2025 CCHY MA 4E5N EM Prelim P1 Sol

* 2025 Prelim Mathematics / 4052/01 / Sec 4E5N [Turn_over 2025 Preliminary Examination Secondary Four Express / Five Normal Academic CANDIDATE NAME FORM CLASS / SUBJECT GROUP / INDEX NUMBER MATHEMATICS 4052/01 Paper 1 18 August 2025 2 hours 15 minutes Candidates answer on the Question Paper. READ THESE INSTRUCTIONS FIRST Write your name, class and index number on 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 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. You are reminded of the need for clear presentation in your answers. Up to 2 marks may be deducted for improper presentation. 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 π , use either your calculator value or 3.142. Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 1 3 2 3 3 2 3 4 Q9 Q10 Q11 Q12 Q13 Q14 Q15 Q16 3 2 2 3 6 6 3 3 Q17 Q18 Q19 Q20 Q21 Q22 Q23 Q24 4 3 3 3 3 3 4 5 Q25 Q26 Presentation Deduction –1 / –2 Total 90 8 5 This document consists of 20 printed pages. CHUNG CHENG HIGH SCHOOL (YISHUN)

2 2025 Prelim Mathematics / 4052/01 / Sec 4E5N [Turn_over Mathematical Formulae Compound Interest Total amount 1 100 n rP= + Measurement Curved surface area of a cone πrl= 2Surface area of a sphere 4 πr= 21Volume of a cone 3 πr h= 34Volume of a sphere 3 πr= 1Area of triangle sin 2ABC ab C= , where is in radiansArc length rθθ= 2 , where is in radians1Sector area 2 r θθ= Trigonometry sin sin sin abc ABC= = 2 22 2 cos Aa c bcb += − Statistics Mean fx f= ∑ ∑ 22 Standard deviation fx fx ff  = −  ∑∑ ∑∑

3 2025 Prelim Mathematics / 4052/01 / Sec 4E5N [Turn_over 1 Calculate 3 9.26 51.76 2.02− , giving your answer correct to 5 significant figures. 8.8362− Answer …………………………… [1] 2 (a) Express 252 as a product of its prime factors. 22237×× Answer ………………………………… [1] (b) The highest common factor (HCF) of two numbers is 21. The lowest common multiple (LCM) of the two numbers is 252. Both numbers are less than 100. Find the two numbers. 2 2 37 2 37 A B = × = ×× ____________ LCM = 22252 2 3 7=×× HCF = 21 3 7= × The two numbers are 63 and 84. Answer ………………………………… [2] 3 Given that 627 8 9nn= , find the value of 3n . 1 3 12 2(3 ) 8 (3 )nn= × 363 83nn= × 631 38 nn−= 3 13 8 n = 3 13 8 n = 1 2= Answer ………………………………… [2]

4 2025 Prelim Mathematics / 4052/01 / Sec 4E5N [Turn_over 4 (a) Simplify 2(4 ) (4 )(4 )n na na−+ − . 2 22 2 16 [(4 ) ]n na a = −− = Answer ………………………………… [1] (b) Hence, without the use of a calculator, evaluate 275 (78)(72).− ( ) 2 75 [(75 3)(75 3)]= −+ − M1 23= 9= Answer ………………………………… [2] 5 Cindy invested $4200 in ABN Bank for 3 years. ABN Bank pays 1.8% per year compound interest. She would have earned the same amount of interest if she had invested the same amount of money for 3 years and 6 months in HKSB Bank which pays r% per year simple interest. Calculate the value of r. Interest = 3 1.84200 1 4200100 +− = 230.9068944 4200 3.5 230.9068944100 r×× = 1.5707952 1.57 r = = Answer …………………………… [3] 6 Simplify 2(4 5)(5 4 7)x xx− +− . = 32 220 16 28 25 20 35x x xx x+ −− −+ 3220 9 48 35xx x= −−+

