SET A

1

PERATURAN PEMARKAHAN PEPERIKSAAN PERCUBAAN SPM 2017

PROGRAM INTERVENSI TERBILANG AKADEMIK SELANGOR

(PINTAS)

MATEMATIK TAMBAHAN KERTAS 2

NO SOLUTIONS MARKS

1 xy – 8 = 2 (2x - y) = 3x + 1

x

xyor,yx

9321

113821 yyy

x

xxxyxor

93211324

018701252 22 xxoryy

0920432 xxoryy

X = -2 , 9

42

3,y

P1

P1

K1

K1

N1

N1

6

2 (a) r = 2

25412

122

25512

121

n

or

n

n = 8 or n= 7

Number of rows = 15

K1

N1

N1

3

6

(b) a =1, n =8 or a = 2, n = 7

( 27 ) or 2 (27 - 1)

(Note: or correct listing P1 K1)

128

P1

K1

N1

3

SET A

2

NO SOLUTIONS MARKS

3

(a) 14- Markah Ben = 7 or 10

7

ShimaMarkah + 62

Markah Ben = 7 dan Markah Shima = 8

K1

N1

2

6

(b) 2107

21721421228272725

**

4.071

K1

N1

2

(c) min = 20, varians = 66.29

N1,N1

2

4

1221 Akos

Akos

Asina

2 sin A kos A = sin 2A

K1

N1

2

8

(b)

P1

(sin

graph)

P1 (2 cycle)

P1 reflect

P1 translasi 4

2

3

212(c)

k

k

K1

N1 2

5 (a) A (30,40) dan C(60,20)

P1 1

7

(b) D (90, 60)

22 6090

108.17

P1

N1

K1

3

(c) DA : DC = 2 : 1

3

8050

3

402(20)

3

302(60)

,

or

P1

K1

N1

3

x

y

1

O 2

2

SET A

3

NO SOLUTIONS MARKS

6 (a)

3

1normalm or xx

dx

dy623

Solve 3623 xx

x = 1

P ( 1, -2)

P1

K1

N1

3

7

7

33

1=-2*(b)

k

k

K1

N1

2

(c) y + 2 = - 3( x – 1)

y= - 3x + 1

K1

N1

2

7 (a) methodvakidotherorsin

5

3

2

36.87o or 0.6436 rad

1.287

(Note: methodvakidotheror K1N1N1)

K1

N1

N1

3

10

(b) 5 (*1.287)

6.435 cm

K1

N1

2

(c) 1.855

21

8551252

12

8551252

11

AA*

.*sinAtriangleofArea

.*AsektorofArea

11.19 cm2

P1

K1

K1

K1

N1

5

8 (a) x2 + 4 = 4x

k = 2

K1

N1

2

(b) A1 = 2

0

32

02 4

34

x

xdxx

K1

K1

SET A

4

NO SOLUTIONS MARKS

A2 = 2

0

22

0 2

4482

2

1

xdxxor

𝐴1 − 𝐴2 = ∫(𝑥2

2

0

+ 4 ) 𝑑𝑥 −1

2(2)(8)

Area of the shaded region = 2 [∫ (𝑥22

0+ 4 ) 𝑑𝑥 −

1

2(2)(8)]

5.333 unit3

K1

K1

N1

5

10

(c) Volume = 𝜋 ∫ (𝑦 − 4)𝑑𝑦5

4 = [

𝑦2

2− 4𝑦]

5

4

16

2

1620

2

25

0.5 𝜋 // 1.5708 // 1.571

K1

K1

N1

3

9

(a) (i) n = 10, p = 0.7 , q = .03

1091

8108

xPxPor

xP......xPxPxP

rrr ..CUse

1010 7030

0.85065 // 0.8507

(ii) 6.72 = n(0.7)(0.3)

n = 32

K1

K1

N1

K1

N1

5

10

(b) X ~ N ( 56 , 32 )

students.

.

