1,000?lan<u

bviwKJ

w. (ml) (d)

EJ- (1)

*hunlir 53 @hurmAttnGr);auumGuu 1s: (n 76 ~ h r n - drra uu~uuu30:r?nrmof 45:li3~181J 58

loo Q@Tters 1,000 9aSRrna

m&nS&

(Measures of motion)

a'rnb3-J (speed) nia~m:u:wi&'57nni~b~dmflu%a9band9 rniu~4~~uni~a'm:u:widdauuin~fiu~un'do~a~i I i a b s flu6hhb9) i?i,a~um~d&Ius (nu. / vu.) v4o~uwaio3uifi( w ~ ~ h u i f i ) gAfluni~<fi?Rdim ih

k ~ ~ m : l d x ~ a a~ IdU L~! ~ L ~ ~ % W \ F U L ? ~ L O ~ D ~

~ku~i~3ab~irelsr~~ahrUi~dah

u i d q n &umni&lw (nu. / m ~f )i o ~ ~ w s d o qldiil ~ ~ d o u % & m i~~~iJrf:u~:~~*iy%$dmlf ~% fia~diil~itd ~1aiu~%~mh9~nfojikdoi~~:~bu I I o bd &h9u& 050'

das*ftm w

(Compound measure) -id

nwanm~nu4osMaumnn~dau Kaohi79~du~ m s i ~ ~ a ~ f i u n i ~ m ~ $ ~ d ~ : n 0 ~ 1 b ~ u 4 ~ n"E1~:u:wi~uar~aai ni3Tn~%d-=i:nouEnoeii~ d 9 a; ~i~i~~sd~d~9~i;~an"u8.~aab~a:d~uims

(Time)

d [Minute (min)] Tu 1 &T%9 $I 60 u l i

~24&%ohs(2ehourdock) mnibam 24 &hTu 1 %&b'tbi am d

o pm

~~&:Td~a~rnr~amin o % 23 Kaam o 8s 9 9:

; dwau&~ 0 d 3 f i 01,w,... L~~~"I:wT~H~B M [Second (SorS~C)] 1 u i f i m o n ~ a s 24 n 24Twiu ttiihbm 4 ti?uar :L ,r Iu 1 uis ii ao i u i i iuii~~um.iaddn$~n aom*rn blSu~apliTn~h:ui~~~sni~~h~o~~'aT~ ui%:Ubb&hTnaT*n kmtx~du b m 2 f '83, pdifim 20 ~4Tu~mfilw:~$m~h 1420 1 ~ $ 3dond~adi-iiu M T ~ T ~ ~ ~ ~ a n :.+,,-' 8

ii-.

hi?id [Millisecond (ms or msec)] Tu 1 Suiq JJ 1,000Q a t % d Qnt5udauni% a drr

k i d i m ~ f a ~ ~ a a m n~du i q ~89mdblil~ehll~adab~9d n dwuamYo~answ~ mh'l 12 & d h(12-hour dock) s:mmram~QuQaTuil I u d f i r ~ f i ~ 2~ i h -$as7 p:l 12 QqTu9 ramaudx~sanazwhs~iersfiu (24.00 w.) t i g ~ i (12.00 ~ a ~u.) 4d.ti am dsmwn ~l~pl:i%.ddl"ante meridiemn w l m r n ~ s %"dau ~iers~u* ~amTuiasisas~a-iis~$us?'un"s~M"ek)%

&Id pm ~~NwI~~IMIw:~~-~I

uifiIl1

1400

uifin?

1800 1900

U*M

"post meridiem"

waJiu~ai~% "mhw"usa'odw ~apli~rhui!~:~iiuung~g~ daoliia.du npli ~ i i u u I 6 6.15 ~ h am 9m&i'b6bfhd .ylw~[ilua~ 6 ul%nl 15

*Au4'~1o\lpi~~ndlru 56: n~fiuu,g~ndiuuls: rm41iir3~21: ~ ? i u ~ & a ~56(pÂśmmi&n): n 8maid? 73

u*ni

r m,

i3vmhdm& ( A l s e b r a i c e e o n )

ihk6Wi1u ( D q e d m variable)

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mw6-a(Constant) imd!Pii~&~auo b2EPd a~n-13 y = 2x + 4, 4 bhdlAdK3

(wqaqe pue laqurnu 40

=tw) mnqwmm.-

bfflddmh (Algebraic fractions)

rmdau~rviik r~iuisnlr~nurnsg~wfow7~

iinm (~i~o$ii~uu) rmrd?ri?u(iii!otjiii~d~~) ~au9'iuaurfluah+o8aBnw(R'a~fluan'u

I n t a t links

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I fWms (Equations)

fn%%Wm%

(Realranging an equation)

R"di~fluai~i~~(~aa~ni~Ifio~~u~mKa~bd~bdek9 hb~m~mulfi&abbdduo~hi&iui~"~~m ~ n $ o w a ~ i ~ ~ v&fiunji i i f i u rnsnidiemKa~~d-=du

m%-

(Solving an quation)

fiia~ni~i8al'?rbnJ%~3era aiui%dfia4~n?s~iowidi as&aiab~d~d&i fh8unii ni3~bn"aa~nia

.I :"I. .f

'I.

:'-*t , ,*:.

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wilt~(Algebraic Graphs)

w x @ -

g d ~ 5 n ~ ~ m A ~ ~ g u I p i x~i~k 0p 1%ual ~i ul ~

unu x uu y = o

m $ ~ n r r r s w l ~ % h(Toplot m a linear graphMan-)

M S ~ X I M I W W I S I ~(Drawing ~ a

w'aoeiw~hdaqmasmi%G~r8uy = 2~ + 2

quadratic graph)

(Quadratic

;i '?!

graphs)

n~i~o\ra~ni~rii~~am::~4upd~u@ ': : :: y = ax2 + bx + c ~ d aa, b, c ~hdiwrFaial~a:: a o