5 2025 Prelim Mathematics / 4052/01 / Sec 4E5N [Turn_over 7 Rearrange the formula 1 3 3 76 xy zw = − to make z the subject. 3 27 7 6 xy zw= − 337 6 27xz xw y−= 337 27 6xz y xw= + 3 3 27 6 7 y xwz x += Answer z = ……………………… [3] 8 (a) A polygon has n sides. Two of its exterior angles are 50° and 70°, and the remaining exterior angles are each 16°. Find the value of n. 50 70 16( 2) 360n++ −= 16 272 17 n n = = Answer ………………………………… [2] (b) The diagram shows one interior angle of each of three regular polygons, A, B and C. The polygons fit together at point O, leaving a space marked by angle x. A is a regular nonagon, B is a square and C is an equilateral triangle. Find angle x. (9 2) 180360 90 609x −×= − ++ = 70° Answer ………………………………… [2]

6 2025 Prelim Mathematics / 4052/01 / Sec 4E5N [Turn_over 9 An area of 1 km2 is represented by 4 cm2 on a map. (a) Calculate, in km2, the actual area of a volcanic crater which is represented by a circle of area 0.3 cm2 on the map. 1 cm2 : 0.25 km2 Actual area = 0.25×0.3 = 0.075km2 Answer ……………………………km2 [1] (b) Find the scale of the map in the form 1: n . 1 cm2 : 0.25 km2 1 cm : 0.5 km 1 : 50 000 Answer ………………………………… [2] 10 The base and the height of a triangle are each reduced by 40% followed by an increase by 50%. Find the percentage reduction in the area of the triangle. Original area = 1 22 bhbh××= New area = 1 (0.6)(1.5) (0.6)(1.5)2 bh×× 0.81 2 bh= Percentage reduction = 1 0.81 100%1 − × = 19% Answer …………………………………% [2]

7 2025 Prelim Mathematics / 4052/01 / Sec 4E5N [Turn_over 11 Mrs Lim draws this graph to show her monthly water bill for the first four months of the year 2024. State one aspect of the graph that may be misleading and explain how this may lead to a misinterpretation of the graph. No equal intervals indicated on the vertical axis and if the values start from 0. Unable to read the cost of water in the months before April. OR Not clear if the size of the water droplets, is referring to the area of the droplets or the height of the droplets. Unable to determine the annual water bill. 12 Starlight Café sells latte drinks in two geometrically similar mugs. The height of the larger mug is 1.5 times the height of the smaller mug, h. Latte in a smaller mug and in a larger mug are sold at $3.30 and $13.20 respectively. Mandy thinks that it is more value for money to buy latte in 4 smaller mugs than one larger mug. Is Mandy correct? Justify your decision with calculations. 3 1 2 1.5 V h Vh = 3 33.375 h h= Volume of 4 small mugs > Volume of 1 large mug 4 > 3.375 Cost of 4 small mugs = $3.30 × 4 = $13.20 Cost of 1 large mug = $ 13.20 Mandy is correct. For the same amount paid for the latte, more latte is obtained from 4 small mugs of latte than from 1 large latte. h 1.5 h smaller larger

8 2025 Prelim Mathematics / 4052/01 / Sec 4E5N [Turn_over 13 { } { } { } { } , Prime Numbers Odd Numbers Square Numbers 1, 2, 3, 4, 8 15, 27, 43, 49,121 L M N ξ = = = = (a) Complete the Venn diagram to illustrate this information. There are no elements in the shaded portion of the diagram. [2] (b) List the elements in ()ML ′∪ {4, 8} (c) Find the value of ( )n () ()L N LN′∪∪ ′∩ . { } { } ( ) , , ( ) 1, 4, 8 15, 27, 49,121 ( ) 2, 3, 8 15, 27, 43 n () () 3 LN LN L N LN ′ = ′ = ∪∩∪′′ ∪ = ∪ (d) The numbers in ξ are each printed on one card. If a card is picked at random