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1 SULIT 7/ Form four Additional Mathematics Paper Nama Calon : 0 hours Tingkatan : PEPERIKSAAN SELARAS AKHIR TAHUN SEKOLAH-SEKOLAH MENENGAH NEGERI MELAKA ADDITIONAL MATHEMATICS Paper hours JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU. Kertas soalan ini mengandungi 5 soalan.. Jawab semua soalan.. Bagi setiap soalan berikan SATU jawapan sahaja.. Jawapan hendaklah ditulis pada ruang yang disediakan dalam kertas soalan. 5. Tunjukkan langkah-langkah penting dalam kerja mengira anda. Ini boleh membantu anda untuk mendapatkan markah. 6. Sekiranya anda hendak menukar jawapan. Batalkan kerja mengira yang telah dibuat. Kemudian tulislah jawapan yang baru. 7. Rajah yang mengiringi soalan ini tidak dilukiskan mengikut skala kecuali dinyatakan. 8. Markah yang diperuntukkan bagi setiap soalan atau ceraian soalan ditunjukkan dalam kurungan. 9. Satu senarai rumus disediakan di halaman hingga. 0. Buku sifir matematik empat angka disediakan.. Penggunaan kalkulator saintifik yang tidak boleh diprogramkan adalah dibenarkan.. Kertas soalan ini hendaklah diserahkan pada akhir peperiksaan. Kod Pemeriksa Soalan Markah Penuh Jumlah 80 Markah Diperoleh Kertas soalan ini mengandungi 8 halaman bercetak 7/ SULIT
2 SULIT 7/ The following formulae may be helpful in answering the questions.the symbols given are the ones commonly used. Rumus-rumus berikut boleh digunakan untuk membantu anda menjawab soalan.. Simbol-simbol yang diberi adalah yang biasa digunakan. ALGEBRA b. x = b ac a 8 log a b = log log c c b a a m a n = a m + n a m a n = a m - n (a m ) n = a nm 5 log a mn = log a m + log a n 6 m log a n = log a m - log a n 7 log a m n = n log a m 9 T n = a + (n-)d 0 n S n = [a ( n ) d] T n = ar n- n n a( r ) a( r ) S n = r r a S r, r <, (r ) dy dv du y = uv, u v dx dx dx du dv v u u dy y, dx dx, v dx v dy dx dy du du dx CALCULUS Area under a curve b = y dx or a b = x dy a 5 Volume generated b b = y dx or a a x dy GEOMETRY Distance = Midpoint x (x, y) = x r ř x y xi yj x y ( x y x ) ( y ) y, y 5. A point dividing a segment of a line nx mx ny my ( x,y) =, m n m n 6. Area of a triangle = ( x y x y x y ) ( x y x y x y 7/ SULIT )
3 SULIT 7/ STATISTICS x = x = = N x fx f ( x x) N = N x _ x w I I w n n! P r ( n r)! n n! C r ( n r)! r! 0 P(A B)=P(A)+P(B)-P(A B) = f ( x x) f = fx f x p (X=r) = r C p q n r n r, p + q = N F 5 M = L C fm P 6 I 00 P 0 Min(mean) = np npq z = x x x N fx Arc x length, s = r f Area of a sector, L = r _ x x) x x sin A + cos N A = N ( sec A = + tan A f ( x x) fx 5 cosek A = + fcot A 6 sina = sinacosa N F 7 cos A L = cos C fa sin A m = cos A- = - sin A P I 00 P tan A 8 tana 0= tan A f TRIGONOMETRY x 9 sin (A B) = sinacosb cosasinb 0 cos (A B) = cos AcosB sinasinb tan (A B) = a sin A b sin B tan A tan B tan Atan B c sinc a = b +c - bc cosa Area of triangle = absin C 7/ SULIT
4 SULIT 7/. Set Q. 5 Answer all questions. Jawab semua soalan Set P Diagram Rajah Diagram shows the relation between set P and set Q. State Rajah menunjukkan hubungan di antara set P dan set Q. Nyatakan ( a ) the image of imej bagi ( b ) the type of relation Jenis hubungan itu Answer : ( a ) [ marks ] ( b ) 7/ SULIT
5 SULIT 5 7/. Given f : x x + and f ( a ) = a, where a is a constant. Find Diberi f : x x + dan f ( a ) = a, dengan keadaan a adalah pemalar Cari ( a ) the value of a nilai a ( b ) f - ( ) Answer : ( a ) [ marks ] ( b ). Given that f ( x ) = x -, find the values of x if f ( x ) =. Diberi f ( x ) = x -, cari nilai-nilai x jika f ( x ) = [ marks ] Answer : 7/ SULIT
