Set 3_K2_jwpn

1449 SULIT Marking Scheme

Peperiksaan Percubaan SPM

KEMENTERIAN PELAJARAN MALAYSIA

PEPERIKSAAN PERCUBAAN

SIJIL PELAJARAN MALAYSIA 2011

MATHEMATICS 1449

MARKING SCHEME

Paper 1

1 A 11 A 21 B 31 A

2 B 12 D 22 B 32 D

3 C 13 D 23 D 33 D

4 C 14 D 24 D 34 D

5 D 15 B 25 C 35 B

6 B 16 A 26 C 36 C

7 A 17 A 27 B 37 B

8 B 18 D 28 C 38 C

9 B 19 A 29 C 39 A

10 A 20 D 30 C 40 D

A - 9 , B - 10, C - 9, D - 12



1449/1 SULIT

2

Paper 2

1 (a)

Straight dotted line 1x correctly drawn.

Region correctly shaded.

Note:

1. Accept solid line 1x for K1. 2. Award P1 to the shaded region bounded by two correct lines. (Must

include part of region R)

K1

P2

3

0

4

6 x

2 4y x

2 12y x

y



1449/1 SULIT

3

2 (a)

(b)

FEB or BEF

8

3tan or equivalent

20.56 or 2033

P1

K1

N1

3

3

3n2 7n 6 = 0 or equivalent

( 3n + 2 )( n 3 ) = 0 or equivalent

OR

)3(2

)6)(3(4)7()7( 2

x or equivalent (K1)

n = 3

2

n = 3

Note:

1. Accept without = 0 .

2. Accept three terms on the same side, in any order.

3. Accept )3)(3

2( nn with n =

3

2 or n = 3 for Kk2.

K1

K1

N1

N1

4



1449/1 SULIT

4

4

1863 qp or 62qp or equivalent

Note

Attempt to equate the coefficient of one of the unknowns, award K1.

84p or 328q or equivalent

OR

pq2

13 or qp 26 or

2

143pq or

3

142qp

or equivalent. (K1)

Note

Attempt to make one of the unknowns as the subject, with 2 terms on the

other side, award K1

84p or 328q or equivalent . (K1)

OR

14

3

2

13

12

)3(1)2(2

1

1

q

p (K2)

Note

Attempt to write the matrix equation, award K1.

2p

4q

Note:

4

2

q

p as final answer, award N1.

K1

K1

N1

N1

4



1449/1 SULIT

5

5

35.27

22

3

4

2

1

)7)(6)(710(2

1

35.27

22

3

4

2

1 + )7)(6)(710(

2

1

389.72 389.74

Note:

1. Accept for K mark.

2. Accept correct values from incomplete substitution for K mark.

3. Correct answer from incomplete working, award KK2.

4. Accept answer within range.

K1

K1

K1

N1

4

6 (a)

(b)

(c)

1073 and 10km = 104m

OR

50 = 5 or 1073 (P1)

OR

50 = 5 or 10km = 10

4m (P1)

If 42x , then 2x . // Jika 42x , maka 2x .

False // Palsu

3 is a factor of 12 // 3 adalah faktor bagi 12

P1

P1

P1

K2

5



1449/1 SULIT

6

7 (a)

(b)

(c)

5k

)3(5

04PRm or 2

PRmx

y*

)3(

0 or cmPR )3(*0

Note: Accept * PRm using ( -3 , 0) and ( *k , 4) only

62xy or equivalent

6

Note:

Do not accept )6,0(

P1

P1

K1

N1

N1

5

8 (a)

(b)(i)

(ii)

{ (S,E) , (S,F) , (S,4) , (S,5) , (P,E) , (P,F) , (P,4) , (P,5) , (6,E) , (6,F) , (6,4) ,

(6,5) }

12

4 or

1

3

12

3 or

1

4

P1

N2

N2

5



1449/1 SULIT

7

9 (a)

(b)

