TJC 2020 IP4 IM EOY Questions with Answers .pdf

1 [Turn over TemasekJC/IP4/IM/EoY/2020 TEMASEK JC INTEGRATED PROGRAMME YEAR FOUR 2020 END-OF-YEAR EXAMINATION INTERMEDIATE MATHEMATICS Date: 1 October 2020 Duration: 2 hours 30 minutes No additional materials required. READ THESE INSTRUCTIONS FIRST. Write in dark blue or black pen in the spaces provided in the paper. You may use a soft pencil for any diagrams or graphs. Do not use staples, paper clips, highlighters, glue or correction fluid. Answer all the questions. 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 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. The total score for this paper is 100 marks. This paper consists of 13 printed pages. Question Marks 1 2 3 4 5 6 7 8 9 10 11 12 Presentation Deduction – 1 Total Name: ________________________ Class: ________________________ ________________________ Parent’s Signature

2 [Turn over TemasekJC/IP4/IM/EoY/2020 MATHEMATICAL FORMULAE Compound Interest 1 100 n rAP =+  Mensuration Curved surface area of a cone = rl Surface area of a sphere = 24 r Volume of a cone = 21 3 rh Volume of a sphere = 34 3 r Area of triangle ABC = 1 sin2 ab C Arc length r= , where  is in radians Sector area 21 2 r = , where  is in radians Trigonometry sin sin sin a b c A B C== 2 2 2 2 cosa b c bc A= + − Statistics Mean fx f=  Standard deviation 22fx fx ff  =−   

3 [Turn over TemasekJC/IP4/IM/EoY/2020 Answer all questions in the spaces provided. Show all working clearly. 1 (a) Express 4 2 3 3 3 5 + + in the form 3ab + , where a and b are integers. [4] (b) Express ( ) ( ) 55 3 5 0 52 2 x x x − + in the form 5cx d+ , where c and d are integers. [4] 2 Figure 1 (not drawn to scale) shows a solid metal paperweight with a uniform cross - section and height 3 cm. Figure 2 (not drawn to scale) shows the cross -section of the paperwei ght where ABC is the arc of a circle of radius 4 cm and centre O. AC is a straight line of length 4 cm. (i) Show that the uniform cross-sectional area of the paperweight is 240 π 4 3 cm3  + . [2] (ii) Find the total surface area of the paperweight , leaving your answer cor rect to 3 significant figures. [4] (iii) The paperweight is melted and recast into several identical solid cones. The cones have a base radius of 2 cm and height of 5 cm. Find the