skema add maths trial spm 2013 penang k12 w

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MAJLIS PENGETUA SEKOLAH MALAYSIACAWANGAN PI]LAU PTNANG

MODUL LATIHAN BERFOKUS SPM 2013

ADD ITIONAL I\{ATHEIVIATIC S

KERTAS 1

1VIARK SCTTN'ME

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)a

ADDITIONAL MATHEMATICS PAPER I 2OI3

3472n

Question Solution and Mark Scheme SubMarlur

TotalMark

I (a)

(b)

64

f:*-)r' OR f(x)=tr'

I

I 2

2 (a)

(b)

7

1

81: l-4n--3

I

2 3

3 (a)

(b)

x+3

-30

B2:

BI

2-L=85

t(S1 :3

I

3 4

42.907 and - A.5734

- (-7) *B2:.

BI: 3x2

2(3)

-'lx-5 = 0

- 4(3)(-5)

3 3

s (a)

o)

P=-1, Q=L6

r=-1

)

I 3

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347211

6I

x < --3

or ,> I2

B2

BI (3x+r)(2x-3)>0

3 3

7-:

3

: 3n+ 5(n +2) -2n

: 33' or 3s(n+2)

B2

BI or 32"

3 3

I+ or t,-'{*) or i-lrl2, (tog, p-logrt)"H

Bl : logo p -logo5 or #

3 3

e (a)

o)

36

54

B1: +1- -

3

I

2 3

10 (a)

o)

1456

972

B2:

B1 :

l4s6 -

2b'-r

hb' - r)] or re =+(gf-'

) or a=4andr=3

I

3 4

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11 (a)

(b)

P:7

217

Br , +[zt:l

+ (r r - r)4]- f,frrr,

+ (4- r)41

OR

i?re)+(7-l)41

19+23+27+31 +35+39+43

I

2 3

12 (a)

o)

!' :-5x + lox

p = 2, q: 5 (both)

BZ i p:2 or q:5

Bl , ?-o --s Il-p {=-5(l)+10 0=-5p+10

t

3 4

13 (a)

o)

3

i6y+8x+7 =0

v-l= -*A+z)B1 . Z J

I

2 3

t4 48.19", 180", 31 1.81" / 48ol 1"180p, 31 l"4g'

B3 : 48.19o, 180" (both)

7BZ : cos 0 = a or cosd = -t or 48.19" 148" 1l' or 180"

3

Bl : cosa = 3(t-cos' e)-t

4 4

ls (a)

(b)

1.A47 rad

45.50

B2' ltd (z.ors)+loxuysin6oo

Br , *Af(z.ols) or ]trxulsin6oo

I

3 4

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347Zlt

16 (a)

(b)

(i)

3i_+4j

5

BI

I

2 3

t7 (a)

(b)

sI -81

t0 40+-y7- 7--

BI 8I * lr.tl-81)

I

2 3

18 (1, 6)

B2 : 2x+3=5 or x=1 or f=6

Bl , i dr=2x+3\, &:

3 3

19' 72n

B2

B1

3On x 2

hf

3 3

20 4

3

BZ: -l+ *b4=-3m

B1mx'

2

44

[,* &-2[ s@) ell

3 3

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2t

n=-2

Br'ffi.i")

n---2

FJZ; m-1 or5

3m---)

3 3

22 (a)

o)

-7

367 ( qt\'6 -[eJ

m+92

BI:

3.804

B1

2

2 4

23 (a)

(b)

"crx"cr+"co

27405

44s

B1

I

23

(a)

o)

24

t56t-I ::96

80 70x-360 360

100 I st-360 I 18

7

162

BI

I

2 3

(a)

(b)

25

11z+m+m+ - =l

1

8

3

8

B1

I

2 3

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341U1ADDITIONAL MATHEMATIC S

Kertas 2September

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MAJLIS PENGETUA SEKOLAH MALAYSIACAWANGAN PULAU PINANG

MODUL LATIHAN BERFOKUS SPM 2OI3

MARI( SCHE,ME

ADDITIONAL MATHEMATIC S

Paper 2

Two hours and thirty minutes

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Mark Scheme

2

SE,CTION A ( 40 MARKS )

341212

v:or

v

5-xor.x:5-y

Eliminate y or x

x*(5-x)+x*7=0

or

*(5- y)y+*(5-y)+ 7:0or

*(-r-7\x+ I l=5

\x)

x--1r7or

Y:6,-2OR

!:6r-2or

x: - | ,7

Solve the Quadratic Equation

Us-ins factorisation

(x+ lXx-7):0OR

(y+2)(y-6):0

Using formula

20)

OR

- (-4) r2(r)

Comnleting the square

(r- 3)2 -32 -7 -oOR

b,-2)' -22 -12 = o

- (-6) t Jc-otz - qe)(t)

- 4(1X-12)

OW-l if steps to solve quadratic equation are not shown.

