Tanjong Katong Secondary School Paper 1

CANDIDATE NAME MATHEMATICS 4048/01 Paper 1 Thursday 4 August 2022 2 hours READ THESE INSTRUCTIONS FIRST Write your name, class and register number on all the work you hand in. Write in dark blue or black pen. You may use a pencil for any diagrams or graphs. Do not use staples, paper clips, highlighters, glue or correction fluid/tape. Answer all questions. If 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 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 , use either your calculator value or 3.142, unless the question requires the answer in terms of . 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. Mathematical Formulae TANJONG KATONG SECONDARY SCHOOL Preliminary Examination 2022 Secondary 4 CLASS INDEX NUMBER This document consists of 18 printed pages. www.KiasuExamPaper.com 735

2 4048/1/Sec 4 Prelims 2022 Compound Interest Total Amount = P n r      + 1001 Mensuration Curved surface area of a cone = rl Curved surface area of a sphere = 4r2 Volume of a cone = 3 1 r2 h Volume of a sphere = 3 4 r3 Area of triangle ABC = 2 1 ab sin C Arc length = r, where  is in radians Sector area = 2 1 r2 , where  is in radians Trigonometry A a sin = B b sin = C c sin a2 = b2 + c2 − 2bc cos A Statistics Mean =   f fx Standard Deviation = 22       −     f fx f fx www.KiasuExamPaper.com 736

3 4048/1/Sec 4 Prelims 2022 1 Calculate 322.3 1 ( 4.5) 7 20 ( 3)− + − − −   − , giving your answer correct to 4 decimal places. Answer [1] 2 4 workers can pack 3 containers for shipping in 15 days. Find the number of workers needed to pack 10 containers of the same size in 20 days. Answer [2] 3 A, B, C and D are points on a circle. AC is a diameter of the circle and angle DBC = 68. Find angle ACD. Answer [2] [Turn over B A C D 68 www.KiasuExamPaper.com 737

4 4048/1/Sec 4 Prelims 2022 70 60 Type of Drinks 50 4 The graph shows the number of each type of drinks purchased in a food court. State a misleading feature of the graph and explain how this will affect the reader’s interpretation of the graph. [2] 5 The diagram shows a square and a figure that is made up of six smaller squares. The ratio of the perimeter of the square : perimeter of the figure is 6 : 7. Find the ratio of the area of the square : area of the figure. Answer : [2] Soda is Everyone’s Favourite Drink www.KiasuExamPaper.com 738

5 4048/1/Sec 4 Prelims 2022 6 Three similar unbiased six-sided dice are thrown at the same time. If each dice is numbered 1, 2, 3, 4, 5 and 6, find the probability that (a) the total of the three numbers shown is 3, Answer [1] (b) the three dice show the same number, Answer [1] (c) the total of the three numbers shown is 4. Answer [2] 7 (a) 2y = 812 + 812 Find the value of y. Answer y = [1] (b) Simplify 224 4 8 8 39 a b a b+−  . Answer [2] [Turn over www.KiasuExamPaper.com 739

6 4048/1/Sec 4 Prelims 2022 8 A pyramid has a volume of 76 cm3, correct to the nearest cubic centimetre. (a) Find the least possible volume of the pyramid. Answer cm3 [1] (b) The base area of the pyramid is 26 cm2, correct to the nearest square centimetre. Find the greatest possible height of the pyramid. Answer cm [2] 9 The square of the diameter of a container varies directly to the amount of paint needed to cover the outside of a container. When 37.5 ml of paint is used to cover the outside of the container, the diameter of the container is 25 cm. Calculate (a) the diameter of a container when the amount of paint needed is 8.64 ml, Answer cm [2] (b) the amount of paint needed for a container which has a radius of 20 cm. Answer ml [2] www.KiasuExamPaper.com 740

7 4048/1/Sec 4 Prelims 2022 10 Solve the equation 32534 xx −=− . Answer [3] 11  = { x: –1 ≤ x ≤ 7, x } A = { x: –1 < x < 6 } B = { 2x: 0 < x ≤ 3 } List the elements in (a) ',A Answer [1] (b) ,AB Answer [1] (c) 'AB . Answer [1] [Turn over www.KiasuExamPaper.com 741

8 4048/1/Sec 4 Prelims 2022 12 A fruit store sells apples in packs of 3 at $1.60 before GST. Lim has a $10 note and wants to buy as many apples as possible. (a) Find the amount of change he will receive if the GST is 7%. Answer $ [2] Lim notices that the GST will increase to 9% in 2024. He commented that if he still uses a $10 note to pay for his apples, the amount of change he receives will decrease by 2%. (b) Do you agree with his comment? Justify your answer with calculation. Answer [2] 13 Bank SDB pays an interest of 1.5% per year for the amount of money in deposit accounts at the end of each year and a bonus interest of 10% of the initial principal amount at the end of 10 years. Luke opened an account with the bank and deposited $10 000 into it. Find the amount of money Luke has in the account at the end of 12 years. Answer $ [4] www.KiasuExamPaper.com 742

9 4048/1/Sec 4 Prelims 2022 14 In the United States, the distance between Disneyland and the Universal Studios is 55 km. (a) On a map, the distance between these two theme parks is 11 cm. The scale of the map is 1 : n. Find the value n. Answer n = [2] (b) The area of the Disneyland Park is 0.65 km2. Find the area of the theme park on another map of scale 1 : 20 000. Answer cm2 [2] [Turn over www.KiasuExamPaper.com 743

10 4048/1/Sec 4 Prelims 2022 15 The cumulative frequency graph represents the amount of savings 50 teenagers can save in a year. (a) Use the curve to estimate (i) the median savings, Answer $ [1] (ii) the number of teenagers who save less than $360. Answer [1] (b) 34% of the teenagers save more than $n in a year. Find n. Answer n = [1] (c) Sometime later, it was found that there was an error in the data collection process and the amount of money every teenager has saved in the year is $100 lesser. Describe the effect this change would have on the cumulative frequency curve. [1] Savings ($) Cumulative Frequency www.KiasuExamPaper.com 744