SPM Add Maths Pass Year Questions

8/9/2019 SPM Add Maths Pass Year Questions

1/61


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SPM 1998

1. Given the functions h(t ) + 2t 5t 2 andv(t ) + 2 6t

'ind(a)

the va%ue of h(t ) hen v(t ) + 11/(b) the va%ues of t so that h(t ) + v-1(2)(c) function hv

1. Given the functions f ( x) + " x 5 and

g ( x) + 2 x 3 , find

(a) f g -1( x)

(b) the va%ue of x so that gf (- x) + 25

SPM 1999

1. Given the function f : x → k – mx. 'ind (a) f -1() in te#$s of k and m [2 $a#*s]

(b) the va%ues of k and m, if f -1(14) + - 4and f (5) + -13 [4 $a#*s]

2. (a) 0he function g is defined as

g : x → x 3. Given the function

fg : x → x2 " x &. 'ind

(i) function f ( x)

(ii) the va%ue of k if f (2k ) + 5k [& $a#*s]

SPM 2000

1. Given the function g -1( x) +3

*5− and

f ( x) + 3 x2 – 5. 'ind(a) g ( x) [2 $a#*s]

(b) the va%ue of k hen g ( x2) + 2 f (- x)[3 $a#*s]

2. Given the function f : x → 4 – 3 x. (a) 'ind

(i) f 2( x)

(ii) ( f 2)-1( x)

(iii) ( f -1)2 [" $a#*s]

SPM 2001

1. Given the function f : x → ax b, a / and f 2 : x → 6 x –

'ind

(a) the va%ues of a and b [3 $a#*s](b) ( f -1)2( x) [3 $a#*s]

2. Given the function f -1( x) + -

1

−

−, x ! p

and g ( x) + 3 x. 'ind

(a) f ( x) [2 $a#*s]

(b) the va%ue of p if ff -1( p2 –1) + g [(2- p)2]

( c) #ane of va%ue of p so that fg -1( x) + x

no #ea% #oots

[5 $a#*s]

SPM 2002

1. Given the function f ( x) + 4 x -2 and g ( x) + 5 x 3. 'ind

(i) fg -1( x)

(ii) the va%ue of x so that fg -1(2

) +

5

2

[5 $a#*s]

2. (a) Given the function f : x →3 x 1, find

f

-1

(5) [2 $a#*s]

(b) Given the function f ( x) + 5-3 x and g ( x) + 2ax b, he#e a and b is a

constants. f fg ( x) + – 3 x, find the

va%ues of a and b[3 $a#*s]

2


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SPM 2006

Paper 1

1. n dia#a$ 1, set 7 shos the i$ae ofce#tain e%e$ents of set

>G@A 1

(a) ia#a$ shos the function x

xm xh

−→:

, /≠ x , he#e m is a constant

>G@A 2

'ind the va%ue of m

[2 $a#*s]

Paper 2

1. Given that 23: −→ x x f and

15

: +→ x

x g , find

(a) )(1

x f −

[1 $](b) )(

1 x g f − [2 $]

( c) )( xh such that "2)( += x xhg [3 $]

SPM 2007

Paper 1

1. >ia#a$ 1 shos the %inea#

function h.

(a)


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3. 0he fo%%oin info#$ation is about the

function h and the co$osite function2h

'ind the va%ue of a and b[3$]

SPM 2008

Paper 1

1. >ia#a$ 1 shos the #ah of thefunction 12)( −= x x f , fo# the

do$ain 5/ ≤≤ x .


6/61

SPM 1994

1. f α and β a#e the #oots of the Cuad#aticeCuation 2 x2 – 3 x – " + /, fo#$ anothe#

Cuad#atic eCuation ith #oots3

β and

3

α

[4 $a#*s]

SPM 1995

1. Dne of the #oots of the eCuation

x2 px 12 + / is one thi#d of the othe#

#oot. 'ind the ossib%e va%ues of p.[5 $a#*s]

2. Given that2

1and -5 a#e the #oots of the

Cuad#atic eCuation. E#ite a Cuad#aticeCuation in a fo#$ ax2 bx c + /

[2 $a#*s]

3. 'ind the #ane of va%ue of k if the

eCuation /322 =−++ k kx x has no #ea% #oots

[3 $a#*s]

4. 8#ove that the #oots of the eCuation

(1 – p) x2 x p + / has a #ea% and

neative #oots if / F p F 1 [5 $a#*s]

SPM 1996

1. Given that a and b a#e the #oots of the

eCuation x2 – (a b) x ab + /.f m and n a#e the #oots of the eCuation

(2 x – 3)( x 4) k + / and m + 4n, find

the va%ue of k

[5 $a#*s]

2. 'ind the va%ues of so that

(3 – ) x2

– 2( 1) x 1 + / has toeCua% #ea% #oots.

[2 $a#*s]

SPM 1997

1. Given that m 2 and n - 1 a#e the #oots

of the eCuation x2 5 x + -4. 'ind the ossib%e va%ue of m and n.

SPM 1998

1. 0he eCuation of px2 px 3q + 1 2 x

have the #oots p

1and C

(a) 'ind the va%ue of p and q

(b) Het, b usin the va%ue of p and q in (a)

fo#$ the Cuad#atic eCuation ith #oots p and -2q

SPM 1999

1. Dne of the #oots of the eCuation 2 x2 6x + 2k - 1 is doub%e of the othe#

#oot, he#e k is a constant. 'ind the #ootsand the ossib%e va%ues of k.

[4 $a#*s]

2. Given the eCuation x2 – " x & + h(2 x – 3)

have to eCua% #ea% #oots. 'ind the va%ues

of h.[4 $a#*s]

3. Given that α and β a#e the #oots of theeCuation x2 – 2 x k + /, hi%e 2I and 2J

a#e the #oots of the eCuation x2 mx 6+/.

'ind the ossib%e va%ues of k and m.

[" $a#*s]

SPM 2000

"

CHAPTER 2: QUADRATIC EQUATIONS


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1. 0he eCuation 2 x2 px q + / has the

#oots -" and 3. 'ind

(a) the va%ues of p and q [3 $a#*s] (b) the #ane of va%ues of k if the

KCuation 2 x2 px q + k has no #ea%

#oots [2 $a#*s]

SPM 2001

1. Given that 2 and m a#e the #oots of theeCuation (2 x -1)( x 3) + k ( x – 1), he#e k

is a constant.

'ind the va%ues of m and k [4 $a#*s]

2. f α and β a#e the #oots of the Cuad#atic

eCuation /132 2 =−+ x x , fo#$ anothe#Cuad#atic eCuation ith #oots

3I 2 and 3J 2.[5 $a#*s]

SPM 2002

1. Given the eCuation x2 3 + k ( x 1) has

the #oots p and q, he#e k is a constant,

find the #ane of va%ue of k if the eCuation has to diffe#ent #ea% #oots.

[5 $a#*s]

2. Given that2

α and

2

β a#e the #oots of the

eCuation kx( x – 1) + 2m – x.

f α β + " and αβ ! 3, find the va%uesof k and m.

[5 $a#*s]

SPM 20031.


8/61


9/61

1. 9uad#atic function f ( x) + 2[( x – m)2 n],

ith m and n a#e constants, have a$ini$u$ oint ("t ,3t 2).

