ACSI 2021 Y3 Core Mathematics Paper 2 Solution

FINAL EXAMINATION 2021 YEAR 3 INTEGRATED PROGRAMME CORE MATHEMATICS PAPER 2 XXXXXX xxth 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. _____________________________________________________ This question paper consists of 4 printed pages. [Turn over

ACS(Independent)MathDept/Y3IPCoreMathPaper2/2021/FinalExamination 2 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 advised 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 figures. [2] 5.4623 −9.6636 = −0.565 (b) Simplify ( ) 3 2 1 1 2 4 82 4 3 (3 ) 3 x y yx −   , expressing your answer in positive indices. [3] (3𝑥 𝑦2) 3 9𝑦 (1 3 𝑥2) = 27𝑥3 𝑦6 3𝑦𝑥2 = 27𝑥3 3𝑦7𝑥2 = 9𝑥 𝑦7 Most students just use calculator to find the answer, a small group of students still give the wrong answer. Careless in expanding the number 3 for both cube and square. Some students did not leave it in positive indices.

ACS(Independent)MathDept/Y3IPCoreMathPaper2/2021/FinalExamination 3 (c) Simplify 13 21 27 2(3 ) 39 yy yy + +− + . [3] (33)𝑦+1 + 2(33𝑦) 3𝑦+2(32)𝑦−1 = 33𝑦+3 + 2(33𝑦) 3𝑦+232𝑦−2 = 27(33𝑦) + 2(33𝑦) 33𝑦 Let 𝑥 = 33𝑦 = 27𝑥 + 2𝑥 𝑥 = 29𝑥 𝑥 = 29 (d) Solve for x if 2 651xx+− = . [4] 5𝑥2+𝑥−6 = 50 𝑥2 + 𝑥 − 6 = 0 (𝑥 − 2)(𝑥 + 3) = 0 𝑥 = −3 or 𝑥 = 2 Careless in factorising the 3 or expanding the power-power rule wrongly. Some students see the question as 3y instead of 33y Easy question to solve.

ACS(Independent)MathDept/Y3IPCoreMathPaper2/2021/FinalExamination 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] (𝑚2 − 𝑛2) (𝑛2(𝑝 − 1) + 𝑚2(𝑝 − 1) 𝑝 − 1 ) = (𝑚2 − 𝑛2) ((𝑛2 + 𝑚2)(𝑝 − 1) 𝑝 − 1 ) = (𝑚2 − 𝑛2)(𝑛2 + 𝑚2) = 𝑛4 − 𝑚4 (b