: :8

fmWWMi (Cubic graphs) mid~nui~~~s::n~u~auww'n'bi5~ x3 nnd V

m5-d (To plot a cubic graph) m~j~mi~pnultnn"~"i'b6~~~~u~hnaid

gnul~%um::~1uu'Iufnl y = &+bx2+cx+d

d hPii~(Alu~:: az d ~i5i~ymriinuuunu Y L ~ a, O b, c L:I

fnlhun'qn"uo~rmdgn~i~6 L y =9

i i i m i m (Cubic cuve)

~~~YJ~~TA"J~~~~~JB~J~~I~J'Iu$$.~I~D~ d2uI*od&Pimo~

a 'Ildaunis y=&+bx2+cx+d

~ ~ W W (Exponential ~ W U graphs)

m H h m & (Reciprocal graphs)

ifWmsn'm (Quadratic Equations)

~ ~ ~ 7 3 6 1 ~ d ~ ~ d ~ e h l ~ ~ ~ % M $ ~ ~ i ? ~ ~ 3 ~ ~ d ~ ~ ~ ~ n S ? & d ~ D

d1&arm8uuoqTu$

ax2 + bx + c = o ida a

+ o aunn

rii&~mv?naum~aim~~m~~~~~lr8ia~~i~~~~a'i~~~ i in n (roots) n - l ~ ~ ~ ~ a u m ~ d i ~ ~ ~ ~ ~ m M " ~ ~ ~ ~ u ~ ~

---(~Y~~ZPI )

r n s t i i ~ b h h m q p(Completing i the square) - ?

1'-

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- ,-

gmaumarlr&am9~~1rna~~ii~un~~Tpd~

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= 0

aunsm6u (Simultaneous Equations) a u r n n r a i u ~ ~ i h r a u r i a ~ ~ w ~ i u ~ ~ ~ zi;+Js ~~~1~~

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rrw~~m-~~num

(Solving by

r n s ~ ~ h r r y s f ~ e(Solving ~ ~ l l s by elimination)

sulastttution)

(To eliminate terms that are the same or opposite) - 2 ~ I. f i ~ w ~ J ~ u ~ d o uih n " u2x iqil 2x ?-2x ii a 2 u i ~ n a u m ~ m ~ o o n n n 8 n a ~ n i & l68li7~9ld"$~Qs3d$l~fi'ld L$u 2~ 4Y - 2 ~551151761~1 ~auniddaa~ui~an~dw" i f ~ o @ / i , ~9~~i ur i f i a ~ n i 2x s - 3y a 5 3.~1~a~~plaodw9~d~~dou~u~uu'1dddua:~'1"Ifia~ x + 3y = 16 l~@â&#x201A;ŹId1\347~ ~~nw~Gdi~B0uirui~1~auflu(d~in~~1dw~6 ~h2 ~ + 5 1~ 3- ~ 1 5 w=i&ir~~u'1uaunisM"~1o~) 7~ - 13 15 (2x -3y) + (x + 3y) = 5 + 16 7x = 15 + 13 3x = 21 7x = 28 x = 7 2. r i ~ u d i a a d ~ a i r d s f i ~ ~ ~ d ~ u 8 n m 9:bdi uni7~u"~ x = 4 u au~a6 a~~n~ d 4. ~ ~ ~ u d n o ~ & a i ? ~ d ~ ~ ~ ~ ~ h a s ~ ~ d~i v~r ina ~ ~ ~ n ~ s ~ & LTh 2x-3y-5 ~~:~lhi~odW"?i?i?d~dn63~~9 (2 x 7) - 3y = 5 !,2d lj x = 4 6ddu (2 x 4) + y = 15 1 4 - 3y = 5 8 + y -15 3y 14-5 y = 15-8 3 y = 9 Y P 7 y = 3 kaouun~aun17Be, x = 4 LL~: y = 7 Pi.iwouuasauni.i Wo x = 7 iia: y = 3 5. a~aswou6ii7rsm4muni~~~~udiu~~ x ua: y 3. ~ssavaoun'~~ou%&~un~~~~~upi~ao~ x bia: y 13 "lurna~n13i~m "launisu-dn E t b"du 2 0 - 7 - 1 3 6 k U ~ x = 4 L L Q t y = 7 ~h 7 + 9 = 16(Ajuu x = 7 $ddwdiaod@nhm I ~ra: y 3 ~~~fiuaii~sau~~nfio~

h a ~ r n % ~ ~ =ymo~niil41ufln lfi y = 5x-13 2. L L M U ~ ~ DyJ a~luanmun17~& ~2jld fil y = 5x-13 2x + y - 1 5 LLWU~ITO~y 9:lh 2x + (5x - 13 ) = 15

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~ n d m (Elimination continued)

rvlslllfi3.J~~

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plot sr graph d simubnwrus linear

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Qaunis"bd1fi y o@?~Si.ida y =

x-1

3-x

~ n i m i & w (More simultaneous

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equations)

1um~~b~1ur78~umfii&~m (Linear and quadratic equations)

a"aodi;ldu

9whwuni4

y=x+3 (1 y=x2-4x+7 (2) LLMUP~IWEN y ~inaun14(1) a~luaun13 (2)

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x2+3= x2-4x+7 3=x2-4x+7-x 3=x2-5x+7

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x2 + (X - I ) ~ x2 + (X - 1) (X - 1) x2+x2-X-x+1 2x2 - 2x + 1 2x2 - 2 ~ - 24

= 25

25 =25 = 0 = 0

(Inequalities) oa~nw~hh~l~~~6~fiiam~~~efid~9d~&~fi~w"

tYai?ah~h ~~uiioauni34 - 3y a 12 - y au 4 oon~inr?'saodw 3y a 12 - y - 4 uan y w'Jaadii9 3 y + y 2 1 2 -4 Y

-2y

#XI-rn

(Example: Inequality

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w!ll

riJuriiiu (Functions)

- .-. *.

m r-

prer (ResuN)

!. t -

-m7$t-5-,T!

(Illustrating functions)

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200 + 1 = 201 ~ ~ ~ o d ~ 8 ~ ~ d n " b 1 9 " 8 ~ n d 1 6 % ~ 1 ? ~s s 1 7 $ n u ~ o ~ ( 9 " ~ ~ ~ 6 1 ~ u W ~ C 9 1 A ~ D 9 f i y a ~ ~ ~ h b ~ I and f r s w : r ~ u f i b ~ m ~ d ~ @ m (codomain) ~ ~ ~ u i ~ a w'auosb~olw+u~dua 8aohdbiu f(x) = 2x

k w (Domain)

(Composite function)

-fm~l