(a) state the va%ue of m and n in te#$s of t

(b) if t + 1, find the #ane of va%ue of k sothat the eCuation f ( x) + k has a distinct

#oots

2. 'ind the #ane of va%ues of x if

(a) 2(3 x2 – x) M 1 – x

(b) 4 y – 1 + 5 x and 2 y 3 x

3. Given that y + x2 2kx 3k has a

$ini$u$ va%ue 2.

(a) Eithout usin diffe#entiation $ethod,

find to ossib%e va%ue of k .(b) 7 usin the va%ue of k , s*etch the

#ah y + x2 2kx 3k in the sa$eais

(c)


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11/61

c) the eCuation of the ais of

s$$et# [3 $]

SPM 2006

1. >ia#a$ 3 shos the #ah of Cuad#atic

function )( x f y = . 0he st#aiht %ine4−= y is a tanent to the cu#ve )( x f y =

a) #ite theeCuation

of the

ais of

s$$et# of the cu#ve

b) e#ess )( x f in the fo#$

cb x ++ 2)( , he#e b and c a#econstants.

[3 $a#*s]

3. 'ind the #ane of the va%ues of x fo# x x x +>+− 4)4)(12(

[2 $a#*s]

SPM 2007(paper 1)

1. 'ind the #ane of va%ues of x fo#

hich x x +≤12 2

[3 $a#*s]

2. 0he Cuad#atic function

42)( 2 −+= x x x f can be e#essed

in the fo#$ nm x x f −+= 2)()( ,he#e m and n a#e constants.

'ind the va%ue of m and of n[3 $a#*s]

nse# m+PPPP.. n+PPPP..

SPM 2008 (paper 1)

1. 0he Cuad#atic function

r q x p x f ++= 2)()( , he#e p, q and r a#e constants, has a $ini$u$ va%ue of

-4. 0he eCuation of the ais of s$$et#is x + 3


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SPM 1993

1. ia#a$ 2 shos the net of an oened bo ith cuboids shae. f e#i$ete# of

the net bo is 4 c$ and the tota% su#facea#ea is 135 c$3, La%cu%ate the ossib%e

va%ues of v and w.

SPM 1999

12

1 $

1 $ 1$

1 $


13/61

1. Given the cu#ve y2 + (1 – x) and the

st#aiht %ine x

y+ 4. Eithout d#ain the

#ah, ca%cu%ate the coo#dinates of the

inte#section fo# the cu#ve and the st#aiht

%ine.2.


14/61

1.


15/61

2. (a) f h + %o m 2 and k + %o m 3, state in

te#$s of h and Oo# k

(i) %o m 6

(ii) %o " 24

(b)


16/61

2 %o 3 ( x y) + 2 %o 3 x %o 3 y,

sho that x 2 y 2 + & xy

(b) Eithout usin scientific ca%cu%ato# o#

fou#-fiu#e $athe$atica% tab%es, so%ve

the eCuation%o 6 [%o 3 (4 x – 5)] + %o 4 2

(c ) fte# n ea# a ca# as bouht the

#ice of the ca# is @A "/ ///n

&.

La%cu%ate afte# ho $an ea#s i%%the ca# cost %ess than @A 2/ /// fo#

the fi#st ti$e

SPM 1998

1. Given that %o x 4 + $ and %o y 5 + y


17/61

1. (a) Given that %o 35 + k . f 5 12 −λ + 15,

'ind λ in te#$s of k

(b)


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SPM 1993

1. 34$ti3ns t3 this q$esti3n by sca4e

drawing wi44 n3t be accepted8oint 5 and oint have a coo#dinate of

(4,1) and (2, 4). 0he st#aiht %ine * is

e#endicu%a# to 5 cuttin -ais at oint *. 'ind

(a) the #adient of 5

(b) the eCuation of st#aiht %ine *( c) the coo#dinates of *

SPM 1993

1. '#o$ the above dia#a$, oint & (1, /)and oint (-2, /) a#e the to fied oints.

8oint 5 $oves such that 5& : 5 + 1:2

(a) have acoo#dinates (2, 2), (5, 3), (4, -1) and (, C)

#esective%. Given that 7L> is a

a#a%%e%o#a$, find(a) the va%ue of and C

(b) a#ea of 7L>

SPM 1993

2. 0he above dia#a$ sho, a

a#a%%e%o#a$ &' .(a) 'ind the va%ue of . Nence

#ite don the eCuation of

& in the fo#$ ofinte#cets

(b) ' is etended to oint 5

so that divides the %ine '5 in the #atio 2 : 3. 'ind

the coo#dinates of 5

SPM 1994

2. (a)0he above dia#a$, 8, 9 and @a#e th#ee oints a#e on a %ine

42 =− x y he#e 89 : 9@ + 1:4 'ind

(i) the coo#dinates of oint 8(ii) the eCuation of st#aiht

%ine assin th#ouh the

oint 9 and e#endicu%a# ith 8@

(iii) the coo#dinates of oint @

(b) oint < $oves such that its distance

1

CHAPTER !: COORDINATE EOMETR"


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SPM 1997

1. n the dia#a$, 7 and 7L a#e tost#aiht %ines that e#endicu%a# to each

othe# at oint 7. 8oint and oint 7 %ie on

x-ais and y-ais #esective%. Given the

eCuation of the st#aiht %ine 7 is

/623 =−+ x y (a) 'ind the eCuation of 7L [3$](b) f L7 is #oduced, it i%% inte#sect the x-

ais at oint @ he#e @7 + 7L. 'ind the

coo#dinates of oint L [3$]

2. 0he dia#a$ shos the st#aiht %ine

#ahs of 89< and 9@0 on the La#tesian

%ane. 8oint 8 and oint < %ie on the x-ais

and y-ais #esective%. 9 is the $idoint of8<

(a) 'ind

(i) the coo#dinates of oint 9 (ii) the a#ea of Cuad#i%ate#a% D89@

[4$]

(b)Given 9@:@0 + 1:3, ca%cu%ate thecoo#dinates of oint 0

(c) oint $ove such that its distance

f#o$ oint < is2

1 of its distance f#o$

oint 0.

(i) 'ind the eCuation of the

%ocus of the oint(ii) Nence, dete#$ine hethe#

the %ocus inte#sects the

x-ais o# not

SPM 1998

1. n the dia#a$, L> and 7LK a#e st#aiht

%ines. Given L is the $idoint of >, and

7L : LK + 1:4'ind

(a) the coo#dinates of oint L

(b) the coo#dinates of oint K

(c ) the coo#dinates of the oint ofinte#section beteen %ines 7 and K>

#oduced

[3$]2. 8oint 8 $ove such that distance f#o$

oint 9(/, 1) is the sa$e as its distance

f#o$ oint @(3, /). 8oint < $ove so thatits distance f#o$ oint 0(3, 2) is 3 units.

Socus of the oint 8 and < inte#sects at

to oints.

(a) 'ind the eCuation of the %ocus of 8

(b)


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22/61

2. 0he dia#a$ shos a t#aeTiu$ #"+,.

Given the eCuation of #" is /123 =−− x y'ind

(a) the va%ue of k [3$]

(b) the eCuation of #, and hence, find

the coo#dinates of oint # [5$](c) the %ocus of oint 5 such that t#ian%e

"5, is a%as e#endicu%a# at 5

[2$]

SPM 2001

1. Given the oints 5 (, /) and (/, -"). 0he

e#endicu%a# bisecto# of 5 inte#sects the

aes at # and ".'ind

(a) the eCuation of #" [3$]

(b) the a#ea of #7"∆ , he#e 7 is theo#iin. [2$]

2. 34$ti3ns t3 this q$esti3n by sca4edrawing wi44 n3t be accepted.


