SULIT / ADDITIONAL MATHEMATICS Kertas September jam Dua jam tiga puluh minit SEKOLAH-SEKOLAH MENENGAH ZON A KUCHING PEPERIKSAAN PERCUBAAN SIJIL PELAJARAN MALAYSIA 0 JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU. Kertas soalan ini adalah dalam dwibahasa.. Soalan dalam bahasa Inggeris mendahului soalan yang sepadan dalam bahasa Melayu.. Calon dikehendaki membaca maklumat di halaman belakang kertas soalan ini.. Calon dikehendaki menceraikan halaman dan diikat sebagai muka hadapan bersamasama dengan kertas jawapan. Kertas soalan ini mengandungi halaman bercetak / 0 HAK CIPTA ZON A KUCHING SULIT

SULIT / The following formulae may be helpful in answering the questions. The symbols given are the ones commonly used. Rumus-rumus berikut boleh membantu anda menjawab soalan. Simbol-simbol yang diberi adalah biasa digunakan. ALGEBRA b ± b ac log c b x = log a b = a logc a a m a n = a m + n a m a n = a m n (a m ) n = a mn log a mn = log a m + log a n m log a = log a m log a n n 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 ) CALCULUS KALKULUS y = uv, dy dx = dv u dx du du v dx dv u + u dy y =, = dx dx, v dx v dy dx = dy du du dx Distance / Jarak = v + ( x x ) ( y y ) Midpoint / Titik Tengah x (x, y) = + x y, + y A point dividing a segment of a line Titik yang membahagi suatu tembereng garis nx (x, y) = + mx ny, + my m + n m + n Area under a curve / Luas di bawah lengkung b = y dx or (atau) a b = x dy a Volume generated / Isi padu kisaran b = π y dx or (atau) a b = π x dy a GEOM ETRY GEOMETRI. Area of triangle / Luas segi tiga = ( ) ( ) x y + x y + x y x y + x y + x y r = x + y x i + yj r = x + y / 0 HAK CIPTA ZON A KUCHING SULIT

SULIT / x = N x = σ = x fx f ( x x ) = N x N x STATISTICS STATISTIK w I i i I = wi 9 n! P = ( n r)!! C = ( n r)! r! n r n r n 0 P(A B) = P(A) + P(B) P(A B) σ = f ( x x) f = fx f x P(X = r) = n Cr p r q n r, p + q = Mean / Min µ = np m = N F L + C fm Q I = 00 Q 0 σ = npq z = X µ σ TRIGONOMETRY TRIGONOMETRI Arc length, s = rθ Panjang lengkok, s =jθ Area of sector, A = r θ Luas sector, L = sin A + cos A = sin A + kos A = sec A = + tan A sec A = + tan A j θ cosec A = + cot A kosek A = + kot A sin A = sin A cos A sin A = sin A kos A cos A = cos A sin A = cos A = sin A kos A = kos A sin A = kos A = sin A tan A tan A = tan A 9 sin (A ± B) = sin A cos B ± cos A sin B sin (A ± B) = sin A kos B ± kos A sin B 0 cos (A ± B) = cosa cosb sina sinb kos (A ± B) = kos A kos B sin A sin B tan (A ± B) = a sin A = b sin B tan A ± tan B tan Atan B = c sin C a = b + c bc cos A a = b + c bc kos A Area of triangle / Luas segi tiga = absinc / 0 HAK CIPTA ZON A KUCHING [Lihat sebelah SULIT

