2010 pat t4 matematik skema

JABATAN PELAJARAN MELAKA

PEPERIKSAAN SELARAS AKHIR TAHUN

TINGKATAN 4, 2010

MATHEMATICS

SKEMA PEMARKAHAN

MATHEMATICS PAPER 1

1 A 11 B 21 A 31 B

2 C 12 B 22 D 32 D

3 A 13 D 23 C 33 D

4 B 14 B 24 B 34 B

5 A 15 D 25 C 35 C

6 A 16 C 26 C 36 B

7 D 17 D 27 A 37 A

8 A 18 B 28 C 38 D

9 C 19 D 29 B 39 D

10 C 20 C 30 D 40 C

MATHEMATICS PAPER 2

No Peraturan Pemarkahan Markah

1 (a)

(b)

1

2

3

2 1684 yx or equivalent

33 y or equivalent

OR

oryxory

x 242

48

equivalent K1

33 y or equivalent K1

OR

13

8

24

45

)4)(4()5)(2(

1K2

1

2

y

x

K1

K1

N1

N1

4

Q

P

R

Q

P

R

No Peraturan Pemarkahan Markah

3 < MUN

tan < MUN =

< MUN = 15.640 or 150 39’

Note: NU = 25 seen award 1 mark.

1

2

1

4

4(a)

4(b)

4(c)

False

If x5 = -32 then x = -2If x = -2 then x5 = -32

450

1

11

1

15

5(a)

5(b)

5(c)

5(d)

or

Some

5 is greater than zero

n = 0, 1, 2, …

1

1

1

11

5

6 x2 – 3x = 0x(x – 3) = 0x = 0x = 3

1111

4

No Peraturan Pemarkahan Markah

7(a)

7(b)

7(c)

k = 7

mPQ =

3 = (-2) + c

y = x + 4

0 = + 4

x-intercept = -8

1

1

111

11

7

8 (a) 50x

(b)

60

2

120

y

y

(c)

80

40120120360

12060180

z

z

orQRS

P1

K1

N1

K1

K1

N1

6

910912

2

1

727

22 2

727

2210912

2

1 2

452

K1

K1

K1

N1

4

No Peraturan Pemarkahan Markah

10(a)

3

2

72

)(

Bn

48

(b) 46)(,20)( BnRn

66

20)( RP or

33

10

K1

N1

K1

N1

4

11 (a) 77

222

360

120 or 12

7

222

360

90

5127127

222

360

907

7

222

360

120

52.5721

1157

(b) 777

22

360

120 or 1212

7

22

360

90 or 127

2

1

1272

11212

7

22

360

9077

7

22

360

120

48.12221

10122

K1

K1

N1

K1

K1

N1

6

No Peraturan Pemarkahan Markah

12 (a) 57

Note: 55 – 59 , give P1

(b)

I

II

III

IV

V

VI

VII

VIII

Upper boundary: ( I until VIII )

Cumulative frequency: ( I until VIII )

(c) Graph:

Uniform scale and correct axis

Plot all 9 points correctly

Smooth curve

(d) (i) 166

(ii) 63.5 -52.5

= 11

Note: Do not accept answers without an ogive.

P2

P1

P2

P1

K2

N1

P1

K1

N1

12

Mass (g)Frequency

i

Upper

Boundary Cumulative

Frequency

40 – 44 12 44.5 12

45 – 49 20 49.5 32

50 – 54 32 54.5 64

55 – 59 48 59.5 112

60 – 64 44 64.5 156

65 – 69 26 69.5 182

70 – 74 14 74.5 196

75 – 79 4 79.5 200

No Peraturan Pemarkahan Markah13 (a)

Mass (kg)

Jisim (kg)

Frequency

Kekerapan

Midpoint

Titik Tengah

I35 – 39

0 37

II40 – 44

5 42

III 45 – 49 7 47

IV 50 – 54 18 52

V 55 – 59 13 57

VI 60 – 64 4 62

VII 65 – 69 2 67

VIII 70 – 74 1 72

IX 75 – 79 0 77

Class Intervals: ( III until IX )

Frequency: ( I until IX )

Midpoint: ( I until IX )

(b)50

)172()267()462()1357()1852()747()542(

=50

2670

= 53.4

P1

P2

P1

K2

N1

No Peraturan Pemarkahan Markah(c) Graph:

Uniform scale and correct axis,

Plot all 9 points correctly using midpoint or class interval as x – axis

Correct polygon.

(d) Modal class is 50 – 54

OR

Any correct information from the frequency polygon

Note: Do not accept answer without a frequency polygon.

P1

K2

N1

P1

12

14(a)

14(b)

14(c)

(i) 4n(2m + 3)

(ii) (k – 5)(k – 2)

(i) {23, 29, 31}

(ii) {30, 31, 35}Note: = {20, 23, 25,29, 30, 31, 35} seen award 1 mark

(iii) 2Note: = {23, 29} seen award 1 mark

(i)

(ii) mPQ = -3

6 = -3(1) + c

y = -3x + 9

1

1

1

2

2

2

1

1

112

No Peraturan Pemarkahan Markah

15(a)

15(b)

15(c)

4 tan 260 or 1.951

tan x =

x = 65.920 or 650 55’

<DHJ

Tan <DHJ =

<DHJ = 36.870 or 360 52’

1

1

2

1

2

1

1

2

1

12

44.5 49.5 54.5 59.5 64.5 69.5 74.5 79.5

20

40

60

80

100

120

140

160

180

200

Graph for Question 12

Number of Potatoes

Mass

SELAMAT MAJU JAYA

37 47 52 57 62 67 72 77

2

4

6

8

10

12

14

16

18

20

Graph for Question 13

42

Number of student

Mass