SKEMA PERCUBAAN SPM 2017 MATEMATIK TAMBAHAN KERTAS 2
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1 SKEMA PERCUBAAN SPM 07 MATEMATIK TAMBAHAN KERTAS SOALAN. a) y k ( ) k 8 k py y () p( ) ()( ) p y , y,, Luas PQRS 8y 8 y Perimeter STR y y , y, y
2 . a).. h( h) h h h h h h 0 h () ( ) ( ) ()() h y y y y y y y (y ) y 7 y 6y 0 y (9y 6y ) y y 8y y y y (7) ( 6) ( 6) (7)() y (y + ) y = y + y = y = 7 atau setara (7 + ) (7 ) = 6 ( )( ) = 0 =, abaikan nilai y =, abaikan nilai Luas 8.7 y y Perimeter y y 6 y 6 8 y
3 Gantikan dalam 6 7, ,. y., y. Ukuran Bilik, Panjang =. + =. m Lebar =. + =. m SOALAN. (a) a = 6000 r =.0 n = = 7 T 7 = = RM ( T n > n > n > Error! (n ) log 0.0 > log 0 n > Error! n > 0.8 n >.8 n = (c) T = = RM6.68 Total interest earned = = RM6. a) T () 9 T0 c) 9() 9 0 S0 ( 9) 0 n () ( n )() n 0. a) (k + ) (k + ) = (k + ) (k )
4 k = 6 d = a + (6 )() = a = c) n S n ( ) ( n )() S n n 7n. a) a a d a d a d 8 a d 0 8 d 76 d a 6 S 6 000cm T cm. a) Number of sheep sold d = 0, a = 0 for the first month = T 0 0(0) = 80 The number of sheep left after month is = 60 n Sn a ( n ) d S (000) ( )( 0)
5 SOALAN. a). a) new new 8 8 new 9. N 0 0 i) N 7 0. N 0 k 6 k 6 ii) N a) N F L C fm
6 f f a) L = 9. atau F = 6 atau f m = atau c = (). 6() 0(7) () (7) 8() () 0(7) () (7) 8() (.) 0 8. atau c).. a) i) 6 6 ii) 6 00 N SOALAN
7 . a) i) ()( 6) y ()(9),6, 6, y R(6,) ii) (8 8 0 ) ( 6 8 0) 8 ( ) ( y ) y y a) ( 80 8) (0 8 6) m, m y ( 7) y c) ( ) ( y8) y y a) c) 0(0) () () () 0() (0) (0) () () (), 7, AP = PC atau ( 0) ( y ) ( ) ( y ) ( 0) +(y ) = [( ) + (y ) ] + y 0 y + 00 = 0. a) Q(, 0) or P(0, -6) 0 y 8 (, 0) =, R = (, 9) ( ) ( y 0) ( ) y y 0
8 . a) c) Luas AOB unit AC : CB : C 6, PA PB 8 8, y 8 y 8 6 y y 0y 7 6y y 6y 6 SOALAN. a) cos cos cos 9 cos No of solution =. a) 0 - cos 0 cos No. of solutions =. a) Bentuk graf sin Amplitud
9 Lakaran dalam julat 0 π Persamaan y Garis lurus y dalam julat 0 π penyelesaian. Sine curve seen One and a half cycle in 0 π Ma value, Min value y 9 π 9 OR sin π or equivalent Sketching the straight line from the *equation involving and y. K Number of solutions = Curve and straight line sketched correctly N O y 9 π π π π y π sin π y 9 π. a) y sin
10 sin sin y Draw y on the same aes Number of solution = SOALAN 6. a) dy 9 atau 9 0 d p dan q (kedua-dua jawapan betul), dan, (kedua-dua jawapan betul) d y 8 d dan 7 (kedua-duanya betul), adalah titik minimum, adalah titik maksimum. a) y y y y 6 y 6 dy y limit d 0 dy 6 d
