SULIT /2 ( 2) ( 2) 4(1)( 12) 2(1) Note: 1. If the solutions of x and y are matched wrongly, then SS1 from full marks.


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1 7/ Modul Peningkatan Prestasi Matematik Tambahan (Kertas ) SPM 6 Zon B Kuching Sarawak y y P Substitute () into () * * y * y y ( ) ( ) ()( ) () ( ) ( ) ()( ) y ().,. y.66,.66 Note:. If the solutions of and y are matched wrongly, then SS from full marks. 5 (a) Let w f ( ) Then f ( w) w w w f ( ) (Shown) 7/ (C) 6 Hak Cipta SM Zon B Kuching Sarawak [ Lihat halaman sebelah
2 7/ (i) gf ( ) g 5.5 (ii) gh( ) f ( ) h( ) h( ) h( ) 8 6 (a) π R () 56π R a 6 r S / (C) 6 Hak Cipta SM Zon B Kuching Sarawak
3 7/ (a) Equation of the curve y 6 d c () () c c y At turning point, dy d 6, When, When, y () () y () () Second derivative, d d y 6 6 When, When, d y 6() 6 d d y 6() 6 d 6 6,, is the maimum point. is the minimum point. 8 7/ (C) 6 Hak Cipta SM Zon B Kuching Sarawak [ Lihat halaman sebelah
4 7/ 5 (a) tan A tan B sin A sin B cos A cos B sin Acos B cos Asin B cos Acos B sin( A B) cos Acos B (i) Shape of sine graph P Amplitude = P.5 cycle f π P (ii) y equivalent π P Crect gradient crect y intercept Number of solutions = 8 y y sin O π π π π 5π π y π 7/ (C) 6 Hak Cipta SM Zon B Kuching Sarawak
5 5 7/ 6 (a) cos 6 cos rad Area of maj sect POR 6. *.68 Area of triangle POR 6 6 sin*96.8 Area of immersed crosssectional region 6. *.68 66sin* cm 7 7/ (C) 6 Hak Cipta SM Zon B Kuching Sarawak [ Lihat halaman sebelah
6 6 7/ 7 (a) T (5) () () ( ),, (shown) Area of QOR unit (c) m ( ) 5 m m y y (d) ( ) ( y ) 8 6 y y 9 y 8 y 7/ (C) 6 Hak Cipta SM Zon B Kuching Sarawak
7 7 7/ 8 (a) A B,, Area under the curve from to * A ( ) d * d * (*) (*) 6 Area of the region required by the question * 6 * * (c) Volume generated π y d π d π 8 6 d π () 6() () 6() π () () π 5 7 π 5 7/ (C) 6 Hak Cipta SM Zon B Kuching Sarawak [ Lihat halaman sebelah
8 8 7/ 9 (a) Range (i) Midpoints 5.5, 5.5, 5.5, 5.5, 5.5 P Mean, (5.5) 8(5.5) (5.5) (5.5) 7(5.5) Variance, (5.5) 8(5.5) (5.5) (5.5) 7(5.5) (ii) New variance * P (c) The height of the bars are proptional to respective frequencies P Boundaries midpoints class intervals are crectly labeled (bars are of the same width) P Crect way of finding mode Mode.5 7/ (C) 6 Hak Cipta SM Zon B Kuching Sarawak
9 9 7/ f mode.5 7/ (C) 6 Hak Cipta SM Zon B Kuching Sarawak [ Lihat halaman sebelah
10 7/ (a) n p 5 q 5 P (i) (ii) P( X 8) P( X 8) P( X 9) P( X ) 8 9 C8 C9 C P( X 5) P Z P Z.5 P Z.5.9 P Z Number of students.9 7 P( X a). P Z a 6 8. a a The minimum marks to get grade A, a 7.5 7/ (C) 6 Hak Cipta SM Zon B Kuching Sarawak
11 7/ (a) log y Note:. In the table, the decimal number being rounded off must not be less precise than the nearest.5 f Y.. The N mark is given f all crect X and Y.. If the value(s) of X and Y are not shown through a table, then the N mark is given f all the crect points on the graph. At least one *point crect, using crect aes log y against in crect direction and ientation, and with unifm scales All 6 *points plotted accdingly Line of best fit (c) log y log a log b ( equivalent) P (i) log a log y intercept *.75 *.75 a.985 Note:.985 a.6 (ii) log b m b.995 Notes:. Graph can only be read with precision until half of the smallest grid division.. Do not accept readings obtained by calculation from the wrong graph.. SS from full marks if not using the given scale. 7/ (C) 6 Hak Cipta SM Zon B Kuching Sarawak [ Lihat halaman sebelah
12 7/ log y.5. 7., c.75.5., / (C) 6 Hak Cipta SM Zon B Kuching Sarawak
13 7/ (a) a dv dt t At maimum velocity, t t a. vma At initial acceleration, t. (c) a () When stopping instantaneously, v. t t 6 t t t, t t t Distance from point O v dt 6 t t t () () 6() / (C) 6 Hak Cipta SM Zon B Kuching Sarawak [ Lihat halaman sebelah
14 7/ (a) (i) PR 7 8 (7)(8)cos75 PR 7.5 (ii) * sin sin QPR QPR sin 8.5sin ' Note: 7.8 QPR 7.9 QRP 8 *7.9.9 Area of Area of PQR PRS (8.5)(7.5)sin.9 (7)(8)sin75 Area of quadrilateral PQRS (8.5)(7.5)sin.9 (7)(8)sin Note:.6 Area.6 (c) Let the shtest distance from point Q sin.9 h 8.5 OR h 8.5sin.9 to the line PR be h. (7.5) h * (8.5)(7.5)sin Note: h / (C) 6 Hak Cipta SM Zon B Kuching Sarawak
15 5 7/ (a) I: y II: y III: y y At least one straight line crect from the *inequalities involving and y Draw all three lines crectly from the *inequalities Shade the crect region (c) (i) When, 7.5 y ymin 8 Note: N if answer ymin 7.5 (ii) Objective function 5 5y k Optimum point, kma 5 5 RM 78 Notes:. F (c)(i) and (c)(ii), accept the codinates only if they are integers.. SS if in (a), symbol "<", ">" is used instead of " ", " " me than three inequalities are given (ecept y ) OR in, not using the given scale aes are reversed not using graph paper 7/ (C) 6 Hak Cipta SM Zon B Kuching Sarawak [ Lihat halaman sebelah
16 6 7/ y y 5 y 5 5 R 5 5y k ma y, 5 55y / (C) 6 Hak Cipta SM Zon B Kuching Sarawak
17 7 7/ 5 (a) y 5. y z z 5.5 I 8(5) (5) 6(5) () K.8 (c) (i) Food.8 6. Food RM (ii).85 I 6, equivalent I6, 5.7 7/ (C) 6 Hak Cipta SM Zon B Kuching Sarawak [ Lihat halaman sebelah
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