Do not open this examination paper until instructed to do so. â¢ You are not permitted access to any ... Section B: answer one question. â¢ Use fully labelled diagrams and references to the text/data where appropriate. ... direct taxes and cutting
May 9, 2016 - Instructions to candidates. â¢ Write your session number in the boxes above. â¢ Do not open this examination paper until instructed to do so. â¢ Section A: answer all questions. â¢ Section B: answer all of the questions from one of
May 1, 2017 - Tom operates Anubis as a sole trader, selling cell/mobile phone cases on the internet. The market is increasingly competitive. The retail price of phone cases is predicted to fall in the second quarter of 2018. Employees at Anubis will
May 11, 2004 - A. It reduces the number of erythrocytes in the blood. B. It reduces the number of platelets in the blood. C. It increases the amount of plasma in the blood. D. It reduces the number of lymphocytes in the blood. 28. How do the followin
350. 11 k k. +. +. = 34. â k. (A1). (C4). = 4. [4 marks]. 3. â²f x( ) = â +. 2. 3 x. (M1). f x( ). 2. 2. 3. 2 x. x c. â. = +. +. Notes: Award (M1) for an attempt to integrate. Do not penalise the omission of c here. 1. (A1). 1 3 c. =â + + c.
Instructions to candidates. â¢ Do not open this examination paper until instructed to do so. â¢ A clean copy of the business and management case study is required for this examination paper. â¢ Read the case study carefully. â¢ Section A: answer
A clean copy of the business management case study is required for this examination paper. â¢ Read the case study ... growth (line 52). . (b) With reference to John, explain the key functions of management.  ... (c) Using the information above
Mathematics Standard level Paper 2 Wednesday 11 May 2016 (morning)
Candidate session number
1 hour 30 minutes Instructions to candidates yyWrite your session number in the boxes above. yyDo not open this examination paper until instructed to do so. yyA graphic display calculator is required for this paper. yySection A: answer all questions in the boxes provided. yySection B: answer all questions in the answer booklet provided. Fill in your session number on the front of the answer booklet, and attach it to this examination paper and your cover sheet using the tag provided. yyUnless otherwise stated in the question, all numerical answers should be given exactly or correct to three significant figures. yyA clean copy of the mathematics SL formula booklet is required for this paper. yyThe maximum mark for this examination paper is [90 marks].
Please do not write on this page. Answers written on this page will not be marked.
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, for example 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 questions in the boxes provided. Working may be continued below the lines if necessary. 1.
[Maximum mark: 6] A random variable X is distributed normally with a mean of 20 and standard deviation of 4. (a)
On the following diagram, shade the region representing P (X ≤ 25) .
Write down P (X ≤ 25) , correct to two decimal places.
[Maximum mark: 8] Note: One decade is 10 years A population of rare birds, Pt , can be modelled by the equation Pt = P0 e kt , where P0 is the initial population, and t is measured in decades. After one decade, it is estimated that (a)
Section B Answer all questions in the answer booklet provided. Please start each question on a new page. 8.
[Maximum mark: 15] A factory has two machines, A and B. The number of breakdowns of each machine is independent from day to day. Let A be the number of breakdowns of Machine A on any given day. The probability distribution for A can be modelled by the following table.
a P (A = a)
Find k .
A day is chosen at random. Write down the probability that Machine A has no breakdowns.
Five days are chosen at random. Find the probability that Machine A has no breakdowns on exactly four of these days.
Let B be the number of breakdowns of Machine B on any given day. The probability distribution for B can be modelled by the following table.
b P (B = b) (c)
Find E (B) .
On Tuesday, the factory uses both Machine A and Machine B. The variables A and B are independent. (d)
Find the probability that there are exactly two breakdowns on Tuesday.
Given that there are exactly two breakdowns on Tuesday, find the probability that both breakdowns are of Machine A.
– 11 – Do not write solutions on this page. 9.
[Maximum mark: 14] A particle P moves along a straight line so that its velocity, v ms−1, after t seconds, is given by v = cos 3t − 2 sin t − 0.5 , for 0 ≤ t ≤ 5 . The initial displacement of P from a fixed point O is 4 metres. (a)
Find the displacement of P from O after 5 seconds.
The following sketch shows the graph of v .
v 3 2 1 0
–1 –2 –3 –4 (b)
Find when P is first at rest.
Write down the number of times P changes direction.
Find the acceleration of P after 3 seconds.
Find the maximum speed of P.
Turn over 12EP11
– 12 – Do not write solutions on this page. 10. [Maximum mark: 16]
6 −3 The points A and B lie on a line L , and have position vectors −2 and 4 respectively. −1 2 Let O be the origin. This is shown on the following diagram. diagram not to scale
L B A
(a) Find AB .
The point C also lies on L , such that AC = 2CB .
3 (b) Show that OC = 2 . 0 →
Let θ be the angle between AB and OC . (c)
Find θ .
ˆ Let D be a point such that OD = k OC , where k > 1 . Let E be a point on L such that CED is a right angle. This is shown on the following diagram. diagram not to scale
Show that DE= (k − 1) OC sin θ .
The distance from D to line L is less than 3 units. Find the possible values of k .