SULIT /1 MATHEMATICAL FORMULAE RUMUS MATEMATIK
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1 SULIT 449/ MTHEMTIL FORMULE RUMUS MTEMTIK 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. RELTIONS PERKITN m a n a m a n 0 Pythagoras Theorem Teorem Pithagoras a m a n a m n c a b m n mn n ( a ) a P n S d b ' 4 P P ad bc c a y y 5 istance / jarak m x x x x y y 6 Midpoint / Titik tengah 4 x, y x y y x, m m y intercept x intercept pintasan y pintasan x 7 verage speed distance travelled time taken Purata laju jarak yang dilalui masa yang diambil 8 9 Mean Min Mean sum of data number of data hasil tambah nilai data bilangan data Sum of classmark frequency sum of frequencies Min hasil tambah nilai titik tengah kelas hasil tambah kekerapan kekerapan
2 SULIT 449/ SHPES N SPE BENTUK N RUNG rea of trapezium = sum of parallel sides height Luas trapezium = hasil tambah dua sisi selari tinggi ircumference of circle = d = r Lilitan bulatan = d = j rea of circle = r Luas bulatan = j 4 urved surface area of cylinder = rh Luas permukaan melengkung silinder = jt 5 Surface area of sphere = 4 r Luas permukaan sfera = 4 j 6 Volume of right prism = cross sectional area length Isipadu prisma tegak = luas keraain rentas panjang 7 Volume of cylinder = r h Isipadu silinder = j t 8 Volume of cone = r h Isipadu kon = j t 9 Volume of sphere = Isipadu sfera = 4 4 r j 0 Volume of right pyramid = base area height Isipadu pyramid tegak = luas tapak tinggi Sum of interior angles of a polygon Hasil tambah sudut pedalaman polygon = n 80 [Lihat sebelah
3 SULIT 4 449/ arc length circumfere nce of circle angle subtended at 60 centre panjang lengkuk lilitan bulatan sudut pusat 60 area of sector area of circle luas sektor luas bulatan angle sudut pusat 60 subtended at 60 centre 4 Scale factor, k Factor skala, k ' P P ' P P 5 rea of image = k area of object Luas imej = k luas objek
4 SULIT 5 449/ nswer all questions. Jawab semua soalan. Round off 6999 correct to three significant figures. Bundarkan 6999 betul kepada tiga angka bererti. 700 B Express in standard form. Ungkapkan dalam bentuk piawai B = B Given that x is a number in base such that 8 < x < 0, the possible value of x is iberi bahawa x ialah nombor dalam asas dengan keadaan 8 < x < 0, nilai yang mungkin bagi x ialah 0 B [Lihat sebelah
5 SULIT 6 449/ 5 Express 5 + as a number in base five. Ungkapkan 5 + sebagai nombor dalam asas lima. 5 B In iagram, B is a quadrilateral and B is parallel to E. alam Rajah, B ialah sebuah sisiempat dan B adalah selari dengan E. B x o 5 o 75 o 45 o E iagram Rajah The value of x is Nilai x ialah 65 B
6 SULIT 7 449/ 7 In iagram, PQRS is a rhombus. alam Rajah, PQRS adalah sebuah rombus. T 70 o 5 o P x o S Q 65 o iagram Rajah R The value of x is Nilai x ialah 5 B [Lihat sebelah
7 SULIT 8 449/ 8 In iagram, B and E are tangents to the circle with centre O, at B and respectively. alam Rajah, B dan E adalah tangen untuk bulatan berpusat O, masing-masing di titik B dan. E F o O 8 o x o B iagram Rajah The value of x is Nilai bagi x ialah 0 B 58 6
8 SULIT 9 449/ 9 In iagram 4, P is the image of P under a certain translation. Q is the image of Q under the same translation. alam Rajah 4, P ialah imej bagi P di bawah satu translasi tertentu. Q ialah imej bagi Q di bawah translasi yang sama. y 8 P 6. Q 4 P x iagram 4 Rajah 4 Find the coordinates of Q. arikan koordinat Q (, 0) B (, 0) ( 5, ) (0, ) [Lihat sebelah
9 SULIT 0 449/ 0 iagram 5 shows the point X which is the image of point Y under a reflection. Rajah 5 menunjukkan titik X adalah imej bagi titik Y di bawah satu pantulan.. U.. V X. Y. T S etermine the axis of the reflection. Tentukan paksi pantulan tersebut. iagram 5 Rajah 5 B TV SU SV TU