.ZP

ZPXPi

15450030850

30850

50

32

564040

ii) P(X > m) = 0.12

marksm

m

mZP

6.93

175.132

56

12.032

56

K1

N1

N1

K1

N1 5

SET A

5

NO SOLUTIONS MARKS

10 (a)

lg(x+1) 0.3 0.48 0.60 0.70 0.78 0.85

lg y 0.85 0.76 0.70 0.65 0.61 0.58

N1

N1

2

10

(b) Refer graph paper

Plot log10 y against log10 (x+1) (at least one point)

6 points plotted correctly

Line of best fit N1

K1

N1

N1

5

(c) blogxlogaylog 101010 1

P1

K1

N1

K1

N1

5

11 (a)(i) 1

3OP OA AB

= 10 2x y

(ii) 3

5AQ AB BC

= 6 6y x

K1

N1

N1

3

10

1 (ii)

2

1

2

1 (i)

10

b

blog

a

a

i)

SET A

6

NO SOLUTIONS MARKS

b) (6 6 )AR h y x

= 6 6hx hy

AR AO OR AO kOP

= 10 (10 2 )x k x y

(10 10) 2k x k y

6 h = 2 k

– 6 h = 10 k – 10

h = 5

18, k =

5

6

K1

K1

K1

N1, N1

10

(c) OS OA AS

10 10 (6 6 )y x m y x

5

3m

K1

N1

12 (a) 125100

168

x or 100

90

99y

210RMx

y = 110

K1

N1

N1 3

10

(b) m + n = 35

115100

4011010512025125

nm

8m + 7n = 265

8(35 – n) + 7n = 265

m = 20

n = 15

K1

K1

K1

N1

N1 5

(c) 115100

120I

= 138

K1

N1

2

SET A

7

NO SOLUTIONS MARKS

13 (a) 200 500 x

700 yx

2002 yx

N1

N1

N1 3

(b) Graf (satu garis betul)

(semua garis betul)

(rantau betul)

K1

N1

N1

3

10

( c )(i) Maximum number of arts students= 450

(ii) (500, 200)

k = 800x + 600y

= 800(500)+600(200)

= RM 520 000

N1

N1

K1

N1

4

14

(a) (2t + 3)(t – 2) = 0

t = 2

a = 4 t – 1

= 4(2) – 1

= 7 m s – 2

K1

K1

N1

3

(b) a = 4t – 1 = 0

111

2

//8

49//

8

16

6)4

1()

4

1(2

4

1

ms 6.125 ms msv

v

st

K1

K1

N1

3

(c) dttts )62( 2

ttt

623

2 23

S2 = 3

28122

3

16

S3 = 2

1418

2

918

K1

K1

K1

4

SET A

8

NO SOLUTIONS MARKS

d = m 2.83 m m 1//6

77//

6

512)]

2

14(

3

28[

3

28

OR

N1

15

(a) AE2 = 202 + AE2 - 2(AE)(20)cos 300

AE = 11.55 cm

K1

N1

2

10

(b) (i) ½ (20)(11.55) sin 300 = 2 ( ½) ( CE)(10) sin 600

6.668 cm

(ii) CD2 = 6.668*2 + 102 - 2(6.668*)(10) cos 60o

8.819 cm

K1, K1

N1

K1

N1

5

0

0

9040

8198

60

6.668*

CDEsin (c)(i)

.

.*

sin

(i)

K1

N1

N1

3

C

EF

D

dtvvdt 3

2

2

0 K1

Correct integration K1

Correct limit K1

Correct answer N1

SET A

9

Question 10

0.1 0.2 0.3 0.4 0.5 0.6 0.7

lg(x+1)

0.1

0.2

0.3

0.4

0.5

0.6

1.0

0.9

0.7

0.8

log10 y

x

x

x

x

x

x

Graph log10 y against log10(x+1)

0.8

SET A

10

n

100

1

200

2

300

3

400

4

y

500

4

600

4

700 800 0

100

1

200

1

300

1

400

1

500

1

600

1

700

1

800

1

R 500,200

x

Question 15

SET A

11