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SULIT 1449/1 LEMBAGA PEPERIKSAAN KEMENTERIAN PELAJARAN MALAYSIA MATHEMATICS SIJIL PELAJARAN MALAYSIA 2009 (ULANGAN) Paper 1 Jun  jam 4 1  JANGAN BUKA KERTAS SALAN INI SEHINGGA !IB ERITAHU 1.  Kertas soalan ini adalah dalam dwibahasa. 2. Soalan dalam bahasa Inggeris mendahului soalan yang sepadan dalam bahasa  Melayu. 3. Calon dikehendaki membaca maklumat di halaman belakang kertas soalam ini . Kertas soalan ini mengandungi 28 halaman bercetak 1 http://mathsmozac.blogspot.com 1449/12!!9 "atu jam lima belas minit www.myschoolchildren.com Kertas soalan mp lain terdapat di :

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SULIT 1449/1

LEMBAGA PEPERIKSAAN

KEMENTERIAN PELAJARAN MALAYSIA

MATHEMATICS

SIJIL PELAJARAN MALAYSIA 2009 (ULANGAN)Paper 1

Jun

 jam4

JANGAN BUKA KERTAS SALAN INI SEHINGGA !IBERITAHU

1.  Kertas soalan ini adalah dalam dwibahasa.

2. Soalan dalam bahasa Inggeris mendahului soalan yang sepadan dalam bahasa

 Melayu.

3. Calon dikehendaki membaca maklumat di halaman belakang kertas soalam ini.

Kertas soalan ini mengandungi 28 halaman bercetak 

h // h bl

"atu jam lima belas minit

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SULIT 1449/1

INFORMATION FOR CANDIDATES

1. This question paper consists of "0  questions.

 

2.  Answer a## questions.

3.  Answer each question by blackening the correct space on the answer sheet .

4.  lacken only $ne space for each question.

#.  If you wish to change your answer! erase the blackened mark that you ha"e

  done. Then blacken the space for the new answer.

$. The diagrams in the questions pro"ided are not drawn to scale unless stated .

%. A list of formulae is pro"ided on pages # to $.

8.  A booklet of four%figure mathematical tables is pro"ided.

  9.  &ou may use a non%programmable scientific calculator.

 MAKLUMAT UNTUK CALON 

'. Kertas soalan ini mengandungi $( soalan.

). *awab semua soalan.

#. *awab dengan menghitamkan ruangan yang betul pada kertas +awapan.

$. agi setiap soalan hitamkan satu ruangan saha+a.

,. Sekiranya anda hendak menukar +awapan! padamkan tanda yang telah dibuat.

 Kemudian hitamkan +awapan yang baru.

-. a+ah yang mengiringi soalan tidak dilukiskan mengikut skala kecuali dinyatakan

/. Satu senarai rumus disediakan di halaman # hingga $.

0. Sebuah buku sifir matematik empat angka disediakan.

1. Anda dibenarkan menggunakan kalkulator saintifik yang tidak boleh

diprogramkan.

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SULIT 1449/1

MATHEMATICAL %RMULAE

The following formulae may be helpful in answering the questions. The symbols gi"en are

the ones commonl& used.

RELATINS

1 nmnmaaa

+=×

2 nmnmaaa

−=÷

3 mnnm aa   ='(

4    

  

 −

−=−

ac

bd 

bcad  A

11

#

'(

'('(

S n

 An A 2    =

$ '(1')(   A 2  A 2    −=

% *istance + 2

21

2

21 '('(   y y 3 3   −+−

 

8 ,idpoint-   

  

    ++=

2-

2'-( 2121   y y 3 3

 y 3

9 erage speed +takentime

 tra/elleddistance

1! ,ean +datao0 number

datao0 sum

11 ,in +s0reuencieo0 sum

'(o0 sum   frequencymark class   ×

12 &thagoras heorem

  c2 + a2  b2

1312

12

 3 3

 y ym

=

14 m +intercept56

intercept5&−

SHAPES AN! SPACE

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SULIT 1449/1

1 rea o0 trapezium + heightsides parallelo0 sum2

1××

2 7ircum0erence + d + 2r 

3 rea o0 circle + r 2

4 7ured sur0ace area o0 c&linder + 2rh

# "ur0ace area o0 sphere + 4r 2

$ olume o0 right prism + cross sectional length

% olume o0 c&linder + j2h

8 olume o0 cone +3

1j2 h

9 olume o0 sphere +34 r 3

  1! olume o0 right p&ramid +3

1 base area height

  11 "um o0 interior angles o0 a pol&gon + (n 5 2' 18!o

  12

3$!

centreatsubtendedangle

circleo0 ncecircum0ere

lengtharc=

  13

3$!

centreatsubtendedangle

circleo0 area

sector o0 area=

  14 "cale 0actor - k + 2A

 2A)

  1# rea o0 image + k 2  area o0 object.

  ns;er a#l uestion

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SULIT 1449/1

1 <ound o00 % 21$ correct to three signi0icant 0igures .

 undarkan / )'- betul kepada tiga angka bererti.

A %21

B %22C % 21!

! % 22!

2 =6press 3! $!! in standard 0orm.4ngkapkan #( (-( dalam bentuk piawai.

A 3.!!$ 1! #

  B 3.!!$ 1! 4

C 3.!!$ 1! 5 4

! 3.!!$ 1! 5 #

 

3 %1!4

!!2#.!

−× 

A   $.2# 1! 512

B   $.2# 1! 52

  C  $.2# 1! 2

  !   $.2# 1! 12

4 >t is gien that the mass o0 the earth is #.9%$ 1! 24 kg and the mass o0 the moon is

%.3#! 1! 22

?ind the di00erence bet;een the masses- in kg. 5iberi bahawa +isim bumi ialah #.9%$ 1! 24 kg dan +isim bulan ialah %.3#! 1! 22 kg .

Cari be6a antara +isim itu! dalam kg 

A  1.3%4 1! 22

B  1.3%4 1! 24

C  #.9!2# 1! 22

!  #.9!2# 1! 24

& "tate the alue- in base 1!- o0 the underlined digit n the number 1!11!2. 7yatakan nilai! dalam asas '(! bagi digit yang digariskan dalam nombor 1!11!2

A 2

B 4

C $

! 8 

' 11!!12  1112 +

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SULIT 1449/1

A 111!!2

B 1111!2

C 1!!!!!2

! 1!!1!12

>n *iagram 1  28ST   is pentagon and 4S9 is an euilateral triangle . @A< and

<" are straight lines . 5alam a+ah '! 28ST ialah pentagon dan . 4S9 ialah segi tiga sama sisi . :8 dan S9 ialah

 garis lurus .

