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. [2] (iv) State the equation of a tangent to the circle that is parallel to the -axisx . [1] [2018 CBA2: Modified] 2 Sketch the following graphs, stating the equation(s) of asymptotes (if any) and intersection(s) with the axes. (a) ( ) ( ) 22 2 3 36xy− + + = [4] [2023 WA1] 3 The equation 10xy ab=− , where a and b are constants, can be represented by a straight line when ( )lg 10y+ is plotted against x, as shown in the diagram below. Find the value of a and of b. [6] x x x (1, 2) (2, 5)

4 TemasekJC/IP4/AM/Term 1 WA/2024 [2024 WA3] 4 The variables x and y are related in such a way that when ln y is plotted against l n x, a straight line is obtained as shown in the figure below. Given that this straight line passes through (0, 2) and (14, 10), find (i) the exact value of x when ln y = 6, [3] (ii) the value of a and of n when the relationship between x and y is expressed in the form y = axn. [4] (14, 10) ln y ln x (0, 2)

5 TemasekJC/IP4/AM/Term 1 WA/2024 [Turn over] [2022 WA1] 5 The diagram shows part of a straight line graph of ln y against x2, passing through the points (1, 2) and (4, 6). (i) Express y in terms of x . [3] (ii) Find the exact value of y when 3x= . [1] (iii) Determine, with clear reasoning, if the point (8, 10) lie s on the graph above. [1] [2019 WA1] 6 The diagram below (not drawn to scale ), shows part of a straight -line graph drawn to represent the equation nx y c= . (i) Calculate the values of n and c. [4] (ii) Using the values from part (i), express y in terms of x. [1] (iii) A straight line ln 3ln 2yx=+ is drawn on the same axes. Find the values of x and of y for which 23ncx e x− = . [3] x2 (1, 2) (4, 6) 0 (1, 6) (4, 2) 0

6 TemasekJC/IP4/AM/Term 1 WA/2024 [2022 IP3 WA2] 7 (a) Solve the equation 3(4 1) 2 xxee −= . [3] (b) Solve the equation 33 1 27 11 log log (2 )log 3yy+ + = − . [4] [2022 IP3 WA3] 8 Solve the equation 2 1log 3log 2 2 xx−= . [6] [2021 WA2] 9 Solve the equation 8log log 64 1xx−= . [5] [2020 IP3 WA2] 10 Solve the equation lg 24log 10 5xx=− . [6] [2020 WA1] 11 Solve the equation 4 2 8log log 4 log 1 5xx+ = + . [6] [2017 IP3 CBA4] 12 (a) Solve the equation ln(2 4) ln 2 ln3x x+ − = . [4] (b) Find the exact value of 1 4 log 8 . [3]  End of Paper 

7 TemasekJC/IP4/AM/Term 1 WA/2024 [Turn over] Answers 1 (i) Centre: ( )1, 2− , Radius: 5 (ii) ( )0, 2 2 6+ , ( )0, 2 2 6− , ( )1 21, 0−− , ( )1 21, 0−+ (iii) (iv) 7y= or 3y=− 2 3 0.1a= , 1000b= 4 (i) x = e7 (ii) n = 4 7 , a = e2 5 (i) 242 33x ye + = (ii) 38 3ey= (iii) The point does not lie on the line. 6 (i) 4 3n= , 22 3 or 1530 (3 s.f.)ce= (ii) 22 4 33y e x − = (iii) 16 13 or 3.42 (3 s.f.)xe= , 297 (3.s.f.)y= 7 (a) No real number solution. (b) y = 9 5 8 3 22y − = or 4y= 9 64x= or 1 8x= 10 810x −= or 1000x= 11 4x= 12 (a) 1x= (b) 3 2−