SKEMA K2 PPT 2017

SKEMA MATEMATIK TAMBAHAN TINGKATAN 5 KERTAS 2 PPT 2017

NO MARKAH

1a 55 + − (21 + ) See 19.5 P1
(2 10 ) K1
21.5 = 19.5 + (5)

p=5 N1

b =√3068020 − (1290)2 See 30820 K1
K1
60 N1
K1
= 7.171 K1
P1
2 2 + = 12 K1
9 2 + 2 = ( + )2 K1
N1,N1
= 12 − 2
K1
8 2 − 2 (12 − 2 ) = 0
12 ( − 2) = 0 K1

= 2 N1
= 8
K1K1
3a (27 × 64)
(3 × 4) N1

123
12

3 12= 3

12

b 1
3 + − 2

1
3 + 2

4a 2 2 = 72 K1

= 4 2 + 2(2 ) 36 + 2 36 K1
( 2 ) ( 2 )

=4 2 + 216 N1



b 216 K1
= 8 − 2 = 0
K1
= 3 K1

= 4(3)2 + 216 N1
3 K1
N1
= 108
N1
5a ′( ) = 4 − = 0
U shape P1
n=4 Min point (1, -7) and
y-intercept = -5 P1
2(1)2 − 4(1) + = −7
p = -5

b f(x)

x

1
-5

-7

c (−4)2 − 4(2)(−5 − ℎ) > 0 K1

h<7 N1

6a 8 = 1(2)7 K1
=128 N1
K1
b(i) 1(210 − 1)
10 = 2 − 1 K1
=1023 N1
K1N1
Isipadu = 1023 × 3 × 7 × 5
= 107415

(ii) 1023 × 0.80 = 818.40

7a 45 K1
180 × 3.142

= 0.7855 N1

b 3.142(4) K1

0.7855(8) K1

3.142(4) + 8 + 0.7855(8) K1

= 26.852 N1

c

1 (4)2(1.571 − 90) K1
2

1 (8)2(0.7855) − 1 (4)(4) − 1 (4)2(1.571) K1
2 2 2

1 (4)2(1.571 − 90) + 1 (8)2(0.7855) K1
2 2
1 1
− 2 (4)(4) − 2 (4)2(1.571)

=9.136 N1

8a(i) ( ) = 2 + K1

= 2 + 3 N1

(ii) k= 7 N1
K1
1 K1K1
2 (7)(7) N1
K1
3 2 49
= [ 3 + 3 ] + K1
2 N1
0 P1
K1
=3361 N1
K1
b 1 (2)2(2)
3

= 1 (2)2(2) + 2 − 7
3 [2
3 ]

3

=1023

10a 2 = 2

0 = 2(−6) +
= 12

= 2 + 12

b 2 3−6=0 @ 23 =12

Q(3,18) N1
K1
c = 1 |(36) − (−9)|
2 N1

= 22.5

d √( + 6)2 + 2 = 2√ 2 + ( + 3)2 K1K1

3 2 + 3 2 − 12 + 4 = 0 N1

11a(i) ⃗⃗ ⃗⃗ ⃗ = ⃗ ⃗ ⃗⃗ ⃗ + ⃗ ⃗ ⃗⃗ ⃗ K1
= −6 + 4 N1

(ii) ⃗ ⃗ ⃗⃗ ⃗ 1
2
= 4 − (−6 + 4 ) K1

= 3 + 2 N1

b ⃗⃗ ⃗⃗ ⃗ = 3 + 2 K1

⃗⃗ ⃗⃗ ⃗ = 6ℎ + (1 − ℎ) K1

3 = 6ℎ K1
= 2ℎ K1
N1
2 = 1 − ℎ
1 N1

ℎ=5
2

= 5

12a = 150 = 2 = 0.4 N1N1N1

b 125 + 140(5) + 150(3) + 80(2 ) = 114.5 K1K1

8 + 3

= 4 N1

c 100 × 2061 K1
2011= 114.5

= 1800 N1

d 120 × 114.5 K1
= 100

= 137.4 N1

13a(i) 10 Seen 60 K1
70 = sin 60 K1

= 9.216 N1

(ii) 2 = 42 + 9.2162 − 2(4)(9.216) 130 Seen 130 K1
K1

= 12.18

12.18 9.216 K1
sin 130 =  N1

 = 35.42

b(i) N1
A’ D’

B’

= 1 (4)(9.216) sin(20.84) K1
2 N1

= 6.557