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NAMA : hours KELAS : JABATAN PELAJARAN NEGERI SABAH SIJIL PELAJARAN MALAYSIA 47/ EXCEL ADDITIONAL MATHEMATICS Paper Ogos 0 hours 0 minutes Two hours thirty minutes jam 0 minit Dua jam tiga puluh

1 NAMA : hours KELAS : JABATAN PELAJARAN NEGERI SABAH SIJIL PELAJARAN MALAYSIA 47/ EXCEL ADDITIONAL MATHEMATICS Paper Ogos 0 hours 0 minutes Two hours thirty minutes jam 0 minit Dua jam tiga puluh minit JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU. This question paper consists of three sections: Section A, Section B and Section C. Kertas ini mengandungi tiga bahagian: Bahagian A, Bahagian B dan Bahagian C.. Answer all questions in Section A, four questions from Section B and two questions from Section C. Jawab semua soalan dalam Bahagian A, empat soalan dalam Bahagian B dan dua soalan dalam Bahagian C.. Give only one answer / solution for each question. Beri hanya satu jawapan/penyelesaian bagi setiap soalan. 4. Show your working. It may help you to get marks. Tunjukkan jalan kerja anda. Ia boleh membantu anda mendapat markah. 5. The diagrams in the questions provided are not drawn to scale unless stated. Gambarajah dalam soalan adalah tidak mengikut skala melainkan dinyatakan 6. The marks allocated for each question and sub-part of a question are shown in brackets. Markah yang diperuntukkan untuk setiap soalan dan sub-bahagian ditunjukkan dalam kurungan. 7. A list of formulae is provided on pages to. Senarai rumus diberi dalam muka surat hingga. 9. You may use a non-programmable scientific calculator. Anda dibenarkan menguna kalkulator saintifik yang tidak boleh diprogramkan. This paper consists of 6 printed pages. Kertas ini mengandungi 6 muka bercetak

2 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 yang biasa digunakan. ALGEBRA... ± x = 4. ( a ) b b 4ac a m n m n a a = a + m n m n a a = a = a m n mn 5. log mn = log m + log n a a a m 6. log log m log n = a a a n 7. log m = nlog m a a n 8. log a logc b b = log a 9. T = a+ ( n ) d n n 0. Sn = [ a+ ( n ) d].. Tn S n = ar n c n n ar ( ) a( r) = =, r r r a. S =, r r < CALCULUS KALKULUS dy dv du. y = uv, = u + v dx dx dx du dv v u u dy. y =, = dx dx v dx v. dy dy du = dx du dx 4. Area under a curve Luas di bawah lengkung b = y dx or (atau) = a b a x dy 5. Volume generated Isipadu kisaran = = b π y dx or (atau) a b π x dy a

3 GEOMETRY. Distance / Jarak 4. Area of triangle / Luas segi tiga = = ( x x ) + ( y y ). Midpoint / Titik Tengah x + x y + y = ( xy, ),. A point dividing a segment of a line Titik yang membahagi suatu tembereng garis nx + mx ny + my = m+ n m+ n ( xy, ), ( xy xy xy ) ( xy ) xy xy r = x + y xi + yj rˆ = x + y x x = N x fx = f ( x x) x σ = = x N N f ( x x) fx σ = = x f f STATISTICS STATISTIK I n n = P = r C = r WI i W i i n! ( n r) ( )! n! n r! r! 0. P( A B) = P( A) + P( B) P( A B) P X= r = Cpq p+ q= n r n r. ( ), r N F 5. m L = + c fm Q 6. I = 00 Q o. Mean / Min, μ = np. σ = npq 4. x µ Z = σ

4 TRIGONOMETRY TRIGONOMETRI. Arc length / Panjang lengkok, s = rθ 8. sin ( A± B) = sin Acos B± cos Asin B. Area of sector / Luas sektor, sin A+ cos A= sec A= + tan A cosec A= + cot A 6. sin A= sin Acos A 7. cos cos sin A= A A A= r θ 9. cos ( A± B) = cos Acos B sin Asin B 0. tan A± tan B tan ( A± B) = tan Atan B tan A. tan A= tan A. a = b = c sin A sin B sin C = cos A = sin A. a = b + c bc cos A 4. Area of triangle / Luas segi tiga = sin ab C

