ACSI 2021 Y3 Core Mathematics Paper 2

FINAL EXAMINATION 2021 YEAR 3 INTEGRATED PROGRAMME CORE MATHEMATICS PAPER 2 MONDAY 11th October 2021 1 hour 30 minutes ADDITIONAL MATERIALS: Answer Paper (7 sheets) Graph Paper ( 1 sheet) INSTRUCTIONS TO STUDENTS Do not open this examination paper until instructed to do so. A calculator is required for this paper. Answer all the questions on the answer sheets provided. At the end of the examination, fasten the answer sheets together. Unless otherwise stated in the question, all numerical answers must be given exactly or correct to three significant figures. Answers in degrees are to be given to one decimal place. INFORMATION FOR STUDENTS The maximum mark for this paper is 80. ______________________________________________________________

ACS(Independent)MathDept/Y3IPCoreMathPaper2/2021/FinalExamination 2 This question paper consists of 4 printed pages. [Turn over Full marks are not necessarily awarded for a correct answer with no working. Answers must be supported by working and/or explanations. Where an answer is incorrect, some marks may be given for correct method, provided this is shown by written working. You are therefore advis ed to show all working. Answer all the questions on the answer sheets provided. Begin each question on a new page. 1. [Maximum mark: 12] (a) Evaluate 3 3 ln(3.256) 1.325 (0.25 2.38) e+ − , leaving your answer correct to 3 significant figure. [2] (b) Simplify ( ) 3 2 1 1 2 4 82 4 3 (3 ) 3 x y yx −   , expressing your answer in positive indices. [3] (c) Simplify 13 21 27 2(3 ) 39 yy yy + +− + . [3] (d) Solve for x if 2 651xx+− = . [4] 2. [Maximum mark: 11] (a) Expand and simplify ( )( ) 2 2 2 2 1 n p n m p mm n n m p  − + −+−  − . [3] (b) Find the sum of 35 x x− and 2 6 10 9 25 x x +− − , expressing your answer as a single fraction in its simplest form. [3] (c) Solve the equation ( )( ) 23 5 4 04 2 4 xx x x x + +=− + − , leaving your answers in 2 decimal places. [5]

ACS(Independent)MathDept/Y3IPCoreMathPaper2/2021/FinalExamination 3

ACS(Independent)MathDept/Y3IPCoreMathPaper2/2021/FinalExamination 4 3. [Maximum mark: 9] A circular cylindrical container of base radius xe cm, and height 2xe cm is fully filled with water. (a) Given that the volume of the water in the container is 12900 cm3, find the value of x . [3] The water is poured into a rectangular tank of base area 850 cm2 and height 60 cm. (b) Find the depth of the water in the rectangular tank. [2] (c) A solid metal sphere of radius 14 cm is then put into the rectangular tank. If the sphere is totally immersed in the water, will the water overflow? Explain your answer. [4] 4. [Maximum mark: 7] (a) Solve 33log (5 ) 1 log (1 2 )xx− = − − . [4] (b) Evaluate 2 3 4