A-Level MathematicsYear 2018Q1
Mark scheme notes Underlying principle The mark scheme will clearly indicate the concept that is being rewarded, backed up by examples. It is not a set of model answers. 1. Mark scheme format 1.1 You will not see ‘wtte’ (words to that effect). Alternative correct wording should be credited in every answer unless the MS has specified specific words that must be present. Such words will be indicated by underlining e.g. ‘resonance’ 1.2 Bold lower case will be used for emphasis e.g. ‘and’ when two pieces of information are needed for 1 mark. 1.3 Round brackets ( ) indicate words that are not essential e.g. “(hence) distance is increased”. 1.4 Square brackets [ ] indicate advice to examiners or examples e.g. [Do not accept gravity] [ecf]. 2. Unit error penalties 2.1 A separate mark is not usually given for a unit but a missing or incorrect unit will normally mean that the final calculation mark will not be awarded. 2.2 This does not apply in ‘show that’ questions or in any other question where the units to be used have been given, for example in a spreadsheet. 2.3 The mark will not be awarded for the same missing or incorrect unit only once within one clip in epen. 2.4 Occasionally, it may be decided not to insist on a unit e.g the candidate may be calculating the gradient of a graph, resulting in a unit that is not one that should be known and is complex. 2.5 The mark scheme will indicate if no unit error is to be applied by means of [no ue]. 3. Significant figures 3.1 Use of too many significant figures in the theory questions will not be prevent a mark being awarded if the answer given rounds to the answer in the MS. 3.2 Too few significant figures will mean that the final mark cannot be awarded in ‘show that’ questions where one more significant figure than the value in the question is needed for the candidate to demonstrate the validity of the given answer. 3.3 The use of one significant figure might be inappropriate in the context of the question e.g. reading a value off a graph. If this is the case, there will be a clear indication in the MS. 3.4 The use of g = 10 m s-2 or 10 N kg-1 instead of 9.81 m s-2 or 9.81 N kg-1 will mean that one mark will not be awarded. (but not more than once per clip). Accept 9.8 m s-2 or 9.8 N kg-1 3.5 In questions assessing practical skills, a specific number of significant figures will be required e.g. determining a constant from the gradient of a graph or in uncertainty calculations. The MS will clearly identify the number of significant figures required. 4. Calculations 4.1 Bald (i.e. no working shown) correct answers score full marks unless in a ‘show that’ question. 4.2 If a ‘show that’ question is worth 2 marks. then both marks will be available for a reverse working; if it is worth 3 marks then only 2 will be available. 4.3 use of the formula means that the candidate demonstrates substitution of physically correct values, although there may be conversion errors e.g. power of 10 error. 4.4 recall of the correct formula will be awarded when the formula is seen or implied by substitution. 4.5 The mark scheme will show a correctly worked answer for illustration only. 5. Quality of Written Communication 5.1 Indicated by QoWC in mark scheme. QWC – Work must be clear and organised in a logical manner using technical wording where appropriate. 5.2 Usually it is part of a max mark, the final mark not being awarded unless the QoWC condition has been satisfied. 6. Graphs 6.1 A mark given for axes requires both axes to be labelled with quantities and units, and drawn the correct way round. 6.2 Sometimes a separate mark will be given for units or for each axis if the units are complex. This will be indicated on the mark scheme. 6.3 A mark given for choosing a scale requires that the chosen scale allows all points to be plotted, spreads plotted points over more than half of each axis and is not an awkward scale e.g. multiples of 3, 7 etc. 6.4 Points should be plotted to within 1 mm. Check the two points furthest from the best line. If both OK award mark. If either is 2 mm out do not award mark. If both are 1 mm out do not award mark. If either is 1 mm out then check another two and award mark if both of these OK, otherwise no mark. For a line mark there must be a thin continuous line which is the best-fit line for the candidate’s results. Question Number Answer Ma rk 1 C ࡲ ൗ ∆࢞࢞ ൗ (stress/strain) 1 Incorrect Answers: A incorrect arrangement