*iagram 1

?ind the alue o0  3 .

Cari nilai 3.

A 118

B 128

C 13!

! 1#1

8 >n *iagram 2 - 28 is the tangent to the circle ;ith centre ; - at point 8 .T;S is a

straight line . 5alam a+ah ) ! 28 ialah tangen kepada bulatan berpusat ; ! di titik8 . T;S ialah garis lurus

 

*iagram 2

?ind the alue o0 3.Cari nilai 3.

  A 1%

  B 22

  C 44

  ! #$

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 S T  ;

8 2 

 3° 34°

 2 

 

8

8#!

 3

114!

93!

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SULIT 1449/1

9 *iagram 3 sho;s seen points on a suare grid . 2< is the image o0 2  under a

re0lection. a+ah # menun+ukkan tu+uh titik pada grid segi empat sama .2= ialah ime+ bagi 2 di bawah satu

 pantulan

  *iagram 3

  @hich o0 the points - -B -7 or *- is the image o0 point 8 under the same re0lectionC

 Antara titik A ! ! C atau 5 ! yang manakah ime+ bagi titik 8 di bawah pantulan yang samaC

1! *iagram 4 sho;s t;o pentagons - 2   and 8 - dra;n on a 7artesian plane . 8 is the

image o0 2  under an enlargement .

 a+ah $ menun+ukkan dua pentagon ! P  dan 8! dilukis di atas satah Cartesan. 8 ialah ime+ bagi 2

di bawah suatu pembesaran .

 

*iagram 4

  ?ind the centre o0 the enlargement .Cari pusat pembesaran itu .

( 2 - 3 '

B ( 2 - 4 '

7 ( # - 2 '

* ( 8 - 1 '

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 B

8

 2 

 2 ’ 

C  A

 D

8

%

$

#

4

3

21

8

9

Q

 P 

52 $42!5$ 54

 y

 3

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SULIT 1449/1

11 >n *iagram #-  28 is a right5angle triangle and 8S  is a straight line. 5alam a+ah , ! 28 ialah sebuah segi tiga bersudut tegak dan 8S ialah garis lurus..

?ind the alue o0 cos 3 !

Cari nilao kos  3 !

A2#

24−  

B 2#

%−

 

C 2#

!2#

24 

12 *iagram $ sho;s the graphs  y  + sin 3 and  y  + cos 3  0or !! D  3  D 3$!!  a+ah - menun+ukkan graf y > sin 3 dan y > kos 3 for !(  ? 3 ? 3$!!.

 

*iagram %

is a point on the graph & + cos 3o .he 3%coordinate o0 2  is 18! !

  @hich o0 the points - - B - 7 or * - represent the point C   2 ialah satu titik pada graf y > kos 3 ( . koordinat%3 bagi 2 ialah '0( ( . Antara titik%titik A ! ! C

atau * ! yang manakah mewakili titik 2 @

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*iagram $

 2 

8   S 

% cm 2# cm

 3(

1

 

7−1

 

BE

 y

 3

*

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SULIT 1449/1

A   9MK ∠

B   9M2 ∠C   98K ∠

  !   98.∠

1# *iagram 9 sho;s t;o ertical poles- 28 and a tree B  on a horizontal plane. kiteis tied to the pole at . he edge o0 the kite is stuck on the top o0 the tree . he

angle o0 eleation o0 = 0rom is #! ! . a+ah 1 menun+ukkan sebatang tiang tegak! 28 dan sebatang pokok B! yang terletak di

atas satah mengufuk. Sebuah laying%layang diikat pada tiang itu di 2 . Du+ung laying%

layang itu tersangkut pada puncak pokok . Sudut dongakan B dari 2 ialah ,( ( .

*iagram 9

7alculate the height - in m - o0 the tree 0rom the horizontal plane . Ditung tinggi ! dalam m ! pokok itu dari satah mengufuk .

38.#%

B 41.#%

7 4#.9$* 48.9$

1$ >n *iagram 1! - 28 and ST are t;o ertical poles on a horizontal plane. 5alam a+ah '( ! 28 dan ST ialah dua batang tiang tegak yang terletak pada satah

mengufuk .

 

"tate the angle o0 depression o0 point 8 0rom point S  . 7yatakan sudut tunduk titik 8 dari titik S .

A   8S2 ∠

B   8ST ∠

C   S82 ∠

!   S8T ∠

h // h bl

*

+  

 B 

8

 2 

E

Kite

$! m

3 m

*iagram 1!

 2 

 

8 T 

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SULIT 1449/1

1% he bearing o0 to;n 0rom to;n A is !%#o.

?ind the bearing o0 to;n A 0rom to;n . earing andar 2 dari andar 8 ialah (/,o.

Cari bearing bandar 8 dari bandar 2.

A 1$#o

B 19#o

C 2##o 

! 28#o

18 *iagram 11 sho;s the location o0 point D  on the sur0ace o0 the earth ;ith E as the

centre o0 the earth . a+ah ''!menun+ukkan kedudukan titik D pada permukaan bumi dengan ; sebagai pusat bumi.

  *iagram 11

 K is a point on the sur0ace o0 the earth such that  DK is a diameter o0 the earth ."tate the location o0 point K 

  K ialah titik pada permukaan bumi dengan keadaan DK ialah diameter bumi .

 7yatakan kedudukan titik K .

  A   ( 3! !  7  - 11# ! :  '

B  ( 3! ! S  - 11# ! :  '

  C  ( $! !  7  - $# !  B  '

! ( $! ! S  - $# !  B  '

19 3 6 ( 6 2 ' J 4 ( 3 6 2 ' +

 A  3 3 2 J $ 3  2

 B  3 3 2 J $ 3  J 8

 C  3 3 2 J 12 3  J $

 !  3 3 2 J 12 3  4

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11#°:  

reen;ich ,eridian 

3!o

 

=uator 

 D • 

 N 

 S 

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SULIT 1449/1

2! =6pressmn

n

m   1#

%#

#

1   −−  +

A mn

n

3

12   −

Bmn

n

3

12   −−

Cmn

n

1#

4#  −−

!mn

n

1#

11!   −

21 ien -32

12k 

n

n=

+−

 e6press n  in the o0 k .