5 Section A Bahagian A [40 marks] [40 markah] Answer all questions. Jawab semua soalan. Solve the simultaneous equations x y = 0 and x + y Give the answers correct to two decimal places. Selesaikan persamaan serentak x y = 0 dan x + y Beri jawapan betul kepada dua tempat perpuluhan. = 5xy. = 5xy. [5 marks] [5 markah] Diagram shows the shaded region bounded by the curve y = g(x) and the x-axis. Rajah menunjukkan rantau berlorek yang dibatasi oleh lengkung y = g(x) dan paksi-x. y y = g (x) A O B x Diagram Rajah 5 It is given that the area of region A is unit 8 and the area of region B is units. 5 unit Diberi bahawa luas rantau A ialah 8 dan luas rantau B ialah unit. (a) Find Cari (i) g ( x) dx. (ii) 0 [ g ( x) + 5 ] dx. [4 marks] [4 markah] (b) Given g (x) = x x, find g(x) in terms of x. Diberi g (x) = x x, cari g(x) dalam sebutan x. [ marks] [ markah]

6 (a) Sketch the graph of y = cos x + for 0 x π. [4 marks] Lakar graf bagi y = kos x + untuk 0 x π. [4 markah] (b) Hence, using the same axes, sketch a suitable straight line to find the number of solutions for the equation cos x = 0 for 0 x π. State the number of solutions. [ marks] Seterusnya, dengan menggunakan paksi yang sama, lakar satu garis lurus yang sesuai untuk mencari bilangan penyelesaian bagi persamaan kos x = 0 untuk 0 x π. Nyatakan bilangan penyelesaian itu. [ markah] 4 Agnes is given 50 cubes with sides 5 cm, to form a pyramid as shown in diagram 4. She needs to arrange a cube in the first (top most) row, three cubes in the second row, five cubes in the third row, and so on. Agnes diberikan 50 buah kubus dengan sisi 5 cm, untuk membentuk sebuah piramid seperti yang ditunjukkan dalam rajah 4. Dia dikehendaki menyusun sebuah kubus pada barisan pertama (teratas), tiga kubus pada barisan kedua, lima kubus pada barisan ketiga, dan seterusnya. Find Cari Diagram 4 Rajah 4 (a) the number of cubes in the bottom most row, if the height of the pyramid to be formed is 60 cm. [ marks] bilangan kubus di barisan terbawah, jika tinggi piramid yang dibentuk ialah 60 cm. [ markah] (b) the maximum height of the piramid. tinggi maksimum bagi piramid itu. [4 marks] [4 markah]

7 5 Table 5 shows the distribution of the scores of 40 students in a quiz. Jadual 5 menunjukkan taburan skor bagi 40 orang pelajar dalam satu kuiz. Markah Number of students Bilangan pelajar x y Table 5 Jadual 5 (a) Given that the median score is 6.75, find the value of x and of y. Diberi skor median ialah 6.75, cari nilai x dan nilai y. (b) Calculate the standard deviation of the distribution. Hitungkan sisihan piawai bagi taburan skor itu. [4 marks] [4 markah] [ marks] [ markah] (c) What is the standard deviation if the score of each student is multiplied by and then increased by? [ mark] Apakah sisihan piawai jika skor setiap murid didarabkan dengan dan kemudian ditambah sebanyak? [ markah]

