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
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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