   5iberi -3212 k 

nn =+−

  ungkapkan n dalam sebutan k  

A2

1$

32   

  

 +

−=

k n  

B2

1$

32   

  

 −

+=

k n

C2

23

1$   

  

 +−

=k 

k n

!2

32

1$  

 

 

 

 −+

=k 

k n

22 ien ( )   k k  423

1=− - 0ind the alue o0 k .

 5iberi  ( )   k k  423

1=−  - carikan nilai k.

A1#

2

B 13

2

C11

2

!9

2

2 "impli0& 32#

41!

   

  

×

 pk 

k  pk 

.

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SULIT 1449/1

ermudahkan. 32#

41!

   

  

×

 pk 

k  pk 

A   #3  pk  −

B

  #4  pk  −

C   41!  pk  −

!   411  pk  −  

24 ien 3   28=n

m

 p  - state the alues o0  p - m  and n  .

*iberi 3   28=n

m

 p - n&atakan nilai bagi  p - m - dan n .

A

B

C

!

2& ?ind the solution o0  3 3   23#   <− .7ari pen&elesaian bagi  3 3   23#   <−

A  3  L 1

B  3 M 1

C  3  L J #

! 6 M J #

2' *iagram 12 is an incomplete bar chart representing the number o0 children in a

group o0 0amilies in a housing area . he bar representing the 0amilies that hae 0our

childrens is not sho;n . a+ah 12 ialah sebuah carta palang yang tidak lengkap mewakili bilangan anak dalam keluarga di

 suatu kawasan perumahan . 2alang yang mewakili keluarga yang mempunyai empat orang anaktidak ditun+ukkan .

h // h bl

 p m n

8 2 3

8 3 2

2 3 8

3 2 8

   I  u

  m   b  e  r  o   0   0  a  m   i   l   i  e  s

      i   l  a  n  g  a  n   k  e   l  u  a  r  g  a

$!

#!

4!

3!

2!

8!

%!

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SULIT 1449/1

A

B

C

!

0 >t is gien that set *  + O - P . list all the subsets o0 the set  *  .

 5iberi bahawa set * > O - P . Senaraikan semua subset bagi set * 

A - . / - .

B O P - O P - O - P

C O P - O P - O P

! O P - O P - O P - O - P

1 *iagram 14 is a enn diagram sho;ing the uniersal set Q

 5iberi set A set M dan set 7 dengan keadaan ∪  M > dan M ⊂  G ∩  7H. Fambar ra+ah 9enn

manakah yang mewakili keadaan di atas@

h // h bl

 y

 3E

−2

−2

 y

 3E

−2

2

 y

 3E

−1

−2

 y

 3E

−22

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SULIT 1449/1

A  ∩ A

B   ∪ A

C ∪ A

! ∩ A

2 *iagram 1# sho;s t;o straight lines- A and <- dra;n on a 7artesian plane. Alies

on the &5 a6is.

   a+ah ', menun+ukkan dua gris lurus! 28 dan 2! dilukis di atas satah Cartesan. 8

  terletak di atas paksi%y .

 

ien 'A + 2E<- 0ind the gradient o0 A.

 5iberi ;8 > );! cari kecerunan bagi 28

A92

B1#

4

C4

1#

!2

33 *iagram 1$ sho;s a straight line Kl on a 7artesian plane. a+ah '- menun+ukkan garis lurus K pada suatu satah Cartesan.

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 y

 3E<(−3-!'

(59- 4'A

 

;

  K ( !- p'

R

2 3 3 y > $

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SULIT 1449/1

3$ bo6 contains 3# blue to;els and some ;hite to;els . to;el is chosen at random

0rom the bo6 . he probabilit& o0 choosing a blue to;el is%

# . ?ind the number o0

;hite to;els in the bo6 .

Sebuah kotak mengandungi #, helai tuala biru dan beberapa helai tuala putih . Sehelai tuala dipilih

 secara rawak daripada kotak itu .Kebarangkalian sehelai tuala biru dipilih ialah%

#. Cari bilangan

tuala putih dalam kotak itu .

1!

B 14

7 21

* 2#

3% >t is gien that y aries directl& ;ith 6 and  y + 4 ;hen 6 + 12 . 7alculate the

alue o0 & ;hen 3  + 21 . 5iberi bahawa y berubah secara langsung dengan 3 dan y > $ apabila 3 > ') .Ditung nilai y

apabila 3 > )' ..

1$

B%

1% 

7 %

* $3

38 able 1 sho;s some alues o0 the ariables  3 and  y .

   *adual 1  menun+ukkan beberapa nilai bagi pembolehubah 3 dan y .

  able 1 

?ind the relation bet;een  y  and  3 .Cari hubungan antara y dengan 3 .

& S 6  J 3 

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4

9

4

4

1

31 2

4 1

 3

 y

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SULIT 1449/1

B & S 6  J 2 

7 & S 6  J 1 

* & S 6  J 2

1

39   ( ) ( ) =−−+ #%24312

  ( )313!

B   ( )11!!   −

7   ( )11!4   −−

*   ( )13134   −−

4!   =   

  

 −

+   

  

 −

−−  

 

  

 −   132

#1!3

2!4

31%2

413

!2#

     

  

 −

−%41

242

 

B    

  

 −

−341

222 

7      

  

 −

−31!1

939

*      

  

 −

−111!1

9%9

SIJIL PELAJARAN MALAYSIA (U)2009

,N=,>7",N=,>7"

=< 1 1449/1=< 1 1449/1

I"@=< I"@=< 

h // h bl

EN! % UESTIN PAPER 

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SULIT 1449/1

1 D   11 A   21 D   31 B

2 B   12 C   22 B   32 A

3 C   13 C   23 C   33 C

4 D   14 C   24 A   34 A

5 B   15 D   25 B   35 C

6 C   16 A   26 A   36 B

7 A   17 C   27 B   37 C

8 B   18 D   28 C   38 B

9 C   19 B   29 A   39 A

10 D   20 A   30 D   40 D

 

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LEMBAGA PEPERIKSAAN MALAYSIA

KEMENTERIAN PELAJARAN MALAYSIA

MATHEMATICS

Paper 2

Two hours and thirty minutes

DO NOT OPEN THIS QUESTION PAPER UNTIL YOU ARE TOLD TO DO SO

 JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU 

This question !e" #onsists o$ %& "inte' !(es.

)**+,%

M!the-!ti#s

P!e" %

Jun

%..+

1. 1. This question paper onsist t!o setion" Se#tion A an# Se#tion B.