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347212

Mark Scheme

8, 20, 32

d: 12

*8 + (n- 1)*12:176

Note : Accept complete listing of the terrns

Substitute x:1 into px+ q*and equate to 2

p(1) + q(l)2 :2 Substitnte x:3 into Px + q*and equate to 0

p(3)+q(3)2:g

p_3or

q- -lq: .-,1 .

orp_3

Integrate *3x + 'r1- 1)x2 wrt x--.-.-

42 35XX1'-- --+c'23

Substitute (3, 4) into *y

to find c

3x

3y= 3x2

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341212

Mark Scheme

L : 20.5

* 20.5 +

s.5(6) + ls.s(13) +zs.s * (s) + 3s.5 * (6) + 4s.5(10)

Modal class ll - 20

Use rqid-points

2(-4) + 3(6) 2(0) + 3(s) )' 3+2 )

D(2,3)

Usezlxtnz--1y _ *3 : *-2(i -_*2)

or*3:*(_2)(*2)+c

=!

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Mark Scheme

6 (a) Shape of cosine

2cyclesfor0 <x<2n

Amplitude: 3

Modulus

trtrtrtr

Accept

sine

graph

v-L+l7t

Sketch the straight line

..Number of solutions : 8

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3412126

strcTroNB(40MALKS)

Mark Scheme

x-l 2 3 4 5 6 7

logroy 0.90 0.83 0.78 0.72 4.67 0.60

Plot logrqy against

6 *points plotted correctly

Line of best fit

logroy: loglsh - (x- l) logls& trUse 't = log16ft

Use*z:-log1s&

k- 1.15 10.47

;

Note : SS-l if part of the scale is not uniform or not usingthe scales given or not using the graph paper

347212more examination papers at :www.myschoolchildren.com

347212

loB,o

1.

jlit,li;jii

0t234567 :.

,,.

347212

0.

0

v

0

8

.7

.4

.3

.t

0.

1

i1

t

{

t:tI

IIllt.ltj

{Ititt

!

Ii;1

,

:Jrll:it:Ilt.

.taI

!t

i?

.i I'iill!it

,lli" i ,it'.;l,II,ii ..i

Nit^'i-.*_-"-!..",-.*1.",*_.*.-,..*..".-l -t -*..

..

iiIIt;II

,I

t{.;"

{

ii

i!I

::c

!

ItI

iI

....t"

't' ; Iiii.i!l,...,.r -. [ ,.1.,-.':'l, .l: IIiil,!r,r. t Iit\

T.,iI1.,,t

i\i:l il

"1'I,l

\ *.i:-'i -"

t,.l'iiili,

i:-.-,.1"- -.-L.:;-j.- -- l.I,l:..,,',.',...'i,l

I

, ,. ' ,l

i,.1 \{ :i:\,li it:

l: I

:" i"-*l-.r -. , ,?, :- -:-,--l

;,1.'.-.-r->

i--.---...-t.-:T---1- I t. --.--J*-.:"'

., .,|,

-'-!: -l

:x-*--L

.lIxi--t -:-?t-i

:IJLI :-- -fj --*j

- r- -i:::li,l

I

i-1---1

,I

,l:lr.-i.,t

,i--:_--li

i: 't,."-.iI ;,t

i:lIIiltr l:ii

::l.l

-i-t-t-I

*1----i-

II:l ai-*f, -, -,

"',- -*-:-'..',*...":.

:!!r

'-:::ir----.ia-

i i -ii i{.': ) i!t-i....l-.:

- r'--.-"i- -:--

Ii i: '-++-;

I'I-l-_ -- r- 1


341 212

Mark Scheme

(i) & (ii) RS or QR

R3: -y 3*-y

4

A-

PT=PQ+=QR5'

or equivalent

t4-x * - v

tJ) )-

(i) PU n(l t* ! v)) )- @(ii) P(J=PR+fRS

+ ( 3 \ptr=Z*k[-2.;r)

Equate the coefficient of xand y and solve simultaneouslinear equations

,1ls-- or4

. 15h- - ot16

.15h: -16

k=!4

Use Triangle Law for

Ful IMarI


341212

I

I

Ii

I

I

I

I

i

i

Ques Mark SchemeSub

Ma rksTotalMark

9 (a

(b

(c)

