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2007 SPM TRIAL EXAMINATION Marking scheme

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1.

2

83 =

yx or

3

82 =x

y

y

2

83y+ 2

2

2

83

y

+ 1 = 0

or

3

82xx + 2x2 + 1 = 0

(3y28y) + (3y8)2 + 2 = 0

or

(2x2 8x) + 6x2 +3 = 0

y =3

11, 3

or

x = 23

, 21

x =2

3,

2

1

or

y =3

11, 3

5

JPNKedah 3472/2 Additional Mathematics Paper 2 [Lihat sebelah]

SULIT2

2

P1 Make x or y as

the subject

Eliminate

x or y

Solve quadraticequation

3y 2 + 20y + 33= 0(3y+11)(y+3 )=

0or

4x 2 8x + 3 = 0(2x-3)(2x-1) = 0

or

using formulaor

completing thesquare

N1

N1

K1

K1

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10

8

6

4

2

2 4 6 8 10 1

2007 SPM TRIAL EXAMINATION Marking scheme

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2(a) 1 + 6x x = 1 ( x 6x )

= 1 [ ( x 2

6)

2

2

6 )( ] use x bx = ( x 2

b)

2

2

)( b

= 10 ( x 3 )

Alternative solution

1 + 6x x = p ( x + q )

= p ( x + 2qx + q )

= p q 2qx x

2q = 6 or p q = 1

q = 3 and p = 10

Curve Sketching :

Correct shape :

Passes through ( 0,1) , ( 3, 10 )4

2(b) f1 exists because for x 4, one value of x is mapped to

one and only one value of y

f1 (x) = 3 + x10 2 6

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JPNKedah 3472/2 Additional Mathematics Paper 2 [Lihat sebelah]

SULIT3

3

P1

P1

N1

P1

P1

Comparing coefficient of x

or constant term

N1

N1

K1

K1

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2007 SPM TRIAL EXAMINATION Marking scheme

3(a)

(b)

a + 9d = 15

S =2

19[ 2a + ( 19 1)d ]

= 19 ( a + 9d)

= 19 15

= 285

2

12

1

1

])(1[96

n

= 1914

1 User

raS

n

n

=

1

)1(

n)(21 =

256

1

=8

21 )(

n = 8

7

21

8 )(96==TTn Use1

=n

n arT

=4

3

4

5 9

4

Shape correct :

Amplitude = 2 :

Full cycle in 0 x 2 : 3

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JPNKedah 3472/2 Additional Mathematics Paper 2 [Lihat sebelah]

SULIT4

4

Use Tn = a + ( n 1)d

N1

N1

Use Sn = 2

n

[ 2a + ( n 1)d ]

Substitute 15 for a + 9d

y

2

2

2

2

3 2x

P1

P1

P1

y =3

4x + 2

K1

K1

K1

K1

N1

K1Copare power

K1

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2007 SPM TRIAL EXAMINATION Marking scheme

4(b)3 sin ( x +

2

) = 2x + 3

2 ( x +2

) =3

4x + 2 or y =

3

4x + 2

Draw the straight line y =34x + 2

Number of solutions is 3 3 6

5(a)

(b)

Use AD = AO + OD or

BC= BO + OC

(i) AD = ~3x +

~

10 y

(ii) BC = ~9 x

~5 y

Use OP = OA + ADm

or

OP = OB + BCn

(i) OP = ~)33( xm +

~

10 ym

(ii) OP = ~9 xn +

~

)55( yn

3 3m = 9n

10m = 5 5n

m = 5

2

,

n =5

1

3

7 10

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JPNKedah 3472/2 Additional Mathematics Paper 2 [Lihat sebelah]

SULIT5

5

Equate coefficientof x or y

Eliminatem or n

N1

N1

K1

K1

N1

N1

K1

K1

N1

K1

N1

K1

N1

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2007 SPM TRIAL EXAMINATION Marking scheme

6.

4272

3365005.10

+=m

L = 10.5

F = 336

C = 4

12.91 kg4 4

JPNKedah 3472/2 Additional Mathematics Paper 2 [Lihat sebelah]

SULIT6

6

K1

N1

Use formula

N2,1,0For L, F, C