PROGRAM PENINGKATAN AKADEMIK TINGKATAN LIMA SEKOLAH-SEKOLAH MENENGAH NEGERI SEMBILAN 2014

MATEMATIK Kertas 1

1. D 11. D 21. D 31. B

2. B 12. A 22. A 32. A

3. B 13. C 23. D 33. B

4. C 14. D 24. C 34. C

5. C 15. C 25.B 35. A

6. B 16. C 26. B 36. D

7. C 17. D 27.B 37. D

8. A 18. D 28. A 38. B

9. C 19. C 29.C 39. A

10.D 20. A 30. C 40. A

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2014

1449/2 Matematik Kertas 2

MAJLIS PENGETUA SEKOLAH MENENGAH MALAYSIA CAWANGAN NEGERI SEMBILAN

PROGRAM PENINGKATAN AKADEMIK TINGKAT AN LIMA SEKOLAH-SEKOLAH MENENGAH NEGERI SEMBILAN 2014

MATEMATIK

Kertas2

PERATURAN PEMARKAHAN

3

No Markin Scheme Marks

1 (a)

PI

(b) P2

3

2 (a) L WPR or L RPW

7 tan e= - or equivalent (b) 13

3x2 + I3x + 10 = 0

( 3x + 10) ( x + 1) = 0

-10 x=- , x=-1

3

3x- 12y =12 or 2x -8y=8

14y=-2 or --x=2 2

x=2 -1

y=­2

PI

Kl

Nl

3

Kl

KI

NI Nl

4

Kl

Kl

Nl

Nl 4

4

2

5

• I

6 (a)

(b)I

I

(c)

7 (a)

(b)

!

22 - x 0.6 x 0.6 x 0.3

(-x 0.6 x 0.6xO.3)- (-x-xO.6xO.6xO.3)

7

70 - x

22 - xO.6 xO.6xO.3

100 7

22 70 22

7 100 7

0.10

False

If q3 =-27 then q =,-3 If q = -3 then q3 =-27

(7 -2) x 1800

9000

k= 18

28 = -x3+c or c=6

3

2 Y=- x + 6

3

2 -2 0= -x + 6 or -x=6

3 3

x -intercept = - 9

K1

K1

Kl

N1

4

PI

KI Xl

Kl

Nl o '

5

Kl

KIKI

Nl

Kl

Nl

6

3

--

II

10 ( t - 20) = 1208 (a) Kl

t = 32 s Nl

(b) I 10 -0 Kl 20 - 0

1 -I N1-ms 2 I

1 1(c) (- x 10 x20) + 120 +- (10 + 25) 18

K1

535 m

2 2

N1

. - ' 6

42· 22 Kl13 8· x 2 x 22 x14 or --x2x-x79 (a) 360· 7 360 0 7

." I 42· 22~38· x 2 x 22 x14 K1+ (-~x2x-x 7) +7+14+7i

I 360· 7 360· 7 I Nl

66~ 15

Kl (b)

13 8· x 22 x 14 x 14 or 42· 22 7 x7 --x-x 360· 7 360· 7

K1138· 22 180 22 42 22 -- x -x14x14 - (-x-x7x7) + -x-x7x7 360· 7 360 7 360 7

N1

177-1 or 177.099 10

6 ,

4

10 (a)

s = { 12, 13, 14,15,21,23,24,25,31,32,34,35,41,42,43,45,51,52, 53,54 }

(b) (i) {12,14,21,23,25,32,34,41,43,45,52,54}

11 (a)

(b)

12 3 -=­20 5

(ii) {21, 25, 31, 32,41,42,.43, 51,52,53,54}

11

20

s = 1 t = 2

[~ =~J CJ = [;J ( ; ) = 1 (-3 2fJ

5x(-3)-(-2x6) -6 5 3

x = 2

Y = 3

PI

Kl

Nl

Kl

Nl

5

PI PI

PI

Kl

Nl

Nl

6

5

12 (a)

(b)

(c) (i)

(ii)

