CAIE A Level 9709

Mathematics 2023 · Oct/Nov

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11 Questions Q&A Available
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This CAIE A Level Mathematics paper is focused mainly on mechanics, especially particles moving under forces, motion on rough and smooth planes, friction, connected particles, projectiles, and work/power in inclined-plane and towing-engine contexts. The questions are mostly structured calculation problems, often split into parts that build from modelling the situation to applying Newton’s laws, kinematics, and energy methods; students may also need to interpret diagrams and set up equations carefully from the wording.…

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Questions & Model Answers 11 Qs

Q1
Structured 4 marks
of greatest slope of an inclined plane. The top of the plane is at a vertical height of 1.6m above the level of the bottom of the plane. The speed of the block at the top of the plane is 2ms and the speed of the block at the bottom of the plane is 4ms Find the work done against the resistance to motion of the block.
Q2
Structured 5 marks
2 N40Åmkg The diagram shows a smooth ring R, of massmkg, threaded on a light inextensible string. A horizontal force of magnitude 2N acts on vertical wall. The part ARof the string makes an angle of 30?with the vertical, the partBRmakes an angle of 40 ?with the vertical and the string is taut. The ring is in equilibrium. m.
Q3
Structured 5 marks
30Å 120 N 10 kg A block of mass 10kg is at rest on a rough plane inclined at an angle of 30 ?to the horizontal. A force of 120N is applied to the block at an angle of 20 ?above a line of greatest slope (see diagram). There is a force resisting the motion of the block and 200J of work isdone against this force when the block has moved a distance of 5m up the plane from rest. Find the speed of the block when it has moved a distance of 5m upthe plane from rest.
Q4
Structured 4 marks
4A particle Pof mass 0.2kg lies at rest on a rough horizontal plane. A horizontal force of 1.2N is applied to (a)Given that [3] travelled by Pin the third second of its motion.
Q5
Short Answer 2 marks
5A particle Aof mass 0.5kg is projected vertically upwards from horizontal ground with speed 25ms (a)Find the speed of Awhen it reaches a height of 20m above the ground. [2] When Areaches a height of 20m, it collides with a particleBof mass 0.3kg which is moving downwards in the same vertical line as Awith speed 32.5ms . In the collision between the two particles, Bis brought to instantaneous rest. (b)Show that the velocity of Aimmediately after the collision is 4.5ms downwards.
Q6
Structured 4 marks
(c)Find the time interval between AandBreaching the ground. You should assume thatAdoes not bounce when it reaches the ground.
Q7
Short Answer 1 mark
6A railway engine of mass 120000kg is towing a coach of mass 60000kg up a straight track inclined at an angle of !to the horizontal where sin!=0.02. There is a light rigid coupling, parallel to the track, connecting the engine and coach. The driving force produced by the engine is 125000N and there are constant resistances to motion of 22000N on the engine and 13000N on the coach.
Q8
Structured 4 marks
At an instant when the engine is travelling at 30ms , it comes to a section of track inclined upwards at an angle "to the horizontal. The power produced by the engine is now 4500000W and, as a result, the engine maintains a constant speed. ".
Q9
Short Answer 1 mark
7A particle denoted byvms , where +1.8t The acceleration of Xis zero att=pandt=q, wherep<q. (a)Find the value of pand the value ofq. [4] It is given that the velocity of Xis zero att=14. (b)Find the velocities of Xatt=pand att=q, and hence sketch the velocity-time graph for the motion of
Q10
Structured 5 marks
(c)Find the total distance travelled by Xbetweent=0 andt=15.
Q11
Short Answer 1 mark
Additional Page If you use the following lined page to complete the answer(s)to any question(s), the question number(s) must be clearly shown. Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge Assessment International Education Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. Local Examinations Syndicate (UCLES), which is a department of the University of Cambridge.
Paper Details
Board CAIE
Level A Level
Subject Mathematics
Code 9709
Year 2023
Session Oct/Nov
Q&A 11 questions
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