ACSI 2020 Y3 Core Mathematics Paper 2 Solution

FINAL EXAMINATION 2020 YEAR 3 INTEGRATED PROGRAMME CORE MATHEMATICS PAPER 2 MONDAY xxth October 2020 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/Y3IPCoreMathPaper2/2020/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: 6] (a) Evaluate 2 4 (0.3578) 7.647 43.96  , leaving your answer correct to 3 significant figures. [2] 0.354019 2.57492 = 0.137 (b) Express 2 1 1 10 3 2 2 4 x x x x ++++ − − as a single fraction in its simplest form. [4] 1 𝑥 + 2 + 1 2 − 𝑥 + 10 + 3𝑥 𝑥2 − 4 = 1 𝑥 + 2 − 1 𝑥 − 2 + 10 + 3𝑥 (𝑥 − 2)(𝑥 + 2) = 𝑥 − 2 − 𝑥 − 2 + 10 + 3𝑥 (𝑥 − 2)(𝑥 + 2) = 6 + 3𝑥 (𝑥 − 2)(𝑥 + 2) = 3 (𝑥 − 2) Some student take square of the expression to get rid of the square root first. They need to know that this is an expression, hence they cannot do that! Very careless 1 2 − 𝑥 = − 1 𝑥 − 2 Some students did not leave it in the simplest form

ACS(Independent)MathDept/Y3IPCoreMathPaper2/2020/FinalExamination 3 2 [Maximum mark: 7] (a) Solve the equation 923 2x x−= , giving your answers correct to two decimal places. [4] 2𝑥(2𝑥) − 9 = 3(2𝑥) 4𝑥2 − 9 = 6𝑥 4𝑥2 − 6𝑥 − 9 = 0 𝑥 = −(−6) ± √(−6)2 − 4(4)(−9) 2(4) 𝑥 = −0.93 or 𝑥 = 2.43 (b) Expand and simplify 2 1 2 1 2 4 3 3 3 3 3 3p q q q p p  + − +      . [3] 𝑝 2 3𝑞 2 3 − 𝑞 1 3𝑝 4 3 + 𝑝2 + 𝑞 − 𝑞 2 3𝑝 2 3 + 𝑞 1 3𝑝 4 3 = 𝑝2 + 𝑞 3 [Maximum mark: 9] (a) Simplify ( ) ( ) 32 12 44 2 3 24 (4 ) xx xx − −  , expressing your answer in positive indices. [3] 8𝑥−6 × 4𝑥12 16𝑥−8 × 𝑥12 = 32𝑥6 16𝑥4 = 2𝑥2 The question specifically asked for 2 dp. Some student left it as 3 sf. Easy question, but