SECTION A : 75 MARKS BAHAGIAN A : 75 MARKAH INSTRUCTION: This section consists of THREE (3) structured questions. Answer ALL questions. ARAHAN: Bahagian ini mengandungi TIGA (3) soalan berstruktur. Jawab SEMUA soalan. CLO1 C1 QUESTION 1 SOALAN 1 a) Referring to Figure 1(a), identify the following trigonometric functions. Merujuk kepada Rajah 1(a), kenalpastikan fungsi trigonometri berikut. i. Sin 60⁰ ii. Cos 30⁰ ii. Tan 30⁰ Figure 1(a) / Rajah 1(a) [6 Marks] [6 Markah] 2
CLO1 C2 (b) Table 1(b) is the ratios summary of special angle in trigonometric, calculate the value of each expression without using a calculator. Jadual 1(b) menunjukkan nisbah sudut istimewa dalam trigonometri, kirakan nilai setiap yang berikut tanpa menggunakan kalkulator. Table 1(b) / Table 1(b) 30⁰ 45⁰ 60⁰ Sin 1/2 1/ 2 3/2 Cos 3/2 1/ 2 1/2 Tan 1/ 3 1 3 (i) Cos 2 π 4 + Tan2 30 [3 Marks] [3 Markah] (ii) Cos 60. Sin π 6 [3 Marks] [3 Markah] (iii) Tan 2 30 2sin 2 45 [3 Marks] [3 Markah] (iv) 5(cos 45 ) 2 + 3 (tan 30 ) 2 4 tan 45 [2 Marks] [2 Markah] (v) Sin 120⁰ [3 Marks] [3 Markah] 3
CLO1 C3 (c) Referring to Figure 1(b), POQ is a triangle to that PO = 7 cm, OQ = 6 cm and PQ = 9 cm. Calculate the angle of P. Berdasarkan Rajah 1(b), POQ adalah sebuah segitiga di mana PO = 7 cm, OQ = 6 cm dan PQ = 9 cm. Kirakan sudut P. O 6cm [5 marks] [5markah] 7cm Q P 9cm Figure 1(b) Rajah 1(b) 4
QUESTION 2 SOALAN 2 CLO1 C1 (a) Convert each of the following angles in degree to radian or radian to degree: Tukarkan setiap sudut berikut dalam darjah ke radian atau radian ke darjah: i. 132 [2 marks] ii. 45.6 [2 marks] iii. 1.75 rad [1 marks] [1 markah] CLO2 C2 (b) Refer to Figure 2(a) and Figure 2(b), calculate the perimeter for each of the following shaded regions. Merujuk kepada Rajah 2(a) dan Rajah 2(b), kirakan perimeter bagi setiap kawasan berlorek yang berikut: i. 3 cm 2.5 rad 4 cm Figure 2(a) / Rajah 2(a) [7 marks] [7 markah] ii. 6 cm 53 Figure 2(b)/ Rajah 2(b) [8 marks] [8 markah] 5
CLO2 C3 (c) Figure 2(c) shows a sector OEFG with centre O and radius 21 cm. Find the area of the shaded region. Rajah 2(c) menunjukkan sector OEFG dengan pusat O dan jejari adalah 21 cm. Kira luas kawasan yang berlorek. 21 cm 105 Figure 2(c) / Rajah 2(c) [5 marks] [5 markah] 6
QUESTION 3 SOALAN 3 CLO2 C1 (a) Express the following parallel vectors in term of u: Ungkapkan vektor selari berikut dalam sebutan u: i. CD [2 marks] ii. EF [2 marks] 7
CLO2 C2 (b) Given p = (4, 8), q = (1,5), and r = ( 2,4). Find each of the following. Diberi p = (4, 8), q = (1,5), and r = ( 2,4). Carikan setiap yang berikut. i. p + q [3 marks] [3 markah] ii. p r [3 marks] [3 markah] iii. 6q + ( r ) [5 marks] [5 markah] iv. 2p 4r + q [5 marks] [5 markah] CLO2 C3 (c) Coordinates A (2, 3), B (5, 1) and C (4, -2) are the coordinates in a triangle ABC. Find the dot product of AB and BC. Koordinat A (2, 3), B (5, 1) dan C (4, -2) adalah koordinat dalam segitiga ABC. Cari produk titik AB dan BC. [5 marks] [5 markah] 8
SECTION B : 25 MARKS EACH QUESTION BAHAGIAN B : 25 MARKAH SETIAP SOALAN INSTRUCTION: This section consists of TWO (2) structured questions. Answer ONE question. ARAHAN: Bahagian ini mengandungi DUA (2) soalan berstruktur. Jawab SATU soalan. QUESTION 4 SOALAN 4 CLO2 C1 a) Solve the inequality below: Selesaikan ketaksamaan dibawah: i. 4 < x+2 [ 2 marks] ii. 6y < 30 [ 3 marks] [3markah] iii. -2y < -16 [ 3 marks] [3 markah] CLO3 C2 9
b) i) Use number line to find a combined solution of two inequalities: x > 1 and x > 7 [ 4 marks] Dengan menggunakan garis nombor selesaikan ketaksamaan dibawah: x > 1 and x > 7 [4 markah] ii) List all integer of y that obey the inequalities of 3y 4 < y 5 + 2y. [11 marks] Senaraikan semua integer y yang mematuhi ketaksamaan 3y 4< y 5+2y. [11markah] CLO3 C3 c) Given 5 x < 10 and 7 < y 11 where x and y are integers. Find the maximum values of x+y [2 marks] Diberi 5 x < 10 dan 7 < y 11. Jika x dan y ialah integer, cari nilai maksimum bagi x + y 10
QUESTION 5 SOALAN 5 CLO3 C1 (a) Simplify, Permudahkan, i. ( 3 2 ) + ( 2 1 ) [2 marks] ii. ( 4 5 2 ) (1 6 6 1 2 ) [2 marks] iii. ( 6 3 ) ( 1 2 ) [2 marks] 2a b b iv. ( ) + (a 3c 4d c d ) [2 marks] CLO3 C2 (b) If A = ( 3 6 1 ) and B = (2 ), determine: 1 9 3 4 Jika = ( 3 6 1 ) and B = (2 1 9 3 4 ), dapatkan: i. matriks A x B matriks A x B [6 marks] [6 markah] ii. inverse matrix A x B. matrix songsang A x B. [9 marks] [9 markah] 11
CLO3 C3 (c) Solve Selesaikan 3 x ( 12 6 0 1 ) 3 x ( 12 6 0 1 ) [2 marks] SOALAN TAMAT 12
FORMULA SHEET FOR PBM2014: BASIC MATHEMATICS 2 TRIGONOMETRY Pythagoras Theorem c a θ b c 2 = a 2 + b 2 sec θ = cosec θ = 1 cos θ 1 sin θ CIRCULAR MEASURE Arc Length of a Circle s r Area of a Sector 1 A r 2 2 Area of a Segment 1 2 1 A r r 2 sin 2 2 cot θ = 1 tan θ Trigonometric Identities tan θ = sin θ cos θ cos 2 θ + sin 2 θ = 1 1 + tan 2 θ = sec 2 θ 1 + cot 2 θ = cosec 2 θ FORMULA OF TRIANGLE VECTOR Sine Rules a sin A b sin B c sin C A B a 1a b b c c 1. 2 1 2 1 2 Cosine Rules a 2 = b 2 +c 2 2bc cos A Area of Triangle = 2 1 a b sin C MATRIX Inverse Matrix A 1 = 1 [ d b A c a ] 13