8 6 Diagram 6 shows a trapezium ABCD. R is the midpoint of BC. AR intersects BQ at point P. Rajah menunjukkan sebuah trapezium ABCD. R ialah titik tengah bagi BC. AR bersilang dengan BQ di titik P. D C Q R P A Diagram 6 Rajah 6 B It is given that AD = y, AB = 6 x, DC = AB, AD = QD Diberi bahawa AD = y, AB = 6 x, DC = AB, AD = QD (a) Express in terms of x and y : Ungkapkan dalam sebutan x dan y : (i) (ii) AC. AR. (b) It is given that AP = h AR and AP = Find the values of h and of k. Diberi bahawa AP = h AR dan AP = pemalar. Cari nilai h dan nilai k. [ marks] [ markah] AQ + k QB, where h and k are constants. [4 marks] AQ + k QB, dengan keadaan h dan k ialah [4 markah]

9 Section B Bahagian B [40 marks] [40 markah] Answer four questions. Jawab empat soalan. 7 Use graph paper to answer this question. Guna kertas graf untuk menjawab soalan ini. x y Table 7 Jadual 7 Table 7 shows the values of two variables x and y which are related by the equation x+ s =, where r and s are constants. y r Jadual 7 menunjukkan nilai-nilai bagi dua pemboleh ubah, x dan y yang dihubungkan oleh x+ s persamaan =, dengan keadaan r dan s adalah pemalar. y r (a) Using a scale of cm to 0. unit on the x-axis and cm to 0.5 unit on the y -axis, plot against x. y Hence, draw the line of best fit. [5 marks] Dengan menggunakan skala cm kepada 0. unit pada paksi-x dan cm kepada 0.5 unit pada paksi- y, plotkan melawan x. y Seterusnya, lukis garis lurus penyuaian terbaik. [5 markah] (b) Use the graph in 7(a) to find the value of Gunakan graf di 7(a) untuk mencari nilai (i) r. (ii) s. (ii) y when x = 0.5. y apabila x = 0.5. [5 marks] [5 markah]

10 8 Diagram 8 shows a semi circle EFG with centre O. Rajah 8 menunjukkan semi bulatan EFG berpusat O. E O θ G F Diagram 8 Rajah 8 Given that the length of arc EF is twice that of arc FG and the area of sector FOG is cm, find Diberi bahawa panjang lengkok EF adalah dua kali lengkuk FG dan luas sektor FOG ialah cm, cari [Use/ Guna π = ] 7 (a) the value of θ, in terms of π. [ mark] nilai θ, dalam sebutan π.. [ markah] (b) the length, in cm, of OE. panjang, dalam cm, bagi OE. [ marks] [ markah] (c) the area, in cm, of the shaded region. [ marks] luas, dalam cm, rantau berlorek. [ markah] (d) the perimeter, in cm, of the shaded region. perimeter, dalam cm, rantau berlorek. [4 marks] [4 markah]

11 9. Solution by scale drawing will not be accepted. Penyelesaian secara lukisan berskala tidak akan diterima. Diagram 9 shows three points P, Q( -, ) and R which lie on the straight line y = x, such that PQ : QR = :. Rajah 9 menunjukkan tiga titik P, Q ( -, ) dan R yang terletak pada garis lurus y = x, dengan keadaan PQ : QR = :. R y Q(-, ) P O x Diagram 9 Rajah 9 (a) Find Cari (i) the coordinates of P. koordinat P. [ mark] [ markah] (ii) the equation of the straight line which passes through Q and is perpendicular to the line RP. [ marks] persamaan garis lurus yang melalui Q dan berserenjang kepada garis RP. [ markah] (iii) the coordinates of R. koordinat R. [ marks] [ markah] (b) A point S moves such that its distance from Q is always units. Find Suatu titik S bergerak dengan keadaan supaya jaraknya dari Q sentiasa unit. Cari (i) the equation of the locus of S. persamaan lokus bagi S. [ marks] [ markah] (ii) the coordinates of the point(s) of intersection of locus S with the x-axis. [ marks] koordinat titik/titik-titik persilangan lokus S dengan paksi-x. [ markah]