11 0 6 0, 6, 6 6 0, 6 dy d y P d y d P. a) 6 d dy y 97, sin 97 6, 0, sin ,, gan Pu Titik y gan Pu Titik y d dy
12 c) d y d 6 When 0 0,, d y d a) d y When, d 97, dy p d p 9 p 9 p dy d y c y c c 6 0
13 . y dy d y m y y solve simultaneous 0 0, y, y (0,) y (,) y 7 SOALAN 7. a) p0.6 q 0. i) 6 P( ) C ii) P( ) P( ) P( ) P( 6) C C C i) P P z 0 0 P 0.7 z P( z 0.7) P( z )
14 ii) P( y ) 0.7 y 00 Pz y y 88.. a) i) 8 p( ) C (0.) (0.9) 0.0 ii) p( y ) p( y 6) p( y 7) p( y 8) C6(0.9) (0.) C7(0.9) (0.) C8(0.9) (0.) i) p( ) p z 8 pz (.) 0.07 ii) 00 p( t) 600 t pz t t 7.6. a) i) 8 P( X ) C 0.9 ii) i) P( X ) P( X 0) P( X ) C0 C P( X 60) P Z P Z 0.8
15 ii) 7 6 P( X 7) P Z P Z a) i) P( ) C (0.7) (0.) C (0.7) (0.) C (0.7) 0.6 ii) n(0.7)(0.) 0. n / i) 80 8 P 80 P( z ) 0.09 ii) w 8 P ( ) 0. w 8.8 w a) i) P( X ) C (0.6) (0.) ii) P( X ) C(0.6) (0.) 0.0 i). P( X ) P SOALAN 8. a) ii) P( m) 0.6 m. PZ m m. s t Skala pada kedua-dua paksi seragam Semua titik diplot betul Garis lurus penyuaian terbaik
16 c) i) s t a bt Kelihatan garis menyentuh paksi- t s = 80 a = 80 Keceruanan = b = 0 ii) a) 6 /y Correct and uniform scale All points correctly plotted Line of best fit i) b y a b y a a gradient a. a a = b Y int ercept a b b.86 ii) 0.9. (a) ² y y q p ( m q., c p 9 p 9 (c) 0., y 9.6. (a) log log0 y log y nlog log a 0 0 0
17 ( m n 0.8 c log a a 7.9. (a) p 6 7 p q p q ap b ( m a 0.7 c b 0.60 (c).8., p. SOALAN 9. a) TR 0 y, SQ 0 y SU m( 0 y) atau SU 0m my SU (0) n( 0y) SU n 0ny atau SU ( n) 0ny c) n = 0m dan m = 0n n, m 6 d) TR PQ atau TU ntr : 0y 0y 6. a) i) 6 m 0 m 8 ii) OQ OP PQ 0i j MN MR RN QR RO (0 i j ) c) i) PT PR RT ( PO OR) RT i j
18 ii) OP 6i 8j PT i j OP PT. a) i) QL QR RL QR QP b ( a) b a ii) i) ii) SN SR RN PQ QR ab QM hql h a b h a hb QM QN NM QR kns ( k( a ka ( k) b Equating the coefficients of a and b h k h k h, k c) PQ a PS b Area of parallelogram PQRS. sin a) i) AC AB BC pq
19 ii) AE AD q iii) i) ii) BE BA AE p q BF kbe k q p kq kp AF hac h p q hp hq c) AF AB BF p kq kp k p kq ( shown). a) i) OF OQ y ii) OE OP PE OP PQ OP 6y y i) ii) PG hpf PO OG h PO OF OG h PO OF PO h hy OG koe k y k ky
20 h hy k ky h k h k h h h k SOALAN 0. a) 8 9 (0) ATAU (0) (0) ATAU atau atau atau.7 9 (0) 90 c). a) (.66) (.66) () atau (0) ATAU (0) - 9 () ATAU () (0) - atau () (0) Arc AB = K (arc AB or CD) Arc CD OE = OD Perimeter =
21 c) Area of sector AOB = Area of OCE. a) i) coswpx WPX 70'.rad ii) WQY WQZ YQZ ' '.9rad Perimeter of the shaded region WX XY WY 8(.) (.9) 8.8cm c) Area of the shaded region cm. a) AB tan OB rad AB AB cm OA.88cm
