ADDITIONAL MATHEMATICS 4049/01 - SEAB · 2019. 12. 31. · S ADDITIONAL MATHEMATICS 4049/01 Paper 1 For examination from 2021 SPECIMEN PAPER 2 hours 15 minutes Candidates answer on
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S
ADDITIONAL MATHEMATICS 4049/01Paper 1 For examination from 2021SPECIMEN PAPER
2 hours 15 minutesCandidates answer on the Question Paper.
No Additional Materials are required.
READ THESE INSTRUCTIONS FIRST
Write your centre number, index number and name in the spaces at the top of this page.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 fluid.DO NOT WRITE ON ANY BARCODES.
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.
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.
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MINISTRY OF EDUCATION, SINGAPOREin collaboration withCAMBRIDGE ASSESSMENT INTERNATIONAL EDUCATIONGeneral Certifi cate of Education Ordinary Level
This document consists of 17 printed pages and 1 blank page.
5 On a certain date, 160 cases of influenza were recorded in a city. This number increased with time and after t days the number of recorded cases was N. It is believed that N can be modelled by the formula N = 160ekt. The number of cases recorded after 5 days was 245.
(a) Estimate the number of cases recorded after 7 days. [4]
Influenza is declared an epidemic when the number of cases reaches 400.
(b) Estimate after how many days influenza is declared an epidemic. [2]
The diagram shows a triangular plot of ground, ABC, in which AB = 12 m, AC = 16 m and angle BAC = 90°. A gardener considers using a rectangular part, APQR, of the triangle, where P, Q and R lie on AB, BC and AC respectively, for growing vegetables.
(a) Given that the length of AR is x m and the length of AP is y m, show that y = 12 – x43 . [3]
(b) Given that x can vary, find the largest possible area of the vegetable plot. [4]
In the diagram, A, B, C, D and E lie on a circle such that AB = BC and BA is parallel to CE. The tangent to the circle at A meets CE produced at T. Angle TAE = θ.
13 In a race, a cyclist passes a point A at the top of a hill with a speed of 5 m/s. He then increases his speed and passes the finishing post B, 10 seconds later, with a speed of 20 m/s. Between A to B, his velocity, v m/s, is given by v = 0.1t 2 + pt + q , where t is the time in seconds from passing A, and p and q are constants.
(a) Show that q = 5 and find the value of p. [3]
(b) Find the acceleration of the cyclist when his speed is 11.6 m/s. [4]
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