INSTRUCTION: This section consists of FIVE (5) structured questions. Answer FOUR (4) questions only.
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1 DBM10: MTHEMTICS FOR COMPUTING SECTION : 100 MRKS BHGIN : 100 MRKH INSTRUCTION: This section consists of FIVE (5) structured questions. nswer FOUR (4) questions only. RHN : Bahagian ini mengandungi LIM (5) soalan erstruktur. Jawa EMPT (4) soalan sahaja. QUESTION 1 SOLN 1 C1 (a) State the definition of hexadecimal and it. Nyatakan maksud heksadesimal dan it. [4 marks] C () Convert the ase numers elow: Tukarkan nomor-nomor asas di awah: i into decimal numer kepada nomor desimal. [ marks] [ markah] ii into hexadecimal numer kepada nomor heksadesimal. [ marks] [ markah] iii into hexadecimal numer kepada nomor heksadesimal. [ marks] [ markah] SULIT
2 i [ marks] ii [ marks] SULIT DBM10: MTHEMTICS FOR COMPUTING (c) Calculate the values of x and y of the following numers. Kirakan nilai x and y agi nomor-nomor erikut. i. 111 xxx = [ marks] [ markah] ii y58 [ marks] [ markah] (d) Solve the following inary arithmetic operations in inary form. Selesaikan operasi aritmetik yang erikut dalam entuk perduaan. [ markah] [ markah] iii F [5 marks] [5 markah] SULIT
3 DBM10: MTHEMTICS FOR COMPUTING QUESTION SOLN C (a) In Diagram (a), O is the centre of the circle and PQR is a straight line. Calculate the value of x and y. Dalam Rajah (a),o adalah pusat ulatan dan PQR adalah satu garis lurus. Hitungkan nilai x dan y. T P 76 Q x 44 O y S R Diagram (a)/ Rajah (a) [6 marks] [6 markah] CLO 1 C () In Diagram (), D and BC are the arcs of two circles of radius O and OB respectively. If is the midpoint of OB and arc D = 1.5 cm, calculate the area of sector OBC. Dalam Rajah (), D dan BC adalah lengkung agi ulatan yang masing-masing eradius O dan OB. Jika adalah titik tengah agi OB dan lengkung D=1.5cm, kirakan luas agi sector OBC. B 9 cm O ϴ D Diagram ()/ Rajah () C [4 marks] 4 SULIT
4 DBM10: MTHEMTICS FOR COMPUTING CLO (c) i. In Diagram (c) (i), PWUV and RSTW are squares. rea of RSTW is 6 cm. Find the area of PWUV in cm. Dalam Rajah (c) (i), PWUV dan RSTW ialah segiempat sama sisi. Luas RSTW ialah 6 cm. Cari luas PWUV dalam cm. V T U S P Q W 6 8 R Diagram (c) (i)/ Rajah (c) (i) [7 marks] [7 markah] ii. Diagram (c) (ii) shows a container in a shape of cuoid and another in a shape of a cylinder. The cuoid is full of water. ll of the water in the cuoid is poured into the cylindrical container. Compute the height in cm of the water level in the cylindrical container. [Use π=/7]. Rajah (c) (ii) menunjukkan satu ekas erentuk kuoid dan satu lagi ekas erentuk silinder. Kuoid diisi penuh dengan air. Semua air di dalam kuoid dituang ke dalam ekas silinder. Kira ketinggian (cm) paras air di dalam ekas silinder. [gunakan nilai π=/7] 1 cm 14 cm cm 7 cm Diagram (c) (ii)/ Rajah (c) (ii) [8 marks] [8 markah] 5 SULIT
5 DBM10: MTHEMTICS FOR COMPUTING QUESTION SOLN CLO 1 C (a) Calculate the following expressions in the form of a i. Kirakan ungkapan- ungkapan erikut dalam entuk a i. i. ( 4 8 i) ( 5 10i) 1i [ marks] [ markah] ii. ( 8 i)(5 i) [ marks] [ markah] iii. i (4 5i) [4 marks] CLO () Sketch rgand s diagram for the following complex numers and express it in polar, trigonometric and exponential forms. Lakarkan gamarajah rgand agi nomor kompleks yang dieri. Seterusnya ungkapkan dalam entuk kutu, trigonometri dan eksponen. i. z = 4 9i [7 marks] [7 markah] ii. z = 4 8i. [8 marks] [8 markah] 6 SULIT
6 DBM10: MTHEMTICS FOR COMPUTING QUESTION 4 SOLN 4 CLO 1 C (a) Differentiate the following with respect to x. Bezakan setiap yang erikut terhadap x. i. x 5 y [4 marks] x ii. 4 y x (x 1) [6 marks] [6 markah] CLO CLO () (c) Determine dx Carikan dx dy for function 4 y x dy agi fungsi 4 Calculate the following: Kirakan yang erikut: y using Chain Rule. y x dengan menggunakan kaedah Petua Rantai. [5 marks] [5 markah] i. 5 x x dx 1 [6 marks] [6 markah] 8 ii. ( 4x) ( ) dx [4 marks] 7 SULIT
7 DBM10: MTHEMTICS FOR COMPUTING QUESTION 5 SOLN 5 CLO C (a) Given and. Calculate: Dieri dan. Kira: i. [1 mark] [1 markah] ii. C [ marks] [ markah] CLO C () Calculate the inverse of matrix Z if the determinant of matrix Z is -1 and Z. Kira songsangan agi matriks Z jika penentu kepada matriks Z ialah -1 di dan. [7 marks] [7 markah] CLO c) Calculate the value of x, y and z y using Cramer s Rule. Kirakan nilai x, y dan z dengan menggunakan Petua Cramer. 5x - y + 7z = 6x - y + 9z x + 8y - 4z = = [15 marks] [15 markah] SOLN TMT 8 SULIT
8 DBM10: MTHEMTICS FOR COMPUTING FORMUL CIRCLE Length of an arc 1. s r rea of a sector, rea of a segment 1. 1 r 1 r ( 1. sin ) SURFCE RE ND VOLUME 1. Cylinder :. Sphere : rh r, V r h 4r, V 4 r. Cone : 1 rs r, V r h 4. Pyramid : area of 4 triangles + area of ase V 1 area of ase height COMPLEX NUMBER Modulus 1. z a 1. rgument arg z a 1 tan 1. DIFFERENTITION y ax dy dx n anx Complex no. In other form. Chain Rule : 1. Polar form : n1,. y ( ax ) dy dx dy dy du dx du dx z 4. Product Rule : y u v i.exponential form : z e y uv vu.trigonometric form : (cos isin ) Multiplication & Division 1. a a a a a a a. a z u 5. Quotient Rule : y v vu uv y INTEGRTION Indefinite Integration x n 1 n1 n MTRIX 1. x dx C Inverse Matrix adj v n n ( ax ) a( n 1) an( ax ). ax dx C efinite Integratio n Cramer s Rule 1. f ( x) dx F( ) F( a) a 1 1. x y z RE UNDER CURVE 1.long x-axis:.long y-axis: a a ydx xdy n1 9 SULIT 1 n
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