SULIT / THE UPPER TAIL PROBABILITY Q(z) FOR THE NORMAL DISTRIBUTION N(0, ) KEBARANGKALIAN HUJUNG ATAS Q(z) BAGI TABURAN NORMAL N(0, ) z 0 9 0.0 0. 0. 0. 0. 0. 0. 0. 0. 0.9.0.........9.0... 0.000 0.0 0.0 0. 0. 0.0 0. 0.0 0.9 0. 0. 0. 0. 0.09 0.00 0.0 0.0 0.0 0.09 0.0 0.0 0.09 0.09 0.00 0.90 0. 0. 0. 0.09 0.00 0.09 0.9 0.090 0. 0. 0. 0. 0.09 0.09 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.00 0.90 0. 0.9 0. 0. 0.0 0. 0. 0.0 0. 0.9 0. 0. 0.09 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.00 0.0 0.00 0.0 0. 0.090 0.0 0. 0.9 0. 0. 0.0 0. 0. 0.9 0.09 0.09 0.0 0.00 0.0 0.0 0.0 0.0 0.0 0.0 0.09 0.00990 0.0 0. 0.0 0.9 0.00 0.9 0. 0.9 0.00 0. 0.9 0. 0.0 0.090 0.09 0.0 0.00 0.009 0.09 0.0 0.00 0.0 0.0 0.009. 0.000 0.009 0.00 0.00 0.00.....9 0.00 0.00 0.00 0.00 0.00 0.000 0.00 0.00 0.00 0.00 0.00 0.000 0.00 0.000 0.00 0.000 0.00 0.00 0.00 0.009 0.00 0.00 0.000 0.00 0.00 0.0 0.0 0.0 0. 0. 0.9 0. 0. 0.9 0. 0.9 0. 0.0 0.0 0.0 0.00 0.09 0.00 0.0 0.0 0.00 0.0 0.0 0.0099 0. 0. 0.9 0.9 0. 0. 0. 0. 0.99 0. 0. 0.0 0.0 0.09 0.0 0.09 0.0 0.09 0.0 0.00 0.09 0.0 0.09 0.009 0. 0. 0.9 0. 0.9 0. 0. 0.0 0.9 0.0 0. 0.0 0.00 0.0 0.00 0.0 0..0 0.0 0.00 0.0 0.09 0.00 0.0 0.009 0. 0. 0.9 0.0 0. 0.0 0. 0. 0.9 0. 0.0 0.90 0.00 0.0 0.09 0.0 0.0 0.0 0.00 0.09 0.0 0.0 0.0 0.00 0. 0. 0.9 0. 0. 0. 0. 0. 0. 0. 0.9 0.0 0.09 0.0 0.0 0.09 0.0 0.0 0.09 0.0 0.0 0.0 0.00 0.00 0.00 0.009 0.00 0.00 0.009 0.009 0.000 0.009 0.009 0.009 0.00 0.009 0.009 0.00 0.00 9 Minus / Tolak.0 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.000 0.000 0.0000 0 f ( z) exp z π = f 0.000 0.009 0.000 0.000 0.009 0.009 0.00 0.00 0.0099 0.00 Q(z) 0.000 0.00 0.00 0.009 0.009 / 0 HAK CIPTA ZON A KUCHING SULIT 0 0 0 0 0 0 0 9 0 9 0 9 0 0 9 9 0 9 Example / Contoh: If X ~ N(0, ), then 9 Jika X ~ N(0, ), maka y Q( z) = f ( z) dz P(X > k) = Q(k) x k z P(X >.) = Q(.) O k = 0.09 0 9 0 9 9 0 9 0 9 0 9 0 0 9 9 9 9 0 9

SULIT / Section A Bahagian A [0 marks] [0 markah] Answer all questions. Jawab semua soalan. Solve the simultaneous equations x y = and x y + xy =. Give the answers correct to three decimal places. Selesaikan persamaan serentak x y = and x y + xy =. Beri jawapan betul kepada tiga tempat perpuluhan. [ marks] [ markah] Given f(x) = 9 x x can be expressed in the form of f(x) = b a(x + p) where a, b and p are constants. Diberi f(x) = 9 x x dapat diungkapkan dalam bentuk f(x) = b a(x + p) dengan keadaan a, b and p ialah pemalar. (a) State the value of a, b and p. Nyatakan nilai a, b and p. [ marks] [ markah] (b) Sketch the graph of f(x) = 9 x x. [ marks] Lakarkan graf bagi f(x) = 9 x x. [ markah] Diagram Rajah A strip of metal is cut and bent to form some semicircles. The diagram shows the first four semicircles formed. The radius of the smallest semicircle is cm. The radius of each subsequent semicircle is increased by cm. [ Use π = ] Satu jalur logam dipotong dan dibengkok untuk membentuk beberapa semi bulatan. Rajah menunjukkan empat semi bulatan pertama yang telah dibentukkan. Jejari semi bulatan yang terkecil ialah cm. Jejari semi bulatan yang berikutnya bertambah sebanyak cm setiap satu. [ Guna π = ] / 0 HAK CIPTA ZON A KUCHING [Lihat sebelah SULIT