VV  Kertas soa$an ini %en&an#un&i #ua 'aha&ian " Bahagian A

dan Bahagian B

2.  Ans!er a$$ question in Se#tion A an# four   questions (ro%

Se#tion B/

2. 2. This question paper is 'i$in&ua$.

). *rite +our ans!ers in the spaes pro,i#e# in the question paper.

-. *orin& step %ust 'e !ritten $ear$+.

/. Dia&ra% &i,en is not aor#in& to sa$e un$ess state#.

0. ars (or eah question are &i,en in 'raet.

2. A $ist o( (or%u$ae is &i,en in pa&es 3 an# ).

4. Non pro&ra%%a'$e sienti(i a$u$ator is a$$o!e#.

5 This question paper %ust 'e han# up at the en# o( the e6a%.

Section Question Full

mark 

Marks

obtained

A

1 3

2

3

3

! !

" !

# "

$

% "

1& "

11 "

B

12 12

13 12

1 12

1! 12

1" 12

Total

 '(M) *++++++++++++.

F,-M* +++++++

SIJIL PELAJARAN MALAYSIA

0ULANGAN1 %..+

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SULIT 2 )**+,%

MATHEMATICAL 2ORMULAE

The (o$$o!in& (or%u$ae %a+ 'e he$p(u$ in ans!erin& the questions. The s+%'o$s &i,en are the

ones o%%on$+ use#..

RELATIONS1   n%n% aaa   +=×

2   n%n% aaa  −=÷

3 %nn% aa   =./

     

  

 −

−−

=−

a

'# 

'a#  A

11

!( )S n An A 7  ././   =

"   ./1.0/   A 7  A 7    −=

# 2

12

2

12 ././istance   + + 6 6   −+−=

$ Midpoint     

  

    ++=

2

2./ 2121   + + 6 6

 + 6

% (era4e speed 5 takentime

 traelleddistance

 

1& Mean 5datao6 number

datao6 sum

 

11 Means6re7uencieo6 sum

6re7uency.marko6/classsum   ×=

12 Pytha4oras Theorem222

'a   +=

1312

12

 6 6

 + +%

−=

1erceptint

erceptint

−−

−= 6

 +%

SHAPES AND SPACE

)**+,% 6Lih!t se7e8!h

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SULIT  )**+,%

1 (rea o6 trape8ium 52

1× sum o6 parallel sides × hei4ht

2 9ircum6erence o6 circle 5 r #    π  π   2=

3 (rea o6 circle 5 2r π  

9ured sur6ace area o6 cylinder 5   rhπ  2

! Sur6ace area o6 sphere 5 2 r π  

" Volume o6 ri4ht prism 5 cross sectional area × len4th

# Volume o6 cylinder 5 hr 2

π   

$ Volume o6 cone 5 hr 2

3

1π  

% Volume o6 sphere 53

3

r π  

1& Volume o6 ri4ht pyramid 5 ×3

1 base area × hei4ht

11 Sum o6 interior an4les o6 a poly4on 5 /n : 2 × 1$&;

12o

3"&

center atsubtendedan4lecircleo6 ncecircum6ere

len4tharc =

13o

3"&

centreatsubtendedan4le

circleo6 area

sector o6 area=

1 Scale 6actor k 5 7A

 7A0

1! (rea o6 ima4e 5 k  2 × area o6 ob<ect

)**+,% 9 2&&$ = k 9i PS>PM ?Lih!t se7e8!h

3

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SULIT  )**+,%

Se#tion A

?!2 %ars @

 Ans!er !88 questions in this setion.

) The Venn dia4ram in the answer space shows sets A8 B and 9 . Aien the uniersal

set B 5 A  ∪   B ∪  9 .

Ga%'ar ra:ah ;enn #i ruan& :a!apan %enun:uan set A8B #an 9. Di'eri set se%esta

< = A ∪  B ∪  9.

,n the dia4ram proided in the answer spaces shade 7a#a ra:ah #i ruan& :a!apan8 $orean

/a  A 0

 b  A ∩  / B ∪  9  . 

?3 %ars@

 Ans!er "

 

a

/b

)**+,% 9 2&&$ = k 9i PS>PM ?Lih!t se7e8!h

 B

 A

 B

 A

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SULIT  )**+,%

% Sole the 7uadratic e7uation *Se$esaian persa%aan ua#ratit"

( ) p p   −= 322 2

? %ars@

 Ans!er  *

: 9alculate the alue o6  6  and the alue o6 +  that satis6y the 6ollowin4 simultaneous

linear e7uations   Hitun& ni$ai 6 #an ni$ai + +an& %e%uasan persa%aan $inear serenta 'eriut

132   =+  + 6

%   =− + 6

 ? %ars@

)**+,% 9 2&&$ = k 9i PS>PM ?Lih!t se7e8!h

!

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SULIT  )**+,%

*  ia4ram shows a ri4ht prism with a rectan4le base  KLN  on a hori8ontal plane. The ri4htC

an4led trian4le L> is the uni6orm crossCsection o6 the prism.

 Ra:ah %enun:uan se'uah pris%a te&a #en&an.tTapa se&i e%pat tepat KLN #i atas satah

%en&u(u. Se& iti&a 'ersu#ut te&a L> a#a$ah eratan rentas sera&a% pris%a itu.

a. 'ame the an4le between the plane 7R   and the plane  L>.   Na%aan su#ut #i antara satah 7R #en&an satah L>

 b. 9alculate the an4le between the plane P-M and the plane DMQ Hitun& su#ut #i antara satah 7R #en&an satah L>

?3 %ars@

 Ans!er  *

)**+,% 9 2&&$ = k 9i PS>PM ?Lih!t se7e8!h

"

ia4ram 1

 L

 7 >

" cm

! cm

cm

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SULIT  )**+,%

! /a State whether the 6ollowin4 statement is true or 6alse. N+ataan sa%a a#a pern+ataan 'eriut a#a$ah 'enar atau pa$su.

/b Erite down two implications based on the 6ollowin4 statements *Tu$is #ua i%p$iasi 'er#asaran pern+ataan 'eriut "

 

/c Make s 4eneral conclusion by induction 6or the se7uence o6 numbers

! $ 11 1 +.which 6ollows the 6ollowin4 pattern * Buat satu esi%pu$an u%u% seara aruhan untu urutan no%'or /8481181-8.. +an&

%en&iut po$a 'eriut "

! 5 3 /1 2

$ 5 3 /2 2

11 5 3 /3 2

1 5 3 / 2

. ?" %ars@

 Ans!er  *

/a +++++++++++++++++++++++++..