Find lL!:"

dY -zx-6

dx

-4

(1,-5) trr)

Y--44x-

_$_o-lyg/_: -61-:_0_x:0r 6OR

Solve simultaneous equations

v -= -6!-:t-qll{ y-=:.x =.0, 'l

-EEerl"- .A-:-6:llF-lt -x3 612Ar - 32

Use limi, tI[ . *( f or2)rn [;- r)

OR

I it{ -t["- se_q -olt1riete lq

Az: *"-rrrr*(7)

Ai

U rntlttzt6

l7

2

3

5 l0

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t0 341212

Ques Mark SchemeSub

MarksFull

Mark

r0 (a)

(b)

(c)

(d)

trUse s : r0 to fihd arc

lglell,-qr- 4P-Arc AB - (*6 + l2)(1.05)

18.9

Use cos I "05' : OD o, sin I .g5' - I__t_?_ __ --r__ :?

OD : 5.971 ; CD: 10.409

49 -: -g P- : !-P -! -v-"- 4-n-*6 + *10.409 + *12.029 + *18.9

!?-:(l-611?) --:?.2BD: 12.029

4

Usel =%lO to

find area of sector

AOB

Ar :l t-u + t2)2(l .os)'2\ ',

*Ar_ l%*(oD)*(cD)l

139.02 10


ll 3 47 212

Ques vrww. myschoolchi ld ren.com Mark SchemeSub

MarksFull

I

Markl

1l (a) (i) 8c, 10.+s)s (o.s s)3

0. 1719

(ii) n (0.45)(0.55) : 940.5

(b) (i) 255 - 240

m

10

Y -240(ii)User:fff:r-{-:-2-3-9-9-?19-

-l<z<l

Use 1 -2P(Z> *1)

l - 2(o.l s87)

0,6826 ll 0,6827

. 1t I

(700 x *0.6826) 10

3472t2


t2

SECTION C (20 MARKS)

3 412t2

Ques Mark SchcmeSub

MarksFull

Mark

l2 (a) 5 -2t <0

5t>2

(b)Irt:g-vr i:-?t-ylv- st -f + c Substitute t:0and

v: -4 in*y to

l,:r4 -g-c=-4Fl_t_u-"_ _r_ _:_q -&l-r_

(,-l)0-4):0

4

(c) fl'-'g::r ! ! :?! -' - -1- Y1-'

st2 f.r - ---4t23

Find total distance travelled

Substitutet: *1 or t=*4 into *s

OR

Use t' o,r fl in's

l[iudtlor ti"at,

re t oL tt 6.3333310


341212

Mark Scheme

ur, &xlooQo

x : 1.50

r20(l2s) + I 37.{45) + * l2s(170) + 135(80)

125+45+170+80

126.76il126.8

ur" ?)? x loo - *126 .76s00 @

J(RM) 633.8 // 634.00

llg. B7 .s100

( RM ) 3.20 z:125 tr

l s9.s

347212


l4

' "r

341212

Ques Mark Scheme,' SubMarks

FullMark

l4 (a)

(b)

(c)

(d)

ZPSR : 60o

Y-': :"_':l:'j'l:

PRz -82 +g2

i:_tffl:lf'ri lI- 2(8)(9) cos 60"

PR: 8 544 t/ 8.54

Use sine rule in MQS to find PQ

Pg=gsin 120' sin 48"

PQ : 9.323 ll9.32

Ar : % *(9.323X8) sin l2'

OR

Use sine rule in LPQSto find p.S

OR

Use sine rule or cosine ruleto find Z SPR

Az: Y, (8)(9) sin 60"

OR

*(9.323X9 + *Qs)sin 48"

aR

* 19 .323)*(8. 544)sin (12+* zP)

38.933

sin 60" - 4oR8

%x9 x h: * Area of APSft

l0

38.90

6.928/t 6.93


l5 341212

Ques Mark Scheme SubMarks

Fu llMark

15 (a)

(b)

(c)

3y

20

80 or equivalent

equivalent

equivalentor

trtr

Draw correctly at least one straight linefrom the *inequalities which involvesxand y

Draw correctly all the three*straight linesNote : Accept dashed lines

The correct region shaded

(i) zo < x < 4o @(ii) Maximum point: (20, 60) tr

Use 30 000x + 50 000yfor point in the *region R

l0

Note:ss-r ifin (a), the symbol ":" is not used at all ormore than three inequalities are given

in (b), does not use the scale given or '

does not use graph paper orinterchange between x-axis and y-axis

.

341212


l6 3412.2

it

!

I

itI

tI

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END OF MARK SCHEME

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