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1 Mathematics Paper 1 Oct./Nov ¼ hours JABATAN PELAJARAN MELAKA PEPERIKSAAN SELARAS AKHIR TAHUN TINGKATAN 4, 010 MATHEMATICS Paper 1 One hour and fifteen minutes DO NOT OPEN THIS QUESTION PAPER UNTIL YOU ARE TOLD TO DO SO 1. This question paper consists of 40 questions.. Answer all questions.. Answer each question by blackening the correct space on the answer sheet. 4. Blacken only one space for each question. 5. If you wish to change your answer, erase the blackened mark that you have done. Then blacken the space for the new answer. 6. The diagrams in the questions provided are not drawn to scale unless stated. 7. A list of formulae is provided on pages and. 8. You may use a non-programmable scientific calculator. This question paper consists of 8 printed pages

2 SULIT MATHEMATICAL FORMULAE The following formulae may be helpful in answering the questions. The symbols given are the ones commonly used. RELATIONS 1 a m a n a m n a m a n a m n ( m n mn a ) a 1 1 d b 4 A ad bc c a n( A) P( A) 5 n S 6 P( A' ) 1 P( A) 7 Distance ( x x1) ( y y1) x1 x y1 y 8 Midpoint, ( x, y), 9 Average speed = sum of data 10 Mean = number of data distance travelled time taken 11 Mean sum of(class mark frequency) sum of frequencies 1 Pythagoras Theorem c a b 1 m y x y1 x 1 14 m y int ercept x int ercept

3 SULIT SHAPES AND SPACE 1 Area of trapezium = 1 sum of parallel sides height Circumference of circle = d r Area of circle = r 4 Curved surface area of cylinder = rh 5 Surface area of sphere = 4 r 6 Volume of right prism = cross sectional area length 7 Volume of cylinder = r h 1 8 Volume of cone = r h 9 Volume of sphere = 4 r 1 10 Volume of right pyramid = base area height 11 Sum of interior angles of a polygon = (n ) 180º arc length angle subtended at centre 1 o circumference of circle 60 area of sector angle subtended at centre 1 o area of circle 60 PA' 14 Scale factor, k = PA 15 Area of image = k area of object

4 SULIT 4 Answer all questions. Jawab semua soalan. 1 Round off correct to three significant figures. Bundarkan betul kepada tiga angka bererti. A B C 8070 D Find the value of ( 1.7) 0, and round off the answer correct to two significant figures. Cari nilai ( 1.7 ) 0, dan bundarkan jawapan itu betul kepada dua angka bererti. A 0.08 B 0.09 C D Express in standard form. Ungkapkan dalam bentuk piawai. A B C D = A B C D

5 SULIT 5 5 A rectangular floor with a length of 6 m and a width of 8 m has to be tiled. Find the number of square tiles of side 0 cm that are required to cover the whole floor. Lantai berbentuk segiempat tepat yang mempunyai panjang 6 m dan lebar 8 m hendak dipasang dengan jubin marmar. Cari bilangan jubin segiempat sama dengan sisi 0 cm yang diperlukan untuk menutupi seluruh lantai itu. A B C D In Diagram 1, PQRSTU is a regular hexagon. TUV and RPV are straight lines. Dalam Rajah 1, PQRSTU adalah sebuah heksagon sekata. TUV dan RPV adalah garis-garis lurus. o Find the value of x. Cari nilai bagi x. A 0 B 50 C 60 D 70 Diagram 1 Rajah 1

6 SULIT 6 7 In Diagram, PQRS is a rhombus. Dalam Rajah, PQRS adalah sebuah rombus. Find the value of x. Cari nilai bagi x. A 15 B 0 C 5 D 5 Diagram Rajah

7 SULIT 7 8 In Diagram, ABC and CDE are tangents to the circle centre O at B and D respectively. Dalam Rajah, ABC dan CDE adalah tangen kepada bulatan berpusat O masingmasing di titik B dan D. Diagram Rajah The value of x is Nilai bagi x ialah A 0 B C 58 D 6

