SULIT 1449/2

1449/2 2016 SULIT

1449/2

Matematik

Kertas 2

PPD KINTA SELATAN

PEPERIKSAAN AWAL TAHUN 2016

SIJIL PELAJARAN MALAYSIA

TINGKATAN 5

MATEMATIK 1449/2

Kertas 2

PERATURAN PEMARKAHAN

Markah = 140

2 1 KertasKertas

Peraturan Pemarkahan ini mengandungi 13 halaman bercetak

SKEMA PERMARKAHAN

MATEMATIK KERTAS 1 (1449/ 1)

MATEMATIK 1449/2 (KERTAS 2)

SULIT 1449/2

1449/2 2016 SULIT

Bahagian A

No.

Soalan Peraturan Pemarkahan Markah

1

(a)

(b)

Note: give P1

P1

P2

3

2

Garis lurus x = 2 dilukis dengan betul (penuh atau bintik )

K1

P

R

R

Q P

Q

R

Q P

y = 2x + 5

5x + 2y = 10

5

y

x 2

SULIT 1449/2

1449/2 2016 SULIT

Rantau betul dilorek

Nota:

1. Rantau yang memuaskan mana-mana dua ketaksamaan

berikan P1

2. Tolak 1 markah dari K1P2 jika x = 2 garis penuh.

P2

3

3

Kenalpasti SMN atau NMS

Tan SMN = 16

10 atau setara

32.01º atau 32 atau 32 01′

P1

K1

N1

3

4

0 = −2𝑋2 + 5𝑥 + 12

2𝑥2 − 5𝑥 − 12 = 0

(2𝑥 + 3)(𝑥 − 4) = 0

2𝑥 + 3 = 0 atau 𝑥 − 4 = 0

𝑥 = −3

2 𝑥 = 4

Harga jualan basikal ialah RM 400 seunit jika tiada keuntungan

diperoleh kedai itu.

1

1

2

1

5

5

6x + 3y = 24 or 2x – 6y = 22 or x = 11+ 3y or y = 8 – 2x or any

equivalent

7x = 35 or -7y=14 or any equivalent

x = 5

y = 2

OR

12

31

y

x=

8

11 (K1)

y

x=

)6(1

1

12

31

8

11 (K1)

x = 5 (N1)

y = − 2 (N1)

K1

K1

N1

N1

SULIT 1449/2

1449/2 2016 SULIT

5Note: Answer give N1

2

4

6

Katakan harga bagi 1kg durian ialah 𝑥 dan 1kg duku ialah 𝑦.

2𝑥 + 𝑦 = 18 ………①

𝑥 − 𝑦 = 3 ………②

① + ② 3𝑥 = 21

𝑥 = 21

3

𝑥 = 7

Dari ①, 2(7) + 𝑦 = 18

𝑦 = 18 − 14

= 4

Harga bagi 1kg duku ialah RM 4.

1

1

1

1

1

1

6

7

Isipadu Prisma = (1

2× (10 + 7) × 4) × 5

= 170

1

3× (5 × 10) × 𝑡 atau

50

3𝑡 = 200

= 370 − 170

𝑡 = 12

1

1

1

1

4

8

(a) Sebilangan

(b) Implikasi 1 : Jika 𝑥 < 0 maka x ialah integer negatif.

Implikasi 2 : Jika x ialah integer negatif maka 𝑥 < 0

(c) Kesimpulan : 20 boleh dibahagi tepat dengan 2.

(d) Jika x adalah gandaan bagi 3, maka x adalah gandaan bagi

12.

Palsu

1

1

1

1

1

1

6

9 (a)

0 2x = 8

x = 4

Nota : Tanpa kerja beri K1N1

K1

N1

SULIT 1449/2

1449/2 2016 SULIT

(b) mST

= 2

9 = 2(3)+ c atau )3(

)9(

x

y= 2

y = 2x 3

Pintasan-y = 3

P1

K1

N1

P1

6

10.

(a) (i) {L, L}, 2

11

(ii) {O, A, A, U, E}, 5

11

Note : Jika tiada ruang sampel, K0N0

(b) 2

11+𝑥=

1

8

11 + 𝑥 = 16

𝑥 = 5

Jumlah kad yang berhuruf ‘P’ ialah 5.

K1, N1

K1, N1

K1

N1

6

11.

(a) 45 22

2 21360 7

or 60 22

2 14360 7

45 22

2 21360 7

+ 60 22

2 14360 7

+ 21 + 7 +14

73.17 or 1

736

or 439

6

(b) 245 22

21360 7

or 260 22

14360 7

or 260 22

7360 7

245 22

21360 7

+ 260 22

14360 7

− 260 22

7360 7

250.25 or 1

2504

or 1001

4

K1

K1

N1

K1

K1

N1

6

12

(a) x = 4, y = 26

x = 2, y = - 4

K1

K1

SULIT 1449/2

1449/2 2016 SULIT

Note:

(1) If not stated, give K1K1 for the table

@ if points are correctly marked on the graph

@ the curve passes exactly through the points.

(b) Graph :

Axes are drawn in the correct direction with uniform

scale. in the range − 4 < x < 4 and -11 y 26.