23/61

SPM 2002

1. 0he dia#a$ shos a t#ian%e 7L ith

an a#ea 1 units2 . the eCuation of thest#aiht %ine +" is ./1 =+− x y 8oint , %ies on the x-ais and divides the st#aiht

%ine +" in the #atio m : n. 'ind(a) the coo#dinates of oint "

(b) m : n

2. #(1, 3), " and + a#e th#ee oints on the

st#aiht %ine 12 += x y . 0his st#aiht %ineis tanent to cu#ve /252 =++ p y x at oint ". Given " divides the st#aiht %ines #+ in the #atio 1 : 2.

'ind

(a) the va%ue of p [3$](b) the coo#dinates of oints " and +

[4$]

(c) the eCuation of the st#aiht %ine that asses th#ouh oint " and is

e#endicu%a# to the st#aiht %ine #+

[3$]

3. Given #(-1, -2) and "(2, 1) a#e to fied

oints. 8oint 5 $oves such that the #atioof #5 and 5" is 1 : 2.

(a)


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>ia#a$ 1

La%cu%ate the va%ues of p and q

[4$]

P2#$%&'ion ()

1. s34$ti3ns t3 this q$esti3n by sca4e

drawing wi44 n3t accepted. oint 5 $oves a%on the a#c of a

ci#c%e ith cent#e #(2, 3). 0he a#c asses th#ouh (-2, /) and *(5, k ).

(a) 'ind

(i) the eCuation of the %ocus of the oint 5

(ii) the va%ues of k

["$]

(b) 0he tanent to the ci#c%e at oint

inte#sects the -ais at oint .'ind the a#ea of t#ian%e 7 [4$]

SPM 2004(P1)

1. >ia#a$ 3 shos a st#aiht %ine #ah of

x

y aainst x

Given that2" x x y −= , ca%cu%ate the va%ue

of k and of h [3$]

2. >ia#a$ 4 shos a st#aiht %ine 89 ith

the eCuation 132=+ y x

. 0he oint 8 %ies

on the x-ais and the oint %ies on the y-ais

'ind the eCuationof the st#aiht %ine e#endicu%a# to 5 and

assin th#ouh the oint

[3$]

3. 0he oint # is (-1, 3) and the oint " is

(4, "). 0he oint 5 $oves such that

5# : 5" + 2 : 3.'ind the eCuation of the %ocus of 5

[3$]

P2#$%&'ion A)

4. >i#a$ 1 shos a st#aiht %ine +,hich $eets a st#aiht %ine #" at the

oint , . 0he oint + %ies on the y-ais

24

x

y


25/61

(a) #ite don the eCuation of #" in the

fo#$ of inte#cets [1$](b) Given that 2 #, + ,", find the

coo#dinates of , [2$]

(c) Given that +, is e#endicu%a# to

#", find the -inte#cets of +,[3$]

SPM 2005(P1)

1. 0he fo%%oin info#$ation #efe#s to the

eCuations of to st#aiht %ines, %& and

* , hich a#e e#endicu%a# to eachothe#.

K#ess p in te#$s of k [2$]

P2#$%&'ion ()


drawing wi44 n3t accepted.

(a) 'ind

(i) the eCuation of thest#aiht %ine #"

(ii) the coo#dinates of "[5$]

(b) 0he st#aiht %ine #" is etended to a

oint , such that #" : ", + 2 : 3'ind the coo#dinates of ,

[2$]

(c) oint 5 $oves such that its

distance f#o$ oint # is a%as 5units.

'ind the eCuation of the %ocus of 5

[3$]

SPM 2006(P1)

1. >ia#a$ 5 shos the st#aiht %ine #"

hich is e#endicu%a# to the st#aiht %ine+" at the oint "

0he eCuation of the st#aiht %ine +" is12 −= x y

'ind the coo#dinates of "

[3 $a#*s]

25

%& : k px y +=

* : p xk y +−= )2(

he#e p and k a#e constant


26/61

P2#$%&'ion ()


drawing wi44 n3t be accepted

>ia#a$ 3 shos the t#ian%e D7 he#e D

is the o#iin. 8oint L %ies on the st#aiht %ine7

(a) La%cu%ate the a#ea, in unit2, of

t#ian%e D7

(b) Given that L:L7 + 3:2, find thecoo#dinates of L

(c) oint 8 $oves such that its

distance f#o$ oint is a%astice its distance f#o$ oint 7

(i) 'ind the eCuation of the %ocus

of 8(ii) Nence, dete#$ine hethe# o#

not this %ocus inte#cets the

-ais

SPM 2007


27/61

1. >ia#a$ 13 shos a st#aiht %ine assin

th#ouh (3,/) and (/,4)

>ia#a$ 13

(a) E#ite don the eCuation of the

st#aiht %ine in the fo#$

1=+

b

y

a

x

(b) oint 8( x, y) $oves such that

5 + 5 . 'ind the eCuation of the%ocus of 5 [4 $]

2. 0he oints (/,3), (2,t ) and (-2,-1) a#e theve#tices of a t#ian%e. Given that the a#ea

of the t#ian%e is 4 unit2, find the va%ues

of t .[3 $]

SPM 2008 ia#a$ shos a t#ian%e 75. 8oint

%ies on the %ine 5.

(a) oint 9 $oves such that its

distance f#o$ oint is a%as

2

12

units. 'ind the eCuation of the %ocus

of 9 [3$](b) t is iven that oint 5 and oint

%ie on the %ocus of 9 . La%cu%ate

(i) the va%ue of k ,(ii) the coo#dinates of

[5$]

(c) Nence, find the a#ea, in unit2, oft#ian%e 75 [2$]

2&


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SPM 1993

1. 0he $ean fo# the nu$be#s ", 2, ", 2, 2,

1/, x, y is 5

(a) sho that 12=+ y x

(b) hence, find the $ode fo# the nu$be#s

hen

(i) y x =

(ii) y x ≠

(c) if standa#d deviation is 3&2

1, find

the va%ues of x

2. 0he be%o tab%e shos the $a#*s

obtained b a #ou of students in a $onth%test .

Aa#*s 1-2/ 21-4/ 41-"/ "1-/ 1-1//

Hu$be#

students

5 12 11 4

(a) Dn a #ah ae#, d#a a histo#a$

and use it to esti$ate the $oda% $a#*(b) 7 ca%cu%atin the cu$u%ative

f#eCuenc, find the $edian $a#*,

ithout d#ain an oive(c) La%cu%ate the $ean $a#*

SPM 1994

1. 0he be%o tab%e shos the $a#*s

obtained b a #ou of students in a $onth%test .

Aa#*s 1 2 3 4 5

Hu$be#

of

students

4 " 2 x 1

2

CHAPTER *: STATISTICS


29/61

'ind

(a) the $ai$u$ va%ue of x if $oda%

$a#* is 2(b) the $ini$u$ va%ue of x if $ean

$a#* $o#e than 3

(c) the #ane of va%ue of x if $edian$a#* is 2

2.


