Math Sl Past Paper
IB DIPLOMA PROGRAMME PROGRAMME DU DIPLÔME DU BI PROGRAMA DEL DIPLOMA DEL BI
M07/5/MATME/SP2/ENG/TZ1/XX
22077304
mathematics staNDaRD level PaPeR 2 Tuesday 8 May 2007 (morning) 1 hour 30 minutes
INSTRUcTIONS TO cANDIDATES not open this examination paper until instructed to do so. Do Answer all the questions. Unless otherwise stated in the question, all numerical answers must be given exactly or correct to three significant figures.
2207-7304
8 pages © IBO 2007
http://www.xtremepapers.net
–2–
M07/5/MATME/SP2/ENG/TZ1/XX
Please start each question on a new page. Full marks are not necessarily awarded for a correct answer with no working. Answers must be supported by working and/or explanations. In particular, solutions found from a graphic display calculator should be supported by suitable working, e.g. 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. 1. [Total mark: 25] Part a [Maximum mark: 10]
The following diagram shows part of the graph of a quadratic function, with equation in the form y = ( x − p) ( x − q) , where p , q ∈ .
(a)
Write down (i) (ii) the value of p and of q ; the equation of the axis of symmetry of the curve. [3 marks] [3 marks]
(b)
Find the equation of the function in the form y = ( x − h) 2 + k , where h , k ∈ . Find dy . dx
(c)
[2 marks]
(d)
Let T be the tangent to the curve at the point (0 , 5) . Find the equation of T.
[2 marks]
(This question continues on the following page)
2207-7304
–3– (Question 1 continued) Part B [Maximum mark: 15]
M07/5/MATME/SP2/ENG/TZ1/XX
The function f is defined as f ( x) = e x sin x , where x is in radians. Part of the curve of f is shown below.
There is a point of inflexion at A, and a local maximum point at B. The
IB DIPLOMA PROGRAMME PROGRAMME DU DIPLÔME DU BI PROGRAMA DEL DIPLOMA DEL BI
M07/5/MATME/SP2/ENG/TZ1/XX
22077304
mathematics staNDaRD level PaPeR 2 Tuesday 8 May 2007 (morning) 1 hour 30 minutes
INSTRUcTIONS TO cANDIDATES not open this examination paper until instructed to do so. Do Answer all the questions. Unless otherwise stated in the question, all numerical answers must be given exactly or correct to three significant figures.
2207-7304
8 pages © IBO 2007
http://www.xtremepapers.net
–2–
M07/5/MATME/SP2/ENG/TZ1/XX
Please start each question on a new page. Full marks are not necessarily awarded for a correct answer with no working. Answers must be supported by working and/or explanations. In particular, solutions found from a graphic display calculator should be supported by suitable working, e.g. 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. 1. [Total mark: 25] Part a [Maximum mark: 10]
The following diagram shows part of the graph of a quadratic function, with equation in the form y = ( x − p) ( x − q) , where p , q ∈ .
(a)
Write down (i) (ii) the value of p and of q ; the equation of the axis of symmetry of the curve. [3 marks] [3 marks]
(b)
Find the equation of the function in the form y = ( x − h) 2 + k , where h , k ∈ . Find dy . dx
(c)
[2 marks]
(d)
Let T be the tangent to the curve at the point (0 , 5) . Find the equation of T.
[2 marks]
(This question continues on the following page)
2207-7304
–3– (Question 1 continued) Part B [Maximum mark: 15]
M07/5/MATME/SP2/ENG/TZ1/XX
The function f is defined as f ( x) = e x sin x , where x is in radians. Part of the curve of f is shown below.
There is a point of inflexion at A, and a local maximum point at B. The