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2024 AQA AS FURTHER MATHEMATICS 7366/2M Paper 2
Verified Question Paper and Marking Scheme Attached
June 2024
FURTHER MATHEMATICS
Paper 2 Mechanics
Friday 17 May 2024 Afternoon Time allowed: 1 hour 30 minutes
Materials ⚫ You must have the AQA Formulae and statistical tables booklet for A‑level Mathematics and A‑level Further Mathematics. ⚫ You should have a graphical or scientific calculator that meets the requirements of the specification. ⚫ You must ensure you have the other optional Question Paper/Answer Book for which you are entered ( either Discrete or Statistics). You will have 1 hour 30 minutes to complete both papers. Instructions ⚫ Use black ink or black ball‑point pen. Pencil should only be used for drawing. ⚫ Fill in the boxes at the top of this page. ⚫ Answer all questions. ⚫ You must answer each question in the space provided for that question. If you require extra space for your answer(s), use the lined pages at the end of this book. Write the question number against your answer(s). ⚫ Do not write outside the box around each page or on blank pages. ⚫ Show all necessary working; otherwise marks for method may be lost. ⚫ Do all rough work in this book. Cross through any work that you do not want to be marked. Information ⚫ The marks for questions are shown in brackets. ⚫ The maximum mark for this paper is 40. Advice ⚫ Unless stated otherwise, you may quote formulae, without proof, from the booklet. ⚫ You do not necessarily need to use all the space provided. For Examiner’s Use Question Mark 1 2 3 4 5 6 7 8 9 TOTAL
Do not write outside the Answer all questions in the spaces provided. 1 An elastic string has modulus of elasticity 20 newtons and natural length 2 metres. The string is stretched so that its extension is 0.5 metres. Find the elastic potential energy stored in the string. box Circle your answer. [1 mark] 1.25 J 5.5 J 5 J 10 J 2 State the dimensions of impulse. Circle your answer.
MLT –^2 MLT –^1 MLT MLT^2
[1 mark]
Do not write outside the
4 In this question use g = 9.8 m s–^2
A ball of mass 0.5 kg is projected vertically upwards with a speed of 10 m s–^1 4 (a) Calculate the initial kinetic energy of the ball. [1 mark] box 4 (b) Assuming that the weight is the only force acting on the ball, use an energy method to show that the maximum height reached by the ball is approximately 5.1 m above the point of projection. [2 marks]
Do not write outside the 4 (c) (i) A student conducts an experiment to verify the accuracy of the result obtained in part (b). They observe that the ball rises to a height of 4.4 m above the point of projection and concludes that this
height difference is due to a resistance force, R newtons.
box
Find the total work done against R whilst the ball is moving upwards.
[2 marks]
4 (c) (ii) Using a model that assumes R is constant, find the magnitude of R
[2 marks] 4 (c) (iii) Comment on the validity of the model used in part (c)(ii). [1 mark] Turn over (^) U
Do not write outside the
6 Kepler’s Third Law of planetary motion for the period of a circular orbit around the Earth is given by the
formula, box where,
t is the time taken for one orbit
t = 2 π
r^3
√ Gm
r is the radius of the circular orbit
m is the mass of the Earth
G is a gravitational constant.
Use dimensional analysis to determine the dimensions of G
[4 marks] Turn over U
Do not write outside the There are no questions printed on this page DO NOT WRITE ON THIS PAGE ANSWER IN THE SPACES PROVIDED box
Do not write outside the 8 Two spheres, A and B , of equal size are moving in the same direction along a straight line on a smooth horizontal surface.
Sphere A has mass m and is moving with speed 4 u
Sphere B has mass 6 m and is moving with speed u
The diagram shows the spheres and their velocities. box
4 u u
m 6 m
A B
Subsequently A collides directly with B
The coefficient of restitution between A and B is e
8 (a) Find, in terms of m and u, the total momentum of the spheres before the collision.
[1 mark] 8 (b) Show that the speed of B immediately after the collision is
u (3 e + 10)
[4 marks]
Do not write outside the box 8 (c) After the collision sphere A moves in the opposite direction.
Find the range of possible values for e
[5 marks] Turn over U
Do not write outside the box 9 (c) State one modelling assumption you have made to answer part (b). [1 mark] END OF QUESTIONS
Do not write outside the There are no questions printed on this page DO NOT WRITE ON THIS PAGE ANSWER IN THE SPACES PROVIDED box
Do not write outside the box
AS
FURTHER MATHEMATICS
7366/2M
Paper 2 Mechanics
Mark scheme June 2024 Version: 1.0 Final
MARK SCHEME – AS FURTHER MATHEMATICS – 7366/2M – JUNE 2024
Mark scheme instructions to examiners General The mark scheme for each question shows:
- the marks available for each part of the question
- the total marks available for the question
- marking instructions that indicate when marks should be awarded or withheld including the principle on which each mark is awarded. Information is included to help the examiner make his or her judgement and to delineate what is creditworthy from that not worthy of credit
- a typical solution. This response is one we expect to see frequently. However credit must be given on the basis of the marking instructions. If a student uses a method which is not explicitly covered by the marking instructions the same principles of marking should be applied. Credit should be given to any valid methods. Examiners should seek advice from their senior examiner if in any doubt. Key to mark types M mark is for method R mark is for reasoning A mark is dependent on M marks and is for accuracy B mark is independent of M marks and is for method and accuracy E mark is for explanation F follow through from previous incorrect result Key to mark scheme abbreviations CAO correct answer only CSO correct solution only ft follow^ through^ from^ previous^ incorrect^ result ‘their’ indicates that credit can be given from previous incorrect result AWFW anything which falls within AWRT anything which rounds to ACF any correct form AG answer given SC special case OE or equivalent NMS no method shown PI possibly implied sf significant figure(s) dp decimal place(s) ISW Ignore Subsequent Workings 3
MARK SCHEME – AS FURTHER MATHEMATICS – 7366/2M – JUNE 2024
Examiners should consistently apply the following general marking principles: No Method Shown Where the question specifically requires a particular method to be used, we must usually see evidence of use of this method for any marks to be awarded. Where the answer can be reasonably obtained without showing working and it is very unlikely that the correct answer can be obtained by using an incorrect method, we must award full marks. However, the obvious penalty to candidates showing no working is that incorrect answers, however close, earn no marks. Where a question asks the candidate to state or write down a result, no method need be shown for full marks. Where the permitted calculator has functions which reasonably allow the solution of the question directly, the correct answer without working earns full marks , unless it is given to less than the degree of accuracy accepted in the mark scheme, when it gains no marks. Otherwise we require evidence of a correct method for any marks to be awarded. Diagrams Diagrams that have working on them should be treated like normal responses. If a diagram has been written on but the correct response is within the answer space, the work within the answer space should be marked. Working on diagrams that contradicts work within the answer space is not to be considered as choice but as working, and is not, therefore, penalised. Work erased or crossed out Erased or crossed out work that is still legible and has not been replaced should be marked. Erased or crossed out work that has been replaced can be ignored. Choice When a choice of answers and/or methods is given and the student has not clearly indicated which answer they want to be marked, mark positively, awarding marks for all of the student’s best attempts. Withhold marks for final accuracy and conclusions if there are conflicting complete answers or when an incorrect solution (or part thereof) is referred to in the final answer. 4