30/61

nu$be#s

'#eCuenc 1 3 1 2 2 1

(a) e#ess $edian fo# the set nu$be# inte#$s of m

(b) 'ind the ossib%e va%ues f m(c) 7 usin the va%ues of m f#o$ (b),

find the ossib%e va%ues of $ode

2. (a) 0he fo%%oin data shos the nu$be#

of ins *noc*ed don b to %ae#s

in a #e%i$ina# #ound of bo%inco$etition.

8%ae# : , 6, , 6, , "

8%ae# 7: &, , , 6, &, 6Bsin the $ean and the standa#d

deviation, dete#$ine the bette# %ae#

to #e#esent the state based on thei#

consistenc[3$]

(b) $se a graph paper t3 answer this

q$esti3n0he data in the tab%e shos the

$onth% sa%a# of 1// o#*e#s in a

co$an.

(i) 7ased on the data, d#aan oive to sho

dist#ibution of the

o#*e#sU $onth% sa%a#(ii) '#o$ ou# #ah,

esti$ate the nu$be# of

o#*e#s ho ea#n $o#ethan @A 3 2//

SPM 1998

1. 0he $ean of the data 2, k , 3k , , 12 and

1 hich has been a##aned in anascendin o#de#, is m. f each e%e$ent of

the data is #educed b 2, the ne $edian

is5m .

'ind

(a) the va%ues of m and k [4$]

(b) the va#iance of the ne data [2$]

2.


31/61

"/-&6 14

/-66 5

(a) 7 usin a #ah ae#, d#a a

histo#a$ and esti$ate the $oda%

$a#* [4$](b) Eithout d#ain an oive, ca%cu%ate

the $edian $a#* [3$](c) 'ind the $ean $a#* [3$]

SPM 2000

1. 0he tab%e shos the #esu%ts 1// students

in a test

(a) 7ased on the tab%e above, coco$%ete the tab%e be%o

[2$]

(b) Eithout d#ain an oive, esti$atethe inte#Cua#ti%e #ane of this

dist#ibution.

[4$]

2. 0he tab%e shos the dist#ibution of $a#*s

in a hsics test ta*en b 12/ ui%s.

La%cu%ate

(a) the $ean [4$]

(b) the $edian [3$](c) the standa#d deviation [3$]

of the dist#ibution

SPM 2001

0. (a) Given that fou# ositive intee#s

have a $ean of 6.Ehen a nu$be#

y is added to these fou# intee#s,

the $ean beco$es 1/. 'ind theva%ue of y

[2$] (b) 'ind the standa#d deviation of the

set of nu$be#s be%o:

5, ", ", 4, &

[3$]

2. 0he tab%e shos the f#eCuenc

dist#ibution of the $a#*s obtained b 1// ui%s

Mar+$ N-m/%r o0 -i$

"-1/ 12

11-15 2/

1"-2/ 2&

21-25 1"

2"-3/ 13

31-35 1/

3"-4/ 2(i) La%cu%ate the va#iance [3$]

(ii) Lonst#uct a cu$u%ative f#eCuenc tab%e

and d#a an oive to sho the

dist#ibution of thei# $a#*s. '#o$ theoive, find the e#centae of ui%s hosco#ed beteen " to 24.

[&$]

SPM 2002

1. 0he tab%e shos the dist#ibution of sco#es

obtained b 6 ui%s in a co$etition. 0he

sco#es a#e a##aned in an ascendin o#de#.Given the $ean sco#e is and the thi#d

Cua#ti%e is 11.


32/61

nu$be# of ui%s in a CuiT. 0he nu$be# of

ui%s is 4/. 7 d#ain an oive, find

7 d#ain an oive, find

(a) 0he $edian(b) 0he e#centae of ece%%ent ui%s if

the sco#e fo# the ece%%ent cateo# is

31.5

SPM 2003,p2 $%&'ion A

1. set of ea$ination $a#*s

"54321 ,,,,, x x x x x x has a $ean of 5 and a

standa#d deviation of 1.5(a) 'ind

(i) the su$ of the $a#*s,

x∑

(ii) the su$ of the sCua#es

of the $a#*s, 2 x∑

[3$]

(b) Kach $a#* is $u%ti%ied b 2 and

then is added to it.'ind, fo# the ne set of $a#*s,

(i) the $ean

(ii) the va#iance

[4$]

SPM 2004,p2 $%&'ion A

1. set of data consist of 1/ nu$be#s. the

su$ of the nu$be# is 15/ and the su$ of the

sCua#es of the data is 2 4&2.(a) 'ind the $ean and va#iance of the 1/

nu$be#s [3]

(b) nothe# nu$be# is added to the setof data and the $ean is inc#eased b

1

'ind

(i) the va%ue of this nu$be# (ii) the standa#d deviation of the set

11 nu$be#s

[4 $a#*s]

SPM 2005,

paper 1

1. 0he $ean of fou# nu$be#s is m . 0he

su$ of the sCua#es of the nu$be#s is 1//

and the standa#d deviation is 3k K#ess m in te#$s of k [3]

paper 2,section A

1. >ia#a$ 2 is a histo#a$ hich

#e#esents the dist#ibution of the $a#*s

obtained b 4/ ui%s in a test.

(a) Eithout usin an oive, ca%cu%ate the

$edian $a#* [3$]

(b) La%cu%ate the standa#d deviation of the

dist#ibution [4$]


33/61


34/61

Paper 1

1. set of data consists of five nu$be#s.0he su$ of the nu$be#s is "/ and the su$

of the sCua#es of the nu$be#s is //

'ind fo# the five nu$be#s

(a) the $ean

(b) the standa#d deviation[3 $]

SPM 2008(Paper 1)

1. set of seven nu$be#s has a $ean of 6

(a) 'ind x∑

(b) Ehen a nu$be# k is added to this

set, the ne $ean is .5[3$]

SPM 2008(Paper 2)

1. 0ab%e 5 shos the $a#*s obtained b 4/

candidates in a test.

Given that the $edian $a#* is 35.5, find the

va%ue of x and of y. Nence, state the $oda%c%ass

["$]

SPM 1993

1. 0he dia#a$ shos to a#cs, 5 and *,

of to ci#c%es ith cent#e 7 and ith #adii

7 and 7* #esective%. Given the #atio7 :* + 3:1, 'ind

(a) the an%eθ

in #adian(b) the a#ea of the shaded #eion 5* ["$]

SPM 1994

1.

0he dia#a$ shos a se$ici#c%e ith

cent#e 7 and dia$ete# #7+ . 'ind theva%ue of the an%e θ (in de#ees and

$inutes) so that the %enth of a#c of the

ci#c%e #" sa$e ith the tota% of dia$ete#

#7+ and %enth of a#c of the ci#c%e "+

34

CHAPTER : CIRCULAR MEASU


35/61


36/61

[5$]

2.

0he dia#a$ shos, D7 is a se$ici#c%eith cent#e > and K7 is a %enth of a#c of

the secto# ith cent#e L. 0he eCuation of 7

is 1"12=+

y x

La%cu%ate

(a) the a#ea of #"+ ∆(b) #+"∠ in #adians(c) the a#ea of the shaded #eion

SPM 1997

1. (a) Lonve#t

(i) "4/2/X into #adians(ii) 4.3" #adians into

de#ees

[2$](b)

0he dia#a$ shos to secto#s75 and 7* of to concent#ic

ci#c%e ith cent#e D. Givenθ =∠756 #ad, the %enth of a#c 5

is tice the %enth of #adius 7, and

the %enth of #adius 7 +"

'ind(i) the va%ue of θ

(ii) the e#i$ete# of the shaded

#eion

[4$]2.