n i ~ h $ ~ ~ ~ f l ~ i i * b t d a o d ~ & # u ~ d a i 1 ~ 1 ~ 0 ( N W ~ H hes) duu164au $(XI w?o f[g(x)]~,aa&iqrflodi~n"h ~~u.J"iuaumil19"i~diuQo ~ L ' S Bb~uu A bb~: g rim 1,1,1a%q:Gi4s& f WYaoh~~iPd ~ & ? ' i u a % d ~ i ~ ~ i w a i ~ o ~ ~ a ~L ~L F~~ Pa~ Q~~u~ I u i a u &I f(x) = x2 LLW: g(x) = 3x - 1 am~~w'~i?oa~6od%ki~r~i1"11mTm~~~~iw $(x) = f(3x - 1) = ( 3 -~ I ) ~ h0riwbiPd / ua: @(XI = g(9) = 3x2 - 1 f(x)=x+l a

n''ufis& T W ~ ~ ~ ~ ~ Q ~ f B-I(x) J ~ ~ U U L Caohurdu wmiSu~aoimo&ii% f(x) = 3x + 5

1. y = f(x), y = 3x + 5 2. ~G'dmmAu~d~ x UR: y .KJWU~ x = 3y + 5 3. mimoil y, 3y = x - 5

474

y = -5 =f"(x), f-'(x) = X 7

(Map or mapping)

~ ~ W II

dm(Flow chart or

~bsnaniw1,m~s~i~mo4~~di~~um~~u

moqmnbaWs~~~LL61r~&

i~dnra~~~arn~ou~Qrnduu~uh~~a@d~& rtqJrnumuua5li)dd&

fx) = 3x + I I

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*Id$

(hrhr):

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52:

rim 12: d n o & d

fnmn -

-Fd-

and graphs)

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gm~b) ~M-~IW~L~~IJ\~I~~RU~~~LII~W

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m ~ i m w nia>om?d w h u M (&7u at]Aa<ons?rJ

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W y = f d t a

h-rn

%rn*

h a c ~ d

(Cubic function)

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*&Aqiup

(Reciprocal function) f(x) = &O a LOUP;IRJ~

4 d h - a ( ~~i r~d efunction)

'31diw y = ayx)

ndnm-mww IU Y A a m ~ m a ~ h a > 1 nn&: wan es~u~nnu Y I e < 1 nm&:f9ff ~ ~ ~ 7 u r rY m r

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.I .I

ni=i~~dnlas y

= f(,) 1 s ; nj a z l ~?~Jo~BL~R~~W~P)~PJ

, or cirwlar function) YX) sin x. XX) = cosine x f(x) = tangent x T

%&&;lupJ

luXt'f7aaI ~7rJ~zmaanRw ru --

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7 7

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-1

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(

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1 flTadWd%bi~(To hkfind the area under (Omdhts and

a c u y ! graph)

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b & w ~ m ~ ' & & f ~&mnm*1dd9:rnd~qwdera~up13~8~ iB~:w fig?An - j l n T J " d ~ a L ~ U N R l wS

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C w ~hmun%rnmihunoi~zfiu"~~*

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(Data)

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(Quantitative data)

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@isCrete data)

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e (mnj-) of data))

pistribution (of a

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(Collecting data)

bmmmmw (Questionnaire)

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(Data logging)

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fwJ(ampling)

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frm@h&i!l

(Random sampling or simple random sampling)

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= 18 = 15 =

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wmw L:

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=lpling)

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HANDLING DATA

fn&nfju$~pl (Grouping data) n m u u o n u ~ i & m +(0-

frequency.

d i s t r i i o n table)

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m l r o n s r o ~ (Frequency d table) ~ ~ ~ ~ b ~ ~ ~ 7 2 6 a t d R f J " l l ~ L ~ ~ ~ l 3 ~ ~ 3 7 ~

(~aiu$m ~ n i s ~ a n ~ adud1 i u am w ~ s ~ n ~ ~ w(E r n quency ui cfistribution)

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4 v m ~ m u (w W i a n of a dkbibution) hnauammru~nb~qd~4~1~wdi&u~imuia

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modal dm)

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dirm&~mmmusn~~~~mud~~in~e~

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(Measures of Spread)

mh1-

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bdu 3 E

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g h ' iL h 4 @ (3, 5 , 8)

abfi (Index)

nisns31u (distribution) 96. loo,

n~rnsrddoumj(associative laws)

addition) 14. 15. 46 15

distributions) 100