12 0 (a) Given that the probability of passing a particular science test, is 4. If 8 candidates are chosen at random, calculate Diberi bahawa kebarangkalian lulus suatu ujian sains ialah 4. Jika 8 orang calon dipilih secara rawak, hitungkan (i) the standard deviation of passing this test. sisihan piawai lulus ujian itu. (ii) the probability that exactly 7 students pass. kebarangkalian bahawa tepat 7 orang calon lulus. (iii) the probability that less than 7 students pass. kebarangkalian bahawa kurang daripada 7 orang calon lulus. [ mark] [ markah] [ marks] [ markah] [ marks] [ markah] (b) The masses of papayas in Eco Orchard forms a normal distribution, with a mean of 950g and a standard deviation of 65g. Papayas with mass more than 850g are exported. Jisim buah betik di Dusun Eco didapati bertaburan normal dengan min 950g dan sisihan piawai 65g. Buah betik yang jisimnya melebihi 850g akan diekspot. (i) Find the probability that a papaya chosen at random from Eco Orchard will be exported. [ marks] Cari kebarangkalian bahawa sebuah betik yang dipilih secara rawak dari Dusun Eco akan diekspot. [ markah] (ii) Determine the number of papayas that will not be exported out of a sample of 00 papayas. [ mark] Tentukan bilangan buah betik yang tidak akan diekspot dari suatu sampel 00 buah betik. [ markah]. (iii) Given that 0% of the papayas have a mass greater than w g, find the value of w. [ marks] Diberi bahawa 0% buah betik mempunyai jisim lebih daripada w g, cari nilai w. [ markah]

13 Diagram shows the tangent to the curve y = 5 x, which passes through point R(, 6). The tangent intersects the x-axis at point Q. Rajah menunjukkan tangen kepada lengkung y = 5 x, yang melalui titik R(, 6). Tangen itu bersilang dengan paksi-x pada titik Q. Diagram Rajah (a) Find the gradient of the curve at R. [ marks] Cari kecerunan lengkung pada R.. [ markah] (b) Determine the coordinates of Q. Tentukan koordinat Q. (c) Find the equation of the normal to the curve at R. Carikan persamaan garis normal kepada lengkung pada R. [ marks] [ markah] [ marks] [ markah] (d) Given that the area of the shaded region is unit, find the value of h. [4 marks] Diberi bahawa luas rantau berlorek ialah unit, cari nilai h. [4 markah]

14 Section C Bahagian C [0 marks] [0 markah] Answer two questions. Jawab dua soalan. A particle moves along a straight line and passes through a fixed point O. Its velocity, v m s, is given by v = t 6t + 5, where t is the time in seconds after passing through O. [Assume motion to the right is positive] Suatu zarah bergerak di sepanjang suatu garis lurus dan melalui satu titik tetap O. Halajunya, v m s, diberi oleh v = t 6t + 5, dengan keadaan t ialah masa dalam saat selepas melalui O. [Anggap bahawa gerakan ke arah kanan ialah positif]. Find Cari (a) the initial velocity, in m s. [ mark] halaju awal, dalam m s. [ markah] (b) the minimum velocity, in m s. [ marks] halaju minimum, dalam m s. [ markah] (c) the range of values of t during which the particle moves to the left. [ marks] julat nilai t ketika zarah bergerak ke arah kiri. [ markah] (d) the total distance, in m, travelled by the particle in the first 5 seconds. [4 marks] jumlah jarak, dalam m, yang dilalui oleh zarah dalam 5 saat pertama. [4 markah]