B incorrect arrangement D incorrect arrangement for strain 2 C ࢚ൌ ૢൈ 1 Incorrect Answers: A -no factor of 2 B - no factor of 2 and incorrect equation D - incorrect equation 3 D – Two points ࣅ apart oscillate with the same amplitude 1 Incorrect Answers: A – Points on a wave do not all oscillate in phase B – A node is formed from destructive interference C – Stationary waves may also be formed from longitudinal waves 4 A – amount of energy of a photon needed to release an electron 1 Incorrect Answers: B- an electron does not release a photon C – reference to frequency incorrect D - reference to frequency incorrect and electron does not release a photon 5 B – decreasing the speed of the electrons in the beam 1 Incorrect Answers: A – the number of electrons does not affect the angle C - the number of electrons does not affect the angle D – increasing the speed would decrease the distance between the rings 6 C - ࣊ ( ൈ࣊ሻ 1 Incorrect Answers: A – the waves would be in antiphase B – the waves would be a quarter of a wave out of phase D – the waves would be a 20th of a wave out of phase 7 B - ࢜ൌࢌ 1 Incorrect Answers: A – wavelength is 2l C - wavelength is 2l D - wavelength is 2l 8 C - µൌ ܚ܉܌ܑ܍ܖܜ 1 Incorrect Answers: A – incorrect use of ݒൌට ் ஜ B – incorrect use of ݒൌට ் ஜ D - incorrect use of ݒൌට ் ஜ (Total for Multiple Choice Questions = 8 marks) Question Number Acceptable Answers Additional guidance Mark 9 This question assesses a student’s ability to show a coherent and logically structured answer with linkages and fully-sustained reasoning. Marks are awarded for indicative content and for how the answer is structured and shows lines of reasoning. Indicative Content Band does not obey Hooke’s law Or there is a non-linear relationship between force and extension (The band is elastic so) the extension returns to zero when the force is removed or size/shape is unchanged For a given force the extension when loading is less than when unloading or for the same extension more force required when loading Area under the loading curve is greater than the unloading curve Or Loading increases the elastic strain energy (of the band) The band absorbs more energy when being loaded than it releases when unloaded Or Unloading: some strain energy transferred by heating Energy released by heating represented by the area between the lines (1) (1) (1) (1) (1) (1) The following table shows how the marks should be awarded for structure and lines of reasoning Number of marks awarded for structure of answer and sustained line of reasoning Answer shows a coherent and logical structure with linkages and fully sustained lines of reasoning demonstrated throughout 2 Answer is partially structured with some linkages and lines of reasoning 1 Answer has no linkages between points and is unstructured 0 6 Total for question 9 6 Question Number Acceptable Answers Additional guidance Mark 10(a) Use of ∆ܧൌ ଵ ଶܨ∆ݔ 4.6 J (1) (1) Example of Calculation ∆ܧൌ ଵ ଶൈ29 N ൈ0.32 m ൌ4.6 J 2 10(b) Use of ܨൌ݇∆ݔ 0.30 m (1) (1) Example of Calculation 29 N 0.32 m ൌ27 N ∆ݔ ∆ݔൌ0.30 m 2 Total for question 10 4 Question Number Acceptable Answers Additional Guidance Mark 11(a) Max 2 Use large angles of incidence or use a wide range of angles Use narrowest possible ray Repeat and calculate mean Work in a dark room. Use monochromatic light (2) 2 11(b)(i) Either Resolution of protractor 1° Recognises that the results are recorded to the same precision as the resolution of the protractor Or Resolution of protractor 0.5° Recognises that the results are not recorded to the same precision as the resolution of the protractor (1) (1) (1) (1) MP2 dependent on MP1 2 11(b)(ii) Use of percentage uncertainty equation with 0.5° as the resolution percentage uncertainty = 2% (1) (1) Example of calculation 0.5 29 ൈ100% ൌ1.72% 2 11(c)(i) Appropriate line of best fit (1) 1 11(c)(ii) Calculates a gradient using at least half the drawn line ηൌ1.37 to 1.47 leading to a conclusion that glass is silica Or conclusion consistent with their value for η (1) (1) (1) Example of calculation .ଽି.ହ .