m l ~ d a (cancelling u fractions) 17 n i s n ' ~ m C r n ~ a u d ~ ~ ~ : : nh i~m @ a a d u a t n i(trial ~ and h ' L s j r v i 7 ~ u ~ o w ' 1 \ r ~ ~ ~ i t ~ improvement) 79 nmmao~dism(pilot surveys) 97 (elimination of like terms with ccefficients not equal or n i r v i 7 r h Q ~ a \ r a ~ s(completing d

nflao\rrmR$fi (laws of arithmetic)

msrnn~rs\rd~7uiiutJ (bimodal

108.109, 110,111 nisnssiu (spread) 102, 108

nqnisaWkmnimn (commutative laws of

frequency) 99

101,102.103.104.105.106.

14, 15, 46

nisusnusdR?iuifaa\rn~u(grouped

n ' o u r ~ w ~(ante u meridiem) (am)

(trapezium rule) 95

nsau (cons) 56, 59. 68

M Z F I W ' L D ~ W ~(isometric ~ paper) 50

nTu (grams) (g) 72 nsirln1sns:s1uw'ioup1un1~ msnszsiu (scattergraphs or diagrams) 110, 111

opposite)m ~ ~

nisrhn$ (taxation) 117 nisriiYni~nw6au(indirect

(simpliication) 77

nisrrnuh (tu-on)

taxation) 117

nisrfiusmsado~a(collecting

curve) 64

n?sliirawdoqa (representing data)

data) 97

nisrrfiaums (solving and

105-111

equations)79.85-86

n1~LIif.I(enlargement) 44.52 services taxes) 117

n?.sduun~o&au~iwnda~uau,

nsihodId~adauIhodId (sine graph or sine curve)

63, 64

nrw;lni&~$w (graphs algebraic) 80-84

nslrlwnau (circle graphs) 89 nsd~mmr?al-~alur~a(s~eedtime graphs) 94

(box plots or box

and-whisker diagrams) 110

nn6mPiiuini5d (standing

curve) 64

ndm (boxs)llO nqu (clusters 98) n~u~7~iiuu~io$uq?uiiur] (modal group or class) 100

nduhoriw (samples) 97.98

niman (addition) 14, 15. 16 n i f i f l n (tallies) 99 n ~ s ~ u , u ? r u & d ( ~ r n a tarea) i n ~ 55 nisilarflmfiiiuu (rounding decimals) 20, 86

nis~fiu~rficnmisusnrrs\r (comparing dibutions) 102

rnsrdduuPi15oua:: (percentage

charges) 117 change) 28 nw~~i7~aru~aiu~uiuuus1n n w r d d u u r r d ~ ~ u ~ i ~ d u ~ r u u UIW~~W(changesin standard lalnrrrnu (calculating frequency from a histogram)

graphs) 64.

n?.sgruama+ (scalar rnukkiiion) 46

nn~@nsa"rtio#a (handing data) 96-115

ni59'wnidoSja (grouping data) 99 t-rrdh~um~(-in9 79

deviation) 104

n i s u M u m n 5 i d (variations on

107

ns7v~Godau~di~~1o\rr~nu~ww' nisgru (multiples) 11 (tangent graph or tangent

77.79. 81,

85.86, 87. 88, 89

ns~d~IsnIGodauTd~~~o\r m ? u w u , n i % d r n s (salesand

Idd(cosine graph or sine

m the square) ~ ~8689y nim"il$kqj!u$orji\rdiu

-1

rnsbrdad (transformation) 43-44 r n s f i i d (displacement) 43 msrsun8ads:nw (factors) 11.78 nisr~udo@alu~ndutJ(labelling pdygons) 35

nisa\r?@nsd(plotting graphs) 80 nisams7m (discounts) 116

n13m (subtraction)(-) 14. 15. 16 rnsn'mmm (translation) 43.44

n m 3 (division)(-)14 15, 16, 76 nn1Mosfu (naming angles) 70

(measurement)72-73

&@I

rnÂś%yu (measuringangles) 47 msmrrlubjnq~(imperial msaswement system) 72-73 m ~ l d % ~ a d 3 t n(drawing w compound loci) 51

rn3~3ht5a1snl3rnw(construction of oompound loci) 51

nnrrfiounb (refkction) 43.44 nnaA~1~~mrn'ouaunruw (glide

(kilograms) (kg) 72

n*IaLUcirr (kilometres) (km) 72

obrvation) 97

sampling) 98

ni~~datma ( cn o n ~ e n i ~ ~ ~ sampling) 98

n n ~ u n u u n ~(cluster u sampling)

UftU Y

~ n f i . I I o j ~ h ~ .(gradient I\r (m)

Ln'&uriuou (certainties) 112 (Y-axis)31

1LftU Z (Z-ads)31

unaou (gallons)(@) 72

ni.~QumT~an~ (quota sampling)

'1lulU (parallel)

30.33. 39. 41. 44.

45, 50,51. 57. 81 107. 109

~I~~UUWMII&WW

(mutti-

sampling) 98

nwuacm, diu1~nkeimk (back -to-back stem-and-leaf

96,

S o t ( a 1 3 W (quantitative data) t)?c~L+Jil&b$ (ordinal data) 96 %ayah (raw data) 96 ht(~~doLdaJ (continuous data) 96, 101, 106. 107

4ot(~dmniau(discrete data) 96, 101. n13LLNBd h-~rld?ut%%~)?a9'1~?~ 106 uln (stem-and-leaf displays or diirarns)lCB % ~ y q i q (secondary $ data) 96 *D~(FUI~QC@ (nominal data) 96 m5uaBds:u:mw~u~?m(distan~~ Q ~ o ~ ( ~ L(primary ~DJB data) ~ ~96 time graph) 73 $oy&S~unw~&a~nd nlmyu (rotation) 43. 44 displays) 108

m d f i e i m (finding ~ area under graphs) 94-95

wnudh%~b (dative frequency) 112

wd?prth@robabi~ity) 10,112-117 miuri79:r&.nro~mmao~ (experimental probability) 112 nnuriwr~t!u~w~ncqni~d (extremes

'IIWL.II~(upperbounds) 16 awr~nrj?J(lower bounds) 16 of probability) 112 Sqa (data) 96-97 n&: p? i l Jm- 3 t (total probability) Qo~mnrmvl(infomation from 113 wr#ni?p:thr#~ (-in9 graphs) 94-95 tya~%qcunw( q u a l i i data) probabilities) 114