15 Use graph paper to answer this question. Gunakan kertas graf untuk menjawab soalan ini. A tuition centre offers tuition in Chemistry and Mathematics. The number of students taking Chemistry is x and the number taking Mathematics is y. The enrolment of the students is based on the following conditions: Sebuah pusat tuition menawarkan subjek Kimia dan Matematik. Bilangan pelajar bagi subjek Kimia ialah x orang dan bilangan pelajar subjek Matematik ialah y orang. Bilangan pelajar adalah berdasarkan kekangan yang berikut: I : The total number of students is not more than 00. I : Jumlah pelajar tidak melebihi 00 orang. II : The number of students taking Mathematics is not more than three times the number of students taking Chemistry. II : Bilangan pelajar subjek Matematik tidak melebihi tiga kali bilangan pelajar subjek Kimia. III : The number of students taking Mathematics must exceed the number of students taking Chemistry by at least 0. III : Bilangan pelajar subjek Matematik mesti melebihi bilangan pelajar Kimia sekurangkurangnya 0 orang. (a) Write three inequalities, other than x 0 and y 0, which satisfy all the above constraints. [ marks] Tuliskan tiga ketaksamaan, selain x 0 dan y 0, yang memenuhi semua kekangan di atas. [ markah] (b) Using a scale of cm to 0 students on both axes, construct and shade the region R which satisfies all the above constraints. [ marks] Dengan menggunakan skala cm kepada 0 pelajar pada kedua-dua paksi, bina dan lorek rantau R yang memenuhi semua kekangan di atas. [ markah] (c) Using the graph from (b), find Dengan mengunakan graf di (b), cari (i) the range of number of students taking Mathematics if 40 students enrolled for Chemistry. [ mark] julat pelajar Matematik jika 40 pelajar telah mendaftar untuk Kimia. [ markah] (ii) the maximum total fees collected per month if the monthly fees per student for Chemistry and Mathematics are RM0 and RM5 respectively. [ marks] Jumlah maksimum kutipan yuran sebulan jika yuran sebulan bagi seorang pelajar Kimia dan Matematik ialah RM0 dan RM5 masing-masing. [ markah]

16 4 Diagram 4 shows a trapezium PQRS where PQ is parallel to SR. Given that PQ = 4.8 cm, PR = 0. cm, SPR = 05, and PSR = 7, calculate [Give all answers correct to 4 significant figures] Rajah 4 menunjukkan sebuah trapezium PQRS di mana PQ ialah selari dengan SR. Diberikan PQ = 4.8 cm, PR = 0. cm, SPR = 05, dan PSR = 7, hitungkan [Berikan semua jawapan betul kepada 4 angka bererti] Diagram 4 Rajah 4 (a) the length, in cm, of PS. [ marks] panjang, dalam cm, PS. [ markah] (b) the length, in cm, of QR. [ marks] panjang, dalam cm, QR. [ markah] (c) the area, in cm, of trapezium PQRS. [ marks] luas, dalam cm, trapezium PQRS. [ markah] (d) Sketch triangle P S R which has a different shape from triangle PSR such that P S = PS, P R = PR and P ' S ' R ' = PSR. Hence find PR S. [ marks] Lakar segi tiga P S R yang mempunyai bentuk yang berlainan daripada segi tiga PSR dengan keadaan P S = PS, P R =PR dan P ' S ' R ' = PSR. Seterusnya cari PR S. [ markah]

17 5 Table 5 shows the price indices and the percentages of usage for four ingredients used to make a kind of dessert. Jadual 5 menunjukkan indeks harga dan peratusan kegunaan bagi empat jenis bahan yang digunakan untuk membuat sejenis pencuci mulut. Ingredient Bahan Price index in the year 007 based on the year 005 Indeks harga dalam tahun 007 berasaskan tahun 005 Percentage (%) Peratusan (%) C 60 0 D 50 0 E x 0 F 5 40 Table 5 (a) Calculate Jadual 5 Hitungkan (i) the cost of ingredient C in the year 005 if the cost in the year 007 was RM400. kos bagi bahan C pada tahun 005 jika kosnya pada tahun 007 ialah RM400. (ii) the price index of ingredient D in the year 007 based on year 006 if its price index in the year 006 based on the year 005 was 40. indeks harga bagi bahan D pada tahun 007 berasaskan tahun 006 jika indeks harganya pada tahun 006 berasaskan tahun 005 ialah 40. [4 marks] [4 markah] (b) The composite index for the cost of making the dessert in the year 007 based on the year 005 is 4. Indeks gubahan kos pembuatan pencuci mulut itu pada tahun 007 berasaskan tahun 005 ialah 4. (i) Calculate the value of x. Hitungkan nilai bagi x. (ii) Find the cost of making the dessert in the year 007 if the cost in the year 005 was RM5. Cari kos pembuatan pencuci mulut itu pada tahun 007 jika kosnya pada tahun 005 ialah RM5. [4 marks] [4 markah] (c) The cost of making the dessert increased by 50% from year 007 to year 00. Calculate the composite index for the cost of making the dessert in the year 00 based on the year 005. [ marks] Kos membuat pencuci mulut itu telah meningkat sebanyak 50% dari tahun 007 ke tahun 00. Hitungkan indeks gubahan membuat pencuci mulut itu pada tahun 00 berdasarkan tahun 005. [ markah] END OF QUESTION PAPER KERTAS SOALAN TAMAT