0he dia#a$ sho se$ici#c%e 89@

ith cent#e D and secto# 9


37/61

0he dia#a$ shos a secto# '%& ith

cent#e ' and to secto#s 5%' and ', ofto ci#c%es ith cent#e 5 and #esective%.

Given the an%e of $a=o# Y ' is 3." #adians.

'ind (a) the #adius of secto# '%&

[2$](b) the e#i$ete# of the shaded

#eion [2$]

(c) the a#ea of secto# 5%' [2$]

(d) the a#ea of the shaded #eion[4$]

SPM 1999

1.

0he dia#a$ shos the osition of a si$%e endu%u$ that sins f#o$ 5 to . f the

an%e 57 is / and the %enth of a#c 5 is

14.4 c$, find(a) the %enth of 7 [3$]

(b) the a#ea of #eion set b the

endu%u$[2$]

2.

0he dia#a$ shos a t#aditiona% Aa%a *ite,

au bu%an, that has an ais of s$$et# 7*.

Given that #5" is an a#c of a ci#c%e ithcent#e 7 and #adius 25 c$. #" is a

se$ici#c%e ith cent#e H and dia$ete# 3/

c$. is an a#c of ci#c%e ith cent#e * and#adius 1/ c$. Given that the %enth of a#c

,+ is 1.&5 c$.

La%cu%ate(a) #7"∠(b) the a#ea of se$ent #;"


38/61

(b) the an%e θ in #adians [3$]

(c) the a#ea of secto# #-+ [2$]

(d) the a#ea of the shaded #eion[4$]

SPM 20011.

0he dia#a$ shos a secto#, 75* of a

ci#c%e ith cent#e 7 and #adius 5 c$. Given

the %enth of a#c 5* is &." c$, find(a) 57*∠ in #adians

[2$]

(b) the a#ea of the shaded #eion[4$]

2.

0he dia#a$ shos a ci#c%e, ", ith

cent#e 7 and #adius " c$. &7 is an a#c of a

ci#c%e ith cent#e . Given #" is a#a%%e% to

&, #" + " c$ and &7)∠ + 12//

(a) 'ind #7"∠ [1$](b) La%cu%ate the a#ea of se$ent 70

[4$]

(c)


39/61

n the dia#a$, #"+, is a #ectan%e and

7#-, is a secto# of a ci#c%e ith cent#e 7

and #adius " c$. Given 7 is the $idoint of #+ .La%cu%ate

(a) #7,∠ in #adians

[2$](b) the e#i$ete# of the shaded

#eion [4$]

( c) the a#ea of the shaded #eion[4$]

SPM 2003

a%r 1

1 >ia#a$ 1 shos a secto# *7

ith cent#e 7

>ia#a$ 1

0he %enth of the a#c * is &.24 c$ and the e#i$ete# of

the secto# *7 is 25 c$. 'ind the va%ue of θ in #ad

[3$]

a%r 2#$%&'ion A)

1. >ia#a$ 1 shos the secto# 57, cent#e

7 ith #adius 1/ c$ 0he oint * on 75 is such that

7* : 75 + 3 : 5

>ia#a$ 1

La%cu%ate(a) the va%ue of θ , in #ad,

[3$]

(b) the a#ea of the shaded #eion , inc$2. [4$]

SPM 2004 a%r 11. >ia#a$ 1 shos a ci#c%e ith cent#e 7

Given that the %enth of the $a=o# a#c #" is

45.51 c$, find the %enth, in c$, of the

#adius.(use π + 3.142)

[3$]

a%r 2#$%&'ion ()

1. >ia#a$ 4 shos a ci#c%e 5* , cent#e 7 and #adius 5 c$. %& is a tanent to the

ci#c%e at . 0he st#aiht %ines, %7 and &7,

inte#sect the ci#c%e at 5 and *

#esective%. 75* is a #ho$bus. %& is

36


40/61

an

a#c of

a

ci#c%e, cent#e 7 La%cu%ate

(a) the an%e α , in te#$s of π

[2$]

(b) the %enth, in c$, of the a#c %&[4$]

(c) the a#ea, in c$2, of the shaded #eion

[4$]

SPM 2005

a%r 1

1. >ia#a$ 1 shos a ci#c%e ith cent#e 7

0he %enth of the $ino# a#c #" is 1" c$ andthe an%e of the $a=o# secto# #7" is 26// .

Bsin π + 3.142, find

(a) the va%ue of θ , in #adians,

(Give ou# anse# co##ect to fou#sinificant fiu#es)

(b) the %enth, in c$, of the #adius of the

ci#c%e [3$]

a%r2 #$%&'ion ()

1. >ia#a$ 1 shos a secto# 57 of aci#c%e, cent#e 7. 0he oint %ies on 75 ,

the oint 7 %ies on 7 and #" is

e#endicu%a# to 7.

0he %enth of 7# + c$ and

"

π =∠ 576 #adian

t is iven that 7# : 75 + 4 : &(Bse 142.3=π )La%cu%ate

(a) the %enth, in c$, of #5

(b) the e#i$ete#, in c$, of the shaded#eion,

(c) the a#ea, in c$2, of the shaded #eion

SPM 2006

a%r 1

1. >ia#a$ & shos secto# 7#" ith

cent#e D and secto# #=> ith cent#e a

>ia#a$ &

Given that D7 + 1/ c$, Z + 4 c$,

1.1=∠ =#> #adians and the %enthsof

a#c 7 + & c$, ca%cu%ate(c) the va%ue of θ in #adian

(d) the a#ea in c$2, of the shaded

#eion

4/


41/61


42/61

SPM 266* a%r 2

1. >ia#a$ 4 shos a ci#c%e, cent#e D and#adius 1/ c$ insc#ibed in a secto# 87

of a ci#c%e, cent#e 8. 0he st#aiht %ines,

8 and 87, a#e tanents to the ci#c%e at oint 9 and oint @, #esective%.

[use ]142.3=π

La%cu%ate

(a) the %enth, in c$, of the a#c 7

[5 $]

(b) the a#ea in c$ 2 , of shaded #eion

[5 $]

SPM 266 a%r 1

1. >ia#a$ 1 shos a ci#c%e ith cent#e 7

and #adius 1/ c$.

Given that 5 , and * a#e oints

such that 75 + 5 and ∠ 75* + 6//,

[Bse ]142.3=π 'ind

(a) ∠ 7*, in #adians (b) the a#ea, in c$2 of the co%ou#ed

@eion

[4$]

SPM 266 a%r 21. >ia#a$ shos to ci#c%es. 0he

%a#e# ci#c%e has cent#e = and #adius 12

c$. 0he s$a%%e# ci#c%e has cent#e > and

#adius c$. 0he ci#c%e touch at oint *.0he st#aiht %ine 5 is a co$$on

tanent to the ci#c%e at oint 5 and oint

.

