Year 11 IBDP Mathematics Analysis And Approaches SL Paper .

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Year 11 IBDP Mathematics Analysis andApproaches SL – Paper 1EXAMINATIONSemester 1 2020Question and Answer BookletSTUDENT NAME:TEACHER(S):Mr. BillerMr. RodgersTIME ALLOWED:Reading time 5 minutesWriting time 90 minutesINSTRUCTIONS Do not open this examination paper until instructed to do so.You are not permitted access to any calculator for this paper.Section A: answer all questions. Answers must be written within the answer boxesprovided.Section B: answer all questions in the answer booklet provided. hereUnless otherwise stated in the question, all numerical answers should be given exactly orcorrect to three significant figures.A clean copy of the mathematics: analysis and approaches formula booklet is requiredfor this paper.The maximum mark for this examination paper is [79 marks]. ions for the exam hereSTRUCTURE OF BOOKLET / MARKING SCHEMEExam SectionSection ASection BNumber of questions to beansweredALLALLTotal marks5524

Full marks are not necessarily awarded for a correct answer with no working. Answers must be supported byworking and/or explanations. Where an answer is incorrect, some marks may be given for a correct method,provided this is shown by written working. You are therefore advised to show all working.Section AAnswer all questions. Answers must be written within the answer boxes provided. Working may becontinued below the lines, if necessary.1. [Maximum mark: 13]For each of the following equations, solve for x. Leave your answers as exact values.(a)x2 – 7x –12.[2 marks](b)3𝑥 2 181.[3 marks](c)1log5( ) log5(x – 1) 3 025.[4 marks](d)100𝑥 11 10𝑥 10 0.[4 marks]

2.[Maximum mark: 6]The following table shows four series of numbers.(a)Complete the table by stating the type of series that is shown: arithmetic, geometric orneither.Series(b)Type of series(i)1 11 121 1331 14641 (ii)1 1 5 1 4 3 12 2(iii) 𝜋 0 𝜋 2𝜋 (iv)10 5 2.5 1.25 Can the sum to infinity be found for any of these series? If so, find its sum.[4 2 6 marks]3.[Maximum mark: 7]𝒏 𝟏(a) A series is generated by the following rule ).𝒏 𝟐(𝟑(i)Write down the first four terms.[3 marks](ii)Show, using a test, that the series generated is either arithmetic, geometric or neither.[2 marks](b)Write the following series in sigma notation form:14 11 8 5 .[2 marks]

4.[Maximum mark: 9](a) Use the Completing the Square Method and hence write down the co-ordinates of the vertex fory 3x2 – 6x – 1.[6 marks](b) Find the x-intercepts of y 3x2 – 6x – 1.[3 marks]

5.[Maximum mark: 12](a) On the grid below, sketch both the graph of f(x) 2x 1and g(x) log2(x 1).Show your working to find:(i)co-ordinates of any intercepts, and(ii)equations of asymptotes.[10 marks]This question continues on the next page.

(b) Write down co-ordinates of where f(x) g(x).[2 marks]

6.[Maximum mark: 8]For the following questions 𝒇(𝒙) 𝒙𝟐 𝟐, 𝒙 0 and 𝒈(𝒙) 𝒙 𝟐(a) Evaluate:(i)f(2)(ii)g(2).[2 marks](b) Find fog(x).[4 marks](c) Hence state gof(x) and explain whether or not f(x) and g(x) are inverse functions of each other.[2 marks]

Do not write solutions on this page.Section BAnswer all questions in the answer booklet provided. Please start each question on a new page.7.[Maximum mark: 7]Consider h(x) 18 2x2 – 4mx, for m 0. The equation h(x) 0 has two repeated roots.(a)Find the value(s) of m.[5 marks](b)What is the range of h(x) for your value(s) of m in part (a).[2 marks]8.[Maximum mark: 9]𝟑Let f(x) log2 ( 𝒙𝟐 ), for x 0.(a)Show that f –1(x) (23)0.5x.[4 marks](b)Write down the range of f –1.[1 mark]Let g(x) log2 x, for x 0.(c)Find the value of (g f –1)(4), giving your answer as an integer.[4 marks]9.[Maximum mark: 8](a)Solve x2 – 5x 2 x – 3 for all x R.[2 marks](b)Hence find the co-ordinates of the vertex of f(x) x2 – 6x 5[2 marks](c)f(x) is transformed in order by the following transformations to become g(x):(i) a translation 3 units to the left(ii) a translation 3 units to the up(iii) a horizontal reflection(iv) a vertical dilation by factor of twoShow working to find an equation for g(x).[4 marks]

Year 11 IBDP Mathematics Analysis and Approaches SL – . A clean copy of the mathematics: analysis and approaches formula booklet is required for this paper. The maximum mark for this examination paper is [79 marks]. ions for the exam here STRUCTURE OF BOOKLET / MARKING SCHEME Exam Section Number of questions to be answered Total marks Section A Section B ALL ALL 55 24 . Full marks .

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