GMSS 2024 4E5N EM P1 PRELIM ANS

[Turn Over Candidate Name WORKED SOLUTIONS & SUGGESTED ANSWER SCHEME Class Index Number MATHEMATICS Paper 1 4052/01 4 Express 5 Normal (Academic) Candidates answer on the Question Paper. 2 hours 15 minutes Setter: Ms Nainee Ismail Monday, 5 August 2024 READ THESE INSTRUCTIONS FIRST Write your class, 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. Answer all the questions. The number of marks is given in brackets [ ] at the end of each question or part question. 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 total of the marks for this paper is 90. 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 , use either your calculator value or 3.142. For Examiner’s Use 90 This document consists of 20 printed pages including the cover page. Geylang Methodist School (Secondary) Preliminary Examination 2024

GMS(S)/Math/P1/Prelim2024/4E5N/Answer Scheme 2 Mathematical Formulae Compound Interest Total amount = 1 100 n rP + Mensuration Curved surface area of a cone = rl Surface area of a sphere = 4r 2 Volume of a cone = 1 3 r 2h Volume of a sphere = 4 3 r 3 Area of triangle ABC = 1 2 ab sin C Arc length = r, where  is in radians Sector area = 1 2 r 2, where  is in radians Trigonometry sin sin sin a b c A B C== a 2 = b 2 + c 2 – 2bc cos A Statistics Mean = fx f   Standard deviation = 22fx fx ff  −  

GMS(S)/Math/P1/Prelim2024/4E5N/Answer Scheme 3 [Turn Over Answer all the questions. 1 Expand and simplify (4x – y) (3x + 4y). Answer ……………………………………… [2] 2 (a) Find the lowest common multiple (LCM) of 108 and 140. Answer ……………………………………… [1] (b) Find the highest common factor (HCF) of 108 and 140. Answer ……………………………………… [1] 3 Solve 142 3 x−= . Answer x = …………………………………… [1] (4x – y) (3x + 4y) = 12x2 – 3xy + 16xy – 4y2 = 12x2 + 13xy – 4y2  4x – y 3x 12x2 – 3xy 4y 16xy – 4y2 12x2 + 13xy – 4y2 142 3 142 3 23 x x x −= −= =  x = 6 6 By Prime Factorisation, 2 108 140 2 54 70 3 27 35 3 9 35 3 3 35 5 1 7 7 1 1 By Prime Factorisation, 2 108 140 2 54 70 27 35 LCM = 22 × 33 × 5 × 7 = 4 × 27 × 5 × 7 = 3780 HCF = 22 HCF = 4 3780 4

GMS(S)/Math/P1/Prelim2024/4E5N/Answer Scheme 4 4 10 23 34 40 25 35 17 44 23 (a) Find the median of the set of numbers. Answer ……………………………………… [1] (b) Find the range of the set of numbers. Answer ……………………………………… [1] 5 (a) A hotel made breakfast milkshake for its guests. A mixture of mango juice, milk and yogurt in the ratio 7 : 5 : 3 are mixed together. 2.5 litres of milk is used in the mixture. (i) How much yogurt is used in the milkshake? Answer ………………………………… litres [1] (ii) How much breakfast milkshake is made? Answer ………………………………… litres [1] (b) Another milkshake is made using apple juice, peach juice and milk. The ratio of apple juice : milk = 2 : 3. The ratio of milk : peach juice = 5 : 4. Find the ratio of apple juice : milk : peach juice. Answer ………… : ………… : ………… [1] Ascending Order: 10 17 23 23 25 34 35 40 44 10 17 23 23 25 34 35 40 44 Range = Highest – Lowest = 44 – 10 = 34 25 34 Apple : Milk : Peach ( )52 : ( )53 : : ( )35 : ( )34 10 : 15 : 12 5 units → 2.5 litres 1 unit → 2.5 0.5 litres5 = 3 units → 0.5 × 3 = 1.5 litres Total number of units = 7 + 5 + 3 = 15 units 1 unit → 0.5 litres 15 units → 15 × 0.5 → 7.5 litres 1.5 7.5 10 15 12

GMS(S)/Math/P1/Prelim2024/4E5N/Answer Scheme 5 [Turn Over 6 Find the equation of the straight line passing through (7, –7) and (– 4, 15) . Answer ……………………………………… [3] 7 The graph shows the growth in milk tea consumers regionally. Adapted from source: https://www.mdpi.com/ (a) State one misleading feature of the graph. ………………………………………………………………………………………… ………………………………………………………………………………………… [1] (b) Based on your answer in part (a), explain how this feature affects the reader’s interpretation of the graph. ………………………………………………………………………………………… ………………………………………………………………………………………… [1] ( ) 21 21 Gradient, 15 7 47 15 7 11 22 11 yym xx −= − −−= −− += − = − Gradient, m = – 2 y – intercept, c: y = mx + c –7 = (–2)(7) + c –7 = –14 + c c = –7 +14 c = 7 Equation: y = mx + c y = –2x + 7 y = – 2x + 7 Evidence: Value does not specify if its actual value or percentage. No y-axis, not indicative of the length of bar and value cannot be verified for accuracy. Title states growth which indicates a basis of comparison which is not shown. [Any comment with substantial and mathematically sound justification can be accepted] Any Interpretation or Conclusion with substantial and mathematically sound justification based on the Evidence mentioned in part (a) can be accepted. Growth of Milk Tea Consumers from Southeast Asian Countries f250f ..750.. ..1515.. ..3000.. ..3900.. ..8000..

GMS(S)/Math/P1/Prelim2024/4E5N/Answer Scheme 6 8 The Venn diagram shows the elements of  = {integers x: 1 ≤ x ≤ 15} and two sets A and B. (a) Use one of the symbols below to complete each statement.      (i) { 15 } …………… A  B [1] (ii) 1 …………… (A  B)’ [1] (b) Suggest a description to define set A . ………………………………………………………………………………………… ………………………………………………………………………………………… [1] 9 The number of social media users globally grew from 4.72 billion in January 2023 to 5.04 billion in January 2024. The number increased by r % every month during that period. Find the value of r. ( 1 billion = 1× 109 ) Answer r = ………………………………… % [2]   A = {integer x: x is a multiple of 3 OR x is divisible by 3}  A B 3 6 9 15 12 5 10 1 2 4 7 8 11 13 14 Social media is a system which experiences exponential growth. [No penalty for not using the info (1 billion = 1× 109 ) given: Total amount 1 100 n rP =+  12 995.04 10 4.72 10 1 100 r =  +  12 12 12 5.04 14.72 100 5.04 14.72 100 5.04100 1 4.72 r r r =+ =+  −= r = 0.5481408453 r = 0.548 0.548

GMS(S)/Math/P1/Prelim2024/4E5N/Answer Scheme 7 [Turn Over 10 The following diagram shows the positions of Earth, E, and Venus, V, and their orbit around the Sun, S. The radius of Venus’ orbit is 1.082 × 108 km. [Follow the degree of accuracy of the values specified in this question and leave your answers in standard form where necessary.] (a) If the angle  is 46.054°, calculate the distance between Earth and the Sun. Answer …………………………………… km [1] (b) State the value of  when Earth is furthest from Venus and calculate this distance. Answer  = ……………………