Skema SET 2 Kertas 2

Skema SET 2 KERTAS 2 3472/2

SECTION A [40 MARKS]

No. MARKING SCHEME MARKS

1 P1 or y = x

x + y = 6xy P1

= 6y KI or = 6x

24y2 – 18y – 3 = 0 or 24x2 – 18y + 3 = 0

(4y – 1)(2y – 1) = 0 K1 or (2x – 1)(4x – 1) = 0

y = , N1 or x = ,

x = , N1 or y = ,

6

2

(a) = –3x2 + 6x – 1

= K1 or 3[(x – 1)2 + (1)2]

= N1

(b)

(c) 6x – 4 – 3x2 = p

3x2 6x + p + 4 = 0

(6)2 – 4(3)(p + 4) < 0 Using b2 – 4ac < 0 K1

– 12p < 12

p > 1 N1

6

1

(1, 2)

1 (2, 1)

P1 for the shape

P1 for the curve passing through (1, 2) and any other 2 points.



3(a) (2t, 6) = or = 4

2t = K1 or 3t = 4

t = N1

= 1 N1(do not accept )

(b) 3RQ = 2QN

3 = 2 K1

x2 + y2 – 4y – 257 = 0 or x2 y2 + 4y + 257 = 0 N1

(c) Area =

= | 0(12) + (4)(10) + ( )(0) + ( )(2)

(4)(2) ( )(12) ( )(10) 0(0) | K1 or use any triangle 2

follow through from the value of t in ( a )

=

= 21 unit2 N1

7

2

P1 (any 2 are correct)



4(a) T1 = 2r +

T2 = 2(r + 1) +

T3 = 2(r + 2) +

T4 = 2(r + 3) +

11(4 + ) = 2r + + 2(r + 1) + + 2(r + 2)

+ + 2(r + 3) + K1

22(4 +) = 16r + 4 r + 24 + 6

64 + 16 = r(16 + 4)

OR

a = 2r + or d = 2 + P1

S4 = = 44 + K1

r = 4 N1

r4 = 7 N1

(b) 120 + 30 = K1

P1 for d =

n = 8 N1

7

3



5 (a) mean new = (previous mean 20) 2

= (5 20) 2 K1

= 98 N1

new = 7 5 K1

= 35 N1

(b) L = 395 or F = 13 or f = 11 P1

K1

5223 N1

7

6 (a) K1 for using trigonometric ratio (sin, cos or tan)

tan =

2·162 rad. N1

(b) s = 8 2·162 K1

= 17·30 N1

(c) K1 for area of KMON or area of minor sector MON

= 2 15 8 or = 82 2·162

K1 for area of KMON area of minor sector MON

= 120 69·18

= 50·82 N1

7

4


SECTION B [40 MARKS]


7(a) (i) t = K1

A = 2πr + 2πr N1

(ii)

K1

r = 4 N1

A = 96π N1

(b) (i) = 4

P (1, 4) P1

(ii) V = π K1 for V or V = π(4)2(1)

= 16π + 16π [x] K1 for the integral

= K1 for V + V

= 29 π unit N1

10

9 (a) (i) 5Cr prq5 r , p + q = 1

p = 04 , q = 06

K1

0·3456 N1

(ii) 1 – [P(X = 0) + P(X = 1)] or

P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)]

1 – [ (0·4)0(0·6)5 + (0·4)1 (0·6)4] K1

0·66304 N1

10

5



9

(b) (i) Use

K1

000982 N1

(ii) P(X > m) = 0·7

= 0·7 K1

= 0·524 K1

m = 2·657 N1

10(a) (i) = 2x + 3y N1

(ii) = 2x + y N1

(b) = m

= m(2x + 3y) P1

= +

= 2x + n(2x + y) K1

= (2 – 2n)x + ny N1

m(2x + 3y) = (2 – 2n)x + ny

2m = 2 – 2n K1

m + n = 1 N1

10


6


10

(c) = +

= – x + y + 2x K1

= x + y N1

= (2x + 3y)

= or = 3 . N1

11

(a)

= K1 for sec x = in

expansion

=

= N1

= cos x

10

7



11 (b) 3 sin 2 = tan

3 (2 sin cos ) = K1 for 2 sin cos and

6 sin cos2 sin = 0

sin (6 cos2 1) = 0 K1 factorisation

sin = 0, cos =

0, 180 or 65·91, 114·09, 245·91 P1

= 0, 65·91, 114·09, 180, 245·91 N1(exactly 5 solutions)

(c)

K1 for sine shape graph

P1 for a straight line equation y = 2

N1 for equation of the straight line y = 2

N1 no. of solution = 3

10

SECTION C [20 MARKS]


12(a) use

or or

K1

x = RM 6·00 N1

y = RM 5·50 N1

z = 130 N1

10

8

0

2

1

2


12(b) Use

P1

= K1

= 132·1 N1

(c) Use

K1

or 360 P1

= 121·7 N1

10

13 (a) TSU = 180 – 94 – 25

= 61 P1

K1

SU = 15·97 cm N1

(b) 62 = 122 + 15·972 2(12)(15·97)cos RUS K1

RUS = 18·70 N1

(c) RUT = 25 + 18·70 = 43·7

RT2 = 122 + 142 2(12)(14)cos 43·7 K1

RT = 9·853 cm N1

(d) (12)(15·97)sin 18·7 or (14)(15·97)sin 25 K1

(12)(15·97)sin 18·7 + (14)(15·97)sin 25 K1

77·97 cm2 N1

10

9



14(a) = 16 – 8t = 0 K1 (for 16 – 8t = 0)

t = 2 s N1

vmax = 16 ms1 N1

(b) s = dt K1

= 8t2 – t3 + c

t = 0, s = 0 c = 0

s = 8t2 – t3 N1

= 36 m N1

(c) 8t2 – t3 = 0 K1

t = 6 s N1

(d) 4t(4 – t) < 0 K1

t > 4 N1

10

10

Skema SET 2 Kertas 2

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