96, 97, 108

25, 80. 81

m1u8 (frequency)(o 96 RTl~8t3:lu (cumulative frequency) 99

L L m X (X-axis) 31

mrwn& (classboundaries) 99,

M 5 & b l ~ ~(interview) ni ~3d1m (surveys) 97. 98 nwju (sampling) 98 nl5Qkloti.IJLfiu.I:~11 (stratifined

49. 50. 70

~ i m ~ n (semicircle) au 51, 65.70 Pis'JrnJtl~u(hemispheres) 69 R?l%J? (capacity) 59. 72

mb?(spirats) 10

m 1 W (magnitude) 45, 46

reflection) 44

n i ~ k ~ (observation) nn 97 nrs&~n&d?tli?uu (participant

LLWaJsfU (ann~ of angles) 32, 48,

(computer

199 L~AFI (compass)53

ma~mii~dofio (credit) 116 R?l~LLdtlSlj'l~~ (variance) 103 A?IU011 (length) 72. 96

R ? I ~ L ~ (acceleration) 73. 95

mnuL~a(velocity) 73.95 ~ n u i i ~ fpias) i u ~97, 98 ~31Udl L%( s u m )112 P~~MUIU~U ( d ~ s i t y59. ) 73. 94.

Rouwfiw$iao~r%n (complements of set) 13

~oSa(chord) 65, 69, 70, 95 dlfiJflalJ&nrn& (mid-interval value) 99, 101, 104, 107

dlA~&(Constarrt)10, 24, 75, 83, 84

d l h (wages) 117 d1L~du(mean) 100, 101. 102, 103.

h?~~llrra? (natural a numbers)

104,111

d i ~ h m ~ n d i d(outsers) u 110

6, 12, 78

b ~ ~ r w ( up ahn d i i numbers)

~ I U I ~ (commission) I 116

~ i l d u 4 ~ y t l ~ ? o(quartiles) f [ ~ d 102

h.nuaqd @e&d numbers) 11 ~?u?u~emnu:: (ircational numbers)

~ I L ~ ~ ~ L U U U I W ~ ?(standard ~

deviation) 103. 104

dnl~zbmfin(place value) 6.9.

16,

P ~ ~ ~ s ~(Ma cpup r o w equal to) (=) 72

9. 66

dIl.404 (mortgages) 116. 117 ?flfilrqfl (origin) 31 ?~1~4na?~.ao4Ro5m (midpoint of a

i-iguLtsri3nb (coefficients) 75,81.

ga&mo4r8um4 (intersectionsof lines) 48, 49. 51

85.86. 88

r~~omuiuGounii (less than) (<) 90 12

U r h (money) 28.29, 116-117 ~ u r j 8 u d n (personal ~ ~ ~ a bans)

117

billu (sides) 34, 35. 37. 49. 60.62

E7iu-n (hypotenuse) 45,60 6ilu~~~billu (included angles) 37 B~~UBIUBIUU~~$~I~LM~UU~UQI~

(Pythagorean triples or triads) 38

Tmrw (domain) 92. 93 bw4?urdu? (codomains) 92

?a#murmY (y-intercept) 80.81 gfl#flmrmu X (x-intercept)80

?muom(vertices)(sing.vertes)91

h (tons) 72

9@14?~5r~lU (coplanar points) 30 gFd?ul&Wld (collinear points) 30 gfl~u8na1~4lm?4nau (centre of a

m%rdw'

circle) 70

?fl&I$B (point of contact) 71

(trigonometry) 60-64

m & m (piece-work) 117 hg(u (multipliers) 28.29 #?gm~?adhu(common multiples) A.5.U. (LCM) 11

&dsrnwmsgcu (multiplying

117

thh(principal) 28 ~d6i%q~nwad~:TumnS

asnrh (interest) 28, 29, 116, 117 6iIihltnl&7 (retail price index)(RPI)

chord) 70

~ I ~ ? J L ?(overtime) ~I 117

r ~ ~ o m u ~ u i @races)({ l n n ~ }) r~dou4(motion) 73

factor) 29 (mutual

(averages) 73.99.100-101

funds) 117

r h d o (inflation) 117

hd~:nourilvu~: (prime factors) I1 h d l t n ~ d l : @ f l ~(identifying ~ factors) 85

&TUG (hours) 74

#?dlrnauj?u (common factor) 11. 24

11u~ri1~dqd6~u (Pay AS YOU Earn) (PAYE) 117

4 1 ~ (number) 7 ~ 6-31 ~lu?ui184~04 (square number) 8. 10. 21, 38, 78. 85

blu?uri?~4alu(cube mumber) 8 blumd (odd number) 7 blu?u$ (even number)7 4711x444 (real number) 9. 12.92 b~u?udu(integers) 6, 12, 19 b 7 ~ 3 ~ (amemth kb number) 6 bluaudrh (excess) 116

6ar~d.r(variables) 75. 79. 80, 87. 88, r%m (sets) 12-13, 92, 98

r~mtiat~lo~u~vm (subsets) (C) 12, 13. 92

rm+N (empty sets) ({ Jor a 1 2 ~mfiu~ml (centimetres) (cm) 72 rauw'fim.r (centiliies) (CI) 72

hmiiUd16q (significant figure) 6, 9. 16, 23

& ~ i ? r f f n a l u(three-figure ~l~~~ bearings) 53

#?r~kt(numerators) 9. 17. 18. 62 #?cj?u(denominators)9.17.18

qlufiuu (mode) 100, 108 qwao4 (base two) 6 g d u (base ten) 6

h i ? ~ (The n highest common factor) M.5.N. (HCF) 11 m ~ n ~ n l m(contingency l tables) 99

mlnd6fQanw(two-way tables) 99 1difn-d (under a graph) 94-95

rn18~( i d e m ) 75

d u J h (midnight) 74

h o cup (u) 13

~ V i l f (equals i singn)(=) 79

ui%ni12 dalw / u19n1 24

n3am:uQn (cylinders) 58. 67 wr4naa.I (spheres)59,69 n.sdr4n~1k(heptahedra)40 n~ahrwaTm(Platonic solids) 40 nsdudnvrii~(octahedra) 40 n s d d W (icosahedra ~ 140 n~dhn~~MZi7 (dodecahedra) 40 n3a8UMSil (decahedra) 40 n w d d i ~(tetrahedra) 40 n s d d ~ ~ i u u ~(cuboids) m ~ n 41.58

Euler's) 40