18 KERTAS JAWAPAN ADDITIONAL MATHEMATICS PAPER SPM YEAR 0 No. Solution and Mark Scheme Sub Total y = x OR x = y + (P) substitute correctly : x + (x ) = 5x(x ) OR y + y + + y = 5 ( y) (K) Solve the quadratic equation : ( 7) ± ( 7) 4()(4) x = OR () (K) ( ) ± x = ( ) 4()() () x = 0.7,.78 y = 0.6, 6.4 (N) (N) 5 5 (a) (i) = (P) 4 8 (K) (ii) + [ 5x ] 0 = 8 + [ 5() 5(0) ] (K) = (N) 4 (b) x x g ( x) = x + c (K) 0 = ( ) ( ) ( ) + c OR 0 = (0) ( 0) (0) + c OR 0 = () () () + c y = x x x (N) (K) 7

19 No. Solution and Mark Scheme Sub Total (a) y 4 y= x O Shape of cos x Amplitude and periods for 0 x π. Modulus cos x (Modulus cos x) + (P) (P) (P) (P) 4 (b) y = (K) draw the straight line y = (K) No. of solutions = 8 (N) 7 4 (a) T = + () (K) = (N) n (b) [() + ( n )()] 50 (K) accept =, < n manimum = 5 (K) Height of pyramid = 5 5 (K) = 75 (N) 4 6 [ accept any other Mathematical method for (a) and (b) ]

20 No. Solution and Mark Scheme 5 (a) L m = 5.5, OR f m = x OR F m = 8 OR x+ y = (P) 6.75 = x = 8 y = 4 (N) (N) (40) 8 (5) x (K) Sub 4 Total 7(8) + () + 8(8) + 0() + 4(8) 40 (b) σ = 7(8) + () + 8(8) + 0( + 4(8) 40 = 6. (N) Calculate fx (maximum mistake) Using formula σ (c) 6. = 8.99 / 8.94 (N) (K) (K) 8 6 (a) (i) AC = AD + DC = y + 4 x ~ ~ (P) (ii) find BC ( 6 x + y + 4 ~ ~ x ) ~ OR find CB ( 4 x y + 6 ~ ~ x ) ~ (K) 5 x + ~ y ~ (N) (b) AP = h AR OR AP = AQ + k QB = 5h x + ~ h y = y k y + 6k ~ ~ ~ x ~ (K) 5h = 6k OR h = k (K) h = (N) 9 0 k = (N) 9 4 7

No. 7 (a) Solution and Mark Scheme Sub Total.64.78.4 4 5.7 5.67 y x 0. 0. 0.4 0.5 0.7 0.

