HCA-IBE June Preliminary (4049 P1)

June Holiday Preliminary Examination Series (JHPES) For the Singapore-Cambridge GCE Ordinary Level DECLASSIFIED to Public (20 October 2024) CANDIDATE NAME ADDITIONAL MATHEMATICS 4049 / 01 Paper 1 20 August 2024 4049-S4-PR-1-01 Preliminary Examination Public 2 hours 15 minutes READ THESE INSTRUCTIONS FIRST Write in dark blue or black pen. You may use an HB pencil for any diagrams or graphs. Do not use staples, paper clips, glue, or correction tape/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 use of an approved scientific calculator is expected, where appropriate. You are reminded of the need for clear presentation in your answers. DO NOT WRITE ON ANY MARGINS. THEY ARE SOLELY FOR THE MARKERS’ USAGE. The number of marks is given in brackets [ ] at the end of each question or part question. The total number of marks for this paper is 90. NO ADDITIONAL MATERIALS ARE NEEDED. Question Mark attained Maximum Marker’s Feedback 1 10 2 5 3 8 4 9 5 9 6 6 7 8 8 7 9 8 10 3 11 8 12 6 13 3 TOTAL 90 Marker’s Signature

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tan(3𝜃) = 3 tan(𝜃) − tan3(𝜃) 1 − 3 tan2(𝜃) ln(1 + tan2(𝑘𝜃))

∫ 4 tan3(𝜃) − 12 tan(𝜃) 4 − 3 sec2(𝜃) 𝜋 9 0  𝑑𝜃

𝑦 = √3 sin(𝑥) + cos(𝑥) + 1 𝑅 sin(𝑥 + α) + 1

log5(4 − 𝜔) − 2 log5(𝜔) = 1 𝑦 = 6 log2(𝑥) − log2(7) ,  𝑥 > 0.