n~aFi?lNh:Lh (theoretical probability) 112

nqr~jwra~dn11nT~ (Fythagoras' theorem) 37, 38,45, 60,68 nHfiuu(decimals) 6. 9, 19, 20.27. 74, 102. 112

n d (reaming ~ decimals) 9.19 nffl%td&l (non-periodic or non-repeating decimals) 19

nfI%d@~

(non-terminating

decimals or infinite decimals)

u"m%I

(weight) 72

expressions) 75, 76, 77, 78. 79. 90 $2 (inches)(")72

L ~ ~ N L % ~ (tessellation) L& 36, 39

114

wadrTidUhdq (successb~ outcomes) 112

bJa3aU (sum)(Z)14,38, 55,101 praiTwjtr8'(quotient) 15

~mt%dthW (possible outcomes)

UU?8dM~QLLU?h(vertcal) 30, 31,

50.95.106.109.110

rruaum (horizontal) 30,53. 81. 84.

115

~raranrmoS(resultant vectors) 46 W U ~ ~ ~ Q U L (pension ~U&

schemes) 117

95,106,107.1 10

c d (accounts) 28, 29, 116, 117 ~ d 0 0 ~ % (savings 6 accounts) 117

rrwd (maps) 53 u w k (plans) 41 u m m w r ? u u ' (Venn diagrams) 13

rrPlwJ$nd(pie charts) 105 rrwfl$rrviJ(bar charts ) 99,106.

h7dllim'lu (charge cards or store card)116

lh3%7~h1 (stock markets)ll7 lkflnu'u4a (recording data) 99 L&IJS:~U (insurance premiums) 117 ~~iJ~$~(bisectors) 48, 51

~~lIll6fwnIx (questionnaires) 97 ~ u u ~ ~ d l a l a l 3(utility q d i bills) ~ 117 ~ d U r & U ( binomial ) 75. 78

107, 108

~~PnrrJij~~hr&"m (muh@te bar

1106

rrprugijuhn'?uds:n~u (component bar charts) 106 ~~wug~~~hn'awd'~:nw (sectional bar chart) 106

umqiirrviJn'auhtnsu (stacked bar chart) 106

pictog tog ram or plctogaph) 105

n H f i ~ N w(finite decimals or

fiffn13 (direction) 53 flml (theta) 60.61

Pld~~idU (outcomes) 112. 113,

~ U ' ~ & R $ B (algebraic I

19 terminating decimaJs)l9

pmgCU (products) 14 prehd (diience) 14

h184 (1'2124-hour clocks) 74

W ~ J l l d (hexahedra) l 40

rnma~uwCi(polyhedron) 41 n~filM(il1(pentahedra) 40 nrpt@o\twu~aos' (EIJI~~ theorem)40 nq$ojQD~Lâ&#x201A;Ź4& (theorems

W bJR (result) 92

U (minutes) (min) 74

rddrfh6 (percent) 27

u w ~ i j @ w (ideograph) 105 d33ln3 (population) 97, 98

U%.I(prisms) 41. 58. 67 fiulOl3 (volume) 58-59. 94. 9 5 dm6 (pounds)(lb) 72 ~flddb1di(impossibilities) 112

L~P~U~~~IU~~~~M~~UP~~~MW~

(flow chart or diagram) 92

8lIWPIOd f (image of

WdM"ldLmu'oufb(un1ike terms)75

ws~dLm8ouh(like terms) 75 wlu (pi) (Tr) 9, 19, 55, 66 w151~Ual @arabolas) 82 wiIuTmu (palindromes) 9 d8tWod x (xcoordinste) 31 fifiWB0d y (ycoordinate) 31

fifiGW&~k(~srtesiancoordinates) d n ' q ~XY (coordinates XV) 30.31 f i 8 B ~ l n(rectangular coordinate system) 31

fhlfl (pints)(@)72 fl8~0Jn13~9nLL94 (range of a distribution) 102, 108. 110 f i f l t J 5 L M ~ l J ~ ? 0(interquartile ~6

range)(lQR) 102. 109. 110

%mfiii(~ (algebra) 75-95 dltfin (pyramids) 41, 59, 68 (area) 55-57.68.69

&Aij?(su&ce

-)57

%& (functions) 92 fi~& (functions) (9 80.82.84,

fi~&L%d%~~%(circular function) 60-64, 93 functions) 60-64, 93 (composite

~m(feet)(sign.foot)(')72

a?@(mass) 23, 59, 72, 73, 94, 95,

y m ~ (interior 1 ~ angles) 34.35,37,

dfju3.l~ (median) 100, 108,109, u i n n i i (greater than)(>) 90 ulmmd?u (scale) 52 fi6 (dimensions) 31. 41, 54 f i a h f u (milligrams) (mg) 72 ~ ~ A ~ U J B(millimeters) IS (mm) 72

fia%mS ( m i l l i l i ) (ml) 59. 72 fiaQ?u$i (milliseconds) (ms or msec) 74

50. 71 Y U - ~ U (angle-angle-side - ~

(AAS))

38 ~ u L L(&emate ~ ~ J angles) 33

y u w (negative angles) 32

~"U'QJHI

(null angles) 32

yuguU'mwl(zer0 angles)32 y u E J ~ " 7(dihedral angles)40 yuLLMau (acute angles) 32, 35 bum3 (metres) (m) 72 ~P~OL& (discontinuities) ~J 64

yu (angles) 32-33. 48. 53.64. 105 yunn'u (refiex angles) 32.35 yu@apil$q (pairs of angles) 33

I r i r h h (not equat to) 90 'lu"[w3umnud (protractors) 47, 49.

rfUNu(elevation) 41

I r i i n i t ~ I u n ~ o (noclaims ~hd

50.105

% ~ J w u ~ ~ u & (side J elevations) 41

bonus) 117

~ ~ L d ~ (front f i lelevation)41 ~ ~ l yualn (right angles) 30, 32, 41, 48,

'lu6 (miles) 72

50. 51, 56, 57. 64, 70. 71 angle-hypotenuse-side) (RHS)

yumu (flat angles) 32 y u m ~(straight angles) 32 yu*1urru* (vertically

undirSJaoa (squaring) 8 uom (apex) 41 uoa~3u~mBo ( balance ) 116 u o a h (frustmm)41 ~Lfl~.lloJL~.er~1 (union of sets) ~ L I % ~ I ~ L % H (union of sets)(U) 13

