SEKTOR SEKOLAH BERASRAMA PENUH BAHAGIAN SEKOLAH KEMENTERIAN PELAJARAN MALAYSIA PEPERIKSAAN AKHIR TAHUN TINGKATAN MATEMATIK.

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1 Matematik Kertas Oktober 006 ¼ jam SEKTOR SEKOLH ERSRM ENUH HGIN SEKOLH KEMENTERIN ELJRN MLYSI EERIKSN KHIR THUN TINGKTN MTEMTIK Kertas Satu jam lima belas minit JNGN UK KERTS SOLN INI SEHINGG IERITHU. Kertas soalan ini mengandungi 40 soalan.. Jawab semua soalan. 3. Jawab dengan menghitamkan ruangan ang betul pada kertas jawapan. 4. agi setiap soalan hitamkan satu ruangan sahaja. 5. Sekirana anda hendak menukarkan jawapan, padamkan tanda ang telah dibuat. Kemudian hitamkan jawapan ang baru. 6. Rajah ang mengiringi soalan tidak dilukiskan mengikut skala kecuali dinatakan. 7. Satu senarai rumus disediakan di halaman hingga halaman uku sifir matematik empat angka boleh digunakan. 9. nda dibenarkan menggunakan kalkulator saintifik ang tidak boleh diprogram. Kertas soalan ini mengandungi 6 halaman bercetak [Lihat sebelah

2 SULIT MTHEMTIL FORMULE The following formulae ma be helpful in answering the questions. The smbols given are the ones commonl used. RELTIONS. a m a n = a m + n. a m a n = a m - n 3. (a m ) n = a m n ( x x) 4. istance = 5. Midpoint x (x, ) = x 6. verage speed =, distance traveled time taken 7. Mean = sum of data number of data 8. thagoras Theorem c = a + b 9. m x x 006 Hak ipta Sektor S SULIT

3 SULIT 3 SHE N SE rea of trapezium = sum of parallel sides height ircumference of circle = d = r 3 rea of circle = r 4 urved surface area of clinder = rh 5 Surface area of sphere = 4r 6 Volume of right prism = cross sectional area length 7 Volume of cuboid = length width length 8 Volume of clinder = r h 9 Volume of cone = 3 r h 0 Volume of sphere = 4 r 3 3 Volume of right pramid = base height 3 Sum of interior angles of a polgon = (n ) arc length = angle subtended at centre circumference of circle 360 area of sector angle subtended at centre = area of circle Scale factor, k = ' 6 rea of image = k area of object. [Lihat sebelah 006 Hak ipta Sektor S SULIT

4 SULIT 4 nswer all questions Round off correct to two significant figures The side of a cube is 4.3 cm. The volume, in cm³, of the cube correct to three significant figures is Express as a number in standard form In iagram, is a tangent to the circle at point and SR is a straight line. R S 87 6 Find the value of IGRM 006 Hak ipta Sektor S SULIT

5 SULIT 5 6 The area of a rectangular nurser plot is.08 km². Its width is 00 m. The length of the nurser plot, in m, is In iagram, O is the centre of the circle. and are tangents to the circle at and respectivel. E O Find the value of. IGRM In iagram 3, RST is a pentagon. STU is a straight line. T S U 3 Find the value of x R IGRM 3 x [Lihat sebelah 006 Hak ipta Sektor S SULIT

6 SULIT 6 9 In iagram 4, RSTU and VWX are regular hexagon and pentagon respectivel. S R X W T U m V The value of m is IGRM iagram 5 shows the graphs of = sin x and = cos x. O 360 The x-coordinate of point is IGRM 5 It is given that cos = where 80 70, find the value of Hak ipta Sektor S SULIT

7 SULIT 7 In iagram 6, KLMN is a straight line and JK = KM. J K cm L 3 cm M x N The value of tan x is IGRM 6 3 Simplif p (p ) 3 p 4. 3p 3p 4p 4p 4 iagram 7 shows a triangle KLM and a shaded triangle, drawn on square grids. M L K IGRM 7 Triangle KLM is the image of the shaded triangle under an enlargement. Which of the points,,, or, is the centre of the enlargement? [Lihat sebelah 006 Hak ipta Sektor S SULIT