/b Gmplication 1 H I%p$iasi 1

+++++++++++++++++++++++++..

Gmplication 2 H I%p$iasi 3

+++++++++++++++++++++++++..

/c +++++++++++++++++++++++++..

+++++++++++++++++++++++++..

)**+,% 9 2&&$ = k 9i PS>PM ?Lih!t se7e8!h

#

(ll trian4le hae sides o6 e7ual len4thSe%ua se&i ti&a %e%pun+ai sisi?sisi +an& sa%a pan:an& 

% : 3 I & i6 and only i6 % I 3% @ ) :ia #an han+a :ia % )

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SULIT  )**+,%

$ ia4ram $ shows a solid cuboid. ( hal6Ccone solid (K9 is taken out 6rom the

cuboid.

 Ra:ah 4 %enun:uan se'uah pepe:a$ 'er'entu u'oi#. Se'uah pepe:a$ 'er'entu separuh on

#ie$uaran #aripa#a u'oi#$ itu.

  ia4ram $

Lsin4 π 5#

22 calculate the olume in cm3 o6 the remainin4 solid.

Aie the answer correct to two decimal places .

 en&&unaan π  =#

22 8 hitun&an isipa#u8 #a$a% %) 8 pepe:a$ +an& tin&&a$.

 Beri :a!apan 'etu$ epa#a #ua te%pat perpu$uhan .

? %ars@

 Ans!er *

)**+,% 9 2&&$ = k 9i PS>PM ?Lih!t se7e8!h

1&

 D

% cm9 

 B

 A

# cm

! cm

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SULIT  )**+,%

% ia4ram % shows two boJes P and Q . KoJ P contains 6our cards labeled with letters

and boJ Q contains three cards labeled with numbers. Ra:ah 5 %enun:uan #ua ota 8 7 #an > . Kota 7 %en&an#un&i e%pat a# 'er$a'e$ #en&an huru(

#an Kota > %en&an#un&i ti&a a# 'er$a'e$ #en&an no%'or.

Two cards are picked at random a card 6rom boJ 7  and another card 6rom boJ > . . Dua eepin& a# #ipi$ih seara ra!a 8 satu a# #aripa#a ota 7 #an satu $a&i #aripa#a ota >.

 a Dist the sample space and the outcomes o6 the eents .

Senaraian ruan& sa%p$e #an esu#ahan peristi!a .

 b =ence 6ind the probability thatSeterusn+a'8 ari e'aran&a$ian 'aha!a

/i a card labeled with letter ) and a card labelled with an een number

are picked satu a# +an& 'er$a'e$ #en&an huru( E #an satu a# +an& 'er$a'e$ #en&an no%'or

 &enap #ipi$ih

/ii a card lebelled with letter ) or a card labelled with an een number are picked satu a# +an& 'er$a'e$ #en&an huru( E atau satu a# +an& 'er$a'e$ #en&an no%'or

 &enap #ipi$ih

  ?! %ars @

 Ans!er *

/a

/b /i

  /ii

)**+,% 9 2&&$ = k 9i PS>PM ?Lih!t se7e8!h

11

K ) S T " #

KoJ P KoJ Qia4ram %

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SULIT  )**+,%

). Gn dia4ram 1& ,Q-S is a s7uare . O7>S is a sector o6 a circle with center O .. Da$a% ra:ah 1 8 O>RS ia$ah se&i e%pat sa%a . O7>S ia$ah setor 'a&i se'uah 'u$atan 'erpusat #i O

Lsin4 π  5#

22 and 4ie the answer correct to two decimal places . 9alculate

 Den&an %en&&unaan π  5 #

22 #an 'eri :a!apan 'etu$ epa#a #ua te%pat perpu$uhan . Hhitun&

/a the perimeter in cm o6 the whole dia4ram    peri%eter 8 #a$a% % 8 se$uruh ra:ah 8

/b the area in cm 2  o6 the coloured re4ions .  $uas 8 #a$a% cm 2 . a!asan +an& 'er!arna .

? " %ars @

 Ans!er  *

/a

/b

)**+,% 9 2&&$ = k 9i PS>PM ?Lih!t se7e8!h

12

O

S  R

>

 7 

3&&

1 cm

ia4ram 1&

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SULIT  )**+,%

11 ia4ram 11 shows the speedCtime 4raph 6or the moement o6 a particle 6or a period o6

1! seconds. Ra:ah 11 %enun:uan &ra( $a:u @ %asa per&eraan se'uah Carah #a$a% %asa 1/ saat.

  ia4ram 11

 /a state the uni6orm speed in ms C1  o6 the particle .   N+ataan $a:u sera&a% 8 #a$a% %s ?1? 8 Carah itu .

/b calculate the rate o6 chan4e in speed in %s−2  in the 6irst ! seconds.

 Hitun& a#ar peru'ahan $a:u8 #a$a% %s− 3

#a$a% te%poh/ saat +an& perta%a . 

/c calculate the alue o6 t  i6 the distance traeled in the last 1& seconds is 1& m. Hitun& ni$ai t 8 :ia :ara +an& #i$a$ui #a$a% te%poh 1& saat terahir itu ia$ah 1- % .

? " %ars @

(nswer *

/a

/b

/c

)**+,% 9 2&&$ = k 9i PS>PM ?Lih!t se7e8!h

13

Speed H La:u  / ms −1 

Time H asa / s& ! t 

2&

12

1!

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SULIT  )**+,%

Se#tion B

?$ %ars@

(nswer any $ou" 7uestions 6rom this section.

 Ja!a' %ana?%ana empat  soa$an #aripa#a 'aha&ian ini.

)%  /a Table 12 in the answer space shows the alues o6 J and o6 + 6or the e7uation

 +  5 2 6 2  3 6  −  1& . Find the alue o6 r   and o6  s   Ja#ua$1 3 #i ruan& :a!apan %enun:uan ni$a?ni$ai 6 #an + persa%aan +  5 2 6 2  3 6  −  1&

9ari ni$ai 'a&i r #an s  ?2 %ars @

/b  or this part o( question8 use the &raph paper pro,i#e# on pa&e 21 . ou %a+ 

use a ($e6i'$e ur,e ru$e.

Untu eraian soa$an ini8 &unaan ertas &ra( +an& #ise#iaan pa#a ha$a%an 21 .An#a'o$eh %en&&unaan pe%'aris ($esi'e$ .