SULIT / (a) If the radius of the largest semicircle is cm, find the number of semi circles formed. [ marks] Jika jejari bagi semi bulatan yang terbesar ialah cm, cari bilangan semi bulatan yang telah dibentuk. [ markah] (b) Calculate the total cost needed to form all the semicircles in (a) if the cost of the metal strip is RM per meter. [ marks] Hitungkan jumlah kos yang diperlukan untuk membentuk semua semi bulatan dalam (a) jika kos jalur logam ialah RM semeter. [ markah] (a) tan x Prove that cot x =. sec x [ marks] tan x Buktikan kot x =. sek x [ markah] (b) (i) Sketch the graph of y = cos x for 0 x π. [ marks] Lakarkan graf bagi y = kos x untuk 0 x π. [ markah] (ii) Hence, find the possible values of k such that the equation cos x + k = 0 has only two solutions for 0 x π. [ marks] Seterusnya, cari nilai-nilai k yang mungkin supaya persamaan kos x + k = 0 mempunyai dua penyelesaian sahaja untuk 0 x π. [ markah] Diagram is a histogram showing the wages per day of a group workers in a firm. Rajah ialah histogram yang mewakili upah harian bagi sekumpulan pekerja dalam sebuah firma. Frequency kekerapan 0 0. 0. 0. 0. 00. 0. Wages in RM Upah dalam RM Diagram Rajah Based on the histogram, calculate Berdasarkan kepada histogram, hitung / 0 HAK CIPTA ZON A KUCHING SULIT

SULIT / (a) the mean wages per day of the worker. [ marks] min upah harian pekerja, [ markah] (b) the variance of the distribution. [ marks] varians bagi taburan itu. [ markah] Diagram shows a triangle OKL in which OK = a and OL = b. P is a point on KL such that KP = hkl in which h is a constant. Rajah menunjukkan sebuah segi tiga OKL dengan OK = a dan OL = b. P ialah satu titik pada KL supaya KP = hkl dengan keadaan h ialah pemalar. K P O L Diagram Rajah (a) Express OP in terms of h, a and b. Ungkapkan OP dalam sebutan h, a dan b. [ marks] [ markah] (b) Given a vector v = (h + ) a + b is parallel to OP, calculate the values of h. Hence, by using the bigger value of h, find the ratio of PL : KL. [ marks] Diberi satu vektor v = (h + ) a + b adalah selari denganop, hitung nilai-nilai h. Seterusnya, dengan menggunakan nilai h yang lebih besar, cari nisbah PL : KL. [ markah] / 0 HAK CIPTA ZON A KUCHING [Lihat sebelah SULIT

SULIT / Section B Bahagian B [0 marks] [0 markah] Answer any four questions from this section. Jawab mana-mana empat soalan daripada bahagian ini. Use graph paper to answer this question. Gunakan kertas graf untuk menjawab soalan ini. Table shows the values of two variables, x and y, obtained from an experiment. Variables x and y are related by the equation y = ( p + ) x, where p and n are constants. Jadual menunjukkan nilai-nilai bagi dua pembolehubah, x dan y, yang diperoleh daripada suatu eksperimen. Pembolehubah x dan y dihubungkan oleh persamaan n y = ( p + ) x, dengan keadaan p dan n ialah pemalar. Table Jadual (a) Based on Table, construct a table for the values of log0 x and log 0 y. [ marks] Berdasarkan Jadual, bina satu jadual untuk nilai-nilai log0 x dan log 0 y. [ markah] (b) Plot log 0 y against log0 x by using a scale of cm to 0.0 unit on the log0 x- axis and cm to 0.0 unit on the log0 y- axis. Hence, draw the line of best fit. [ marks] Plot log y melawan log x dengan menggunakan skala cm kepada 0.0 unit 0 x.0.0.0.0.0 0.0 y.. 9. 0 pada paksi-log 0 x dan cm kepada 0.0 unit pada paksi -log0 y. Seterusnya, lukis garis lurus penyuaian terbaik. [ markah] n (c) Use the graph in (b) to find the value of Gunakan graf di (b) untuk mencari nilai (i) y when x =.9, y apabila x =.9, (ii) n, (iii) p. [ marks] [ markah] / 0 HAK CIPTA ZON A KUCHING SULIT