(d)

x -2 2

9 I 0.:7: I -7

Graph (Refer graph on Lampiran 1 )

Axes drawn in the correct directions with uniform scales for -3::;x::;3 and -26::;y::;28

All 8 points and *2 points correctly plotted or curve passes through aU the points for -3 ::;x ::; 3 and -26::;y::; 28

A smooth and continuous curve without any straight line and passes through all 10 correct points using the given scale for -3 ::; x::; 3 and -26::; Y ::; 28

Notes:

1. 8 or 9 points correctly plotted, award K1

2. Ignore curve out of range

y = 4.4 ± 0.1

x = - 2.3 ± 0.1

Draw the straight line y = -5x

Shaded region correctly

K1K1K1

PI

I K2

N1

PI

PI

K1

N2

12

6

13 (a) ---7(7,5 ) (2,3 ) ---7 (-3,1) P2(i} T T

P2(7,5 ) It (9,1) r (4, -1)(ii)

P2(a) V : Reflection in the line BE(b) (i) P3(b) W : Enlargement of scale factor 3 with centre P

Area ofan image =3 2 x 35 K1(ii)

K1Area Of The Shaded Region = (3 2 x 35)- 35 .

I 'Nl280

I

."

12

7

14 (aJ

I I

Class interval Selang kelas (umurJ

Frequency Kekerapan

Midpoint Titik tengah

21 -30 3 25.5 31 -40 5 35.5 41 - 50 6 45 .5 51 - 60 9 55.5 61 -70 7 65.5 71- 80 6 75.5 81 -90 4 85.5 PIP2PI

(b)

(c)

(d)

Note:

Allow two mistakes in frequency for PI

·3x25.S+·Sx3S.5+·6x4S.S+"9xSS.S+·7x6S.S+"6x7S.5+·4x8S.S K2

•3+ • 5 + 6+ •9+ • 7 + • 6 + " 4

2280 or - ­

40

57 year Nl

Histogram (Refer graph on Lampiran 2)

Axes are drawn in the correct direction, uniform scale for PI 20.5::; x ::;90.5 and 0::; y::; 10

Horizontal axis is labelled using midpoint! upper boundary and K2 "7 bars drawn correctly using mid point/upper boundry.

Note: "5 or • 6 bars drawn correctly, award Kl

Correct histogram using the given scale for 20.5 ~ x ~ 90.5 Nl

17 outpatients Nl

12

8

15 (a)

(b) (i)

Q IK r--~__~_-,R I L

I

SIMP I N --------<I IIii-

Correct shape with a rectangle NMLK.

NK=ML>KL= NM

The measurement is accurate to ± 0.2 cm (one way) and the angles at all vertices of the rectangles are 90° ± 1°.

SIR

I

BIC

P I Q

N I K MIL

Correct shape with trapeziums PS.MN and triangle BAM All solid lines

MS = MA > MB > NP

Measurements correct to ± 0.2 em (one way) and LN ,LM ::: 90° ± 1°

Kl

Kl

Nl

A /~

Kl

Kl

N2

9

--------------------------

IS(b) Oi)

SR

C B I

PQ

'I

K/UD NIMIA .

KlCorrect shape two rectangles KLPS and SPQR

•Note: "

KICB joined with dotted line.

KIRL=SM>CB > CL = BM>QD = PN

N2Measurement correct to ± 0.2 cm. (one way) and all angles at vertices of rectangles is 90° ± 1°.

!

12

10

16

. '

(a) (i)

(ii)

(b)

(c) (i)

(ii)

(55 0 N, 65° E)

70 x 60

4200 nautical miles

Bx60=6000

100 - 55

45 oS.

115° - 85° .

(115° - 85°) x60 cos 55°

1032.44 nautical miles

1032.44 + 6000 690= or

t

10.l9 hours

1032.44 +6000

690

I

P1P1

K1

N1

K1

K1

N1

K1 -

Kl

N1

,.

K1

N1

12

11

Lampiran 1 Graph for Question 12

12

Graph for Question 14 Lampiran 2

I I