15 (a)

1449

SULITMarking Scheme

Peperiksaan Percubaan SPM PAGE 71449

SULITMarking Scheme

Peperiksaan Percubaan SPM

KEMENTERIAN PELAJARAN MALAYSIA

PEPERIKSAAN PERCUBAAN

SIJIL PELAJARAN MALAYSIA 2011

MATHEMATICS 1449MARKING SCHEME

Paper 1

1A11A21B31A

2B12D22B32D

3C13D23D33D

4C14D24D34D

5D15B25C35B

6B16A26C36C

7A17A27B37B

8B18D28C38C

9B19A29C39A

10A20D30C40D

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

Paper 21 (a)Straight dotted line correctly drawn.

Region correctly shaded.Note:

1. Accept solid line for K1.

2. Award P1 to the shaded region bounded by two correct lines. (Must include part of region R)

K1

P23

2 (a) (b) or

or equivalent

20.56 or 2033

P1K1

N1

3

3 3n2 7n 6 = 0 or equivalent

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

or equivalent (K1)

n = n = 3 Note:

1. Accept without = 0 .

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

3. Accept with n = or n = 3 for Kk2.

K1K1

N1

N14

4 or or equivalentNote

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

or or equivalent

OR

or or or

or equivalent. (K1)Note

Attempt to make one of the unknowns as the subject, with 2 terms on the other side, award K1

or or equivalent . (K1)

OR

(K2)Note

Attempt to write the matrix equation, award K1.

Note:

as final answer, award N1.

K1

K1N1

N1

4

5

+

389.72 389.74Note:

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

N14

6 (a) (b)

(c)and 10km = 104m

OR50 = 5 or (P1)

OR 50 = 5 or 10km = 104m (P1)If , then . // Jika , maka .

False // Palsu

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

P1

P1

P1

K25

7 (a)

(b)

(c)

or

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

or equivalent

Note:

Do not accept

P1

P1

K1

N1

N15

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) }

or

or

P1

N2

N2

5

9 (a)

(b)

or

+ + 28 +28 + 14

or or 121.31 121.33

or

EMBED Equation.3

EMBED Equation.3

or 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

33

10 (a) (b)

(c)4

or equivalent

50

or or equivalentd = 648

P1

K1

N1

K2

N16

11(a)

(b)

Note : Determinant or 2, award P1.

or

or or 2.5

or or

Note:

1. Do not accept or

2. as final answer, award N1.

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

P1

P2

P1

K1

N1

N13

4

12 (a) (b)

(c)

(d)

6.4

Graph

Axes drawn in correct directions with uniform scales for and .

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

A smooth and continuous curve without any straight line and passes through all 9 correct points using the given scale for .

Note:

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

2. Ignore curve out of range.

(i)

(ii) 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.

Identify equation

Straight line correctly drawn.

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

Note:

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

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

P1

P1

P1

K2

N1

P1

P1

K1

K1

N1

N1

2

4

2

4

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.

Note:

or or equivalent, give K1

P1

P2

P3

P3

K2

N1

3

6

3

14 (a) (b)

(c)

(d)

Class IntervalSelang KelasMidpointTitik Tengah

Frequency

Kekerapan

I

30 34 320II

35 39 37

4III

40 44

42

6IV

45 49

47

5V

50 54

52

9VI

55 59

57

7VII

60 64

62

4VIII65 69

67

0Class Interval : (II to VII)

Midpoint : (I to VIII)

Frequency : (I to VIII)

Note : Allow two mistakes in frequency, for P1

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. (without table)

Frequency polygon Axes drawn in correct directions, uniform scales for and .

*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 and

*20 from * frequency polygon

Note: Do not accept answer without a frequency polygon.

P1

P1

P2

K2

N1

P1

K2

N1

K1

4

3

4

1

15

15 (a)

(b) (i)

(b) (ii)

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 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 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.

Correct shape with hexagon ABCDEF.All solid lines.

Measurement correct to cm (one way) and all angles at the vertices of rectangles are .

Correct shape with rectangles AHGF and FGLD and semicircle AD.

All solid lines.

Note: Accept semicircle drawn not using compass.

and semicircle AD drawn correctly (use compass).

Measurement correct to cm (one way) and

901.

Correct shape with rectangles FGLD, DLKC and QCSR.

All solid lines.

Note:

Ignore straight line AHA and H joined with dashed line to from rectangle AHLD

Measurement correct to cm (one way) and

all angles at vertices of rectangles

K1

K1

N1

K1

K1

N2

K1

K1

K1

N2

3

45

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.

Note:

cos 80 or 136 seen, award K1.

1416.97

20 hour 7 min

P2

P2

K2

N1

K1

K1

K2

N12

2

3

5

(

(

(

(

(

(

-2

-3

-1

1

2

3

4

-4

10

20

30

40

y

-10

-20

9

8

7

-30

-40

0

x

(

(

47

42

37

32

(

6

4

3

2

1

5

0

67

62

57

52

(

(

(

(

(

(

(

(

(

y = 10x + 20

0.65

-2.65

-0.65

11

Question 12

y

EMBED Equation.DSMT4

EMBED Equation.DSMT4

x

(6

4

0

(

(

Question 14

A

F

E

D

C

B

A

H

G

L

D

F

F

G

A

H

D

L

K

C

Q

R

S

PAGE 1449/1

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