SULIT 9 / Diagram shows the curve y = x and the normal to the curve at the point A(, ) Rajah menunjukkan lengkung y = x dan normal kepada lengkung itu pada A(, ). y y = x O A(, ) x Calculate Hitung Diagram Rajah (a) the equation of the normal to the curve at A, [ marks] persamaan normal kepada lengkung pada A, [ markah] (b) the area of the region enclosed by the curve, the normal and the x-axis, [ marks] luas rantau yang dibatasi oleh lengkung, normal itu dan paksi-x, [ markah] (c) the volume of the revolution, in terms of π, if the region in (b) is rotated through 0 about the x-axis. [ marks] isipadu kisaran, dalam sebutan π, jika rantau di (b) dikisarkan melalui 0 pada paksi-x. [ markah] / 0 HAK CIPTA ZON A KUCHING [Lihat sebelah SULIT

SULIT 0 / 9 P Q U T rcm r cm π rad O S R Diagram 9 Rajah 9 Diagram 9 shows a circle STP and an arc QRU with centre O and radius r cm and 0 cm respectively. PR is the tangent to the circle STP at the point P. Given that POR= π radians. Rajah 9 menunjukkan sebuah bulatan STP dan satu lengkok QRU berpusat O dan berjejari r cm dan 0 cm masing-masing. PR adalah tangent kepada bulatan STP pada titik P. Diberi POR= π radian. Find Cari (a) the perimeter, in cm, of triangle OPR, [ marks] perimeter, dalam cm, bagi segi tiga OPR, [ markah] (b) the length, in cm, of minor arc PT, [ marks] panjang, dalam cm, bagi lengkok minor PT, [ markah] (c) the area, in cm, of the shaded region. [ marks] luas, dalam cm, bagi kawasan berlorek. [ markah] / 0 HAK CIPTA ZON A KUCHING SULIT

SULIT / 0 Solutions by scale drawing will not be accepted. Penyelesaian secara lukisan berskala tidak akan diterima. y C D B A O x Diagram 0 Rajah 0 y x Diagram 0 shows a parallelogram OABC and a straight line = intersects the x-axis and the y-axis at point B and point D respectively. Given that point C divides line segment BD such that BC = CD. Find y x Rajah 0 menunjukkan segiempat selari OABC dan satu garis lurus = yang bersilang dengan paksi-x dan paksi-y pada titik B dan titik D masing-masing. Diberi titik C membahagikan tembereng garis BD dengan keadaan BC = CD. Cari (a) the coordinates of C and of A, [ marks] koordinat C dan A, [ markah] (b) the area of parallelogram OABC, [ marks] luas bagi segi empat selari OABC, [ markah] (c) the equation of straight line AB, [ marks] persamaan bagi garis lurus AB, [ marks] (d) the equation of the locus of point R which moves in such a way that its distance from point B is always the distance of OD. [ marks] persamaan bagi lokus titik R yang bergerak dengan keadaan jaraknya dari titik B adalah sentiasa daripada jarak OD. [ marks] / 0 HAK CIPTA ZON A KUCHING [Lihat sebelah SULIT