6 SULIT 6 7/. Form the quadratic equation which has roots - and 6. Bentukkan persamaan kuadratik yang mempunyai punca-punca - dan 6. [ marks ] Answer : 5. Solve the equation ( x ) = 7. Give your answer correct to four significant figures. Selesaikan persamaan kuadratik ( x ) = 7. Beri jawapan anda betul kepada empat angka bererti. [ marks ] Answer : 5 7/ SULIT
7 SULIT 7 7/ 6. The quadratic function f(x) = x + px + q,where p and q are constant, has a maximum point at (, 8 ) Fungsi kuadratik f(x) = x + px + q, dengan keadaan p dan q ialah pemalar mempunyai titik maksimum (, 8 ) (a) State the equation of the axis of symmetry Nyatakan persamaan paksi simetri (b) Find the value of p and of q Cari nilai bagi p dan q Answer : [ marks ] a) b) 6 7. Find the range the values of p if the quadratic equation x + x = 5 + p has two different roots Carikan julat nilai p jika persamaan kuadratik x + x = 5 + p mempunyai dua punca yang berbeza Answer : [ marks ] 7 7/ SULIT
8 SULIT 8 7/ 8. Diagram 8 shows part of the graph of function y= (x k) +, where k is a constant. Rajah 8 menunjukkan sebahagian daripada graf bagi fungsi kuadratik y= (x k) +, dengan keadaan k ialah pemalar. Find Cari (a) the value of k nilai k (b) the equation of axis of symmetry persamaan paksi simetri (c) the coordinates of minimum turning point. koordinat minimum titik pusingan [ marks ] Diagram 8 / Rajah 8 Answer : a) b) 8 c) 7/ SULIT
9 SULIT 9 7/ 9. Given that x + x. Find the range values of x Diberi x + x, cari julat nilai-nilai x Answer : [ marks ] 9 0. Given that log P = log 9 R,express R in terms of P Diberi Answer : log P = log 9 R, ungkapkan R dalam sebutan P [ marks ] 0 7m. Given that log m = p and log m = r, express log m in terms of p and r. 7m Diberi log m = p dan log m = r, ungkapkan log m dalam sebutan p dan r. [ marks ] 7/ SULIT
10 SULIT 0 7/. Solve the equation 5 x+ + 5 x- = 6 Selesaikan persamaan 5 x+ + 5 x- = 6 [ marks ]. Solve the equation + log (x-) = log x Selesaikan persamaan + log (x-) = log x [ marks ]. Find the equation of the normal to the curve y = x -5x - 8 at the point (,-) Cari persamaan bagi garis normal kepada lengkung y = x -5x - 8 pada titik (,-) [ marks ] 7/ SULIT
11 SULIT 7/ 5. The point A(7,7), B(m,) and C(,-) are the vertices of a triangle, where m is an integer. Given the area of the triangle is unit, find the value of m. Titik-titik A(7,7), B(m,) dan C(,-) ialah bucu-bucu sebuah segitiga, dengan keadaan m ialah integer. Diberi luas segi tiga ialah unit, cari nilai m. [ marks ] 5 6. Given point C(8,0) divides the line segment joining A(p,) and B(5,q) internally in the ratio AC : CB = :. Find the values of p and q. Diberi titik C(8,0) membahagi garis yang menyambungkan A(p,) dan B(5,q) mengikut kadar AC : CB = :. Cari nilai bagi p dan q. [ marks] 6 7/ SULIT
12 SULIT 7/ 7. A set of six numbers has a mean of 0. Satu set enam nombor mempunyai minnya 0. a) Find Cari b) when a number m is added to this set, the new mean is. Find the value of m. Bila satu nombor m ditambah kepada set itu, min barunya menjadi. Cari nilai bagi m. [ marks] a) b) 7 8. A set of eight numbers has the sum of the numbers is 96 and the sum of squares of the numbers 600. Satu set yang mengandungi lapan nombor mempunyai jumlah nombor-nombor itu ialah 96 dan jumlah kuasa dua nombor-nombor itu ialah 600 Find Cari a) the mean min b) the standard deviation sisihan piawai [ marks] a) 8 b) 7/ SULIT