8 SULIT 8 5 Express u w uw w as a single fraction in its simplest form. uw uw uw uw u uw uw u uw = (5 ) pq (3p + q) = 3p + q + 5pq 3p q + 3pq 9p q + pq 9p q + 0pq 006 Hak ipta Sektor S SULIT

9 SULIT 9 9 iagram 8 shows a right prism with rectangular base KLMN. 5 cm K N 6 cm 8 cm L IGRM 8 M alculate the angle between the line L and the base KLMN The angle of elevation of the peak of pole from the peak of pole is 60. The two poles are verticall planted in a horizontal ground. Which diagram below represents the situation described? [Lihat sebelah 006 Hak ipta Sektor S SULIT

10 SULIT 0 iagram 9 shows a pole, R on a horizontal plane. 60 R IGRM 9 alculate the angle of depression of from vertex Given that h v, then h = t vt vt v t v t 3 There are two helicopters X and Y at height 300 m and 340 m above sea level respectivel. If the angle of elevation of helicopter Y from helicopter X is 4, calculate the horizontal distance, in m, between the two helicopters Hak ipta Sektor S SULIT

11 SULIT 4 Given that w, express w in terms of. w w w w w 5 In iagram 0, is the image of under a reflection. K L H N M IGRM 0 The axis of reflection is the straight line that joins H and K L M N 6 Express m m n 3n as a single fraction in its simplest form. 3m 4n 3m 3n m 3n 5m 3n [Lihat sebelah 006 Hak ipta Sektor S SULIT

12 SULIT k 7 The solution for k 3 is k 4 8 k 3 5 k 5 k 3 8 The solution for simultaneous linear inequalities 3n + > and 0 8 4n is 3 < n 4 4 < n 3 3 < n < 4 4 < n 3 9 iagram is a pie chart showing the colours of t-shirts chosen b a number of students. Red Yellow lue IGRM If 8 students chose ellow t-shirts, find the number of students who chose red t-shirts Hak ipta Sektor S SULIT

13 SULIT 3 30 Table shows the frequenc distribution of the scores obtained b a group of pupils in a competition. Time (min) Frequenc TLE alculate the mean of the distribution iagram is a bar chart showing the number of candidates who obtained scores to 5 in a Mathematics test. Number of andidates 0 IGRM If the passing score is the mean score, calculate the percentage of students who pass the test Score [Lihat sebelah 006 Hak ipta Sektor S SULIT

14 SULIT 4 3 It is given that the universal set = {x : x 0, x is an integer}, set = {, 3, 6, 7, 9,, 3, 7}, set = {x : x is a prime number} and set R = {x : x multiple of 3}. Find n[( R) ] iagram 3 is a Venn diagram showing the sets, and R such that the universal set = R. R The shaded region represents the set ( R) ( R) ( R) ( R) IGRM 3 34 iagram 4 is an incomplete Venn diagram showing the elements in sets, and R..c.w.s.g..k R.q.m IGRM 4 It is given that the universal set, = R, n() = 6 and n(r) = 3. Find n( R) Hak ipta Sektor S SULIT

15 SULIT 5 35 Find -intercept of the straight line x The straight line has gradient and passes through the point (3, 5). It is parallel to the straight line + mx 4 = 0. Find the value of m iagram 5 shows two straight lines, OR and R, on a artesian plane. R(, 8) O x IGRM 5 The distance and the x-intercept of is 5 units and 9 respectivel. Find the gradient of R [Lihat sebelah 006 Hak ipta Sektor S SULIT

16 SULIT 6 38 Table shows the distribution of a group of students plaing a game. Form One Form Two Girls x os 8 6 TLE student is chosen at random from the group to start the game. The probabilit that a girl from Form One will be chosen is 5. Find the value of x box contains a number of ellow marbles and 0 red marbles. marble is chosen at random from the box. The probabilit of choosing a ellow marble is 3. Then, a number of red marbles is put in the box. If a marble is now selected 5 at random from the box, the probabilit that a red marble chosen is. How man red marbles are there in the box? dice is rolled twice and the sum of the number shown is noted. Find the probabilit that the sum of the numbers being EN OF UESTION ER 006 Hak ipta Sektor S SULIT