8 SULIT 8 9 In Diagram 4, QRT is a tangent to the circle with centre O at R. PUS, OPQ and OUR are straight lines. Dalam Rajah 4, QRT ialah tangent kepada bulatan berpusat di O pada titik R. PUS, OPQ dan OUR adalah garis-garis lurus. 0 Diagram 4 Rajah 4 Find the value of x. Cari nilai bagi x. A 40 B 45 C 50 D 65

9 SULIT 9 10 Diagram 5 shows five triangles, P, A, B, C and D, drawn on square grids. Rajah 5 menunjukkan lima segitiga bertanda P, A, B, C and D dilukis pada grid segiempat sama. Diagram 5 Rajah 5 Triangle P is rotated under an anticlockwise direction of 90º about centre X. Which of the triangles marked A, B, C and D is the image of P? Segitiga P diputarkan 90º pada lawan arah jam pada pusat X. Antara segitiga-segitiga yang bertanda A, B, C dan D, yang manakah imej bagi P?

10 SULIT In Diagram 6, pentagon ABCDE is the image of pentagon AFGHI under an enlargement. Dalam Rajah 6, pentagon ABCDE adalah imej bagi pentagon AFGHI di bawah satu pembesaran. Diagram 6 Rajah 6 If the area of the shaded region is 60 cm, calculate the area, in cm, of pentagon AFGHI. Jika luas kawasan berlorek ialah 60 cm,hitungkan luas, dalam cm, bagi pentagon AFGHI. A.5 B 4 C 40 D 10

11 SULIT 11 1 Diagram 7 shows a right-angled triangle PSQ and PQR is a straight line. Rajah 7 menunjukkan sebuah segitiga bersudut tegak PSQ dan PQR ialah garis lurus. Diagram 7 Rajah 7 Given PQ = 15 cm, and cos xº =, find the value of tan yº. 5 Diberi PQ = 15 cm dan kos xº =, cari nilai bagi tan yº. 5 A B C D

12 SULIT 1 1 Diagram 8 shows the graph of y = sin xº. Rajah 8 menunjukkan graf bagi y = sin xº. Diagram 8 Rajah 8 The value of p is Nilai p ialah A 90º B 180º C 70º D 60º

13 SULIT 1 14 In Diagram 9, PTR is a straight line. Dalam Rajah 9, PTR ialah garis lurus. Diagram 9 Rajah 9 Given that cos x = 1 5 and sin y = 5. Find the length, in cm, of PT. Diberi bahawa kos x = 1 5 dan sin y = 5. Carikan panjang, dalam cm, bagi PT. A 10 B C D 6

14 SULIT Diagram 10 shows a cuboid with a horizontal base PQRS. Rajah 10 menunjukkan sebuah kuboid dengan tapak mengufuk PQRS. Diagram 10 Rajah 10 Name the angle between the plane RQVW and the plane QUR. Namakan sudut antara satah RQVW dan satah QUR. A B C D VQR VUQ VRU VQU

15 SULIT Diagram 11 shows a right-angled triangular prism with a horizontal base PQRS. Rajah 11 menunjukkan sebuah prisma segitiga tegak dengan tapak mengufuk PQRS. Q Diagram 11 Rajah 11 Name the angle between the line KQ and the plane PQRS. Namakan sudut antara garis KQ dan satah PQRS. A B C D KQP KQR KQS KRQ

16 SULIT In Diagram 1, PQS and RT are two vertical poles on a horizontal plane RS. Dalam Rajah 1, PQS dan RT adalah dua tiang tegak pada satah mengufuk RS. Diagram 1 Rajah 1 Name the angle of elevation of point P from point T. Namakan sudut dongak titik P dari titik T. A B C D TPL SPT TPQ QTP