10 SULIT 449/ In iagram 6, pentagon BE is the image of the pentagon FGHI under an enlargement. alam Rajah 6 pentagon BE adalah imej bagi pentagon FGHI di bawah satu pembesaran. y F B I H G E x iagram 6 Rajah 6 If the area of the shaded region is 60 cm, calculate the area, in cm, of pentagon FGHI. Jika luas kawasan berlorek ialah 60 cm, hitungkan luas, dalam cm, bagi pentagon FGHI..5 B [Lihat sebelah
11 SULIT 449/ In iagram 7, PTR is a straight line. Given that cos x = 5 and sin y = 5. alam Rajah 7, PTR ialah garis lurus. iberi bahawa kos x = 5 dan sin y = 5 P S T 5 cm y o Q 0 cm iagram 7 Rajah 7 x o R Find the length, in cm, of PT. arikan panjang, dalam cm, bagi PT. 0 B 6
12 SULIT 449/ Given that tan x = tan 60, where 0 x 70, find the value x. iberi bahawa tan x = tan 60, di mana 0 x 70, cari nilai x. 60 B iagram 8 shows a right prism with a rectangular horizontal base RSTU. The prism has a uniform cross section in the form of trapezium PQRS. Rajah 8 menunjukkan sebuah prisma dengan tapak mengufuk yang berbentuk segiempat tepat RSTU. Prisma tersebut mempunyai keratan rentas seragam trapezium PQRS. W V P Q T U S R iagram 8 Rajah 8 Name the angle between the plane WSR and the plane RSTU. Namakan sudut di antara satah WSR dan satah RSTU. B WRT WRU WSR WST [Lihat sebelah
13 SULIT 4 449/ 5 In iagram 9, MN is a vertical television antenna on top of a building. Given that the angles of elevation of M and N from the point Q are. and 8. respectively. alam Rajah 9, MN ialah antena televisyen yang tegak di puncak sebuah bangunan. iberi sudut dongakan M dan N dari titik Q masing-masing ialah. dan 8.. M N P 50m Q iagram 9 Rajah 9 alculate the height, in m, of the television antenna. Hitungkan tinggi, dalam m, antena televisyen tersebut..4 B
14 SULIT 5 449/ 6 In iagram 0, P, Q and R are three points on a horizontal plane. alam Rajah 0, P, Q dan R adalah tiga titik di atas suatu satah mengufuk. R P iagram 0 Rajah 0 Q Given that Q is due east of R, find the bearing of Q from P. iberi bahawa Q berada di timur R, cari bearing Q dari P. B 00 o 060 o 0 o 40 o [Lihat sebelah
15 SULIT 6 449/ 7 n aeroplane flew 0 nautical miles from P( 80 N, 0 E ) to Q via the North Pole. Find the position of Q. Sebuah pesawat terbang 0 batu nautika dari P( 80 U, 0 T ) ke Q melalui Kutub Utara. ari kedudukan Q. ( 80 N, 0 E ) ( 80 U, 0 T ) B ( 80 N, 70 W ) ( 80 U, 70 B ) ( 78 N, 0 E ) ( 78 U, 0 T ) ( 78 N, 70 W ) ( 78 U, 70 B )
16 SULIT 7 449/ 8 In iagram, NOS is the polar axis of the Earth. Given that PON = 50 and QOR = 0. alam Rajah, NOS ialah paksi bumi. iberi PON = 50 dan QOR = 0. P N 0 o Q O R S 00 o E iagram Rajah Find the position of P. arikan kedudukan P. ( 40 N, 0 W ) ( 40 U, 0 B ) B ( 40 N, 0 W ) ( 40 U, 0 B ) ( 50 N, 0 W ) ( 50 U, 0 B ) ( 50 N, 0 W ) ( 50 U, 0 B ) [Lihat sebelah
17 SULIT 8 449/ 9 4 pq q 6q p B 4q 8q 4q 8q 0 Factorise completely 6mp np 4n + m Faktorkan selengkapnya 6mp np 4n + m (6p + )(m n) B (p )(m + n) (p + )(m + n) (p + )(m n) Given that = B, express B in terms of and. i beri bahawa = B = B, ungkapkan B dalam sebutan dan. B B = 6 B = 8 B = 8
18 SULIT 9 449/ Given that 5(8 m) = 5m 5, find the value of m. iberi 5(8 m) = 5m 5, carikan nilai m. B Express m 4 m 5 4m m as a single fraction in its simplest form. Ungkapkan m 4 m 5 sebagai satu pecahan tunggal dalam bentuk termudah. 4m m B 7m 4 4m 6 7m 4m m 4m 7m 6 4m [Lihat sebelah
19 SULIT 0 449/ (mn ) 4 mn m n = n m B n m n 5 m n m 5 Given that x = ( x ), find the value of x. iberi x = ( x ), cari nilai x. 4 B Given that h is an integer, find all the values of h that satisfy both inequalities h < and 8 7h. 4 iberi h ialah integer, carikan semua nilai h yang memuaskan kedua-dua ketaksamaan h < dan 8 7h. 4 5, 6, 7 B 4, 5, 6, 7 5, 6, 7, 8 4, 5, 6, 7, 8
20 SULIT 449/ 7 Table shows the distribution of marks for 50 students. Jadual menunjukkan taburan markah bagi 50 orang pelajar. Marks Markah Number of students Bilangan pelajar alculate the mean mark. Hitungkan min markah. 7.4 B Table Jadual [Lihat sebelah