SULIT / (a) There are fish of type A and type B in a pond. The ratio of the number of fish of type A to type B is :. If fish are caught at random from the pond, find the probability that Terdapat ikan jenis A dan B di dalam sebuah kolam. Nisbah bilangan ikan jenis A kepada ikan jenis B ialah :. Jika ekor ikan ditangkap secara rawak dari kolam itu, cari kebarangkalian bahawa (i) exactly fish are of type A, tepat ekor ikan adalah jenis A, (ii) not less than fish are of type B. tidak kurang daripada ekor ikan adalah jenis B. [ marks] [ markah] (b) The heights of a group of students have a normal distribution with a mean of cm and a standard deviation of cm. Calculate Tinggi sekumpulan pelajar mempunyai taburan normal dengan min cm dan sisihan piawai cm. Hitung (i) the standard score when the height is cm, skor piwai apabila ketinggian ialah cm, (ii) the height, in cm, of a student whose standard score is 0., ketinggian, dalam cm, seorang pelajar yang mempunyai skor piawai 0., (iii) the probability that the height of a student chosen at random is between cm and cm. kebarangkalian bahawa ketinggian seorang pelajar yang dipilih secara rawak adalah antara cm dan cm. [ marks] [ markah] / 0 HAK CIPTA ZON A KUCHING SULIT

SULIT / Section C Bahagian C [0 marks] [0 markah] Answer any two questions from this section. Jawab mana-mana dua soalan daripada bahagian ini. A particle starting from a fixed point O is moving along a straight line. The velocity of the particle, v m s, is given by v = t where t is the time, in seconds, after passing through O. Sebutir zarah bermula dari titik tetap O dan bergerak dalam satu garis lurus. Halaju zarah itu, v m s, diberi oleh v = t dengan keadaan t ialah masa, dalam saat, selepas melalui O. Find Carikan (a) the displacement of the particle from O when it is instantaneously at rest, [ marks] sesaran zarah itu dari O apabila ia berhenti seketika, [ markah] (b) the time when the particle passes through O again, [ marks] masa apabila zarah itu melalui O semula, [ markah] (c) the total distance travelled by the particle in the first seconds. [ marks] jumlah jarak yang dilalui oleh zarah itu dalam saat yang pertama. [ markah] / 0 HAK CIPTA ZON A KUCHING [Lihat sebelah SULIT

SULIT / Table shows the prices and the price indices of four Ingredients, P, Q, R and S, used to make a particular kind of pudding. Jadual menunjukkan harga dan indeks harga bagi empat bahan, P, Q, R dan S, yang digunakan untuk membuat sejenis puding. Ingredient Bahan Price (RM) per kg in the year Harga (RM) se kg pada tahun Price index in the year 00 based on the year 00 Indeks harga pada tahun 00 berasaskan tahun 00 Weightages Pemberat 00 00 P.0.9 x Q.0.0 0 n R.00 y S.00.0 0 n Table Jadual (a) Find the value of Cari nilai (i) x, (ii) y. [ marks] [ markah] (b) Given that the composite index for the cost of making the pudding in the year 00 based on the year 00 is., find the value of n. [ marks] Diberi indeks gubahan bagi kos membuat puding itu pada tahun 00 berasaskan tahun 00 ialah., cari nilai n. [ markah] (c) (d) Calculate the price of the pudding in the year 00 if its corresponding price in the year 00 is RM.0. [ marks] Hitung harga puding pada tahun 00 jika harganya yang sepadan pada tahun 00 ialah RM.0.. [ markah] The cost of making the pudding is expected to increase by % from the year 00 to the year 0. Calculate the expected composite index for the year 0 based on the year 00. [ marks] Kos membuat puding itu dijangka meningkat sebanyak % dari tahun 00 ke tahun 0. Hitung indeks gubahan dalam tahun 0 berasaskan tahun 00. [ markah] / 0 HAK CIPTA ZON A KUCHING SULIT