22 c) OB OQ OQ OB 6cm BQ cm AP OP OA PQ 6.7cm Perimeter shaded region AP AB BQ PQ cm d) Area of shaded region = Area sector OPQ Area of AOB 6.cm. a) = kos - ( ) 6 =8. =.7 rad QP = 6. cm atau QRY =.7 rad QR =.7 atau PR =.7 QR = 8.97 atau PR = c) ½(+)(6.) atau ½( )(.7) atau ½( )(.7) ½(+)(6.) - ½( )(.7)-½( )(.7) 8.7 SOALAN. a) y b c) ()() ( () () ) atau () () () 9 () () () - ()()
23 d) ( 0 6() ) () () 6(0) () (0). a) dy d m y y ( y) dy y c) ( y) dy (() ) ((). a) k 7. d 7. k 7. k k
24 (i) (ii) B(0,) 0 0, A(,) y dy y dy 0 y y y y a) , k L ( ) d 0 9 L
25 c) V 7 () V 8 ( y ) d y y 7 8. a) y, y ( )( ) 0, () () ( ) d 8 6 8() 8() 6() 6() 8 6 SOALAN. a) y 0 y 0 y 600 c) i) 0
26 ii) y k 0, y 60 0.(60) 0.6(0) 98. a) y 00 y y 0 c) i) y ma = 80 y min = 0 ii) (0,80) 0(0) 0(80) 00. a) y y 0 y 000 c) i) RM70 ii) (,7) y k a) y 0 y y c) i) ii) 00 0y k 00() 0() 000. a) 6 0y y 80 y 0 c) i) y 7 ii) (0,) y k (0) () 8
27 SOALAN. a) X00 0 y X X00 80 z 0() 0(0) 0(0) 80() 00 =.0 c) i) ii) P 0 X P RM X.0 00 =.. a) i) Price inde I = Error! 00 p = Error! 00 = 6 ii) 87 = Error! 00 q = 9.80 I, = Error! = Error! = c) i) I 00 = Error! = 07.9 ii) P 00 = Error!. = RM6.7. a) i) P P06 RM. ii) RM.0 00 P P 0 0 RM.7
28 (06 0) ( ) ( I M ) (0 0) I 9 I M 60 M.9 c) i) ii) 90 I P P RM (a) 960 m ( P0 I 00 P09 = 0, y = 0 (c) 0(6) () 98() 0() (d) a) =6 y = z = 80 n 8n n 00 n () 0(8) 0() 80() 0 c) 80 P P RM.
29 d) P P I SOALAN. a) i) AC = (7) + (6) (7)(6)kos(80) 8.9 ii) sin ACD sin iii) CAD (7)(6) sin 80 atau (8.9)()sin i) ii). a) i) 0 sin 0 QT QT 0 cm ii) cos 0 8 i) 9 sin B sin 0 B = ii) CD = (9)(8.) cos CD = 7.07 cm. iii) ' (8.)(9)sin 69 ()(9)sin a) TSU 6 SU sin9 sin 6 SU.97
30 6.97 ()(.97)cos RUS RUS 8.70 c) RUT.7 RT ()()cos.7 RT 9.8 d) ()(.97)sin8.7 ()(.97)sin a) i) QRS SQ ()() cos SQ 7.60 ii) sinqsr sin 7.60 QSR 6. iii) ()()sin0 ()()sin 8.6 i) Q S ii) Q ' S' R' R S. a) sin R 7 R. QS ( cos. ) QS.6 c).6 8 sinp sin P 8.6 PQS d).6 8 sin SOALAN
31 . a) dv a 6 8t 0 dt t v ma ()( ) 6 s 6t t dt s 8t t 8() () 6 8t t c t 0, s 0 c) s 8t t 0 t 8 t 0 t 0 t 6 d) t( t) 0 0t. a) v t t c v t t ma v, a t 0 v ma v 0 t k k 0 k k 0 k k 0 k c) s t t dt t t t
32 d) s 0 t t t 9t 0 t t t 0 t 9 0 t.8. a) t 0 0t s t t () () 7. c) s t t (8) (8) (7.) or 7. (7. ) d). a) dv a dt v 0 t 8 0 t c) 8 s t dt s t 8t c t 0, s 0 s t 8t v t 8 t s 8
33 d) 7 v dt v dt 0. a) s 0 t t 0 t t 0 t 0, t t s s () () () () c) d) ds 6t t dt 6t t 0 t 6 t 0 t s, s 6 s ( 6) a 66t 6 6t 0 t v 6() ( t)
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