opposite angles) 33

n 8llFi8WB'Jld (cross W o n s ) 41,

ydLfi~30u?~.nra~?Jnnu(su~ended

angles) 33

nim8m?iJ~on$ (uniform cross-

yULh%% (adjacent angles) 33 yuilllJ (obtuse angles) 32.35 angles) 34. 37. 71

yU&luu'u~~ (corresponding

58,69

angles)33

%pllfJUDfl (exterior or external

~&mancu2W (trigonometric

33, 37

y u r h r n ~ s a ~ q w(supplementa~y n

y u m n h m 5 d i u y u ~ i n(rigtit-

92-93

fld&dstnou

n d (taxes) 116,117 d % a i I ~ d (Value u Added Tax) (VAT)117 nhft-1u16 (income tax) I I6.1 I7

110

&M"

9 92

angles)70

yuY3n (positive angles) 32

section) 58

yd3:nw (complementary angles)

3aua: (percentages)(%) 18.27. 28. 29,112, 116, 117

b u a z h n h (reverse percentages) 27 5 3 l l U (plane) 30, 31, 43

5ZÂśJlJ6JflCp72(irnperialunits)

3mII84nfp (imperial units) 72 5rumd (distance) 73 ffig (radius) 51.57,65, 66,67,68,69,70,71

n d a i u (roots cube) 11.22 51ul6 (earnings) 1 16 5iul69inma~r2u(investment

$&IBD~R~W (dodecagons )34

f l l ~ ~ i r n d u(quindecagons) u 34 gr~aurnduu(decagons) 34 $~lldmrnduu (hendecagons) 34 $d~ndU~(quadrilaterals) 34.39, 71

$drndusmnrur~un~u(rhombuses)

iiM1yw't-d(fibonacci sequence) 10

kl-(~itres)(1) 59.72

+,58

~Rlliflfi(cubes) 8,

~ R $ W(arithmetic) 14. 15,16

L&~'IRYJ (indices) 16.21,22 r d f i l ~ ~ m d (fractional au

income) 117 ~ I U ~ % ~ M O(net J Wearnings)

indices or exponents) 21.22

1 16

~ ~ J ~ L M ~ U ~ ~ R(trapeziums) IJMY 39.

nuhEmum (gross eamings)ll6 siul6d~r&r#Bu(salaries) 1 17 $rfiirnduu (nonagons) 34

;~lirnduuscq~a (squares ) 36.39,

$21~61~(similar figures) 44

$drnduuyuain (rectangles) 35,

$L&LM~UU (septagons) 34

LEn'L.Gi(il (digits) 6

rmunriik (powers) 6,16. 19,21.

57.94 56

39.56,67

n.76.84 uarng (and rule) 114 I n k (loci) 51

$~%i~duu (heptagons) 34 $ummm (m inthew) 97 $~rwRnfi(gradient form) 81

pnrnduu (hexagons) 34,

ph~alurndux(polygons) 34-35,

adnflu (circles) 47.51,55, 57.65-

$ L ~ W L M ~ U(octagm.) N 34.36

$ ~ W I U L M ~ U ~ R O U L(convex ?~

?A (ellipses) 69

(function form) 80 $daurnbu (icosagons) 34

pol~gons)35 ~aiurnduudi?urni(equilateral

w r h (brackets) 16 aa~?uu(compasses) 47,48, 49, 50.

@I%I

$in (kites) 39 $~~4$fi(t~0-~Jimensional shapes)

40.41,50. 55,56.57,107

polygons) 35

$naiurndu~a"7tlbrrii(scalene triangles) 37

- t

%J (days)

~!$LLVI!

(unitary method) 26

klfi(sector) 67.68, 105

$ n r ~ ~ ~ d u(triangles) bl 30.34. 37-38,56,60-63

@murndunini!

@am~nduu+u(~hinesetriangle)

~ a i u ~ ~ d ~ ~ u ~ ~ i i ( e ~ u i aranrmnf n ~ u ~(vectors) ar 43. 45-46 Pol~gOnS)35 ranrm~f~oiTu6 (column vectors)

grJmu~nduuhum7tl (parallelograms) 39

~umdu&'I~~iu~nduu

(regular

pdygons) 35.36.40, 41,50

$naiur~duwr~nau~~u(~clic polygons) 34.71

$naiurnduur% (concave

yuain (non-right-angled

~ h n d u (pentagons) u 34

triangles) 62-63

~sp'lR(iiW

~murnduniiania(Pascal's triangle) 10

31J~urnduuyu~in (right-angled triangles) 37.38,45.56. 60-61,70

$ ~ I u L ~ ~ u N ~ U ~(obtuse]IU angled triangles) 37,56

%~r~iurnduuyurrnau (acuteangled triangles) 37

(geomentry) 30-31, 32-44,47-50.51.52-54. 55-57.58-59.60-64.65-71

â&#x201A;ŹI aW (reduction) 52 hKu (sequences) 10 h K a u i n i (order of rotation (4)symmetry) 42

h n f ~(Whiskers) j 110

am (time) 73,74 raairdw (noon) 74

raw (remainder) 7,15 rfldBu (complex fraction) 18 rflwd%~(fraction) 6.9. 17-18.19. 21,24. 27, 112

rflwdau~&~#ua(vulgar fractions) 18

~ f i w d ~(decimal ~ ~ ffractions) i ~ ~ d a u d r m h (equivalent fradb~)17

& k c, -

r~ktdmuM"(proper fractions) 18 r~ktd?~'Ldr~fi(impro~er fraction) 18 ~Hdaubrrfi(top heavy fraction) 18

arnf~?i;niduicuarnmf(scalar or scak quantity) 46 alwu (stones)(st) 72 an1unisdni~~3u (statements) 117 a86 (statistics) 96 nunis (equations) 60,61, 79, 85, 86, 87. 88.89. 90

d?uTfidon (rnajorarcs) 65 h u l & g m i ~ f(cubic i curve) 83

85-86.89

88. 89. 91

EJUnlmnau (circle equations) 84 numstlm& (simultaneousaquations) 87-89

mdanWhmn (mdmtecorcel;bion) 111

8qnsdnwk (mapping notation) 92 ~ Q ~ ~ " & E N L ' P I W (mternotation

69.

(m notation)

8~tlÂś&u7Hl~d

or rotational symmetry) 39, 42

a u ~ m a (refle'on = ~ ~ SYmmetV or reflective symmetry) 42