13 SULIT 7/ 9. The mean of a set of numbers m-, m+, m-, m+ and m- is. Min bagi satu set nombor m-, m+, m-, m+ dan m- ialah. Find Cari a) the value of m nilai bagi m b) the variance of the set of numbers varians bagi set nombor-nombor itu [ marks] a) b) 9 7/ SULIT
14 SULIT 7/ 0. P θ rad O 0 cm Q Diagram 0/ Rajah 0 The diagram 0 shows a major sector POQ with centre O and radius of 0 cm. Given the area of sector is 0 cm. Rajah 0 menunjukkan sektor major POQ dengan O sebagai pusat bulatandan berjejari 0 cm. Diberi luas sektor itu ialah 0 cm. Find Cari a) the value of θ nilai θ b) perimeter in cm of the major sector perimeter major sector dalam cm [ marks ] a) b) 0 7/ SULIT
15 SULIT 7/ 5. O Diagram / Rajah Diagram shows a circle, with centre O and a radius of 0 cm. If the length of the minor arc MNP is cm, find Rajah menunjukkan sebuah bulatan berpusat O dan berjejari 0 cm. Jika panjang lengkok minor MNP ialah cm, cari a) the value of nilai b) the length of a major arc MQP. panjang lengkok major MQP. [ marks ] a) b) 7/ SULIT
16 SULIT 7/ 6. R P Diagram shows Q Diagram /Rajah OQR that has a right angle at Q and OPQ is sector of a circle, with centre O, such that OQ = 5 cm and Rajah menunjukkan POQ = 0.9 radians. OQR yang mempunyai sudut tegak di Q dan OPQ adalah sektor sebuah bulatan, berpusat O, di mana OQ = 5 cm dan POQ = 0.9 radian. O Find Cari a) the length of QR panjang QR, b) the perimeter of shaded region. Perimeter kawasan berlorek. a) [ marks ] b) 7/ SULIT
17 SULIT 7/. Given y = 7 u, where u = x dy -, find dx in terms of x. Diberi y = u, dengan u = x keadaan cari dx dy dalam sebutan x. [ marks ]. Given f(x) = x ( 7 6x ) find f f '() Diberi f(x) = x ( 7 6x ) cari f '() Answer : [ marks ] 7/ SULIT
18 SULIT 7/ 8 5. Given that y = x + x - 5, Diberi y = x + x - 5 dy a) find the value of dx when x =. dy Cari nilai bagi bila x = dx b) express the approximate change in y in terms of p, when x changes a) from to + p where the value of p is small. Ungkapkan dalam sebutan p, perubahan hamper dalam nilai y apabila kepada + p, dengan keadaan p ialah satu nilai kecil. [ marks ] b) 5 END OF QUESTION PAPER / KERTAS SOALAN TAMAT 7/ SULIT
19 7/ Form Additional Mathematics Paper 0 PEPERIKSAAN SELARAS AKHIR TAHUN SEKOLAH-SEKOLAH MENENGAH NEGERI MELAKA Kelolaan PEJABAT PELAJARAN DAERAH JASIN * ALOR GAJAH * MELAKA TENGAH Dengan kerjasama : JABATAN PELAJARAN NEGERI MELAKA TINGKATAN TAHUN 0 ADDITIONAL MATHEMATICS Paper MARKING SCHEME This marking scheme consists of 5 printed pages
20 Number Solution and marking scheme Submarks Full marks a) b) Many to one a) a = - - = a a b) - f (x) = x = and x = x = or x = x f(x) = x or f(x) = - x + x x = 0 SOR = -+6 =, POR = -(6) = - 5 x =.66 and x = -.66 x =.66 or x = -.66 B B a =, b = -, c = -6 or ( ) ( ) ()( 6) () 6 a) x = b) p = - q = -0 7 p > - 8 () [ -5 + p ] > 0 B x + x ( 5 + p ) = 0 OR a=, b=, c=-( 5+p ) 8 (a) k = (b) x = (c) (, ) B
21 9 x (x+)(x-) 0 B x x P R = 8 B log P = log R Log p ( ) log 8 Log P = R log R = log 9 log R B. r + p log m + log m log m + log m log m 7 + log m m log m. X = 5 x = 5 5 x (5 ) + 5 x ( ) = 6 5 B B B OR 5 x ( ) = 6. X = 8 9 9x-9=x log (x-) = log x OR log + log (x-) = log x B. y = x 5 or x y 7 = 0 y + = (x+) dy = - OR m = dx B
22 5. m = 5-9m = or 5-9m= - 5 9m = m 8 7m = 6 p = 0 and q = 9 p = 0 or q = 9 B B B 7 a) 60 p q atau 0 5 p (5) () q, b) m = 8 a) x x m 7 b) a) m = ,0 m m m m m b) x atau x 75 atau B B 0 a).rad b) 6cm (.) a) =.8
23 5 0 b).8 0(.8) a)8 cm QR 5 tan0.9 b)7.5 5(0.9) or RP=cm 8x(x ) -0 5 a) (x ) or 8x 6x (7 6x)(7 0x) 6x (7 6x) - x (7 6x) b)p x p B
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