Ky usin4 a scale o6 2 cm to 1 unit on the 6 : aJis and 2 cm to ! units on

 + :aJis draw the 4raph the 4raph o6 +  5 2 6 2  3 6  −  1& 6or − ≤  6 ≤ 3.en&an %en&&unaan sa$a 3 % epa#a 1 unit pa#a pasi?6 #an 3 % epa#a / unit pa#a

 pasi?+8 $uisan &ra( +  5 2 6 2  3 6  −  1& 'a&i ni$ai 6 #a$a% :u$at −   ≤    6 ≤   3.

  ? %ars@

/c Lsin4 the 4raph drawn in 12 /' 6ind en&&unaan &ra( +an& #i$uis #i 12 F' 8 arian

/i the alue o6 + when 6 5 −1.!

ni$ai + apa'i$a 6 = − 1.!

/ii the alues o6 6 when + 5 &

ni$a?ni$ai 6 apa'i$a + = & ?3 %ars@

/d raw suitable strai4ht line on your 4raph to 6ind alue o6 6 which satis6ies the

e7uation &!$2   2=−+   6 6   6or : ≤  6 ≤ 3.

State the alue o6 6. Luisan satu &aris $urus +an& sesuai pa#a &ra( an#a untu %enari ni$ai 6 +an&

%e%uasan persa%aan &!$2   2=−+   6 6  'a&i @ - ≤   6 ≤   ).

 N+ataan ni$ai 6 itu.

  ?3 %ars@

)**+,% 9 2&&$ = k 9i PS>PM ?Lih!t se7e8!h

1

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SULIT  )**+,%

 Ans!er  *

  /a

 6   −    −3   −2   −1 & 1 2 2.! 3

 + 1& r    −$   −11   −1&  s 1& 1#

Table 12

r   5 ++++++++.  s 5 ++++++++.

/b -e6er 4raph on pa4e 21. Ru:u &ra( pa#a ha$a%an 31.

/c /i  + 5 +++++++++++++.

/i  6 5 +++++++++++++..

F# 6 5 +++++++++++++

)**+,% 9 2&&$ = k 9i PS>PM ?Lih!t se7e8!h

1!

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SULIT  )**+,%

13 ia4ram 13.1 shows the point / − 1 and the strai4ht line  +  5 −  6 drawn

on a 9artesian plane . Ra:ah 13.1 %enun:uan titi F- 8 −  1 #an &aris $urus +  5 −  6 #i$uis pa#a suatu satah 9artesan

/a Trans6ormation T  is a translation     

  −!

1. Trans6ormation R is a re6lection in

the strai4ht line 6 +   −=

. State the coordinates o6 the ima4e o6 point / −

 1 under the 6ollowin4 trans6ormations *

   7en:e$%aan T ia$ah satu trans$asi    

  −

!

1 7en:e$%aan 7 ia$ah satu pantu$an pa#a &aris $urus

 6 +   −=  8 N+ataan oor#inat i%e: 'a&i titi F-8− 1) #i'a!ah pen:e$%aan +an& 'eriut .

 

/i T 

/ii TR.

?3 %ars@

 Ans!er  *

/a /i

/ii

)**+,% 9 2&&$ = k 9i PS>PM ?Lih!t se7e8!h

1#

 +

O % *2−

2

2−

ia4ram 13.1 

"

y 5 − J

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SULIT  )**+,%

/b ia4ram 13.2 shows three 7uadrilaterals KLN  7>  and HJG drawn on a

s7uare 4rid.   Ra:ah 1).3 %enun:uan ti&a sisi e%pat KLN 8 7> #an HJG +an& #i$uis pa#a &ri#

 se&i e%pat sa%a .

/i  HJG is the ima4e o6 KLN  under the combined trans6ormations <U . escribe in

6ull the trans6ormation * HJG ia$ah i%e: 'a&i KLN #i'a!ah &a'un&an pen:e$%aan VL. Huraian se$en&apn+a

 pen:e$%aan

/a L

 

/b E

/ii Gt is 4ien that 7uadrilateral >DM' represents a re4ion o6 2 m 2 . 9alculate the area

in m 2  o6 the re4ion represented by the coloured re4ion .   Di'eri 'aha!a sisi e%pat KLN %e!ai$i suatu a!asan +an& %e%pun+ai $uas 2 m  3 . Hitun&

$uas 8 #a$a% m 3 8 a!asan +an& %e!ai$i o$eh a!asan +an& 'er!arna .

?% %ars@

 Ans!er  *

/b/i /a

/b

  /ii

)**+,% 9 2&&$ = k 9i PS>PM ?Lih!t se7e8!h

1$

 H 

 J 

 S  L

ia4ram 13.2

 P 

 ! 

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SULIT  )**+,%

)*  Table 1.1 shows the 6re7uency distribution o6 marks obtained by a 4roup o6 $

students in a test. Ja#ua$ 1-.1 %enun:uan ta'uran eerapan %arah +an& #ipero$ehi seu%pu$an -4 oran& %uri#

#a$a% satu u:ian.

Marks Fre7uency

"! : "% 2

#& : # "

#! : #% $

$& : $ 12

$! : $% 1&

%& : % #

%! : %% 3

  Table 1.1

/a Kased on Table 1.1 complete Table 1.2 in the answer space . ?1 %ar @   Ber#asaran Ja#ua$ 1-.1 $en&apan Ja#ua$ 1-.3 #i ruan& :a!apan..

/b 9alculate the estimated mean mark o6 the 4roup o6 the students. Hitun&an %in an&&aran %arah 'a&i u%pu$an %uri# itu.

  ?3 %ars@

/b For this part o6 the 7uestion use the 4raph paper proided on pa4e 2%.Untu eraian soa$an ini8 &unaan ertas &ra( +an& #ise#iaan #i ha$a%an 2%.

Lsin4 the scale o6 2 cm to ! marks on the hori8ontal aJis and 2 cm to !

students on the ertical aJis draw an o4ie 6or the data. Den&an %en&&unaan sa$a 3 % epa#a /%arah pa#a pasi %en&u(u #an 3 % epa#a /

 %uri# pa#a pasi %enan,an&8 $uisan satu o&i( 'a&i #ata terse'ut.