42


43/61

[use ]142.3=π Given that θ =∠ 5=* #adian,(a) sho that 3&.1=θ (to to

deci$a% %aces) [2$]

(b) ca%cu%ate the %enth, in c$ of the

$ino# a#c * [3$](c) ca%cu%ate the a#ea, in c$2, of the

co%o#ed #eion. [5$]

SPM 1993

1 Given that34

21)(

2

−−= x

x x f , find f X( x)

SPM 1994

1. (a) Given that 53 2 += x y , finddx

dy

usin

the fi#st #inci%e

(c) 'ind

+121

xdx

d

2. Given4

1"

x y = , find

dx

dy if 2= x . Nence,

esti$ate the va%ue of( ) 46.1

1"

SPM 1995

1. Given1

21)(

3

−−

= x

x x f find f ? ( x)

2. Given )3( x x y −= , e#ess

43

CHAPTER 7: DIFFERENTATIO


44/61


45/61

(b) La%cu%ate the va%ue of x so that

the a#ea of the shaded #eion is a

$ini$u$

[5$]

SPM 1998

1. Given that ,)12(4)( 5−= x x x f find)(

X x f

2.

0he dia#a$ shos a ooden b%oc*

consistin of a cone on to of a c%inde#

ith #adius of x c$. Given the s%ant heihtof the cone is 2 x c$. and the vo%u$e of the

c%inde# is 24π c$ 3

a) 8#ove that the tota% su#face a#ea of the b%oc*, c$ 2 , is iven b

+

+ x

x 1"

3 2π [3$]

b)La%cu%ate the $ini$u$ su#face a#ea of the

b%oc* [3$]

c) Given the su#face a#ea of the b%oc*

chanes at a #ate of 42π c$ 2 s 1− . 'ind

the

of chane of its #adius hen its #adius is

4 c$. [2$]

d) Given the #adius of the c%inde# inc#eases

f#o$ 4 c$ to 4.//3 c$. find thea#oi$ate inc#ease in the su#face a#ea

of the b%oc* [2$]

SPM 1999

1. Given( ) x

x x f

31

2)(

52

−−

= , find

)/(X f [4$]

2. Given 22t t y −= and 14 += t x

(a)'inddx

dy, in te#$s of x

(b) f x inc#eases f#o$ 3 to 3./1,

find the co##esondin s$a%%inc#ease in t . [2$]

3 (a)

0he dia#a$ shos a bo ith a unifo#$

c#oss section #"+,- .Given #" + -, + (3/-" x)

c$, "+ + 3 x c$, +,+ 4 x and # + 2 c$

(i)


46/61

(b) the va%ue of that $a*es

/ a $ai$u$

(c) the $ai$u$ va%ue of /

3 (b) iece of i#e "/ c$ %on is bent to

fo#$ a ci#c%e. hen the i#e is heated,its %enth inc#eases at a #ate of /.1 c$ s1− (use 142.3=π )(i) La%cu%ate the #ate of chane

in the #adius of the ci#c%e

(ii) Nence, ca%cu%ate the #adius of the ci#c%e afte# 4 second

SPM 2000

0. >iffe#entiate the fo%%oin e#essionsith #esect to x

(a)4

31 x+ [2$]

(b)3

524 ++ x

x[2$]

2. Given "43 2 +−= x x y . Ehen 5= x , x inc#eases b 2. 'ind theco##esondin #ate of chane of y.

1. 'ind the eCuation of the tanent to

the cu#ve r x y += 22 at the ointk x = . f the tanent asses th#ouh

the oint (1,/), find r in te#$s of k

4.(a) 0he st#aiht %ine k x y =+4 is theno#$a% to the cu#ve ( ) 312 2 −−= x y at oint #.

'ind

(i) the coo#dinates of oint # and the

va%ue of k

(ii) the eCuation of the tanent at oint #

4.(b) 0he dia#a$ shos a to in

the shae of a se$ici#c%e ith cent#e

7. >ia$ete# #" can be ad=usted so that

oint + hich %ies on theci#cu$fe#ence can $ove such that

#+ +" + 4/ c$. Given that #+ + x

c$ and the a#ea of t#ian%e #"+ is # c$, find an e#essions fo#

dx

d) in

te#$s of x and hence, find the

$ai$u$ a#ea of t#ian%e #"+

SPM 2001

1. Givenr

r r f

25

34)(

−+= find %i$ited va%ue

of )(r f hen ∞→r

2. Given that #ah of function

2

3)(

x

k hx x f += has #adient function

3

2 6"3)(X x

x x f −= he#e h and k a#e

constants,

'ind

a. the va%ues of h and k b. x-coo#dinate of the

tu#nin oint of the #ah

of the function3. (a)

0he dia#a$ shos a ci#c%e inside#ectan%e 7L> such that the ci#c%e

is constant% touchin the to sides

4"


47/61

of the #ectan%e. Given the e#i$ete#

of 7L> is 4/ c$

a. ia#a$ 2 shos a conica% containe#

4&

y + 2 x – x2


48/61


49/61

1. cu#ve ith #adient function2

22 x x −

has a tu#nin oint at (k , )

(a) 'ind the va%ue of * [3 $](b) dete#$ine hethe# the tu#nin oint is a$ai$u$ o# $ini$u$ oint

[2 $]

( c) find the eCuation of the cu#ve

[3 $] SPM 2007

Paper 1

1. 0he cu#ve )( x f y = is such that

dx

dy+ 53 +kx , he#e k is a constant.

0he #adient of the cu#ve at 2= x is 6 'ind the va%ue of k

[2 $]

2. 0he cu#ve "4322 +−= x x y has a

$ini$u$ oint at p x = , he#e p is aconstant.

'ind the va%ue of p[3 $]

SPM 2008

Paper 11. 0o va#iab%es x and y a#e #e%ated b the

eCuation2

1"

x y = .

K#ess, in te#$s of h, the a#oi$atechane in y hen x chanes f#o$ 4 to 4

h, he#e h is a s$a%% va%ue

[3$]

2. 0he no#$a% to the cu#ve x x y 52 −= at oint 5 is a#a%%e% to the st#aiht %ine

12+−= x y . 'ind the eCuation of theno#$a% to the cu#ve at oint 5 .

[4$]

SPM 1993

1.

0he dia#a$ shos a ∆ 5*

(a) La%cu%ate obtuse an%e 5* [2$]

(b)


50/61

2.

0he dia#a$ shos a %and fo#$ t#ian%e, #"+ , divide b th#ee a#ts. #,", "+ , and

#-;+ is a st#aiht %ine

Given that sin 13

12

=∠ "#+ (a) if the fence ant to bui%d a%on the

bounda# "+ , ca%cu%ate the tota% %enth is

needed

(b) La%cu%ate "+#∠ (c ) Given that the a#ea of :+;∆ sa$e

ith the a#ea #,- ∆ . La%cu%atethe %enth of ;+

SPM 19941.

n the dia#a$, "+, is a st#aiht %ine,ca%cu%ate the %enth of +,

2.

0he dia#a$ shos a #a$id ith #"+ ∆as the ho#iTonta% base. Given that #" + 3

c$, "+ + 4 c$ and /6/=∠ #"+ andve#te , is 4 c$ ve#tica%% above ",

ca%cu%ate the a#ea of the s%antin face.

[5$]

SPM 1995

1.

n the dia#a$, sin5

4=∠ #,+ he#e

#,+ ∠ is an obtuse an%e. La%cu%ate(a) the %enth of L co##ect to to deci$a%

%aces [3$]

(b) #"+ ∠ [2$]

SPM 1996

1.