17 SULIT In Diagram 1, EF is a vertical flag pole on a horizontal plane FG. Dalam Rajah 1, EF ialah sebatang tiang bendera tegak terletak di atas satah mengufuk FG. 59 m Diagram 1 Rajah 1 Given the angle of elevation of point E from point G is º. Find the height, in m, of the flag pole EF. Diberi sudut dongakan titik E dari titik G ialah º. Cari tinggi, dalam m, tiang bendera EF. A 1.7 B 6.87 C 50.0 D x (1 x) = A x x B x C 4x D 7x

18 SULIT x(x y) (x y) = A x xy + y B x 8xy y C x xy 9y D x 14xy + 9y 1 n 4 1 Express n 6n Ungkapkan 1 n 4 n 6n as a single fraction in its simplest form. sebagai satu pecahan tunggal dalam bentuk termudah. n n A n n B 4n 8 1n C 4n 8 1n D Given that p 1 pq, express p in terms of q. q Diberi p 1 pq, ungkapkan p dalam sebutan q. q A B C D p q p q 1 1 p 1 q q p 1 q 1 q

19 SULIT 19 Given that u 4 18 u 5, find the value of u. Diberi bahawa u 4 18 u 5, cari nilai u. A 4 B C D Simplify ( x y ) x y. 5 4 Permudahkan ( x y ) x y. A B C D 6 xy x 7 y 6 x 7 y 1 6 x y 5 Given that 16, find the value of k. k k Diberi bahawa A B 1 C D 1 16, cari nilai k. k k

20 SULIT 0 6 List all the integer values of p that satisfy the two inequalities 1 p < 10 and p 1. Senaraikan semua nilai integer p yang memuaskan kedua-dua ketaksamaan 1 p < 10 dan p 1. A, 4, 5, 6, 7, 8 B 4, 5, 6, 7 C 4, 5, 6, 7, 8 D, 4, 5, 6, 7 7 The solution of w 1 w Penyelesaian bagi w 1 w A w B w C w D w is ialah

21 SULIT 1 8 Diagram 14 is a pie chart showing the number of members in three clubs. Rajah 14 ialah carta pai yang menunjukkan bilangan ahli di dalam tiga kelab. Science ss (Sains) 100 o Geography (Geografi) Mathematics (Matematik) The Geography club has 45 members. Calculate the difference between the number of students in Mathematics club and Science club. Kelab Geografi mempunyai 45 orang ahli. Kira perbezaan antara bilangan murid dalam kelab Matematik dan kelab Sains. A 10 B 5 C 5 D 40 Diagram 14 Rajah 14 9 Diagram 15 shows the distribution of a student s quiz marks Rajah 15 menunjukkan taburan markah kuiz seorang murid Diagram 15 Rajah 15 The mode is 5. Find a possible value of m. Modnya ialah 5. Cari kemungkinan nilai bagi m. A 1 B C D 4

22 SULIT 0 The pictograph shows the number of books sold at a bookshop in three consecutive days. Piktograf menunjukkan bilangan buku yang dijual di sebuah kedai buku dalam tiga hari berturut-turut. Monday Isnin Tuesday Selasa Wednesday Rabu represents 10 books mewakili 10 buah buku. The sales on Wednesday make up 60% of the total sale of the three days. The numbers of books sold on Wednesday is Jualan pada hari Rabu adalah 60% daripada jumlah jualan bagi ketiga-tiga hari itu. Bilangan buku yang dijual pada hari Rabu ialah A 60 B 100 C 160 D 5 1 Diagram 16 shows a Venn diagram with the universal set,, set P and set Q. Which of these regions A, B, C, and D represent ' P Q? Rajah 16 menunjukkan gambar rajah Venn dengan set semesta, ξ, set P dan set Q. Mana di antara kawasan A, B, C, dan D mewakili P Q? P Q A B C D Diagram 16 Rajah 16

