Year 11 IB MATHEMATICS SL EXAMINATION PAPER 2

1 Students are not permitted to bring mobile phones and / or any other unauthorized electronic devices into the EXAMINATION room. Year 11 IB MATHEMATICS SL EXAMINATION PAPER 2 Semester 1 2017 Question and Answer booklet STUDENT NAME: _____ TEACHER(S): Mr Rodgers, Ms McCaughey TIME ALLOWED: Reading time 5 minutes Writing time 90 minutes INSTRUCTIONS * Do not open this EXAMINATION PAPER until instructed to do so. * A graphic display calculator is required for this PAPER . * Section A: answer all questions in the boxes provided.

2 * Section B: answer all questions in the answer booklet provided. * Unless otherwise stated in the question, all numerical answers should be given exactly or correct to three significant figures. * A clean copy of the MATHEMATICS SL formula booklet is required for this PAPER . STRUCTURE OF booklet / MARKINGSCHEME Number of questions Number of questions to be answered Total marks 10 10 78 2017 IB standard level PAPER 2 1 Full marks are not necessarily awarded for a correct answer with no working. Answers must be supported by working and/or explanations.

3 In particular, solutions found from a graphic display calculator should be supported by suitable working, if graphs are used to find a solution, you should sketch these as part of your answer. 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 A Answer all the questions in the spaces provided. Working may be continued below the lines, if necessary. 1. [Maximum mark: 7 marks] a) Let 2( ) 289f xxx.

4 (i) Write down the coordinates of the vertex. (ii) Hence or otherwise, express the function in the form 2( ) 2()f xx hk . (4) b) Solve the equation ( ) 0fx . (3) .. 2017 IB standard level PAPER 2 2 2. [Maximum mark: 7 marks] a) Describe two transformations whose composite transforms the graph of ()yf x to the graph of 32xyf . (2) b) Sketch the graph of 3ln2xy (2) c) Sketch the graph of 3ln12xy , marking clearly the positions of any asymptotes and x - intercepts.

5 (3) .. 2017 IB standard level PAPER 2 3 3. [Maximum mark: 8 marks] Jose takes medication. After t minutes, the concentration of medication left in his bloodstream is given by ( ) 10( )tAt , where A is in milligrams per litre. a) Write down (0)A . (1) b) Find the concentration of medication left in his bloodstream after 50 minutes. (2) c) At 13:00, when there is no medication in Jose s bloodstream, he takes his first dose of medication. He can take his medication again when the concentration of medication reaches milligrams per litre.

6 What time will Jose be able to take his medication again? (5) .. 2017 IB standard level PAPER 2 4 4. [Maximum mark: 6 marks] Consider the line L with equation y + 2x = 3. The line L1 is parallel to L and passes through the point (6, 4). (a) Find the gradient of L1. (2) (b) Find the equation of L1 in the form y = mx + b. (2) (c) Find the x-coordinate of the point where line L1 crosses the x-axis. (2) .. 2017 IB standard level PAPER 2 5 5. [Maximum mark: 7 marks] Consider 2( ) 2f xx , for 22x and ( ) sinxg xe , for 22x.

7 The graph of ()fx is given below. a) On the diagram above, sketch the graph of g. (3) b) Solve ( )( )f xg x . (2) c) Write down the set of values of x such that ( )( )f xg x . (2) .. 2017 IB standard level PAPER 2 6 6. [Maximum mark: 5 marks] Solve the equation 4 sinxex , for 02x . (5) .. 7. [Maximum mark: 5 marks] The quadratic equation 2(3)1 0kxkx has two equal real roots. Find the possible values of k. (5) .. 2017 IB standard level PAPER 2 7 Do NOT write on this page.

8 SECTION B Answer all the questions on the answer sheets provided. Please start each question on a new page. 8. [Maximum mark: 16 marks] Let 333( ) loglog 16 log 42xfx , for 0x . a) Show that 3( ) log 2f xx . (2) b) Find the value of( )f and of ( )f . (3) c) The function f can also be written in the form ln()lnaxfxb . (i) Write down the value of a and of b. (ii) Hence on graph PAPER , sketch the graph of ()fx, for 55x ,55y , using a scale of 1 cm to 1 unit on each axis.

9 (iii) Write down the equation of the asymptote. (6) d) Write down the value of 1(0)f . (1) e) The point A lies on the graph of ()fx. At A, . On your diagram, sketch the graph of 1()fx , noting clearly the image of point A. (4) 2017 IB standard level PAPER 2 8 9. [Maximum mark: 9 marks] Consider the function 35()2xfxx . a) Write down the equation of the horizontal asymptote of the graph ()yf x . (1) b) Show that 1( ) 32fxx . (2) c) Hence describe a translation vector which transforms the graph of 1yx to the graph of ()yf x.

10 (2) d) Find an expression for 1()fx and state the domain. (3) e) Describe the transformation which transforms the graph of ()yf x to the graph of 1()fx . (1) 10. [Maximum mark:8] A ball is thrown vertically upwards into the air. The height, h metres, of the ball above the ground after t seconds is given by 22 205 ,0httt (a) Find the initial height above the ground of the ball (that is, its height at the instant when it is released). (2) (b) Show that the height of the ball after one second is 17 metres.