5/


51/61

0he dia#a$ shos a cuboid. La%cu%ate

(a) %6)∠ [4$]

(b) the a#ea of %6)∆ [2$]

2.

n the dia#a$, oints #, ", + , , and - %ieon a f%at ho#iTonta% su#face. Given "+, is a

st#aiht %ine, #+"∠ is an obtuse an%e andthe a#ea of #,- ∆ + 2/

c$2, ca%cu%ate

(a) the %enth of >

(b) ,#- ∠

SPM 1997

1. 0he dia#a$ shos a t#ian%e #"+

La%cu%ate

(a) the %enth of #" (b) the ne a#ea of t#ian%e #"+

if #+ is %enthened hi%e the

%enths of #", "+ and "#+ ∠ a#e $aintained [3$]

SPM 1998

1. n the dia#a$, ", + 5 c$, "+ + &c$,

+, + c$ and #- + 12 c$, ",- and

#,+ a#e a st#aiht %ines. 'ind (a) ",+ ∠ (b) the %enth of #,

2.

0he dia#a$ shos a #a$id /#"+, itha sCua#e base #"+,. /, is ve#tica% and base

#"+, is ho#iTonta%. La%cu%ate

(a) /.8 ∠(b) the a#ea of %ane /8

SPM 1999

51


52/61

1.

0he dia#a$ shos a t#aeTiu$ #"+,

La%cu%ate(a) +",∠(b) the %enth of st#aiht %ine #+

2. %& is a t#ian%e ith side %& + 1/ c$.

Given that sin 45"./=∠ &%) andsin 3"./=∠ %&) ,

La%cu%ate (a) %)& ∠ (b) the a#ea of %&)∆

SPM 2000

1. 0he dia#a$ shos a cc%ic Cuad#i%ate#a%

7L>. 0he %enths of st#aiht %ines >L

and L7 a#e 3 c$ and " c$ #esective%.K#ess the %enth of 7> in te#$s of

(a) α

(b) β

Nence, sho that cos2611=α

2.

n the dia#a$, 5* is a st#aiht %ine.

La%cu%ate the %enth of 5

SPM 2001

1.

0he dia#a$ shos a #a$id ith at#ianu%a# base 5* hish is on a ho#iTonta%

%ane. \e#te / is ve#tica%% above 5 . Given

5 + 4 c$, 5/ + 1/ c$, /* + 15 c$ and//=∠/6*

La%cu%ate(a) the %enth of *(b) the a#ea of the s%antin face

SPM 2002

1.

0he dia#a$ shos a Cuad#i%ate#a% #"+,.Given #, is the %onest side of t#ian%e

#", and the a#ea of t#ian%e #", is 1/ c$2

La%cu%ate

52


53/61

(a) "#,∠(b) the %enth of ",

( c) the %enth of "+

2.

0he dia#a$ shos a #is$ ith a unifo#$t#ianu%a# c#oss-section 5 . Given the

vo%u$e of the #is$ is 315 c$3. 'ind the

tota% su#face a#ea of the #ectanu%a# faces

[5$]

SPM 2003

1. 0he dia#a$ shos a tent \7L in the

shae of a #a$id ith t#ian%e 7L as theho#iTonta% base. \ is the ve#te of the tent

and the an%e beteen the inc%ined %ane

\7L and the base is 5//

Given that /" + /+ + 2.2 $ and #" + #+ +

2." $, ca%cu%ate

(a) the %enth of "+ if the a#ea of the

base is 3 $2

(b) the %enth of #/ and the base is

25/

(c ) the a#ea of t#ian%e /#"

SPM 2004

1. 0he dia#a$ shos a Cuad#i%ate#a% 7L> such that #"+ ∠ is acute

53


54/61

(a) La%cu%ate

(i) #"+ ∠ (ii) #,+ ∠

(iii) the a#ea, in c$2, of Cuad#i%ate#a% #"+,

[$]

(b) t#ian%e #?"?+? has the sa$e

$easu#e$ents as those iven fo# t#ian%e

#"+ , that is, #?+? + 12.3 c$, +?"? + 6.5c$ and "∠ X #?+? + 4/.5/, but hich isdiffe#ent in shae to t#ian%e #"+

(i) ia#a$ 5 shos a Cuad#i%ate#a% 7L>

54


55/61

>ia#a$ 5

0he a#ea of t#ian%e 7L> is 13 c$2 and "+,∠ is acute

La%cu%ate

(a) "+,∠ [2 $](b) the %enth, in c$, of ", [2 $](c) #",∠ [3 $](d) the a#ea, in c$2, Cuad#i%ate#a% #"+,

[3 $]

SPM 2006

1. >ia#a$ & shos Cuad#i%ate#a% #"+,

i. La%cu%ate

(a) the %enth, in c$, of #+

(b) #+"∠ [4 A]ii. 8oint U %ies on L such that

#U " + #"

(i) s*etch #∆ U "+ (ii) ca%cu%ate the a#ea, in

c$ 2 , of #∆ U "+ [" A]

SPM 1993

1. 0he tab%e be%o shos the $onth%

eenses of %iUs fa$i%

55

CHAPTER 11: INDE8 NUM(ER


56/61

"%ar

E9%n$%$

177 1772

'ood @A 32/ @A 34

0#anso#tation @A / @A 3

@enta% @A 2/ @A 322K%ect#icit _ ate# @A 4/ @A 4/

'ind the co$osite inde in the ea# 1662 b usin the ea# 166 as the base ea#.

Nence, if %iUs $onth% inco$e in the ea#

166 is @A //, find the $onth% inco$e#eCui#ed in the ea# 1662 so that the

inc#eases in his inco$e is in %ine ith the

inc#eases in his eenses

[5$]

SPM 1994

1. 0he ie cha#t be%o shos thedist#ibution of the $onth% eenses in the

ZusnisU househo%d in the ea# 166/. 0he

tab%e that fo%%os shos the #ice indices inthe ea# 1663 based on the ea# 166/

Mon'.

%9%n$%$

Pri&% In%9

'ood 13/

Nouse #enta% 115Knte#tain$ent 11/

L%othin 115

Dthe#s 13/

La%cu%ate(a) the co$osite #ice inde, co##ect

to the nea#est intee#, of the

$onth% eenses in the ZusnisU

househo%d

(b) the tota% $onth% eenses in theea# 1663, co##ect to the nea#est

#init, if the tota% $onth%

eenses of the Zus#isU househo%din the ea# 166/ is @A 5/

SPM 1995

1. 0he tab%e be%o shos the #ice indices

and eihtaes of fou# ite$s in the ea#

1664 based on the ea# 166/. Given the

co$osite #ice inde in the ea# 1664 is@A 114

La%cu%ate

(a) the va%ue of n(b) the #ice of a shi#t in 1664 if its

#ice in 166/ is @A 4/

SPM 1996

1. (a) n the ea# 1665, the #ice and #ice

inde of a *i%o#a$ of a ce#tain #ade

of #ice a#e @A 2.4/ and 1"/. Bsin theea# 166/ as the base ea#, ca%cu%ate

the #ice of a *i%o#a$ of #ice in the

ea# 166/.[2$]

(b) 0he above tab%e shos the #ice indices

in the ea# 1664 usin 1662 as the base

ea#, chanes to #ice indices f#o$ the

ea# 1664 to 166" and thei# eihtaes

I'%m Pri&% In%9 ;%ig'ag%


57/61

#esective%.

I'%m Pri&%

In%9

1774

Cang%$ 'o

Pri&% in%9

0rom 1774 'o

177!