? %ars@

/d Lsin4 the o4ie drawn in 1/c 

%en&&unaan o&i( +an& #i$uis #i 1 /c

/i 6ind the third 7uartileari uarti$ eti&a 8

/ii state one in6ormation re4ardin4 the third 7uartile .

n+ataan satu %a$u%at tentan& uarti$ eti&a . ?2 %ars@

 

)**+,% 9 2&&$ = k 9i PS>PM ?Lih!t se7e8!h

1%

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SULIT  )**+,%

/a ia4ram 1!.1 shows a solid ri4ht prism with a rectan4ular base ABHG on a

hori8ontal plane . The sur6ace AB9DE  is the uni6orm crossCsection o6 the prism . AE  

and B9  are ertical ed4es . -ectan4le EDK is a hori8ontal plane and rectan4le

 D9JK   is an inclined plane . Ra:ah 1!.1 %enun:uan se'uah pepe:a$ 'er'entu pris%a te&a #en&an tapa se&i e%pat tepat ABHG

ter$eta pa#a suatu satah %en&u(u . 7er%uaan AB9DE ia$ah eratin rentas sera&a% pris%a itu .Tepi AE #an B9 a#a$ah te&a . Se&i e%pat tepat EDK ia$ah satah %en&u(u #an se&i e%pat tepat

 D9JK ia$ah satah on#on& .

 

ia4ram 1!.1

 

raw 6ull scale the plan o6 the solid.

 Luis #en&an sa$a penuh 8 pe$an pepe:a$ itu. ?3 %ars@

 Ans!er *

/a

/b (nother solid ri4ht prism with trape8ium (ALV as the uni6orm crossCsection is

 <oined to the prism in ia4ram 1!.1 at the ertical plane (-SA . The composite solid

)**+,% 9 2&&$ = k 9i PS>PM ?Lih!t se7e8!h

22

 A

  

 E

 D 9

 B

 K J

 H

1& cm

! cm

3 cm

# cm

! cm

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SULIT  )**+,%

is as shown in ia4ram 1!.2 . The base (K=ALV lies on a hori8ontal plane . VQ

and LP are ertical ed4es and ∠ (AL 5 ∠  ALV 5 %& &

Se'uah pepe:a$ $ain 'er'entu pris%a te&a #en&an trapeCiu% AGU; se'a&ai eratin rentas

 sera&a%n+a #iantu%an epa#a pris%a #a$a% Ra:ah 1!.1  pa#a satah %enanan& ARSG .

Ga'un&an pepe:a$ a#a$ah seperti +an& #itun:uan #a$a% Ra:ah 1!.2 . Tapa ABHGU; ter$eta pa#a

 suatu saatah %en&u(u . Tepi ;> #an U7 a#a$ah te&a #an ∠ AGU = ∠ GU; = %& &

ia4ram 1!.2

raw 6ull scale Luis #en&an sa$a penuh8

/i the eleation o6 the composite solid on a ertical plane parallel to AB as iewed

6rom   .#on&aan&a'un&an pepe:a$ itu pa#a satah %enanan& +an& se$ari #en&an AB se'a&ai%ana

#i$ihat #ari .

? %ars@/ii the eleation o6 the composite solid on a ertical plane parallel to U;  as iewed

6rom  .#on&aan &a'un&an pepe:a$ itu pa#a satah %enanan& +an& se$ari #en&an U; se'a&ai%ana

#i$ihat #ari .

  ?! %ars@

 Ans!er * 

/b /i /ii

)**+,% 9 2&&$ = k 9i PS>PM ?Lih!t se7e8!h

23

 A

  

 E

 D 9

 B

 K J

 H

! cm

3 cm

cm

! cm3 cm

  

G

3 cm

    

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SULIT  )**+,%

): ia4ram 1" shows the locations o6 point 7  / !$ & S 1&& & ) and point V /!$ & ' 3& &

) on the sur6ace o6 the earth . , is the centre o6 the earth .  7> is the diameter o6 the

common parallel o6 latitude !$ & S .

 Ra:ah 10 %enun:uan e#u#uan titi 7  F /4  U 8 1 T #an titi ; F/4 S 8 ) T pa#a

 per%uaan'u%i 8 O ia$ah pusat 'u%i . 7> ia$ah #ia%eter se$arian $atitu#e sepun+a /4

 S  .

/ a State the lon4itude o6 >   N+ataan $on&itu#e 'a&i >.

? 2 %ars @

/b 9alculate the shortest distance in nautical miles 6rom 7 to > measured alon4

the sur6ace o6 the earth .   Hitun& :ara terpen#e88#a$a% 'atu nautia8 8#ari 7 e > #iuur #isepan:an& per%uaan

'u%i .

? 2 %ars@

/c 9alculate the distance in nautical mile 6rom V due east to P measured alon4the common parallel o6 latitude .hitun& :ara 8 #a$a% 'atu nautia 8 #ari ; arah e ti%ur e 7 #iuur sepan:an& se$arian

$atitu#e sepun+a .

? 3 %ars@

/d Point R lies 3%"& nautical miles due north o6  7  . (n aeroplane took o66 6rom

 7  and 6lew due north to R . The 6li4ht took $ hours .Titi R ter$eta )50 'atu nautia e utara 7 . Se'uah apa$ ter'an& 'er$epas #ari 7 arah e

utara e R . Te%poh pener'an&an ia$ah $ :a% .

/i 9alculate the latitude o6 R Hitun& $atitu#e 'a&i R .

/ii 9alculate the aera4e speed in knot o6 the aeroplane 6rom 7  to R . Hitun& purata $a:u 8 #a$a% not 8 apa$ ter'an& itu #ari 7 e R .

?! %ars@

)**+,% 9 2&&$ = k 9i PS>PM ?Lih!t se7e8!h

2

 7 

NN

N

ia4ram 1"

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PEPERIKSAAN SPM ( ULANGAN ) 2009

MARKING SCHEME

MMAATTHHEEMMAATTIICCSS PPAAPPEER R  22 (( 11444499//22 )) 

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MARKAH MAKSIMUM BAGI KERTAS INI : 100 MARKAH

No MARKING SCHEME Mark

1 (a)

(b)

 Note:

 B ∪   C correctly shaded, 1 mark

1

2

3

2 2 p2 + 5 p – 3 = 0

(2 p – 1)( p + 3) = 0

3,

2

1−==  p p  

1

1

1,1

4

327312   =−  y x  or 264   =+  y x  or

2

31  y x

−=   or 94   −=  x y  or equivalent

77   =−  y  or 2814   = x

2= x , 1−= y

OR

⎟⎟ ⎠

 ⎞⎜⎜⎝ 

⎛ ⎟⎟ ⎠

 ⎞⎜⎜⎝ 

⎛ ⎟⎟ ⎠

 ⎞⎜⎜⎝ 

⎛ 

−−

−−=

9

1

24

31

)4)(3()1)(2(

1

 y

 x  2

2= x   11−= y   1

 Note : as final answer, award 1 mark⎟⎟ ⎠

 ⎞⎜⎜⎝ 

⎛ ⎟⎟ ⎠

 ⎞⎜⎜⎝ 

⎛ 

−=

1

2

 y

 x

1

1

1,

1

4

C  B

 A

 AC 

 B

 AC 

 B

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4 (a) ∠ PMQ or ∠ QMP

(b) tan θ =4

56.31° or 56° 19' or 56.3 0r 56° 18'

1

1

1

3

5(a)

5(b)

5(c)

False // Palsu

If m – 3 > 0 then m > 3  //

Jika m – 3 > 0 maka m > 3

If m > 3  then m – 3 > 0 //

Jika m > 3 maka m – 3 > 0

3n + 2, n = 1,2,3,4,...

