CEDAR 2025 EMATH PRELIM P1 MS

CEDAR GIRLS’ SECONDARY SCHOOL PRELIMINARY EXAMINATION 2025 SECONDARY FOUR CANDIDATE NAME Marking Scheme CLASS INDEX NUMBER MATHEMATICS 4052/01 Paper 1 21 August 2025 2 hours 15 minutes Candidates answer on the Question Paper. READ THESE INSTRUCTIONS FIRST Write your name, class and index number 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. Gives answers in degrees to one decimal place. For  , use either your calculator value or 3.142. For Examiner’s Use 990 This document consists of 20 printed pages. [Turn over]

Cedar Girls’ Secondary School 4052/01/S4/Prelim Exam/2025 2 Mathematical Formulae Compound interest Total amount = 1 100 n rP+ Mensuration Curved surface area of a cone = rl Surface area of a sphere = 24 r Volume of a cone = 21 3 rh Volume of a sphere = 34 3 r Area of triangle ABC = 1 sin2 ab C Arc length = r , where  is in radians Sector area = 21 2 r  , where  is in radians Trigonometry sin sin sin a b c A B C== 2 2 2 2 cosa b c bc A= + − Statistics Mean = fx f   Standard deviation = 22fx fx ff  − 

Cedar Girls’ Secondary School 4052/01/S4/Prelim Exam/2025 [Turn over 3 Answer all the questions. 1 (a) Given 22 2 vta s −= , express v in terms of a, t and s. Answer v = ………………… [2] (b) Simplify 22 2 4 4 4 2 xy y x xy y y x −− + − . Answer ………………………… [3] 2 The diameter of a solid sphere is 7.12 cm, measured correct to 3 significant figures. Its density is 2.2 g/cm3. Find the smallest possible mass of the sphere. Answer …...………………….. g [2] 22 2 vta s −= 222as v t=− [transform to non-fractional equation] 22 2v as t=+ 22v as t= + 2( 2 ) 2 xy y x y y x=− −− (factorise into a square) 2( 2 ) 2 xy y x y x y=+ −− 2 2 2 ( 2 ) xy xy y xy +−= − (Attempt to change to common denominator) 2 2 22 ( 2 ) xy y xy −= − (or 2 2 ( ) ( 2 ) y x y xy − − or 2 22 22 44 xy y x xy y − −+ ) Mass 3 4 7.115 2.232=  (See 7.115) 415= g

Cedar Girls’ Secondary School 4052/01/S4/Prelim Exam/2025 4 3 An area of 512 km2 is represented by 50 cm2 on a map. Find the scale of the map in the form 1 : n. Answer ..………. : .………… [2] 4 (a) Factorise completely 32 30 5 6m m m+ + + . Answer …………….………… [2] (b) Given that m is a positive integer, explain why 32 30 5 6m m m+ + + is not a prime number. Answer ……………………..…..……………………..…..……………………..……… ……………………..…..……………………..…..……………………..……… [1] 5 Mary cycles 2.8 km at an average speed of 12 km/h and takes a break. She then continues to cycle a further 1.4 km in 5 minutes. Given that her average speed for the whole journey is 19 3 km/h, find the duration of her break. Answer ..………..….…….. h [2] 512 km2 : 50 cm2 256 km2 : 25 cm2 16 km : 5 cm (Square root) 3.2 km : 1 cm 320 000 : 1 32 6 5 30m m m= + + + 2( 6) 5( 6)m m m= + + + (2 groups of factorisation) 2( 6)( 5)mm= + + Time taken for first part 2.8 7 h12 30== Let x h be her break time. 1 2.8 1.49 713 30 12x += ++ -- M1 19 4.2 160 9 3 x+= 2 15x= (or 0.133 h) Its factors ( 6)m+ and 2( 5)m + are whole numbers more than 1 . Hence, it’s not a prime number. 1 : 320 000

Cedar Girls’ Secondary School 4052/01/S4/Prelim Exam/2025 [Turn over 5 6 (i) The diagram below shows 3 lighthouses A, B and C at sea. AC = 12 km. BC = 18 km. AB = 17 km. The bearing of B from C is 136o. Find the bearing of A from C. Answer ..………..….…….. o [2] (ii) Find the area of the region enclosed by triangle ABC. Answer ..………..….……km2 [2] Area of ABC 1 (12)(18)sin 65.5222 o= = 98.3 km2 A C North B 17 12 18 2 2 212 18 17cos 2(12)(18)ACB +−= = 0.41435 (5 s.f.) 65.522oACB= (3 dp) Bearing of A from C 136 65.522oo=− 070.5o= (1 dp) (with zero in front)

Cedar Girls’ Secondary School 4052/01/S4/Prelim Exam/2025 6 7 On the axes given, sketch the graphs 3xy= and 3y x= , indicating the x- and y- intercepts where relevant. The point (1, 1) is marked in the diagram. Answer [2] 8 (a)  = {all real numbers} A = {all perfect cubes} B = {all rational numbers} C = {all recurring decimals} D = {1, 2, 3, 4, 5, 6, 7, 8, 9} (i) List all the elements contained in the set AD . Answer …………….……………………….………… [1] (ii) Explain why ' CB = . Answer ……………………..…..……………………..…..……………………..…. ……………………..…..……………………..…..……………………..…. ……………………..…..……………………..…..……………………..…. [1] x y O 3xy= (shape and see intersection at above x =1) 3y x= 1 'B are irrational numbers which are non-recurring decimal numbers. Therefore, ' CB = . (Or saying rational numbers are recurring decimals) 1, 8

Cedar Girls’ Secondary School 4052/01/S4/Prelim Exam/2025 [Turn over 7 (b) On the Venn diagram, shade the region(s) which represent ( ) ( )''A B A B   . Answer [1] 9 A quadratic curve 2 3.5y x mx=− + + has a turning point at ( )1.5, p− , where both m and p are constants. Find the value of m and of p. Answer m = …………….. p = …………….. [4] Completed square form: 23() 2y x p=− + + (Completed square form) 2 9( 3 ) 4