77

222

360

180 or 28

7

222

360

60

77

222

360

180+ 28

7

222

360

60+ 28 +28 + 14

3

364 or

3

1121 or 121.31 121.33

2287

22

360

60 or 27

7

22

360

180

2287

22

360

60 277

22

360

180

3

1001 or

3

2333 or 333.53 333.67

Note:

1. Accept for K mark.

2. Accept correct values from incomplete substitution for K mark.

3. Correct answer from incomplete working, award KK2.

K1

K1

N1

K1

K1

N1

3

3

10 (a)

(b)

(c)

4

08

0400 or equivalent

50

3618

d or 36

18

400400 d or equivalent

d = 648

P1

K1

N1

K2

N1

6



1449/1 SULIT

8

11(a)

(b)

3n

2

1m

Note : Determinant )]4)(3()2(5[ or 2, award P1.

13

17

24

35

k

h

13

17

54

32

)4)(3()2(5

1

k

h or

13

17*

matrix

inverse

2

5h or

2

12 or 2.5

2

3k or

2

11 or 5.1

Note:

1. Do not accept 24

35*

matrix

inverse or

10

01*

matrix

inverse

2.

2

32

5

k

h as final answer, award N1.

3. Do not accept any solutions solved not using matrices.

P1

P2

P1

K1

N1

N1

3

4



1449/1 SULIT

9

12 (a)

(b)

(c)

8

6.4

Graph

Axes drawn in correct directions with uniform scales for 44 x and

3232 y .

All 7 points and *2 points correctly plotted or the curve passes through all the

points for 44 x .

A smooth and continuous curve without any straight line and passes through

all 9 correct points using the given scale for 44 x .

Note:

1. 7 or 8 points correctly plotted, award K1.

2. Ignore curve out of range.

(i) 1210 y

(ii) 6.075.0 x

Note

1. Allow P marks if value of x and of y are shown on the graph.

2. Value of x and of y obtained by calculation, award P0.

P1

P1

P1

K2

N1

P1

P1

2

4

2



1449/1 SULIT

10

(d)

Identify equation 2010xy

Straight line 2010xy correctly drawn.

(Check any two points (0, 20), (1, 30), (2, 40), and accurate to 2

1square

grid vertically)

7.06.0 x

5.26.2 x

Note:

1. Allow N marks if values of x are shown on the graph.

2. Values of x obtained by calculation, award N0.

K1

K1

N1

N1

4



1449/1 SULIT

11

13 (a)

(b) (i)

(b) (ii)

(i) (-2, 3)

(ii) (2, 1)

Note:

Point (2, 1) marked or (-2, 3) seen or (-2, 3) marked, award P1

(a) X : Rotation 90 clockwise / 270 anticlockwise at centre (0, 4) //

Putaran 90 arah jam / 270 lawan arah jam pada pusat (0, 4)

Note :

1. Rotation 90 clockwise / 270 anticlockwise //

Putaran 90 arah jam / 270 lawan arah jam //

Rotation at centre (0, 4) //

Putaran pada pusat (0, 4), award P2

2. Rotation // Putaran, award P1.

(b) Y : Enlargement with scale factor 3 at centre P(-3, 2) //

Pembesaran dengan faktor skala 3 di pusat P(-3, 2)

Note:

1. Enlargement with scale factor 3 // Pembesaran dengan faktor skala 3//

Enlargement at centre P(-3, 2) //

Pembesaran pada pusat P(-3, 2), award P2.

2. Enlargement // Pembesaran, award P1.

xx 2* )3(96

12x

Note:

96x or x2* )3( or equivalent, give K1

P1

P2

P3

P3

K2

N1

3

6

3



1449/1 SULIT

12

14 (a)

(b)

Class Interval

Selang Kelas

Midpoint

Titik Tengah

Frequency

Kekerapan

I 30 34 32 0

II 35 39 37 4

III 40 44 42 6

IV 45 49 47 5

V 50 54 52 9

VI 55 59 57 7

VII 60 64 62 4

VIII 65 69 67 0

Class Interval : (II to VII)

Midpoint : (I to VIII)

Frequency : (I to VIII)

Note : Allow two mistakes in frequency, for P1

4*7*9*5*6*4*

4*627*579*525*476*424*37

Note :

1. Allow *midpoint for K1

2. Allow two mistakes for the multiplication of midpoint and *frequency

for K1.