All 7 points and 2 points* are correctly marked

Smooth curve and continuously in range of − 4 < x < 4

with no straight line parts and passing through all the

correct 9 points.

Note:

(i) 7 @ 8 points are correctly plotted, K1

(ii) Other scale used, minus 1 mark from the KN

marks obtained.

(c)

(i) 2.85 2.65x

3.15 3.35x

(ii) 5.3 ≤ 𝑦 ≤ 5.5

(d) The equation y = 3x + 9

Straight line y = 3x + 9 correctly drawn and meet the

curve.

The value of x :

−2.35 ≤ 𝑦 ≤ −2.0 Note:

(i) Allow N mark if x is shown on the graph.

(ii) The value of x obtained by calculation, give N0

K1

K2

N1

K1

K1

K1

K1

K1

N1

12

SULIT 1449/2

1449/2 2016 SULIT

O -1 2 3 1 -2 -3

x

4

y

25

15

30

5

20

10

-5

-10

-4

SULIT 1449/2

1449/2 2016 SULIT

13

(a) x = 2, y = 11,

x = 2, y = - 5

Note:

(2) If not stated, give K1K1 for the table

@ if points are correctly marked on the graph

@ the curve passes exactly through the points.

(b) Graph :

Axes are drawn in the correct direction with uniform

scale. in the range −3.5 x 3.5 and 15 y 18.

All 7 points and 2 points* are correctly marked

Smooth curve and continuously in range of − 3.5 x

3.5 with no straight line part and passing through all

the correct 9 points.

Note:

(i) 7 @ 8 points are correctly plotted, K1

(ii) Other scale used, minus 1 mark from the KN

marks obtained.

(c) (i) 7.4 y 7.6

(ii) –3.5 x –3. 3

(d) The equation y = 5x 5

Straight line y = 5x 5 correctly drawn and meet the

curve.

The value of x : 3.2 x 3.3

0.6 x 0.7

Note:

(i) Allow N mark if x is shown on the graph.

(ii) The value of x obtained by calculation, give N0

K1K1

K1

K2

N1

K1

K1

K1

K1

N1

N1

12

SULIT 1449/2

1449/2 2016 SULIT

O -1 2 3 1 -2 -3

x

4

y

25

15

30

5

20

10

-5

-10

-4

-20

-15

y = 5x 5

SULIT 1449/2

1449/2 2016 SULIT

14(a)

(b)

(i) (1,1)

(ii) (1, 2)

(iii) (4, 1)

(i) X - Pantulan

pada garis y= -1

Y- Pembesaran

Pada Q

Faktor skala = 3

(ii) 210 + ABCD = 3 2 (ABCD) atau setara

ABCD = 4

105 atau 2625

P1

P1

P1

P2

P3

K2

N2

12

15 (a)

I II III

Markah Kekerapan Titik Tengah

31 – 40 2 35.5

41 – 50 4 45.5

51 – 60 9 55.5

61 – 70 12 65.5

71 – 80 8 75.5

81 – 90 3 85.5

91 - 100 2 95.5

Lajur I

Lajur II

Lajur III

Nota: 5 atau 6 kekerapan betul, berikan P1.

(b) Histogram:

Paksi-paksi dilukis dengan arah yang betul, skala seragam

bagi 30.5<x<100.5 dan 0<y<12, paksi-x dilabel mengguna-

kan sempadan bawah atau sempadan atas atau titik-tengah.

Semua 7 bar dilukis betul

Nota: 1) 5 atau 6 atau 7* bar dilukis betul, berikan N1.

P1

P2

P1

K1

N2

SULIT 1449/2

1449/2 2016 SULIT

2) Jika skala lain digunakan, tolak 1 markah KN

yang diperolehi.

(c) (i) 61 – 70

(ii) (2 x 35.5 + 4 x 45.5 + 9 x 55.5 + 12 x 65.5 + 8 x 75.5 +

3 x 85.5 + 2 x 95.5) / 40

= 64.75 atau setara

P2

K2

N1

12

35.5 45.5 55.5 65.5 75.5 85.5 95.5

2

4

6

8

Titik

Tengah

Kekerapan

SULIT 1449/2

1449/2 2016 SULIT

16 (a)

Class

Interval

Selang Kelas

Midpoint

Titik Tengah

Frequency

Kekerapan

10 – 14 12 0

15 – 19 17 5

20 – 24 22 10

25 – 29 27 9

30 – 34 32 11

35 – 39 37 5

* Column 1 (class interval) (all correct)

* Column 2 (mid point) (all correct)

* Column 3 (frequency) (all correct)

(b) (12 x 0 + 17 x 5 + 22 x 10 + 27 x 9 + 32 x 11 + 37 x 5) / 40

= RM27.13

(c) Lukis poligon kekerapan :

* axes are drawn in the correct direction with uniform scale.

* x- axis is labelled with midpoint

* All 7*points are correctly marked.

* The frequency polygon passes through (12, 0) and (42, 0)

P1

P1

P2

K2

N1

K1

K1

K1

K1

SULIT 1449/2

1449/2 2016 SULIT

(d) 16 students whose donation is more than RM29 (or other

correct answers)

16 pelajar telah menderma lebih banyak daripada RM29.

N1

12

TAMAT SKEMA PEMARKAHAN

42