21 SULIT 449/ 8 Histogram in iagram shows the weight, in kg, of 0 students. Histogram dalam Rajah menunjukkan berat, dalam kg, bagi 0 orang pelajar. Number of students Bilangan Pelajar Weight / Berat (kg) iagram Rajah alculate the percentage of students whose weight is more than 44 kg. Hitungkan peratus pelajar yang mempunyai berat lebih daripada 44 kg B
22 SULIT 449/ 9 Which of the following represents the graph of y = x + 6? ntara yang berikut, yang manakah mewakili graf y = x + 6? y R 6 x B 6 y x y - 6 x y - 6 x [Lihat sebelah
23 SULIT 4 449/ 0 It is given that the universal set ξ = {x : x 0, x is an integer}, set H = {x : x is a perfect square}, and set N = {x : x is a multiple of 4}. iberi set semesta ξ ={x : x 0, x ialah integer}, set H = {x : x ialah kuasa dua sempurna}, dan set N = {x : x ialah gandaan 4}. Find n(h N). arikan n(h N). B iagram is a Venn diagram with the universal set, ξ = L M N. Rajah ialah sebuah gambarajah Venn yang menunjukkan set semesta ξ = L M N. L M B N iagram Rajah Which of the region,, B, or, represents set L N M? Rantau yang manakah, B, atau, yang mewakili set L N M?
24 SULIT 5 449/ iagram 4 is a Venn diagram showing set ξ, set R and set S. Rajah 4 ialah sebuah gambarajah Venn yang menunjukkan set ξ, set R dan set S. ξ S R iagram 4 Rajah 4 Which of the following represents the shaded region? Yang manakah mewakili rantau yang berlorek? R S B R S S R S R [Lihat sebelah
25 SULIT 6 449/ In iagram 5, PQ is parallel to RS. The equation of the straight line RS is y = x 7. The point F lies on the x axis. alam Rajah 5, PQ dan RS adalah selari. Persamaan bagi garis lurus RS ialah y = x 7. Titik F berada di atas paksi x. y 0 Q S y = x 7 F(t, 0) x E P R Find the value of t. iagram 5 Rajah 5 ari nilai t. 0 B Find the equation of the straight line with the y intercept of 5 and passes through P(6, ). arikan persamaan garis lurus dengan pintasan y ialah 5 dan melalui P(6, ). y 4 x 5 B y 4 x 5 y x 4 5 y x 4 5
26 SULIT 7 449/ 5 Table shows the number of stamps in an envelope. stamp is taken out from the envelope randomly. Jadual menunjukkan bilangan setem di dalam satu sampul surat. Sekeping setem dikeluarkan secara rawak daripada sampul surat itu. Stamp Setem Number of stamps Bilangan setem 0 sen 0 sen 0 sen 50 sen Table Jadual Find the probability that the selected stamp is less than 50 sen. arikan kebarangkalian bahawa setem yang dipilih itu kurang daripada 50 sen. B [Lihat sebelah
27 SULIT 8 449/ 6 Zaid has a collection of coins from Britain, Indonesia and the Philippines. He picks one coin at random. The probability of picking an Indonesian coin is and the probability of picking a Philippine coin is 9 4. Zaid has 0 British coins. alculate the total number of coins in his collection. Zaid mempunyai satu koleksi duit syiling dari negara Britain, Indonesia dan Filipina. ia memilih sekeping duit syiling secara rawak. Kebarangkalian memilih duit syiling 4 Indonesia ialah dan kebarangkalian memilih duit syiling Filipina ialah. Zaid 9 mempunyai 0 duit syiling British. Hitungkan jumlah bilangan duit syilingnya. 0 B If t varies directly as the cube of s and t = 6 when s =, calculate the value of s when t = 48. Jika t berubah secara langsung dengan kuasa tiga s dan t = 6 apabila s =, hitungkan nilai s apabila t = 48. B
28 SULIT 9 449/ 8 Table shows the values of the variables u, v and w where u varies directly as the square of v and inversely as w. Jadual menunjukkan nilai bagi pemboleh ubah u, v dan w dengan keadaan u berubah secara langsung dengan kuasa dua v dan berubah secara songsang dengan w. u v w 40 4 r 6 4 alculate the value of r. Hitungkan nilai bagi r. B Table Jadual [Lihat sebelah
29 SULIT 0 449/ 9 Given n = 5, find the value of n. iberi bahawa n = 5, cari nilai n. 5 B Given 4 m m 5 9, find the value of m. iberi 4 m m 5 9, cari nilai m. B 5 9 EN OF QUESTION PPER KERTS SOLN TMT
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