ACSI 2020 Promo Paper 2 ans

ACS (Independent) / Mathematics Department / Mathematics HL / Year 5 / 2020 Final Exam / Paper 2 / Solutions 1 FINAL EXAM 2020 YEAR 5 IB DIPLOMA PROGRAMME MATHEMATICS HIGHER LEVEL Paper 2 MARKING SCHEME SECTION A Qn Solution 1. Eqn 1 : 3 8xy = 3 2 22log log log 8xy⇒ += 223log log 3xy⇒ += Eqn 2 : 24log log 3xy+= 22 1log log 32xy⇒ += Using GDC, letting 2logvx= and 2logwy= 3v=− and 12w= So 3 2 1log 3 2 8xx −= −⇒ = = 12 2log 12 2 4096yy= ⇒= = Comments : Generally well attempted.

ACS (Independent) / Mathematics Department / Mathematics HL / Year 5 / 2020 Final Exam / Paper 2 / Solutions 2 Qn Solution 2. Let the two numbers be 122 1, 2 1kk++ ( )( ) ( ) 1 2 12 1 2 12 1 2 2 1 21 4 221 22 1 k k kk k k kk k k + += + + + = ++ + Comments : generally poorly attempted. Common mistakes included : 1. Letting the two odd numbers be (2𝑘𝑘 + 1)(2𝑘𝑘 + 1) 2. Letting the two odd numbers be consecutive (2𝑘𝑘 − 1)(2𝑘𝑘 + 1) 3. Letting 𝑛𝑛 be an even number and then (𝑛𝑛 − 1) is an odd number As they do not fully prove the result on its own. A few students attempted this question by substituting values. This reveals the students’ incorrect concepts as this technique does not prove the result for a high generality. A few students attempted to prove this question using contrapositive. While this attempt is commendable, they proved the result that “the product of two even numbers is even” instead of the correct contrapositive statement “suppose the product of two numbers is even, prove that the two numbers are both even”. Qn Solution 3. (a) From GDC, The product moment correlation coefficient is -0.606 (3 sf) There is moderate negative correlation (b) 0.0831 27.5404yx= −+ (c) (i) ( )0.0831 168 27.5404 13.6y= − += (ii) We find the regression line of x on y From GDC, The regression line is 229.219 4.4202xy= − So the estimated height when 100y= is ( ) ( )4.4202 100 229.219 177 3 sf− += Comment : a surprising number of students used the regression line of y on x to answer part (c), when the regression line of x on y ought to be used. For (a), the key word markers were looking out for was “moderate”.

ACS (Independent) / Mathematics Department / Mathematics HL / Year 5 / 2020 Final Exam / Paper 2 / Solutions 3 Qn Solution 4. (a) There are 2! ways of arranging the man and woman. So there are 2! 13! 12454041600×= ways (b) Fix the position of the women. There are 8! ways of doing so ___ W ___ W ___ W ___ W ___ W ___ W ___ W ___ W ___ Now fix the position of the men in the gaps, for doing so, no two men will be standing next to each other. There are 9 6P ways of doing so The number of ways is 9 6 8! 2438553600P ×= Comment : generally well attempted. Some students rounded the answer off to 3 significant figures when there is no need to as the answer is exact. S