SULIT / In Diagram, ABC and CDE are two triangles. E is the midpoint of AC, AC = DC, AB = 9. cm and ABC = 0. Dalam Rajah, ABC dan CDE adalah dua buah segitiga. E adalah titik tengah AC, AC = DC, AB = 9. cm dan ABC = 0. A 9. cm E B 0 Diagram Rajah C 9 cm D Calculate Hitung (a) ACB, [ marks] [ markah] (b) the length of ED, [ marks] panjang ED, [ markah] (c) the area of quadrilateral ABDE. [ marks] luas sisi empat ABDE. [ markah] A bakery shop produces two types of bread, L and M. The production of the bread involves two processes, mixing the ingredients and baking the bread. Table shows the time taken to make a loaf of bread L and bread M respectively. Sebuah kedai roti mengeluarkan dua jenis roti, L dan M. Penghasilan roti-roti tersebut melibatkan dua proses iaitu pencampuran bahan dan pembakaran roti. Jadual menunjukkan masa yang diambil oleh sebuku roti L dan roti M masing-masing. Type of bread/ Jenis roti Time taken (minutes) / Masa yang diambil (minit) Mixing the ingredients Pencampuran bahan L 0 0 M 0 0 Baking the bread Pembakaran roti / 0 HAK CIPTA ZON A KUCHING [Lihat sebelah SULIT

SULIT / Table Jadual The shop produces x loaves of bread type L and y loaves of bread type M per day. The production of the loaves of bread per day are based on the following constraints: Kedai ini mengeluarkan x buku roti jenis L dan y buku roti jenis M setiap hari. Penghasilan roti setiap hari berdasarkan kekangan-kekangan berikut: I : The maximum total time used for mixing ingredients for both types of bread is not more than 0 minutes. Jumlah masa maksimum yang digunakan untuk pencampuran bahan bagi kedua-dua roti tersebut adalah tidak melebihi 0 minit. II : The total time for baking both types of bread is at least 0 minutes. Jumlah masa untuk pembakaran bagi kedua-dua roti tersebut adalah sekurangkurangnya 0 minit. III : The ratio of the number of loaves of bread type L to the number of loaves of bread type M is not less than :. Nisbah bilangan buku roti jenis L kepada bilangan buku roti jenis M adalah tidak kurang daripada :. (a) (b) Write down three inequalities, other than x 0 and y 0, which satisfy all the above constraints. [ marks] Tuliskan tiga ketaksamaan, selain daripada x 0 dan y 0, yang memuaskan semua kekangan yang dinyatakan di atas. [ markah] Using a scale of cm to represent loaves of bread on both axes, construct and shade the region R that satisfies all the above constraints. [ marks] Dengan menggunakan skala cm untuk mewakili buku roti bagi kedua-dua paksi, binakan dan lorekkkan kawasan R yang memuaskan semua kekangan yang dinyatakan di atas. [ markah] (c) By using your graph from (b), find Berdasarkan graf anda dari (b), cari (i) (ii) the maximum number of loaves of bread type L if 0 loaves of bread type M are produced per day. bilangan maksimum buku roti jenis L jika 0 buku roti jenis M dihasilkan setiap hari. the maximum total profit per day if the profit from one loaf of bread type L and type M are RM.0 and RM.00 respectively. jumlah keuntungan maksimum sehari jika keuntungan yang diperoleh daripada sebuku roti jenis L dan jenis M ialah RM.0 dan RM.00 masing-masing. [ marks] [ markah] END OF QUESTION PAPER / 0 HAK CIPTA ZON A KUCHING SULIT

/ Matematik Tambahan Kertas ½ jam Sept 0 SEKOLAH-SEKOLAH MENENGAH ZON A KUCHING PEPERIKSAAN PERCUBAAN SIJIL PELAJARAN MALAYSIA 0 MATEMATIK TAMBAHAN Kertas Dua jam tiga puluh minit JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU MARKING SCHEME Skema Pemarkahan ini mengandungi halaman bercetak

QUESTION NO. ADDITIONAL MATHEMATICS MARKING SCHEME TRIAL SPM exam Zon A Kuching 0 PAPER SOLUTION MARKS x = + y P y y y y (+ ) + ( + ) = 0 Eliminate x or y ± y = () () () ()( ) Solve the quadratic equation by quadratic formula @ completing the square must be shown y = 0.,. or x =.0, 0.0 Note : OW if the working of solving quadratic equation is not shown. (a) f(x) = b ax apx ap a = ap = or b ap = 9 b = / p = (b), y 9 ( /, /) max and (0, 9) The shape of the function. x