8qnsnI~anrmoi(vector notation) 45 8~cnt~ (inequality d notation) 90 t g h h (proportion) 24. 25. 26, 52. 98. 107

a.@m* 110

dauncjir (reciprcd) 18. 76, 77 d?~%whmau (parts of circles) 65, 70-71

d m l a ~(arcs) 47. 48.49. 50.65.70 d?~Tfi~aoo~ao~%d (quadrant arc) 65

d3u~fi~&htnau(semicircular arc) 65. 70

d ~ u ~ (curved ~ ~surface d ~area) a 67. 68

fi8;111%1~ (lateral faoes) 41

dau (debit) 116

d d j 6 (one-dimensional) 30.31 num (cap) (n)13 nyumiudwiCni (clockwise) 32. 43

8lJ(edges) 40 gmd (interviews) 97 (-triangles)

nyun?uduuifini (anti clockwise) 32,43 W V ~ O Y(whde turns) 32. 71

nj'ioiy (or rule) 114

hu:lwrlsains (census) 97 ~fiuT~~~&fii& (exponential curve) 84

~ J ~ ~ ~ D J L (elements)(E) 'PIW 12, 13,

m'nlh~ou (hundreweights)(cwt) 72

d h (faces) 40

nL l &OIMUw&

auuiBl~nlmyu(rotation symmetry

H Mliamrmrndn (mof measuement) 24, 55, 58. 72-73, 74

P r o m ) 44 SblNIBlS (symmetry 1 37, 39. 42,

r h ~ u ' n(zig-zag) 110 uam~murYu~s"s~-Mii~8n~s (trinomial expressions) 75

kd~m% (direct proportion) 25,

r~~%mbrr21srls?u (invariance

L ~ U B (mirror ~ M ~lines) 42, 43. 44

111

~ u n i ~ ~ f i(linear d l h equations) 81,

34. 55. 65. 66. 67. 68, 70. 71

dau$dr&Id (slant heigh) 41 ,68 nut8fid (correlation) 111 m8*bfiwin (strong cortelation)

of sets) 12

aun13fii~a~d (quadratic equations)

(mino-)

tinil&&

rh3wad (perimeter) 55 rh3ou3JaoJ3Jnau (circumference)

(directed lines) 45

18u~id(line) 30, 31, 32. 33, 34, 48 71

r f i u ~ ~(msversa~s) rn~ 30, 33 ~hnAnofJ(regression line) 111 l h L L ~ d q ~ "(long ~ 3 dia-141 ~ h n u u ~ q (short u h diagonals )41 L~UM:UW~MOJ$MQIULH~UU

(diagonals of polygons) 34. 39

M&L~U\ITU (post meridiem)(pm) 74

Ma1 (W&)(Y~)72 3;?% (arrowhead or delta) 39 ~ n q n ~ (events) sd 112. 113. 114. 115

LM?~I~~U'L%I? (single event) 113 ~~qni~~h:~i~iAaimi~::r~~vi h (equiprobable events) 112 ~ ~ ~ ~ h f l u ' I ~ J '(possibim L8;hu~ space) 115 ~nqrndn%~fi~liauKu (mutually exclusive events) 113, 114

~ $ u l ~ ~ d ~ j d(perpendicular ~ ~ $ d ~ l n ~ ~ ? r n ~ (dependent ~ g a 3 ~ bisectors) 43, 48. 51 r&u~IUgu&n@ld (diameter) 55,65,

66. 69, 70

events) 113, 114. 117

~ n q m d(random j ~ events) 113 ~nqtn~dEa3:(independent events) 113. 114. 115

.spuawwoml a! sqs aqa 6 u ! s ~ o ~ q 40 alnsal e se papeolu~opaq Xew ley1sasru!nAq pasne>ssol l o a6ewep Aue lo) &!l!qe!l ou aney II!M 6u!ys![qndauroqsn'qa~ay3 uo leadde Xew y > ! y ~le!lalew weln2>eu!lo'an!sua#o'ln~wleya alnsodxa Xue lo) l o ' u ~ oU!ueql laylo aa!sqaM Xue 40 aualuo>l o r(l!l!qel!ene ayl 104 A!!!qe!! adam lou saop pue ~ I ~ ! S U O 3ou ~ s! S 6u!ys!lqnd ~J auloqsn .sa!lluno>~ayiopue sn aya u! paraas!6ar1.>ul'e!pawolmWjo n(rewapeJaa1eanenny>oyspue yselj .sa!lluno> laylo pue Sn ay, u! puas!6a~ "XI] 'n(lowaNlea!j 40 yrewapeq palaas!br l o ylewapea e s! laXeld auoleau .sa!Jluno:, raylo pue sn ayl u! paiaas!6a~">ul'lalndw02 alddy p qJewapua ale awlyyng pue ysolu!>ew n(rewapwl

'le!JaleW a>np~Jdal O l UO!SS!UlJad pue UO!lnq!JlUO> J!ayl lOJ paula>uo>slenp!A!pu! pue SUO!I~Z!U~~JO ayl oa 1 q w e ~aJe 6 uays!lqnd aqJ.'uope>y!aou 6u!~ol!o)'uo~!pa alnay Xue u! s!ya 4!a>a1o l lago slays!lqnd aqa1pau!wouaaq aAeq saq6!r Xuejl yooq s!ya u! le!laaew a y l p uaploq lq6!1Mo> aqa a > u 01 ~ apew uaaq seq u q a han3,

19 (

~ n ~nblWllr\Q!&$QLlng )

19 (~033n) ,yr\Q!&$QLlng

911

(saw e6wwxa) ~p~t?iirurw_a

19 ( u r n ) ,nrp~r\oqo~ing ZL ((zo'y) muno p!ny) w ~ u r \ o q m o PZ @!w

ZL (20) ( w n o ) p o o

wpiynbs lo so!@.~p n b )

tyyi~tU.pLrujokunLpLrq

s 11 (SPPO)Guup~.pr~ubui P8 ( s m ) LBQQMlq

(4 bid@)LtABQ11 ~9 (wwldw) ukjwnnoii 09

EL 'ZC

(a)(-

m ! u n ) gWIkunrQ1

vz (uJ:u) (o!w)

LO1 (wmm)RLUllupg

( o w d m ) wLnn!m

06 (hpnbau! alqnop) tymmunsa 06 (4@nhu! ~

~@uo!gprnun) Q L ~ ffilnoppwLunkzo c L ~ B

tU.flLWB

EL (wads e 6 w ) npoitkiLr@,g (hpnbeu! @uo!gpum) r&lnnftrLun!m 96 'vL 'W .9v (Peads) qlu* 16-06 (sewlenhu!) LLU~PQ 9 11 (tldV) (em

Z )!Jl'4~ 4 !(

pnum) c~+:rpyngippiuleno~

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lo MW) flpUQULLIB$

yn-p

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