23 SULIT It is given that the universal set ξ = {x : 1 x 10, x is an integer} Set P = x : x is a factor of 9 Set Q = x : x is a prime number Set R = x : xis a multipleof The set (Q R ) P is Diberi set semesta ξ = {x : 1 x 10, x adalah integer} Set P = x : x adalah faktor bagi 9 Set Q = x : x adalah nombor perdana Set R = x : x adalah gandaanbagi Set (Q R ) P ialah and dan A {} B {1, } C {, 8} D {5, 7}

24 SULIT 4 Which of the following shows the set (X Y) Z? Antara rajah berikut, yang manakah menunjukkan set (X Y) Z? A Y X Z B Y X Z C Y X Z D Y X Z

25 SULIT 5 4 Diagram 17 is a Venn diagram showing the number of elements in set F, set G and set H. Rajah 17 ialah gambar rajah Venn yang menunjukkan bilangan unsur-unsur dalam set F, set G dan set H. F H 6 1 G x 4 Given that the universal set ξ = F G H and n(h ) = n(g H), find the value of x. Diagram 17 Rajah 17 Diberi bahawa set semesta ξ = F G H dan n(h ) = n(g H), cari nilai bagi x. A 4 B 6 C 8 D 1 5 Given that the gradient of the straight line passing through point A (p, 8) and point B(1, 4) is. Find the value of p. Diberi bahawa kecerunan satu garis lurus yang melalui titik A (p, 8) dan B(1, 4) ialah. Cari nilai p. A B C D 4

26 SULIT 6 6 The y-intercept of the straight line x + 4y = 7 is Pintasan-y bagi satu garis lurus x + 4y = 7 ialah A 4 B C D 7 7 In Diagram 18, the straight line GH is parallel to the straight line PR. Find the value of k. Dalam Rajah 18, garis lurus GH adalah selari dengan garis lurus PR. Cari nilai k. y R(k, 9) H(4, 6) P(-16, 0) G(0, 4) O x Diagram 18 Rajah18 A B C 4 D 6

27 SULIT 7 8 Diagram 19 shows 1 identical cards, each labelled with the digit, 5, or 9. A card is chosen at random. State the probability that the card chosen is labelled with a prime number. Rajah 19 menunjukkan 1 keping kad yang serupa yang setiapnya dilabel, 5, atau 9. Sekeping kad dipilih secara rawak. Nyatakan kebarangkalian bahawa kad yang dipilih itu dilabel dengan nombor perdana Diagram 19 Rajah 19 A B C D A bag contains 18 blue balls and a number of green balls. If a ball is chosen at 1 random, the probability of choosing a blue ball is. Find the total number of balls in the bag. Sebuah beg mengandungi 18 bola biru dan beberapa bola hijau. Jika satu bola dipilih secara rawak, kebarangkalian sebiji bola biru dipilih ialah 1. Cari jumlah bola di dalam beg itu. A 6 B 1 C 6 D 54

28 SULIT 8 40 Table 1 shows the results of a Mathematics test of a group of students. Jadual 1 menunjukkan keputusan ujian Matematik bagi sekumpulan pelajar. Passed Lulus Failed Gagal Boys Lelaki Girls Perempuan 16 x 5 Table 1 Jadual 1 A student is chosen at random from the group. The probability of choosing a student who passed the test is 5 4. Find the value of x. Seorang pelajar dipilih secara rawak daripada kumpulan itu. Kebarangkalian memilih seorang pelajar yang lulus ujian ialah 5 4. Cari nilai x. A 4 B 5 C 7 D 10 END OF QUESTION PAPER KERTAS SOALAN TAMAT

29 JABATAN PELAJARAN MELAKA PEPERIKSAAN SELARAS AKHIR TAHUN TINGKATAN 4, 010 MATHEMATICS SKEMA PEMARKAHAN MATHEMATICS PAPER 1 1 A 11 B 1 A 1 B C 1 B D D A 1 D C D 4 B 14 B 4 B 4 B 5 A 15 D 5 C 5 C 6 A 16 C 6 C 6 B 7 D 17 D 7 A 7 A 8 A 18 B 8 C 8 D 9 C 19 D 9 B 9 D 10 C 0 C 0 D 40 C