ହ଼ = 1.47 silica 3 Total for question 11 10 Question Number Acceptable Answers Additional Guidance Mark 12 (a) Electrons exist in discrete energy levels (After the mercury atom is excited) electrons move back to a lower energy level Or (After the mercury atom is excited) electrons move back down from a higher energy level Photons are emitted Frequency of emitted radiation / photons depends on the difference in energy between the energy levels Or reference to ∆ܧൌ݄݂ Since there are only certain energy changes possible, only certain frequencies are possible (1) (1) (1) (1) (1) Accept excited state for higher energy level Accept ground state for lower energy state 5 12 (b) Use of ܧൌ ଵ ଶ݉ݒଶ Use of ܧൌ݄݂ and ܿൌ݂ߣ λൌሺ2.4 െ2.5ሻൈ10ିሺm) leading to a conclusion that radiation is ultraviolet Or conclusion consistent with their value for wavelength (1) (1) (1) (1) ∆ܧൌଵ ଶൈଽ.ଵଵൈଵషయభ ୩ൈሺሺ2.5 ൈ10m sିଵሻଶെሺ2.1 ൈ10m sିଵሻଶሻ ߣൌ6.63 ൈ10ିଷସJ s ൈ3 ൈ10଼ m sିଵ 8.4 ൈ10ିଵଽ J MP4 dependent on MP2 Example of Calculation ∆ܧൌ8.4 ൈ10ିଵଽ (J) ߣൌ2.4 ൈ10ିሺm) 4 Total for question 12 9 Question Number Acceptable Answers Additional guidance Mark 13 (a) Line/surface joining points on a wave that are in phase (1) 1 13(b)(i) Do not stare into laser (1) 1 13 (b)(ii) Lack of other evidence (supporting wave theory) Or Was yet to be reproduced Or There was support / evidence for the particle model (1) 1 13(c)(i) An explanation that makes reference to the following: Path lengths (A-O and B-O) are equal Or Path difference is zero Will arrive in phase Or phase difference is zero (Bright line is position of) constructive interference/superposition (1) (1) (1) 3 13(c)(ii) 600 nm Or 600 × 10-9 m Or 6.0 × 10-7 m Or one wavelength Or λ (1) Do not accept (nλ) Accept any correct equivalent value 1 Total for question 13 7 Additional guidance Mark 14(a)(i) One ray correctly drawn Second ray correctly drawn Completes diagram with image at position 3.6 to 3.8 cm and height of 0.7 to 0.8 cm (1) (1) (1) 3 14(a)(ii) Use of ݉ൌ ௩ ௨ or ݉ൌ ௧ ௧௧ using values from (a)(i) Magnification of 0.47 to 0.53 (1) (1) Example of Calculation ݉ൌ ௩ ௨ ൌ ଷ. .ହൌ0.5 2 14(a)(iii) Real and image on different side of converging lens to object Or rays pass through the image (1) 1 14(b)(i) Focus image of distant/far object on to a screen Measure distance from lens to screen Or Use parallel rays of light Measure distance from lens to the point where the rays converge (1) (1) (1) (1) MP2 dependent on MP1 2 14(b)(ii) Greater refraction To converge (parallel) rays at a point closer to the lens (1) (1) 2 14(b)(iii) Photograph 2 has a greater magnification so v is greater since u is constant So f is greater Hence photograph 2 taken with lens of focal length 200 mm (1) (1) (1) (1) (1) MP5 dependent on MP2 and MP4 5 Total for question 14 15 Question Number Acceptable Answers Additional guidance Mark 15(a) (High intensity of light means) photons strike the photocell at a greater rate One to one interaction between photons and electrons So Electrons released at a greater rate So greater current/charge/power in external circuit (1) (1) (1) (1) 4 15(b) Use of ܫൌ Use of ܲൌ ா ௧ Multiply by 23% 1700 MJ (1) (1) (1) (1) Example of Calculation ܧൌ1300 Wmିଶൈ200 mଶൈሺ8 ൈ60 ൈ60 s ൈ0.23ሻ ܧൌ1700 MJ 4 15(c) Use of ܧൌܲݐ 430 MJ (1) (1) Example of Calculation ܧൌ4 ൈ7500 W ൈሺ4 ൈ60 ൈ60ሻs ܧൌ432 MJ 2 15(d) Use of ܧൌ݉݃∆݄ ܧൌ1.1 ൈ10଼ J (1) (1) Example of Calculation ܧൌ݉݃∆݄ൌ1600 ݇݃ൈ9.81݉ݏିଵൈሺ8500 െ1500ሻ݉ ܧൌ1.1 ൈ10଼ J 2 15(e) Drag increases as speed increases Or Drag increases as density of air increases Requiring a greater forward force So motors require more energy/power so plane should fly at a reduced speed (1) (1) (1) Accept air resistance for drag 3 15(f) Max 1 Develops new technologies Develops alternative energy sources Raises public awareness Secures funding for other projects (1) 1 Total for question 15 16 Question Number Acceptable Answers Additional guidance Mark 16(a) Recognises that F=0 Or Uses D = U – W Use of W = mg with m = 5.2 g Use of U = weight of air displaced by balloon Or U = ସ ଷߩߨݎଷ݃ Or U = ߩܸ݃ and ܸൌ ସ ଷߨݎଷ Or U = mg and ߩൌ and ܸൌ ସ ଷߨݎଷ 0.034 N (1) (1) (1) (1) Example of calculation ܦൌሺర యగൈሺ.ଵଶ ୫ሻ య ൈ ଵ.ଶ ୩ ୫షయ ൈ 9.81 m sିଶ) – ((4+1.2) kg ൈ 9.81 m sିଶሻ ൌ0.034 N 4 16(b) Viscosity of air increases as temperature increases Or Density of air is lower so upthrust is smaller (1) (1) 1 Total for question 16 5 Pearson Education Limited. 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Paper Source:Markscheme-ASPaper2-June2018.pdf
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Exam Specification Info
This question is part of the UK A-Level Mathematics syllabus. In the actual exam, structured questions typically require linking specific keywords to gain full marks. Applaa helps you drill these topics.
Syllabus levelAdvanced Level (A-Level)
SubjectMathematics
Official MarksVariable (2–6 marks)