DYSS EM paper 2 2024

DEYI SECONDARY SCHOOL MATHEMATICS 4052/02 Paper 2 05 Aug 2024 0810 – 1025h 2 hours 15 minutes _________________________________________________________________________ READ THESE INSTRUCTIONS FIRST Write your name, class, index number and calculator model in the spaces at the top of this page. Write in dark blue or black pen in the spaces provided on the Question Paper. You may use a pencil for any diagrams or graphs. Do not use staples, paper clips, highlighters, glue or correction fluid / tape. Answer all 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 π , use either your calculator value or 3.142, unless the question requires the answer in terms of π . The total number of marks is given in brackets [ ] at the end of each question or part question. The total number of marks for this paper is 90. This document consists of 20 printed pages including the cover page. Candidates answer on the Question Paper. Name: Class: Index No.: O 90 For Examiner’s Use Preliminary Examination 2024 Secondary 4 Express

2 Mathematical Formulae Compound interest Total amount = n rP      + 1001 Mensuration Curved surface area of a cone = rl Surface area of a sphere = 4r2 Volume of a cone = 3 1 r2h Volume of a sphere = 3 4 r3 Area of triangle ABC = Cabsin2 1 Arc length = r, where  is in radians Sector area = 21 2 r  , where  is in radians Trigonometry C c B b A a sinsinsin == Abccba cos2222 −+= Statistics Mean = fx f   Standard deviation = 22fx fx ff  −  

3 [Turn over Answer all the questions. 1 (a) Factorise completely 3𝑥3 − 12𝑥𝑦2. Answer ……………………………… [2] (b) Express 𝑥 (1−3𝑥)2 − 1 3𝑥−1 as a single fraction in its simplest form. Answer …………..………………….. [2]

4 (c) Given that 𝑅 = √𝑞2 + 2𝑎 𝑣 , express a in terms of R, v and q. Answer a = …………..…………….. [2] (d) Given that 𝑦 𝑥 = 10 and 𝑧 𝑦 = 5, where 𝑥 ≠ 0 and 𝑦 ≠ 0. Find the value of 𝑦+𝑧 2𝑥+𝑦 . Answer …………..…………….. [2]

5 [Turn over 2 A store sold a laptop at $1530 after offering a discount of 15%. Despite the discount, the store is still able to make a profit of 11%. Calculate (a) (i) the selling price of the laptop before the discount, Answer $ ………………………… [2] (ii) the cost price of the laptop, giving your answer to the nearest dollar. Answer $ ………………………… [2]

6 (b) Richard bought an HDB flat for $720 000. He took a home loan of 80% of this amount from a bank. (i) Calculate the amount of the loan. Answer $ ………………………… [1] (ii) At the end of each month, the bank charges a 2.88% per annum compound interest compounded monthly. If Richard pays $5000 at the end of each month, calculate the amount of loan left at the beginning of the third month. Answer $ ………………………… [4]

7 [Turn over 3 A company has two types of robot vacuum. Model Q takes 5 minutes more then Model P to clean a particular floor surface area of 450 m2. The speed of Model P is 8 m2 per minute faster than Model Q. (a) Taking x to be the rate, in m2 per minute, at which Model Q cleans, write down an expression, in terms of x for the time taken to clean the floor area of 450 m2 with Model P and Model Q respectively. Answer Model P ………..………… minutes [1] Model Q …………..……… minutes [1] (b) Form an equation in x and show that it reduces to 𝑥2 + 8𝑥 − 720 = 0. [3] (c) Solve the equation 𝑥2 + 8𝑥 − 720 = 0, giving your answers to 2 decimal places. Answer ……………..…or …………….. [3] (d) Hence, determine the time required to clean the floor area of 450 m2 with both Model P and Model Q operating together, leaving your answer in minutes and seconds, accurate to the nearest second. Answer …….… minutes ……… seconds [2]

8 North A D C B 20 m 60 m 75 102 4 A, B, C and D are points on level ground with A due north of C and D. ∠𝐵𝐴𝐷 = 75°, ∠𝐵𝐷𝐶 = 102°, AB = 60 m and CD = 20 m. Calculate (a) (i) the bearing of D from B, Answer ………………………… [2] (ii) the length of BD, Answer ………………………m [2] (iii) the length of BC. Answer ………………………m [2] °

9 [Turn over (b) A tree is spotted at point B. The largest angle of elevation from AC to the top of the tree is 40. Find the height of the tree. Answer …………..……………..m [3]

10 5 In the diagram, the position vectors of A and B relative to O are 4a and 5b respectively. OA is parallel to CB and SC is parallel to AB. It is given that OS : SB = 2: 3 and 𝐴𝑇⃗⃗⃗⃗⃗ = 1 3 𝑇𝐵⃗⃗⃗⃗⃗ . (a) Find, in terms of a and b, the vectors (i) 𝑂𝑆⃗⃗⃗⃗⃗ , Answer ………………………… [1] (ii) 𝐴𝑆⃗⃗⃗⃗⃗ , Answer ………………………… [1] (iii) 𝑂𝑇⃗⃗⃗⃗⃗ . Answer ………………………… [2] A O B C S U T 5b 4a