 Note : 3n + 2 only, award 1 mark

1

1

1

2

5

6 (a)

6(b)

2

1=

PQm  

2

1

4

10=

 x

 y  or c+= )4(

2

110

.

82

1+=  x y   or equivalent

82

10   +=  x  

 –16

.

1

1

1

1

1 5

7 (a)

7(b)

⎟⎟⎟⎟

 ⎠

 ⎞

⎜⎜⎜⎜

⎝ 

⎛ 

3

8

3

73

5

3

4

 

 Note: 1. Accept ⎟⎟

 ⎠

 ⎞⎜⎜

⎝ 

⎛ 

87

54

3

1  for 2 marks

2. ⎟⎟ ⎠

 ⎞⎜⎜⎝ 

⎛ 

−−− 87

54

)7)(5()4)(8(

1  or ⎟⎟

 ⎠

 ⎞⎜⎜⎝ 

⎛ 

87

54

3

award 1 mark

⎟⎟ ⎠

 ⎞⎜⎜⎝ 

⎛ =⎟⎟

 ⎠

 ⎞⎜⎜⎝ 

⎛ ⎟⎟ ⎠

 ⎞⎜⎜⎝ 

⎛ 

1

2

47

58

 y

 x 

2

1 6

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⎟⎟ ⎠

 ⎞⎜⎜⎝ 

⎛ ⎟⎟ ⎠

 ⎞⎜⎜⎝ 

⎛ 

−−−=⎟⎟

 ⎠

 ⎞⎜⎜⎝ 

⎛ 

1

2

87

54

)7)(5()4)(8(

1

 y

 x 

 x = –1

 y = –2

1

1

1

8 5 × 7 × 9

92

2

7

7

22

3

1

2

1×⎟

 ⎠

 ⎞⎜⎝ 

⎛ ×××  

5 × 7 × 9 – 92

2732⎟ ⎠

⎜⎝ 

72211×

 ⎞⎛ ×××  

4

1029  or

4

1257   or 257.25 – 257.30

1

1

1

1 4

9(a)

(b) (i)

(ii)

{(B, 4), (B, 6), (B, 7), (E, 4), (E, 6), (E, 7), (S, 4), (S, 6), (S, 7), (T, 4),

(T, 6), (T, 7)}

 Notes : 1. Accept 8 correct listings for 1 mark

{(E, 4), (E, 6)}

12

2  or

6

{(E, 4), (E, 6), (E, 7), (B, 4), (B, 6), (S, 4), (S, 6), (T, 4), (T, 6)}

12

9  or

4

2

1

1

1

1

6

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10(a)

10(b)

147

222

360

30×××  

14141414147

222

360

30++++×××   or equivalent

3

190

  or 3

1

63 or 63.28 – 63.33

14147

22

360

90×××   or 1414

7

22

360

30×××   or 1414

7

22

360

120×××  

14 × 14 + 147

222

360

30×××   – 1414

7

22

360

90×××   or equivalent

3

280  or

3

193 or 93.28 – 93.47

1

1

1

1

1

1

6

1

2

3

11(a)

(b)

(c)

20

05

1220

−  or equivalent

6.15

31

5

8or or   

14020)15(21)5(20   =×−+− t t    or

14020)]515()5[(2

1=×−+−t   

t = 9

1

1

1

2

1

6

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12(a)

12(b)

12(c)

 – 1

 – 5

Both axes with uniform scales and in the right directions for – 4 ≤  x ≤ 3

and – 11 ≤  y ≤ 17

All 7 points and *2 points correctly plotted or curve passes through all the points for – 4 ≤  x ≤ 3 and – 11 ≤  y ≤ 17Smooth curves and continuous curve without any straight line and passes

all 9 correct points using the given scales for – 4 ≤  x ≤ 3 and – 11 ≤  y ≤ 17

(i) –10.5 < y < – 9.5

(ii) ,1.32.3   −≤≤−  x 7.15.1   ≤<  x  

Identify equation 155   +−=  x y   or 15510322   +−=−+  x x x

Straight line correctly drawn 155   +−=  x y1.20.2   ≤<  x  

1

1

1

2

1

1

1,1

1

1

1

12

13(a)

(b)

(i) ( 3, 4 )

(ii) ( 0, 1 )

(i) (a) U : Rotation

180°Centre M

(b) V  : Enlargement

Scale factor 2Centre M

ORU : Enlargement scale factor – 1 centre M

V : Enlargement scale factor 2 centre M

OR

U : Enlargement scale factor 2 centre x 

V : Rotation 180° centre y 

(ii) 24 × 22

  24 × 22 – 24

OR

18

24  or 72

18

24×  

1

2

3

3

1

1

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15 (a)

15(b) (i)

(ii)

3

4

5

12 

4 cm

2 cm3 cm

10cm

3 cm

5 cm

3cm

5 cm

3 cm 7 cm

2 cm

10 cm

4 cm

1 cm

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2

2

3

5

16(a)

16(b)

16(c)

16(d)

80o W

 Note : 80o or

oθ  W , give 1 mark

2 x ( 90 – 58 ) x 60 or equivalent

3840

( 100 – 30 ) x 60 x cos 58

 Note

( 100 – 30 ) or using cos 58 correctkly award 1 mark

2226

 

(i)60

3960  or 66

60

3960

 ~ 588 ° N

(ii)8

3960 

495 

2

1

1

2

1

1

1

1

1

1 12

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Graph for Question 12

x

20

−15

−20

15

10

5

−5

−10

4  x0−1−2−3 1 2 3−4

 y

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5

10

15

20

25

30

35

40

45

X

X

X

X

X

X

X

50