MGS 2025 EMATH PRELIM P2 MS

This question paper consists of 26 printed pages and 2 blank pages. Class Index Number MARK SCHEME Name : METHODIST GIRLS’ SCHOOL Founded in 1887 PRELIMINARY EXAMINATION 2025 Secondary 4 Thursday MATHEMATICS 4052/02 22 August 2025 Paper 2 2 hours 15 minutes 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

2 Methodist Girls’ School Mathematics Paper 2 Sec 4 Preliminary Examination 202 5 Mathematical Formulae Compound Interest Total amount = ( ) 100 r 1+ n P Mensuration Curved surface area of a cone = rlπ Surface area of a sphere = 4 2rπ Volume of a cone = h r2 3 1π Volume of a sphere = 3 3 4 rπ Area of a triangle ABC = 2 1 absinC Arc length = rθ , where θ is in radians Sector area = 21 2 r θ , where θ 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

3 Methodist Girls’ School Mathematics Paper 2 Sec 4 Preliminary Examination 202 5 1 (a) There are 2 500 sheets of paper of the same thickness in a stack of paper. (i) Given that the height of the stack of paper is 25 cm, write down the thickness of a single sheet of paper in metres in standard form. 4 0.25 0.00012500 1 10 − = = × B1 Answer ……......……………. m [1] (ii) The stack of paper weighs 13.1 kg, correct to one decimal place. Find the minimum mass of the stack of paper. 13.05 B1 Answer ………….…...…….. kg [1] (iii) The number 2500 is correct to k significant figures. State a possible value of k. 2, 3 or 4 B1 Answer k = ………….…...…… [1]

4 Methodist Girls’ School Mathematics Paper 2 Sec 4 Preliminary Examination 202 5 (b) Jim is climbing a mountain that is 4 500 metres high. The temperature at the base of the mountain is 7 °C, and as he climbs, the temperature drops at a constant rate. The temperature at the top of the mountain is 15 °C lower than at the base of the mountain. (i) Find the temperature at the top of the mountain. 7C 1 5C 8C° − ° = −° B1 Answer ……........…………. °C [1] (ii) At what height during his climb does the temperature reach 2− °C? 7 ( 2) 4500 270015 −− ×= B1 Answer ….……….…...…….. m [1] (c) In 2023, Sandra earned 20% less than what she earned in 2022. In 2024, she earned 15% more than what she earned in 2023. If she earned $49 680 in 2024, how much did she earn in 2022? 49680 1.15 0.8 54000 ÷÷ = M1 A1 Answer $ ………..….………… [2]

5 Methodist Girls’ School Mathematics Paper 2 Sec 4 Preliminary Examination 202 5 2 (a) (i) Solve the inequality 745 1 2 2xx x−< +≤ − . 745 1 2 2 74 51 51 2 2 54 5 7 2 55 4 14 55 4 14 xx x xx x x xx xx x −< +≤ − −< + +≤ − >− ≤ >− ≤ − <≤ M1 A1 Answer ……….....……….……. [2] (ii) List all the integers that satisfy 745 1 2 2xx x−< +≤ − . 1, 0− B1 Answer ..…………………..…… [1]

6 Methodist Girls’ School Mathematics Paper 2 Sec 4 Preliminary Examination 202 5 (b) 3 2( 1) 4 bac += − (i) Find a when 2b= and 1c=− . 3 2(2 1) ( 1)4 27 14 23 4 a += −− = − = B1 Answer a = ………….…...…… [1] (ii) Arrange the formula to make b the subject. 3 2 3 2 23 23 ( 1) 4 ( 1) 4 4( ) ( 1) 4( ) 1 bac bac ac b b ac += − ++= += + = +− M1 M1 A1 Answer b = ………….…...…… [3]

7 Methodist Girls’ School Mathematics Paper 2 Sec 4 Preliminary Examination 202 5 BLANK PAGE

8 Methodist Girls’ School Mathematics Paper 2 Sec 4 Preliminary Examination 202 5 3 (a) A , B, C and D are points on a circle, centre O. EB and ED are tangents to the circle. Angle DOC = 50° . Find, giving reasons for each answer, (i) angle OEB, 90 (tan rad) 180 90 50 ( sum in a ) 40 40 (tangents from ext point) ODE DEO OEB ∠= °⊥ ∠ = °− °− ° ∠ ∆ = ° ∠= ° M1 M1 A1 Answer …………….………… ° [3] 50° B D C A E O

9 Methodist Girls’ School Mathematics Paper 2 Sec 4 Preliminary Examination 202 5 (ii) angle DAB, 50 (tangents from ext. pt) 100 50 ( at centre = 2 at circumference) COB DOB DAB ∠= ° ∠= ° ∠ = ° ∠ ×∠ M1 A1 Answer ..………….………… ° [2] (iii) angle EBC. 180 50 (base of isos )2 65 90 65 =25 OBC s EBC °− °∠= ∠ ∆ = ° ∠ = °− ° ° B1 Answer ..………….………… ° [1]

10 Methodist Girls’ School Mathematics Paper 2 Sec 4 Preliminary Examination 202 5 (b) The diagram shows the graphs of 48 4 0yx− −= and xy ka= . They intersect at the points A and B. A is a point on the y – axis. Find the values of k and of a. 0 2 48 4 0 0, 4 (0, 4) 2, 100 (2,100) 0, 4 4 4 2, 100 100 4 5 x yx xy A xp B y ka x y ka k xy a a − −= = = = = = = = = = = = = = M1 M1 A1 A1 Answer k = ………….…………. a = ………….…………. [4] A y B (2, p) x