MRSM TRIAL SPM 2011 PAPER 2 ANSWERS 1. 7x2 + 5x 2 = 0

(7x 2)(x + 1) = 0

x = 72 , 1

y = 7

13 , 2

2. Surface area A = 2(2xy + xy + 2x2) = 6xy + 4x2 72 = 2x2y

A = 4x2 + x

216

A = 4x2 + 216x1

2

2

2168

2168

xx

xxdxdA

For min/max value, 0dxdA

02168 2 x

x

278

2163 x

x = 3, Amin = 108 cm2

3. Number of solutions = 8

4. (a) range of scores = 10 6 = 4

(b) 20

1751.8 y

y = 13

(c) 375.189.11.820

1350 2

21 xy

2

5. (a) Area : 5x , 5(x + 2), 5(x + 4), .. T6 = 80 5x + (6 1)(10) = 80 5x = 30 x = 6 (b) Perimeter : 22, 26, 30, … Sn ≤ 450

2n2 + 20n ≤ 450

n2 + 10n 225 ≤ 0

n = 10.8, n ≠ 20.8

n = 10

6. (a) ~~

810 xyTS

~~

86 xyTK

(b) (i) ~~ 3

1083

16 ynxnTQ

(ii) QKTQ

~~

456 xnynTQ

Comparing ~x :

8

3164 nn

~y : nn

31056

n = 119

7.

qpxy

63

qxpy

23

1

Refer graph

(b) (i) Gradient 3p = 0.78, p = 2.34

(ii) y-intercept = 0.53 2q = 0.53 q = 0.265

(iii) when x = 1, 455.01

y

y = 2.198 8. (a) 0.5237 rad

(b) Perimeter = 6 + 10.392 + 8.785 + 6.284 = 31.461 cm (c) Area = 152.496 cm2

3

9. (a) (i) npx

3.5 = 10p p = 0.35 (ii) P(x ≥ 2) = 1 P(x = 0) P(x = 1) = 0.914 (b) (i) P(298 < x < 303) = P(0.5 < Z < 0.75) = 0.4649 (ii) P(x < k) = 0.005

005.0)4300(

kZP

005.0)575.2( ZP

575.2)4300

k

k = 289.3

10. (a)

332

32

xy

(b) 1123

xy , C = (10, 4)

(c) Area = 00

1148001040

21

= 87 unit2

(d) Locus : x2 + y2 8x 16y 20 = 0

11. (a) A = (3, 5)

(b) Area Q = 3

2

)2()52(23 dxx

= 6 unit2

(c) Volume =

0

4

84dyy

12. (a) (i) 012163 2 tt

dtds

t = 6 , t ≠ 32

(ii) 12163 2 ttv

a = 0166 tdtdv [velocity decreasing where a < 0)]

38

t

(b) a = 3t + 2 dttv 23

4

cttvQ 223 2 where VP =VQ = 28 when t = 4

c = 60

60223 2 ttvQ

13.

(a) Using Area A = ab21 sin

= 59, KLM = 180 59 = 121 [Obtuse ] (b) Using Cosine formula, KM = 6.532 cm (c) MN = 194.75.38 22 Using Sine formula , KNM = 51.85 (d) KMN = 180 60 51.85 = 68.15

Area A = 21 (6.532)(7.194)sin 68.15 = 21.807 cm2

14. (a) y = 2, x = 150, z = 0.4

(b) 83

)2(80)3(150)5(1401255.114

kkk

k = 4 (c) Total cost in 2006 = RM1800 (d)

20062008

20062010 2.1 II = 1.2(114.5) = 137.4

15.

(a) x + y ≥ 35 30x + 20y ≤ 2400 y ≥ 2x (b) Refer grapb (c) (i) min. A = 5 (ii) Max. Profit = 10x + 15y, subst. (0, 120) = 10(0) + 15(120) = RM1800

5

6

No.7

0 1 2 3 4 5 6

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

0.55 y1

x