;%ig'ag%$

Eood 1/ nc#eases 1/ 5

Le$ent 11" >ec#eases 5 4

#on 14/ Ho chane 2


58/61

eihtaes. Given the #ice of 8 in the

ea# 166" is @A 12.// and inc#eases to

@A 13./ in the ea# 1666. 7 usin166 as the base ea#, ca%cu%ate the va%ue

of x. Nence, find the va%ue of y if the

co$osite #ice inde is 113

te$ 8#ice inde Eeihtae

x 5

7 6 y

L 123 14 - y

SPM 2002

1. 0he tab%e be%o shos the #ices, #ice

indices and the nu$be# of th#ee ite$s

te$

8#ice (@A)

8#ice

nde Hu$be#

Zea#

1666

Zea#

2///

(7ase

ea#

1666) of ite$s

A 55 66 120 200

B 40 x 150 500

C 80 100 125 y

(a) 'ind the va%ue x

(b) f the co$osite #ice inde of the th#ee

ite$s in the ea# 2/// usin ea# 2/// as the base ea# is 13".5, find the va%ue of y

2. 0he tab%e be%o shos the #ices of th#ee

ite$s , 7 and L in the ea# 166" and

166, as e%% as thei# eihtaes

(a) Bsin the ea# 166" as the base ea#,ca%cu%ate the #ice indices of ite$s ,

7 and L

(b) Given the co$osite #ice inde ofthese ite$s in the ea# 166 based on

the ea# 166" is 14/, find the va%ues

of x and y

[5$]

SPM 2003

1. 0he dia#a$ be%o sho is a ba# cha#t

indicatin the ee*% cost of the ite$s 8,

T.% o0i'%m

Pri&%#RM) in

177!

Pri&%#RM) in

177

;%ig'ag%=

&/ 1/5 >

7 / 1// =

L "/ "&.5/ 2 x

5


59/61

9, @, < and 0 fo# the ea# 166/. 0ab%e 1

shos the #ices and the #ice indices fo#

the ite$s.

I'%m$ Pri&% in

1776

Pri&% in

1775

Pri&% In%9

in 1775

/a$% on

17768 x @A /.&/ 1&5

9 @A 2.// @A 2.5/ 125

@ @A 4.// @A 5.5/ y

< @A ".// @A 6.// 15/

0 @A 2.5/ z 12/

(a) 'ind the va%ue of

(i) x (ii) y

(iii) z

(b) La%cu%ate the co$osite inde fo# the

ite$s in the ea# 1665 based on the ea#

166/

( c) 0he tota% $onth% cost of the ite$s in

the ea# 166/ is @A 45"

(d) 0he cost of the ite$s inc#eases b 2/

f#o$ the ea# 1665 to the ea# 2///.

'ind the co$osite inde fo# the ea#

2/// based on the ea# 166/

SPM 2004

1. 0he tab%e be%o shos the #ice indicesand e#centae of usae of fou# ite$s, 8, 9,

@ and < hich a#e the $ain in#edients in

the #oduction of a te of biscuits

(a) La%cu%ate

(i) the #ice of in the ea# 1663 if its

#ice in the ea# 1665 is @A 3&.&/(ii) the #ice inde of 5 in the ea# 1665

based on the ea# 1661 if its #ice

inde in the ea# 1663 based on theea# 1661 is 12/

[5$]

(b) 0he co$osite inde nu$be# of the %ostof biscuits #oduction fo# the ea# 1665

based on the ea# 1663 is 12. La%cu%ate

(i) the va%ue of

(ii) the #ice of a bo of biscuits in theea# 1663 if the co##esondin

#ice in the ea# 1665 is @A 32[5$]

SPM 2005

1. 0he tab%e be%o shos the #ices and the

#ice indices fo# the fou# in#edients 8, 9,@ and < used in $a*in biscuits of a

te$ 8#ice inde fo# the

ea# 1665 based on

the ea# 1663

8e#centae of

usae ()

5 135 4/

x 3/

* 1/5 1/

13/ 2/

56

0

5

10

15

20

25

30

P Q R S

ITEMS


60/61

a#ticu%a# *ind. >ia#a$ be%o shos a

ie cha#t hich #e#esents the #e%ative

a$ount of the in#edients 8, 9, @, and <used in $a*in these biscuits

n#edients 8#ice e# * 8#ice inde fo# theea# 2//4 based on

the ea# 2//1Zea#

2//1

Zea#

2//4

5 /./ 1.// x

2.// y 14/

* /.4/ /."/ 15/

z /.4/ /

(a) 'ind the va%ue of , and T [3$]

(b) (i) ca%cu%ate the co$osite inde fo# the

cost of $a*in these biscuits in theea# 2//4 based on the ea# 2//1

(ii) Nence, ca%cu%ate the co##esondin

cost of $a*in these biscuits in theea# 2//1 if the cost in the ea# 2//4

as @A 265 [5$]

(c) 0he cost of $a*in these biscuits iseected to inc#ease b 5/ f#o$ the

ea# 2//4 to the ea# 2//&

'ind the eected co$osite inde fo#the ea# 2//& based on the ea# 2//1

[2$]

SPM 2006

1. a#ticu%a# *ind of ca*e is $ade b

usin fou# in#edients 5 , , * and .0ab%e shos the #ices of the in#edients

(a) 0he inde nu$be# of in#edient 5 inthe ea# 2//5 based on the ea# 2//4

is 12/. La%cu%ate the va%ue of w

[2$]

(b) 0he inde nu$be# of in#edient * in

the ea# 2//5 based on the ea#2//4 is 125. 0he #ice e# *i%o#a$

of in#edient * in the ea# 2//5 is

@A 2.// $o#e than its co##esondin

#ice in the ea# 2//4.

La%cu%ate the va%ue of x and of y

[3$]

(c) 0he co$osite inde fo# the costof $a*in the ca*e in the ea#

2//5 based on the ea# 2//4 is

12&.5 La%cu%ate

(i) 0he #ice of a ca*e in the ea#

2//4 if its co##esondin #ice in the ea# 2//5 is @A3/."/

(ii) the va%ue of $ if the

Cuantities of in#edients 5 , ,

* and used a#e in the #atioof & : 3 : m : 2

[3$]

SPM 2007

1. 0ab%e 4 shos the #ices and the #ice

indices of five co$onents, 8, 9, @, < and 0, used to #oduce a *ind of to

n#edient

8#ice e# *i%o#a$ (@A)

Zea# 2//4 Zea# 2//5

5 5.// 9

2.5/ 4.//

* x >

4.// 4.4/

"/


61/61

>ia#a$ " shos a ie cha#t hich

#e#esents the #e%ative Cuantit of

co$onents used

>ia#a$ "

(a) 'ind the va%ue of and of

[3$](b) La%cu%ate the co$osite inde fo# the

#oduction cost of the tos in the

ea# 2//" based on the ea# 2//4[3$]

(c) 0he #ice of each co$onent

inc#eases b 2/ f#o$ the ea#

2//" to the ea# 2//Given that the #oduction cost of one to

in the ea# 2//4 is @A 55, ca%cu%ate the

co##esondin cost in the ea# 2//

[4$]

Comon%n' Pri&% #RM) 0or '%

.%ar

Pri&% in%9 0or '%

.%ar 266! /a$% on

'% .%ar 2664

8 1.2/ 1.5/ 125

9 x 2.2/ 11/

@ 4.// ".// 15/

< 3.// 2.&/ y

0 2.// 2./ 14/

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