Marks Question Examiner Moderator C.Moderator 1 2 3 4 Total /50 Group Assignment Feedback Lecturer’s Comments : ........................................................................................................................................................................................................... ........................................................................................................................................................................................................... 50 KOLEJ MATRIKULASI KEDAH KEMENTERIAN PENDIDIKAN MALAYSIA DM015 MATEMATIK 1 SEMESTER I SESI 2023/2024 GROUP ASSIGNMENT CHAPTER 5 : TRIGONOMETRIC CHAPTER 8 : CIRCLES NAME : . ....................................................................... MATRIC NO. : ...................................... : . ....................................................................... : ...................................... : . ....................................................................... : ...................................... : . ....................................................................... : ...................................... CLASS : ........................................................................ LECTURER : ..............................................................
1 INSTRUCTIONS TO CANDIDATE: This question paper consist of 4 questions. Answer all questions. The full marks for each question or section are shown in the bracket at the end of the question or section. All steps must be shown clearly. Numerical answers can be given the form of π , e, surd, fractions or up to three significant figures, where appropriate, unless stated otherwise in the question. All the answer must be submitted on or before 29 Oct 2023
2 QUESTION 1 1) a) Convert 3 a = − rad to degrees form where a is a natural number. Hence, find the smallest value of a if lies in the third quadrant. [4 marks] b) Solve 2 2 2 3 2cot 30 2cos 60 sin 45 4sec30 4 − − − in the form of 3 a b b − . By multiplying an appropriate conjugate, give your final answer in the form of e f 3 g + where e f and g 0, 0 0. [7 marks] QUESTION 2 2) a) Using an equilateral triangle PQR of sides 2 cm, show that 12 1 tan (90 ) sin (90 ) 2 2 − − − = [4 marks] b) Solve the equation 3 2 3 3 cos = − − ec for − . [5 marks] Q R P
3 QUESTION 3 a) A and B are acute angles with 2 1 cos A = and 3 1 sin B = . Without using calculator, evaluate cos(A + B) . Give your answer in a single fraction. [6 marks] b) Simplify the following expressions into a non-fraction single trigonometry expression: sec cos sec − − [4 marks] c) Prove that (i) 2 2 cot 1 cot cot sec + = [4 marks] (ii) sin cosec cot 1 cos + = − [4 marks]
4 QUESTION 4 Given that equation of circle B is 2 2 ( 3) ( 4) 25 x y + + + = . Show that Circle B passes through the origin O. [2 marks] a) Find centre and radius of this circle B and sketch the graph. [4 marks] b) R is coordinate of the other end of the diameter through origin O. Find R. [2 marks] c) Circle B passed through the x axis − at point M and y axis − at point N. Find coordinate of points M N and . [4 marks] END OF QUESTION PAPER
5 Question Learning Outcome Domain Remembering C1 Understanding C2 Application C3 1 (a), (b) X 2 (a), (b) X 3 (a), (b),(c) X X 4 (a), (b),(c) X To be submitted on 29 OCTOBER 2023
SESI 20PENGAKUAPROGRAM MATRIKULASI KEMENSTUDENT’S DMINISTRY OF EDUCATION MALAYSKursus / Course: MATEMATIK 1 Kod / Code: DM015 Tajuk Tugasan / Assignment Title: TUGASAN KUMPULAN (TOPIPengakuan Pelajar / Student’s Declaration Kami mengaku bahawa tugasan ini adalah hasil kerja kumpulan dijelaskan sumbernya. We declare that this task is my own groupwork except for the citatiNama Pelajar / Student’s Name: Tarikh / Date: 22/11/2022 Nota: Borang ini hendaklah dikepilkan bersama tugasan bertulis / bmemeriksa tugasan.
PTP 22/2023 AN PELAJAR NTERIAN PENDIDIKAN MALAYSIA DECLARATION SIA MATRICULATION PROGRAMME K 5 & 8) kami sendiri kecuali nukilan dan ringkasan yang setiap satunya ions and summaries of which we acknowledged the source. No. Matrik / Matric No.: Tandatangan / Signature: bercetak / model dan diserahkan kepada pensyarah yang