QUESTION NO. SOLUTION MARKS (a) a =, d = = + ( n )() n = 0 (b) a = π, d = π S 0 0 = ( ) + (0 )( ) [ π π ] = 0π the total cost = RM90.0 (a) sin x cos x cos x sin x cos x = x ( sin ) = cot x (b)(i) y y = cos x 0 π π x

QUESTION NO. SOLUTION MARKS Shape of cosine curve Amplitude Period P P P (ii) cosx = k k =, (a) fx = 0.() + 0.() + 0.() + 90.() + 0.() = 0 0 x = 0 =. (b) σ = (0.) () + (0.) () + (0.) () + (90.) () + (0.) () (.0) + + + + 9 = 0. 0 = (a) = a + h( a + b) OP = OK + KP OP = ( h) a + hb

QUESTION NO. SOLUTION MARKS (b) h = h + h (h )( h + ) = 0 h = PL : KL = :

log 0 x 0.0 0.0 0.0 0. 0.90.00 log 0 y 0..9....0 log 0 y Q Correct both axes (Uniform scale) All points are plotted correctly Line of best fit. (a) Each set of values correct (log 0 y must be at least decimal places), log 0 y = n log 0 x + log 0 (p + ).0 where Y = log 0 y, X = log 0 x, m = n and c = log 0 (p + ) (c) (i) X = log 0.9 = 0. = 0. Y =. = log 0 y y =.... (ii) n = gradient n.0 0.0 = =. n = 0. 0 (iii) log 0 (p + ) = Y-intercept log 0 (p + ) = 0.0 p = 0.99. (0.0,.0)..0 0. 0. 0. 0. (0, 0.0) 0 0. 0. 0. 0. 0. 0. 0. 0. log 0 x 0.9.0

QUESTION NO. SOLUTION MARKS (a) or or m normal = +c + (b) B(, 0) = = unit (c) volume of revolution = = = unit QUESTION NO. SOLUTION 9 (a) r = 0 MARKS PR =.0. cm (b) π s = π =0.

(c) Area of shaded region of semi circle = (0) ( π ) () ( π ) =. /.09 cm Area of shaded region PQR π = (0) ()(0) sin 0 =0. / 0.09 cm Total area of shaded region =.+0. =. /.9 cm 0 QUESTION NO. SOLUTION MARKS 0 (a)(i) (ii) ( ) + (0) (0) + () or + + C =, + x + y = or or (, 0) A, (b) = 0( ) + ( )(0) + ( )( ) + ( )(0) 0( ) ( )( ) (0)( ) ( )(0) = 9. (c) m AB = y = x (d) ( ) x ( ) + ( y 0) x y x + + = 0 0

9 QUESTION NO. SOLUTION MARKS (a) (i) C ( ) ( ) = 0. (ii) C ( ) ( ) C ( ) ( ) ( ) 0.90 (b) (i) 0. P (ii) h h =. = 0. (iii) P( z 0.) or P(Z > ) P(Z > 0.) or R( ) R(0.) 0. 0

0 QUESTION NO. (a) t + = 0 SOLUTION MARKS t = s = t + t s = ( ) + ( ) = m (b) t( t + ) = 0 t = (c) s s + s s 0 = 0 + =

QUESTION NO. SOLUTION MARKS (a) x = y =.0 (b).n + 9. = 0n + 9 n = (c). RM.0 RM. (d) I = 0 I = 00. 0. 0

QUESTION NO. SOLUTION MARKS (a) 9. 9 = sin ACB sin 0 ACB =.9 / ' (b) ECD = 0.9 =.0 / ED =. + 9 (.)(9)cos.0 ED =. cm (c) BAC = 0 0.9 =.0 / P Area of triangle ABC = 9. 9 sin.0 =.9 Area of triangle CDE = 9. sin.0 =.90 Area of quadrilateral ABCD =.9 +.90. 0

Answer for question y (a) I. x + y II. x + y III. y x (b) Refer to the graph, 0 or graph(s) correct graphs correct Correct area (c) (i) x = (ii) (, ) P Maximum Profit = RM [.0() + ()] = RM.00 (, ) 0 0 R 0 0 x