PEPERIKSAAN PERCUBAAN BERSAMA SPM NEGERI PERLIS 2012 ADDITIONAL MATHEMATICS PAPER 1

No. Answer Sub-mark Total marks

1. (a) 1 and 7 (b) {e, g, h}

1 1

2

2. (a) 1 B1 : 2𝑥 + 3 = 5 or 𝑓!! 𝑥 = !!!

!

(b) 4𝑥! + 2𝑥 B1 : (2𝑥 + 3)! − 5 2𝑥 + 3 + 6

2 2

4

3.

473 −x

B2: ( ) 5324 −=+ xxg B1: ( )

25312 −=+ xxg

3 3

4. 5143 2 −+ xx B1 : 3𝑥 − 1 𝑥 + 5 = 0

2 2

5. 2or1 =−= hh B2 : ℎ + 1 ℎ − 2 = 0 B1 : 6ℎ ! − 4 ℎ + 2 9 = 0

3 3

6. (a) p = 3 (b) q = 47 (c) x = 5

1 1 1

3

7.

322 ≤≤− x

B2: 3𝑥 − 2 𝑥 + 2 ≤ 0 B1 : 3𝑥2 + 4𝑥 − 4 ≤ 0

3

3

8. n = –2 B1: 32(2n + 1) = 33n or 4n + 2 = 3n or equivalent

2 2

9. x = 10 or x = –2 B3: x2 – 8x – 20 = 0

B2: 452

2

=+xx

B1: log252

2

+xx

= 2

3 3

10. y =

81

2x

B2: log3y – 2 log3x = –4 or equivalent

B1: xy

33

3 log29log

log=+

3 3

11. (a) 4 (b) 559 B2: 𝑠18 - 𝑠5 = 594 − 35 B1: 𝑠18 =

182

[2(-1) + (17)(4)] or 𝑠5 = 52 [2(-1) + (4)(4)]

1 3

4

12. n = 8 B2 :![ !!)

!!!!!!  !

= −3280 B1: r = −3

3 3

13.

427,

43

=−= ba

B3 : either one correct B2 : baxxy += 2

B1 : gradient = 1563

−

−

4 4

14. ji 213 − B1 : jiji 5776 ++−

2 2

15.

(a) 3=p B1 : )2(64 jpiji +=+ λ

(b) 13 B1 : ji 32 +

2 2

4

16. oooo 225,'26198,45,'2618 B3 : oo 45,'2618

B2 : 0)1)(tan1tan3( =−− xx or 1tanor31tan == xx

B1 : xxx 22 tan1tan2tan4( +=−

4 4

17.

nm

38

=

B1 : 123

4−=⎟

⎠

⎞⎜⎝

⎛⎟⎠

⎞⎜⎝

⎛ − nm

2 2

18. (a) 6.5 B1 : 1.084 radians (b) 22.9

B1  :   )084.1)(5.6(21

       

2 2

4

19. −44 B3 : )92()32(4 22 +− xxx B2 : [ ] 4233 )32(12)2()32(44 −−− xxxx B1 : )2()32(4 3−x or 212x

4 4

20. 1cms1 −π

B2 : Use of chain rule :dtdrr ×= π28 or equivalent

B1 : rdrdA

π2= or r = 4cm

3 3

21. 6

B3 : 523)1(

3)3( 33

=−pp

B2 : 603

83

1

3

=⎥⎦

⎤⎢⎣

⎡+px

B1 : 3

3pxis seen

4 4

22. (a) 93 (b) 1296

1 1

2

23. (a) 720 B1 : 6! (b) 240 B1 : 5!×2!

2 2

4

24. (a)

151

(b) 6029

B1 : )43

51

31()

43

54

32()

41

51

32( ××+××+××

1 2

3

25. (a) 0.6915

B1 : )35.1817( −>zP

(b) 34 B1 : 50 × 0.6915

2 2

4