50

Note :

Correct answer from incomplete working, award KK2.

e.g. 5035

1750(without table)

P1

P1

P2

K2

N1

4

3



1449/1 SULIT

13

(c)

(d)

Frequency polygon

Axes drawn in correct directions, uniform scales for 6732 x and

9*0 y .

*8 points correctly plotted using the correct midpoint

Note: *6 or *7 points correctly plotted, award K1.

Frequency polygon passes through all 8 correct points using the given scales

for 6732 x and 90 y

*20 from * frequency polygon

Note: Do not accept answer without a frequency polygon.

P1

K2

N1

K1

4

1



1449/1 SULIT

14

15

Note:

(1) Accept drawing only (not sketch).

(2) Accept diagrams without labels and ignore wrong labels.

(3) Accept correct rotation of diagrams.

(4) Lateral inversions are not accepted.

(5) If more than 1 diagrams are drawn, award mark to the correct ones only.

(6) For extra lines(dotted/dashed or solid) except construction lines, no KN mark is awarded.

(7) If other scales are used with accuracy of 2.0 cm one way, deduct 1 mark from the N mark obtained, for each part attempted.

(8) Accept small gaps or extensions at the corners. For each part attempted:

(i) If 4.0 cm, deduct 1 mark from the N mark obtained.

(ii) If >0.4 cm, no N mark is awarded.

(9) If construction lines cannot be differentiated from the actual lines:

(i) Dotted line: If outside the diagram, award the N mark. If inside the diagram, award N0.

(ii) Solid line: If outside the diagram award N0. If inside the diagram, no KN mark is

awarded.

(10) For double lines or non collinear or bold lines, crooked lines,

deduct 1 mark from the N mark obtained, for each part attempted.



1449/1 SULIT

15

15 (a)

Correct shape with hexagon ABCDEF.

All solid lines.

DECDFEBCAB

Measurement correct to 2.0 cm (one way) and all angles at the vertices of

rectangles are 190 .

K1

K1

N1

3

A

F

E D

C B



1449/1 SULIT

16

(b) (i)

Correct shape with rectangles AHGF and FGLD and semicircle AD.

All solid lines.

Note: Accept semicircle drawn not using compass.

FDAFADAH and semicircle AD drawn correctly (use compass).

Measurement correct to 2.0 cm (one way) and

DLHA ,,, 901.

K1

K1

N2

4

A H

G

L D

F



1449/1 SULIT

17

(b) (ii)

Correct shape with rectangles FGLD, DLKC and QCSR.

All solid lines.

Note:

Ignore straight line AH

A and H joined with dashed line to from rectangle AHLD

QDCQLKGLGKFG

Measurement correct to 2.0 cm (one way) and

all angles at vertices of rectangles 190

K1

K1

K1

N2

5

F G

A H

D L

K C

Q R

S



1449/1 SULIT

18

16

(a)(i)

(ii)

(b)

(c)

80 S

Note: 80 award P1.

(80 N, 84E) // (80 U, 84T)

Note: 80 N / 84 E // 80 U / 84 T, award P1.

80cos60136

Note:

cos 80 or 136 seen, award K1.

1416.97

80cos6044

60160

500

60160)80cos6044(

20 hour 7 min

P2

P2

K2

N1

K1

K1

K2

N1

2

2

3

5



1449/1 SULIT

19

-3 -2 -1 1 2 3 4 -4 0

10

20

30

40

y

-10

-20

-30

-40

x

y = 10x + 20

0.65

-2.65 -0.65

11

Question 12



1449/1 SULIT

20

5

1

2

3

4

6

7

8

9

Question 14



1449/1 SULIT

21

32 37 42 47 52 57 62 67

0

Set 3_K2_jwpn

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