2023 MGS Emath Prelim Exam P1 Solutions

This question paper consists of 22 printed pages and 2 blank pages. Class Index Number Name : __________________________________________ METHODIST GIRLS’ SCHOOL Founded in 1887 PRELIMINARY EXAMINATION 2023 Secondary 4 TUESDAY MATHEMATICS 4052/01 15 August 2023 Paper 1 2 hours 15 minutes Candidates answer on the Question Paper. INSTRUCTIONS TO CANDIDATES Write your class, name and index number in the spaces at the top of this page. 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. 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 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 p , use either your calculator value or 3.142, unless the question requires the answer in terms of p . 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 90. 90 SOLUTIONS

Methodist Girls’ School Mathematics Paper 1 Sec 4 Preliminary Examination 2023 Page 2 of 24 Mathematical Formulae Compound Interest Total amount = ( ) 100 r 1+ n P Mensuration Curved surface area of a cone = rl Surface area of a sphere = 4 2r Volume of a cone = hr 2 3 1 Volume of a sphere = 3 3 4 r Area of a triangle = 2 1 ab sin C Arc length = r , where  is in radians Sector area = 2 2 1 r , where  is in radians Trigonometry C c B b A a sin sin sin == a 2 = b 2 + c 2 – 2bc cos A Statistics Mean =   f fx Standard deviation = 22         −     f fx f fx

Methodist Girls’ School Mathematics Paper 1 Sec 4 Preliminary Examination 2023 Page 3 of 24 Answer all the questions. 1 It is given that M is a prime number and is a digit of the number 508 M45. If the number, correct to 3 significant figures, is 509 000, find the maximum value of M. Answer M = ……….7………. [1] 2 Simplify ( ) 2 3 2 3 2x+− . ( ) ( ) 2 2 2 2 3 2 3 2 3 2 9 12 4 3 18 24 8 18 24 11 x xx xx xx +− = + − + = + − + = − + Answer …….…… 218 24 11xx−+ ……..... [2] 3 Solve the equation 2 31 497 x  = . 2 3 322 2 2 3 1 497 77 77 22 3 1 3 x x x x x − −  = = = −= =− Answer x = …… 1 3− ………. [2]

Methodist Girls’ School Mathematics Paper 1 Sec 4 Preliminary Examination 2023 Page 4 of 24 4 (a) Factorise 236 aayy + completely. ( ) 236 32 aa aa yy yy + =+ Answer …… ( )32aayy + ……..… [1]