MGS 2025 EMATH PRELIM P1 MS

Class Index Number Name : Mark Scheme This question paper consists of 26 printed pages and 2 blank pages. METHODIST GIRLS’ SCHOOL Founded in 1887 PRELIMINARY EXAMINATION 2025 Secondary 4 Wednesday MATHEMATICS 4052/01 20 August 2025 Paper 1 2 h 15 min Candidates answer on the Question Paper. INSTRUCTIONS TO CANDIDATES Write your name, class 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 , 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 90. 90

Page 2 of 28 Methodist Girls’ School Mathematics Paper 1 Sec 4 Preliminary Examination 2025 Mathematical Formulae Compound Interest Total amount = Mensuration Curved surface area of a cone = Surface area of a sphere = 4 Volume of a cone = Volume of a sphere = Area of a triangle = absin C Arc length = r θ , where θ is in radians Sector area = , where θ is in radians Trigonometry a 2 = b 2 + c 2 – 2bc cos A Statistics Mean = Standard deviation = ( ) 100 r 1+ n P rlπ 2rπ h r2 3 1π 3 3 4 rπ 2 1 θ2 2 1 r C c B b A a sin sin sin = = ∑ ∑ f fx 22         − ∑ ∑ ∑ ∑ f fx f fx

Page 3 of 28 Methodist Girls’ School Mathematics Paper 1 Sec 4 Preliminary Examination 2025 1 Simplify ( ) 1 6 32 3 274 3 aa rr − ÷ , giving your answer in positive index. ( ) 1 6 32 22 33 23 2 2 4 274 43 33 4 33 4 9 aa aa r r rr ar xra r a −− − ÷= ÷ = = Answer………………………………. [2] 2 3 3148 4mm−− ×= Use the laws of indices to find the value of m . Show your working. ( ) ( ) 3 31 2 3 33 1 2 2 69 3 2 11 9 2 48 4 22 2 22 22 11 9 2 11 11 1 mm mm mm m m m m −− −− −+ − − ×= ×= = = −= = = Answer m = …………………………. [2] M1 for 3a2 A1 A1 M1 for expressing terms in base 2

Page 4 of 28 Methodist Girls’ School Mathematics Paper 1 Sec 4 Preliminary Examination 2025 3 Two identical containers are filled with a mixture of rose syrup and evaporated milk in the ratio of 5 : 3 and 4 : 7. The contents of the containers are poured into a big bowl and mixed thoroughly. Find the ratio of the rose syrup to the evaporated milk in the big bowl.