*oot1331460101 + UT F MINISTRY OF EDUCATION, SINGAPORE, in collaboration with UNIVERSITY OF CAMBRIDGE LOCAL EXAMINATIONS SYNDICATE General Certificate of Education Ordinary Level CANDIDATE NAME NUMBER NUMBER CENTRE s I INDEX MATHEMATICS 4048/01 Paper 1 October/November 2019 2 hours Candidates answer on the Question Paper. READ THESE INSTRUCTIONS FIRST Write your Centre number, index number and name on all the work you hand in. 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 IN ANY BARCODES. ‘Answer all questions. It working is needed for any question it must be shown with the answer. Omission of essential working will result in loss of marks, The use of an approved scientific calculator is expected, where appropriate. If the degree of accuracy is not specified in the question, and if the answer is not exact, give the answer to three significant figures. Give answers in degrees to one decimal place. For 7, use either your calculator value or 3.142, unless the question requires the answer in terms of m. ‘The number of marks is given in brackets { } at the end of each question or part question. ‘The total of the marks for this paper is 80. This document consists of 18 printed pages and 2 blank pages. en (Cif swovpsre examination and assssmen tot CAMBRIDGE © UCLESe MoE 2ove Do (nwice) 1695504 Turn over L aa= 0011331460102* OA = "7 Mathematical Formulae 2 2 Compound interest E Total amount = P (1+ 8 8 Mensuration Curved surface area of a cone = mri z Surface area of a sphere = 4nr? i Volume of a cone = bnrh 4 “ e=3 E g Volume of a sphere 8 8 Area of triangle ABC = ab sinC Are length = 9, where @ is in radians 3 Sector area = 4776, where 0 isin radians g z g Trigonomenry g 8 z Statistics : rf g Mean = 5:7 2 z g g Standard deviation 5 8 0 NOT WRITE IN THIS MARGIN © UCLES & MOE 2019 we s0aK0V01N9 |SEEDS ERS ES em ee DIO IRIE SRE ES FEES es, (BO NOT WRITE IN THIS MARGIN: (DO NOT WRITE IN THIS MARGIN: ae ee ee 0 ‘Answer all the questions. 00113914601 1 The number of people in a cinema is given as 400, cortect to the nearest hundred. Write down the minimum number of people that could be in the cinema at this time. Answer 50 40 Total spending (Sbillions) 3° 20 10 0000 0000 0000 0000 0000 0000 aoa0 0000 0/00 00/00 Explain how the chart above may be misleading. ES & MOE 2019 sossVOINIIWm * 0011331460104 * wa 3 (a) Simplify (x")) Answer. esc (by 3°=374+3743" Find the value of a Answer a= .. 4 (a) Express 360 as a product of its prime factors. Answer . Oo) 360) (b) The number a is a perfect cube. and q are prime numbers. Find the value of p and the value of g Answer p q 5 The estimated number of Bengal tigers increased from 3200 in 2010 to 3890 in 2016. ‘The number increased by 7% every year. Find the value of r. Answer r= (2) l © UCLES & MOE 2019 g& s0asovOrNnD DONOT WRITE IN THIS MARGIN DO NOT WRITE IN THIS MARGIN DO NOT WRITE IN THIS MARGIN DO NOT WRITE IN THIS MARGIN. DO NOT WRITE INTHIS MARGIN.DO NOT WRITE IN THIS MARGIN: (00 NOT WRITE IN THIS MARGIN DO NOT WRITE IN THIS MARGIN: DO NOT WRITE IN THIS MARGIN: DO NOT WRITE IN THIS MARGIN * 0011331460105 OME - 1 6 Write as a single fraction in its simplest form 5-15 —~ 3 Answer R 7 Abag contains 8 red counters, 9 green counters and 3 yellow counters. (a) Accounter is chosen at random and then replaced. ‘What isthe probability that it is not a yellow counter? Answer. 0) (b)_ x green counters are removed from the bag, The probability of choosing a red eounter is now 2. Find the value of x. Answer X= suse u 8 Use factorisation to solve the equation. 3p? +p-10=0 Answer p | OUCLES & MOE2019 g 0480019 [Turn over_]011331460108 > wl Choose a symbol from the list above to make a correct statement. Answer 33% (b) Solve the inequalities 6 <2x-+11 <19 Answer. 