TJC 2025 IP4 WA1 AM Revision Questions Answers updated 3 Feb 2025

1 TemasekJC/IP4/AM/Term 1 WA/2024 [Turn over] TEMASEK JUNIOR COLLEGE 2025 IP4 TERM 1 REVISION CANDIDATE NAME CG SUBJECT TUTOR’S NAME ADVANCED MATHEMATICS 23 February 2024 45 minutes READ THESE INSTRUCTIONS FIRST Write your name, CG and tutor’s name on all the work you hand in. Write in dark blue or black pen. You may use a soft pencil for any diagrams or graphs. Do not use paper clips, highlighters, glue or correction fluid. Answer all questions. Write your answers in the spaces provided in the question paper. You may request for additional writing materials if there is insufficient space. These should be attached to the back of the booklet. Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angles in degrees, unless a different level of accuracy is specified in the question. The calculator value for π should be used unless the question requires the answer in terms of π . The use of an approved scientific and/or graphing calculator is expected where appropriate. You are reminded of the need for clear presentation in your answers. Marks will be deducted for poor or unclear presentation. The number of marks is given in brackets [ ] at the end of each question or part question. This document consists of 6 printed pages and no blank page. For Examiner’s Use Q1 / 10 Q2 / 7 Q3 / 7 Q4 / 6 Presentation Deduction – 1 Total / 30

2 TemasekJC/IP4/AM/Term 1 WA/2024 MATHEMATICAL FORMULAE 1. ALGEBRA Quadratic Equation For the equation 2 0ax bx c+ + = , 2 4 2 b b acx a −  −= Binomial expansion ( ) 1 2 2 12 n n n n n r r nn n na b a a b a b a b b r − − −     + = + + + + + +           where n is a positive integer and ( ) ( ) ( )11! ! ! ! n n n n rn r r n r r − − + == − 2. TRIGONOMETRY Identities ( ) ( ) ( ) 22 22 22 2 2 2 2 2 sin cos 1 sec 1 tan cosec 1 cot sin sin cos cos sin cos cos cos sin sin tan tantan 1 tan tan sin 2 2sin cos cos 2 cos sin 2cos 1 1 2sin 2 tantan 2 1 tan 1sin sin 2sin 2 AA AA AA A B A B A B A B A B A B ABAB AB A A A A A A A A AA A P Q P += =+ =+  =  = = = = − = − = − = − + ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 1cos 2 11sin sin 2cos sin 22 11cos cos 2cos cos 22 11cos cos 2sin sin 22 Q P Q P Q P Q P Q P Q P Q P Q P Q P Q P Q +− −  + − +  + − − − + − Formulae for ABC sin sin sin a b c A B C== 2 2 2 2 cosa b c bc A= + − Area of 1 sin2ABC ab C=

3 TemasekJC/IP4/AM/Term 1 WA/2024 [Turn over] [2020 WA1] 1 (i) State the coordinates of the centre and the radius of the circle with equation ( ) ( ) 22 1 2 25xy+ + − = . [2] (ii) Find the exact coordinates of the points where the circle crosses the axes. [3] (iii) Hence, sketch the circle, labelling the coordinates of the centre and the points where the circle crosses the axes