add maths final f4 module 3 _ okt 2015 _ p2 _ skema.pdf

7/24/2019 ADD MATHS Final F4 Module 3 _ OKT 2015 _ P2 _ Skema.pdf

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1

Nama Pelajar : Tingkatan 5 : .

3472/2

Additional

Mathematics

Otober 2015

MODUL PENINGKATAN PRESTASI TINGKATAN 4

TAHUN 2015

ADDITIONAL MATHEMATICS

Paper 2

( MODUL 3 )

MARKING SCHEME


2/13

2

SULIT 3472/2

MARKING SCHEME

ADDITIONAL MATHEMATICS PAPER 2 2015

N0. SOLUTION MARKS

1 mn 26 or 26 nm

22632 2 mm

02062 2 mm

01032 mm 025 mm

5m and 2m (both)2n and 16n (both)

P1

K1 Eliminate m/n

K1 Solve quadratic equation

N1

N1

5

2

(a)

(i)

(i)

(ii)

(b)

5)2(2)2( f

= 1

952

952

x

x

7x dan 2x

72 x

3

1)(

1 xgxgh

= 5

3

1x

=15

1x

K1

N1

K1

N1

N1

K1

K1

N1

8


3/13

3

N0. SOLUTION MARKS

3

(a)

(b)

22 0x hx k

S.O.R :

2 3

2

h

2h

P.O.R. :

2 32

k

12k

22 2 12x x m

22 2 12 0x x m

2

2 4 2 12 0m

100 8 0m

12 5m

K1 for finding S.O.R or P.O.R

N1

N1

K1 ( 2 4 0b ac )

K1

N1

6


4/13

4

N0. SOLUTION MARKS

4

(a)

(b)

Quadratic curve a < 0

Maximum point ( 2 , 8 )

Axis of symmetry x = 2

The value of x= -2 , y=0 or x=8 , y= -10

(i) 0 8x

(ii) 2 different roots

P1

P1P1

P1

N1

N1

6


5/13

5

N0. SOLUTION MARKS

5

(a)

(i)

(ii)

(b)

3

2

5125

25 5

a ba b

aa

=a

ba

2

33

5

55

= ba 355

3xy

5log x a ,

5log y b

44

5 5 5 5log log log 125 log125

xx y

y

4 3a b

2 1 212 12x

2 1 2x

1

2x

K1

K1

N1

K1 Use log log loga a am m nn

K1 Use mnm an

a loglog

N1

K1

K1

N1

9


6/13

6

N0. SOLUTION MARKS

6

(a)

(b)

Joseph: 25 3 23 4 24 6 27 1 100 4x

2 2 2 2 2

25 3 23 4 24 6 27 1 2527 22x

Mean100 4

25 14

Standard deviation = 21.254

22.2527

= 340.1

Firdaus: 26 1 24 6 25 8 23 9 100 4x

2 2 2 2 226 1 24 6 25 8 23 9 2523 22x

Mean100 4

25 14

Standard deviation =21.25

4

22.2523

0 8916

Firdauss performance is more consistent.

Prestasi Firdaus lebih konsisten.

The standard deviation is smaller.

Sisihan piawainya adalah lebih kecil.

K1 (usingN

xx

)

K1 (using 22

xN

x

)

N1

N1

N1

N1

6


7/13

7

N0. SOLUTION MARKS

7

(a)

(b)

Correct axes & uniform scale

Draw 5 bar correctly

Show the method to find mode

Mode = 2.25

Midpoint = 1.2, 1.7, 2.2, 2.7, 3.2

Mean=

1.2 5 1.7 8 2.2 20 2.7 10 3.2 7

50

2.26

222222 )2.3(7)7.2(10)2.2(20)7.1(8)2.1(5 fx

22

xf

fx

=2)26.2(

50

7.271

= 5713.0

K1

K1

K1

N1

K1

K1

N1

K1

K1

N1

10


8/13

8

12

14

16

10

8

2

4

6

Weight

Number of

Durian

18

00.95 1.45 1.95 2.45 2.95 3.45 3.95

20


9/13

9

N0. SOLUTION MARKS

8

(a)

(b)

(c)

(i)

(ii)

(d)

2 2 2 2( 6) (6 12) 6 (12 4)

14

h

h

2 3(6) 2 3(12)14 6

5 5

(26, 3)

x yor

m =4

3

4( 3) ( 26)

3y x

4 113/ / 3 4 113

3 3y x y x

89(6, )

3

Area =

1 896( 3) 26(12) 6(4) 6(4) 26( ) 6( 3)

2 3

2541

3

K1

N1

K1

N1

P1

K1

N1

N1

K1

N1

10


10/13

10

N0. SOLUTION MARKS

9

(a)

(b)

(c)

18060

= 1.047

5.237 300rad or

42.31

237.56

RQS or95.20

237.54

PSS

Perimeter = 31.42 + 20.95 +2 +2

= 56.37

21 6 5.2372

94.27

Area

214 5.237

2

41.896

Area

Area = 94.2741.896

= 52.374

K1

N1

P1

K1 Use rs

K1

N1

K1 Use21

2A r

N1 For

94.27 or 41.896

K1

N1

10


11/13

11

N0. SOLUTION MARKS

10

(a)

(b)

6 4 2

6 61

dyx

dx

xx

1

3 4 1

(1 , 1 )

x

y

H

1 1

1 2

1 1

2 2

y

x

y x

2

2

2 3

(6 )

(6 )

V r h

r r

r r

2(12 3 ) 0

(3 )(4 ) 0

0( ) 4

dVr r

dr

r r

r ignored r

2 26(4) (4)

32

V

K1

N1

K1

N1

K1

N1

K1

N1

K1

N1

10


12/13

12

N0. SOLUTION MARKS

11

(a)

(i)

(ii)

(iii)

(b)

(i)

(ii)

6.8

5.40sin

1.12

sin

PQR

04.66PQR

PSRkos )8.4)(4.9(28.44.91.12 222

83.112PSR

46.73sin1.126.82

1AreaPQR

Or

83.112sin8.44.92

1AreaPSR

79.2088.49 AreaPQRS

= 70.67

113.96

K1

N1

K1

N1

See 73.46

P1

Find Area of

PQR or PSR

K1

K1

N1

N1

N1

10

Q

PR


13/13

13

N0. SOLUTION MARKS

12

(a)

(b)

(c)

(d)

10020.2

110 x

00.2x

118

10000.5

90.5

y

y

20.16

13510000.12

z

z

1210

120(18) 110(10) 118(45) 135(27)

100I

= 122.15

10040

15.122 12 Q

86.4812 Q

100

15.122115

10

15 I

=140.5

K1 Use

10010

12

Q

QI

N1

N1

N1

K1

N1

K1

N1

K1

N1

10

END OF MARKING SCHEME

add maths final f4 module 3 _ okt 2015 _ p2 _ skema.pdf

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