10 Ps directly proportional to 0°, (a) When o=},p=2 Find P when Q = 2 Answer (b) A cchange in Q produces a change in P. ‘When the value of Q is multiplied by +, the value of P changes by a factor of m Find m. Answer m u (a) Factorise Answer (b) Factorise completely 6ab-+1-3a-26 AMSWEP soe © LCLES & MOF 2019 UT > 4048/01001N19 | DO NOT WRITE IN THIS MARGIN (20 NOT WRITE IN THIS MARGIN. DO NOT WRITE IN THIS MARGIN DO NOT WRITE IN THIS MARGIN DO NOT WRITE IN THIS MARGINee ene ee BONO T-VIRITE IN THiS MARGIN DO NOT WRITE IN THIS MARGIN: 011331460107 * OMA 7 12 The diagram shows a quadrilateral ABCD. c D, 4 B On the diagram, (a) construct the bisector of angle ADC, tu) (b) construct the perpendicular bisector of AB, i] (©) shade the region inside ABCD that is closer to DC than to Dd and closer to 4 than to B. ia] 3) 13 The point 4 is translated to B (5, —2) by the vector ( ? (a) Find the coordinates of point 4. ne (b) Find the magnitude of (3) Answer . (2) l © UCLES & MOE 2019 B s04u0V0IN [Turn over |4 0011331460108 * North North T a) Ss ‘The diagram shows the positions of three cities, Singapore (S), Delhi (D) and Tokyo (7) Angle SDT = 55°. The bearing of Delhi from Singapore is 317° and the bearing of Tokyo from Singapore is 044°, (a) Find the beating of Singapore from Delhi. a) Answer. (b)_ Find the bearing of Dethi from Tokyo, Answer 15 Sketch the graph of yy =-(x-2)?+9 on the axes below. Indicate clearly the coordinates of the points where the graph crosses the axes and the maximum point on the curve. Oo BI UL " Bg 4048/01/0"NI19 | DO NOT WRITE IN THIS MARGIN. DO NOT WRITE IN THIS MARGIN DO NOT WRITE IN THIS MARGIN DO NOT WRITE INTHIS MARGIN 00 NOT WRITE IN THIS MARGIN* 011391460109 * A Tr z ; B 2 (a) TA and TB are tangents to a circle, centre Q. z ‘Show that triangle OAT and triangle OBT are congruent. [ Give a reason for each statement you make. > Answer 3 z : 2 3 G3] (b) Point P lies on the circumference of the circle so that triangle APT is congruent to triangle BPT. On the diagram, mark the two possible positions for the point P. a l ©UCLES & MOF 2019 soswovioni9 [Turn over |Distance from A (km) 10am lam 12noon ‘The distance-time graph shows the journeys for two people, Nur and Lim, between two villages, A and B. (a) Find Nur’s speed for the first hour of her journey. Answer svete .kan/h [1] (b) (Find the time when Nur and Lim pass each other, Answer (ii) How far are they from village B when they pass cach other? Answer km [1] (©) Lim jogs back to village B at 8kmn/h Change 8 km/h into metres per second, Answer vs [1] l ©UCLES & MOE 2019 40480020019 | DO NOTWRITE IN THIS MARGIN. DO NOT WRITE IN THIS MARGIN DO NOT WRITE IN THIS MARGIN DO NOT WRITE IN THIS MARGIN DO NOT WRITE IN THIS MARGIN* 011331460111 * 7 = {integers x: 4 pt DO NOT WRITE IN THIS MARGIN Show that 4p+2g = 19 Answer 1 Gi) Answer p= q Bl (b) The sum of the first » terms of a different sequence is given by 3n°+7n . Find the 10th term of this sequence. Answer 1 l © UCLES & MOE 2019 44R/0HIOND |ne tee Re ee EE ee a Sit a lt | ee a MONS Mee ee * oor ssa%4s0119* ‘OMIM l UCLES & MOE 2019, & 19 BLANK PAGE, Aorsr1/OnW19* 0911331460120 ° IO 7 BLANK PAGE amisson to reproduce Hams where bird pary owned material protcied by copyright included ras buon sought and cared whore posable, Every reatonabo efert has boon mado by the publeh (UCLES} to ace copyright olde, but any items requing desrance have unwingly been cled, the ‘ublehar wll pleseacto make amends at the salestposebie opportunity CamorgeItamatonal Examination is par ofthe Cambridge Aasesernnt Group, Cambridge Assossmantis the brand name of Univers of Cambridge Local Examinations Syecale (ULES), which tea doparient of the Unwersy of Cambidge Aoig01I0"NNG | OUCLES & MOF 2019