21 No. 7 (a) Solution and Mark Scheme Sub Total y x (N) Graph : Using correct, uniform scale and axes ( with at least point seen ) ( P) All points plotted correctly ( P) Line of best fit ( P) y = ( x) + r s r OR equivalent (P) 5 (b) (i) Use = * m r r = (K) (N) (ii) Use s = * c r (K) s = (N) (iii) y = 0.57 by graphical method (N) 5 0

22 No. Solution and Mark Scheme Sub Total 8 (a) π θ = rad ( P) (b) r π = ( K) r = ( N) π (c) area EOF = () OR area EOF = () π sin ( K) area sector EOF area EOF = π () = 7.04 ( N) () π sin OR equivalent ( K) (d) cos 6 π OR sin π OR equivalent ( K) π arc EF = () OR equivalent ( K) π π π π = () cos + () OR ( ) sin + () 6 OR equivalent ( K) = 80.7 OR 80.8 ( N) (a) (i) P (0,) (P) (ii) m = y = x + (iii) (, ) = (K) (N) x + 0 y +, + + (K) R (, 4) (N) 5 (b) (i) ( x + ) + ( y ) (K) ( x + ) + ( y ) = (K) x + x + y 4y + = 0 (N) (ii) (x +)(x + ) = 0 (K) (, 0) (N) 5 0

23 No. Solution and Mark Scheme 0 (a) (i) σ =.5 (P) (ii) C 4 4 (K) (N) (ii) C C (K) 0.69 (N) (b) (i) z >.58 (K) (N) (ii) (integer) (N) Sub 5 Total (iii) Z > 0.84 (K) w = OR 005 (N) 5 0 (a) dy = x dx 6 (K) (N) (b) 6 0 x = 6 OR equivalent (K) Q 5, 0 (N) (c) m = 6 y = x + 6 (K) (N) (d) A = ( h) (6) 5 OR A 5x x 5 = ( from dx 5 x ) (K) 8( h) + h = 5 = 5(5) 5() 7 = OR equivalent (K) (N) (K) 4 0

24 No. Solution and Mark Scheme Sub Total (a) 5 m s (P) (b) dv = t 6 (K) dt 0 = t 6 (K) t = v max = 4 (N) (c) (t ) (t 5) < 0 (K) accept (t ) (t 5) = 0 < t < 5 (N) 5 (d) = t 6t + 5 dt + 0 t 6t + 5 dt (K) = t 6t 5 + t 0 + t 6t 5 + t 5 (K) = 0 () + 5() (0) + 5(0) (5) + 5(5) () + 5() 0 OR equivalent (K) = m (N) 4 0

No. Solution and Mark Scheme (a) x + y 00 OR equivalent (N) y x OR equivalent (N) y x 0 OR equivalent (N) (b) Draw correctly at least one straight line (K) OR Draw correctly all

25 No. Solution and Mark Scheme (a) x + y 00 OR equivalent (N) y x OR equivalent (N) y x 0 OR equivalent (N) (b) Draw correctly at least one straight line (K) OR Draw correctly all the three straight lines (K) Region R shaded correctly (K) Sub Total (c) (i) 50 y 0 (N) (ii) Maximum fee = 0x + 5y maximum point (50, 50) (N) = 0(50) + 5(50) (K) = RM6750 (N) 4 0

26 No. 4 (a) PRS = 8 (P) Solution and Mark Scheme Sub Total PS 0. = sin 8 sin 7 PS = 0.4 cm (K) (N) (b) QR = (4.8)(0.) cos 8 QR = (N) (K) (c) (0.4)(0.) sin 05 OR (4.8)(0.) sin 8 (K) (0.4)(0.) sin 05 + (4.8)(0.) sin 8 (K) (N) (d) R S R 4 (N) (K) (a) (i) 60 = 00 P 005 P 005 = 50 (N) OR equivalent (K) (ii) 00 OR equivalent (K) (N) 4 60(0) + 50(0) + 0( x) + 5(40) (b) (i) = 4 00 x = 5 (N) (K) P (ii) 4 = OR equivalent (K) P 007 = 7.84 (N) 50 4 (c) 00 OR equivalent (K) (N) 4 0

Answer all questions Jawab semua soalan [80 marks] [80 markah] f(x)

1 Diagram 1 shows the linear functions f. Rajah 1 menunjukkan fungsi linear f. Answer all questions Jawab semua soalan [80 marks] [80 markah] x 7 7 Set P f(x) 9 9 Set Q Diagram 1 Rajah 1 1 2 (a) State