TRIAL ADDMATE SPM 2010 Pahang Paper 2 Answer

8/8/2019 TRIAL ADDMATE SPM 2010 Pahang Paper 2 Answer

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SULIT 3472/2

SULIT 1 3472/23472/2@2010 HAKCIPTA PKPSM PAHANG

SCHEME ANSWER OF PAPER 2

No. PERATURAN PEMARKAHAN MARKAH MARKAHPENUH

1 x=2y-4 or y = 1

Substitute x or y in equation 2

y2

-3(y)*(2y-4) =6 or

or

1

5y2 -12y +6 =0 or 5x 2 +16x+8 =0Solve quadratic equations by using a formula orcompleting the squareUsing a formula

y =1

By completing the squareOr 1

y = 1.69, 0.71 10

x = -0.62, -2.58 1 52

6 4

1, 2

dy x

dxdy

xdx

(a) Equation of the tangenty-2 = 2(x-1)

y =2x

(b) approximate change in x

=8

1

1

1

1

1

or

1

16

3

i

ii

BA AC BC or BA AT BT or BT TC BC oranother valid method

2 AC y x

12

BT x y

1

1

1


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SULIT 3472/2


AP y x

*12

BR k x y

*

1

BR h y x y

BR h y hx

Compare:1

1 ,2

k h k h

1 2,

3 3h k

1

1

2 7

4

(a) 1

1

5 210.5 10516.5

Q

Q

=35.5Interquartile range=35.5 -16.5

= 19

6

5

4

3

2

1

numberofstudents

marks23.5 50.540.530.520.510.50.5

Score mode = *23.5

1

or

1

1

1

3

1 7


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SULIT 3472/2


No.PERATURAN PEMARKAHAN MARKAH MARKA

HPENUH

5

2 2 22

2cos tan sec

2cos 1

cos2

LHS

x x

x

x

or any correct method

Shape of cosineAmplitude (maximum and minimum)ShiftedStraight line (gradient or y-intercept) for

3 cos 2x -1 = or 3 x

y

Number of solutions = 4

1

1

11111

1 8

6(a) used formula 2 1

2n

nS a n d

2

2

12

20 12 8

2 12 1 8 17602

12 4 4 1760 0

2 440 0

22 20 0

22@ 20

n

a

d

nS n

n n

n n

n n

n n

1

1

1n=20


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SULIT 3472/2


(b) Used 1nT a n d

108

108 12 1 8

13

nT

n

n

(c) 20

20

12 19 8

164

T

T

1

1

1

17

Section B

7 10log 2 x

0.30 0.48 0.60 0.70 0.78

10log y 0.54 0.68 0.77 0.86 0.92

Refer to the appendix 1

Minimum 1 point plotted correctly(Correct axes and uniform scales)5 *points are correct plottedLine of best fit (at least 3 points lies on the straight line andthe other must be balance)

2 n y k x

10log log log 2 y k n x 10 10 10log log 2 log y n x k

0.80m n 100.3 logc k 1.995k

1

1

1

11

1

11+1

1

10

8

(a)

20, 9

3

0,3 , 0, 3

x y

y

Q R

solve simultaneous equations

2 3 9

3 4 0

3@ 4

4 3 7

7, 4

y y

y y

y

x

P

1

1

1


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SULIT 3472/2


(b)

or

area of shaded region= 2

=

=

= 2 -0}+

=

(b) Volume of generated

V=

V= -

=

1

1

1

1

1

1

1 10

9

(a)

1 2

2

0,2

1

2

32

23

L

m m

m

y x

Used formula a point dividing a segment of a line

(b) (i)

2 3 1 2 0 10, 2 ,

3 3

6,6

x y

M

1

1

1

1

1


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(ii) use area of triangle

2

1 86

2 3

133

unit

(c) 2

2 2 2

2 2

2

46 6 4 0

3

4 83 3 12 64 0

3 9

WM WK

x y x y

x y x y

1

1

1

1

1 10

10(a) mean, (i)

8 6.40.8

p p

p

(ii)find

0 8 1 7 2 68 8 8

0 1 2

3

1 0.8 0.2 0.8 0.2 0.8 0.2

P X

C C C

or using 3 3 4 5 6 7 8P X P X P X P X P X P X P X

0.9988 or 0.99877

(b) use 5.3 0.0668P z

or4.8

0.1587P z

5.31.5

4.81

Solve simultaneous equation (until 1 variableleft)

0.2, 5

11

1

Or 1

1

1

Or 1

1

1

1

1+1

10

11(a)

Used trigonometric ratios3

tan5

30.96 0 0.54 rad

1

1

2

(b) Used Pythagoras Theorem to find OR2 23 5 5.831OR


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SULIT 3472/2


5.831 5 0.831PQ 5.831 0.54QR

3.149

Used trigonometric ratios to find PRO

tan PRO =

PRO = 59.04 or

1.031 r 3 1.031 3.093SP

Perimeter of shaded region3 3.093 0.831 3.149 10.073

10.07

1

1

Or 1

1

1

4

(c) Area of sector PRS

21 3 1.0312

4.6395

Area of sector QOR

21 5.831 0.542

9.1802

Area of triangle OPR

1 3 52

7.5

Area of shaded region9.182 7.5 4.6395

=6.32

1

Or 1

Or 1

1

1 4

Total marks 10Section C

12 (a) Used sine rulesin sin 325.7 4.9

sin 0.6164

38.06

Q

Q

PQR

1

1


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(b) Used cosine rule

2 2 24.5 2.7 5.7cos

2 4.5 2.7

cos 0.2037

101.76

S

S

PSR

(c) Used sine rule or cosine rule

*

4.9sin 109.94 sin32

8.692

PQ

PQ

(d) Area of triangle PQR

* follow through

Area of triangle PSR

1 4.5 2.7 sin101.752

Area of PQRS1 2

13.13 5.94819.078

A A

1

11

1

1

1

Or

1

1

1

10

13 20, 18, 200 x y z

(b)Ingredient 2007/ 2005 I w wI

A 150 36 5400B 120 72 8640C 200 108 21600D 130 144 18720

360 54360

(b) Used

54360

360

151

Iw I

w

I

I

3

1

1

1

PSR =101.75 0

19.08

or equivalent


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SULIT 3472/2


(c) 20052005

3322100 151

2200

Q

Q

(d)

130151

100196.3

1

1

1

1

10

14

(a)

. 80

1.

2.420 240 20000

21 12 1000

I x y

II y x

III x y

x y

(b) Draw correctly at least one straight line * Draw correctly all three straight linesR correctly shaded.Refer to appendix 2

(c) (i) 31 x 50(ii)

* *

* *

420 53 240 26

28500

420 5 240 75

20100

or

The maximum fees collected is 28500

1

1

1

111

1+1

1

110

15 (a) 0 10v

(b) 8 4a t

08a

(c) , 8-4t =0t = 2

2maxmax

10 8 2 2 2

18

v

v

1

1

1

1

1

1


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SULIT 3472/2


(d)

2

2 2

10 8 2

210 4

3

s vdt t t dt

s t t t

At least two terms changes their index.

Stops instantaneously, 0v

210 8 2 0

5 1 0

5@ 1

t t

t t

t t

2 3210 5 4 5 53

266

3

s

s

1

1

1

1

10

t3

Or=


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Appendix 1Graph 7(a)


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Appendix 2


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Graph 14(b)

END OF SCHEME ANSWER

SKEMA PEMARKAHAN TAMAT

TRIAL ADDMATE SPM 2010 Pahang Paper 2 Answer

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