SPM Add Maths Pass Year Questions

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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 .

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SPM 1994

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

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

"

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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.

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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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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]

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)

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 \$

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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.

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1.

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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)

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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

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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

(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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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.

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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

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(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 ()

2. 34\$ti3ns t3 this q\$esti3n by sca4e

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

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P2#\$%&'ion ()

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

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

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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

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'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.

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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.

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"/-&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.

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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\$]

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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

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

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[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

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

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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 #;"

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(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)

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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

[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

[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

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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

"

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/

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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

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

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[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

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

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(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

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)

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(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"

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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

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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)

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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/

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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

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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

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(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

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(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

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>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

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"%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%

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#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

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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

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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

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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/

"/

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>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/