3472/2(PP)ADDITIONAL

MATHEMATICS

Paper 2

Aug / Sept 20142 hoursPEPERIKSAAN PERCUBAAN SPM TAHUN 2014

ADDITIONAL MATHEMATICSPERATURAN PEMARKAHANKertas 2

QuestionWorkingMarks

1x + 2y = 1 , x2 xy = 1 or equivalentx = 1 2y or y= (1 2y)2 (1 2y)y = 1 or x2 - x( = 1 y (6y-5) = 0 or (3x +2) (x 1) = 0y = 0, y = or x =, x = 1x = 1, x= or y = , y = 0 1

1

1

1

1

5

2(a)(b)

(c)r = x = 1458

r = S5 = 19440

= 19440a = 13 12213 122 < 0.01Taking log both sides + simplifyn = 1411

1

1

1

1

1

7

3(a)3(b) (i)

3(b) (ii)

LHS =

=

= cosec2 x

Shape of curve correct

2 periods with correct magnitude OR vertical shift 1 unitAll correct1 cos 2x = 2 - Straight line y = 2 - correctly sketchedNumber of solutions = 4

11

1

11

111

8

4(a)(b) = 6x + & substitute x = -1 = -5

y 4 = -5 (x + 1)y = -5x -1

V = 2x2h = 2x2 (90 3x)

= 180x2 6x3 = 360x 18x2 = 0

x = 20

Vmax = 24 000 cm3

111

1

1

1

1

7

5(a)(b)

(c) Score

0-19

20-39

40-59

60-79

80-99

No of students

0

51683

55.13Refer to Graph in page 8 1113

6

6(a)(i)(ii)(b)

* or *follow through = Using h = or -4 + , 11

1

1

11+1

7

7(a)(b)

(i)

(ii)

(iii)x2

3

4

5

6

7

Log 10 y

0.890.780.660.550.440.32

(at least two decimal places)Graph - correct axes with uniform scales All points correctly plotted

Line of best fit

Refer to graph on page 9Use Y- intercept = log10 h gradient = log10 kGradient = -0.1140.01k = 1.30 0.05h = 13.18 0.10y = 4.050.0511

1

1 11

1

1

1

1

10

8(a)(i)(ii)

(b) (i)(ii)

(c)

k = -2

Gradient of PQ = Finding equation of PQ : y = any method to find intersection point between line SP and QPP(2, 4)

or 0 = Q(14, -2) Menggunakan formula dengan betul = 60 = 3 or equivalent

x2+y2 = 911

1

1

1

11

1

1

1

10

9(a)(b)(i)

(ii) QPR = cos-1( 1.318 rad RS = 16 sin or = 15.492 Arc length = s = (10) (1.318) 0R arc length TS = 6(1.824) perimeter= 15.492 + 10.944 + 13.18 39.62 cm OR 123.936 - 65.900 - 32.83225.20 cm2

111

1

11

1

1

11

10

10(a)(i)

(ii)

(b)(i)

(ii)

p = 0.9 or q = 0.1

0.7361 =0.9487P( X > 45) = P = P (z > -1)

= 0.8413

No. of students who passed = 0.8413 x 300 = 252 orang

P (X > k ) = 0.1200

k = 77.63 78 marks1

1

1

1

1

1

11

1

1

10

11(a)(i)(ii)

(b)

(c)

f(x) or = y = y = y = Ax = = = = 42

Shaded area = 42 18 = 24 unit2Vy =

= 108

111

11

1

11

11

10

12(a)(i)(ii)

(iii)

(b) v= 3t2 -21t +18 3(t-1)(t-6)=0

t=1, t =6(1)3 -(1)2 +18(1) or (6)3 -(5)2 +18(6)

62.5 6t -21 =0

-18.75 m/s Correct shape

Correct minimum point and the roots or y-intercept All correct11

1

1

1

1

1

1

1

1

10

13(a)(i)(ii)

(b) (i)

(ii)

AC2 = 252 + 92 2 (25)(9) cos 500AC = 20.41 cm

( ACB = 21.890

( BAC = 129.890Finding BC = 16.46cm (Using Sine rule or any relevant method to find a second side) OR = 31.13 OR OR Area of area of = 31.14 62.64 31.49 = 31.151

1

1

1

1

11

1

11

10

14(a) (b)

(c)(i) (ii) w = 8 x

= 10.00 y = x + 5 x 100 = 150 *any one eqn correct

Solving, x = 10

y = 15

50 x RM 65.75131.5 = Solving m = 5 11

1

1

1

1

1

11

1

10

15(a)(b)

(a)x > 20

y 10

x + y 80

x 3y (or y x )

(b) Axes correct and one *straight line correct

Draw correctly all 4 straight lines

Region R is correctly shaded and labelled.

(Please refer to appendix)

(c)(i)20 < x 60

(ii)200 (21) + 400 (59)

The maximum fees collected is RM 27 800

Sila rujuk graf (Lampiran 1)11

1

1

111

1

1

1

10

Appendix / Lampiran 1Graph for Question 15 [LINEAR PROGRAMMING]

2

1

x

2

O

-1

6

1

18

t

v

7

0

-18.75

B

A

A

C

21.890

10.15

16.46

8

8

10.26

50.110

50.110

129.890

28.220

79.780

y

10

20

0

30

40

50

60

70

80

80

50

40

30

70

60

20

10

R

x

100

90

(21, 59)

x+ y = 80

X

x = 3y

x = 20

y = 10

xy

Frequency /

Bilangan murid

2

4

6

8

10

12

19.5

39.5

59.5

79.5

99.5

Mode=50.5

x-axis and y-axis drawn correctly 1M

Histogram drawn correctly 1M

Mode = 50.5 1.0 1M 1M

16

14

Question 5(b)

Marks

[Horizontal axes : Use either class boundaries or midpoints / class marks]

log10 y

Question 7(b)

7

6

1.1

1.0

0.9

0.8

0.7

0.2

0

0.3

0.4

0.5

0.6

x

5

4

3

2

1

NOTE : Skala paksi seragam : MESTI mula dengan 0, 1, 2, dan BUKAN 0, 2, 3, 4, !!!

2