GCE Mathematics Support Event Thursday 8th November 2018 Stormont Sports Pavilion Thursday 15th November 2018 Glenavon Hotel

AGENDA 0930 – 1000 Registration 1000– 1015 Introduction from Subject Officer 1015 – 1130 Reports on C1, C2, C3, C4 1130 – 1215 Reports on S1, M1 (M2) 1215 – 1230 Plenary/Questions 1230 – 1300 Lunch 1300 – 1315 Introduction to GCE Further Mathematics 1315 – 1500 Reports on (M2), F1, F2, F3, S4, M3, M4 1500 – 1530 Plenary/Questions

CCEA website

GCE Mathematics Current specification will be assessed for the last time in 2019 (mop up resits A2 only 2020) The current AS units (C1 & C2) will still be available in 2018 for one year (resits unavailable for AS after 2019) GCE A2 in 2019, resits 2020

‘A’ level Mathematics Information Day 2018

C1 and C2 In 2019 the papers for these two modules will only be taken by those resitting. Hence, we will concentrate on the common mistakes made in 2018 and those that have been made in the past.

C1 This is a non calculator paper so answers in fractions or surds are expected. However, candidates need to consider if their answers are sensible or not. It is basically an algebra paper and candidates do not always find algebra easy. Candidates need to be well practiced in algebraic manipulation if they are to do really well. Reading questions carefully and giving the answers in the required form will improve marks. The last couple of questions on the paper are usually the most testing and require careful thought. Here it is very important to read questions very carefully – Q7 & 8. Watching time is important to ensure that all questions are attempted. 1 mark per minute will leave enough time at the end to correct mistakes.

C1 In the transformation questions, Q1, the most common mistake is involving reflections: in x-axis or in y-axis? Some also have problems with the direction to move in a translation or if the shape gets larger or smaller in a stretch. As there is only one transformation involved here, it is usually easy to choose a point, do the transformation to it and see what it has done. Coordinates questions are usually well done as in Q2. However, be careful if normal or tangent equations are being asked for in calculus questions.

C1 Index questions, Q3(b), often cause problems not because the rules are not known but if a power has two terms e.g 1– x, then candidates fail to put brackets around this power before they, for example, have to take it to a top line or multiply it by a number. The poor use of brackets can lead to the loss of too many marks in many places. Indices are often needed in the calculus questions so care needs to be taken here as well.

C1  

Item Level Data C1 C1 Pure Summer 2018 Question % lowest % highest Mark Mean mark Total 1 (i) 3.57 95.09 2.00 1.92 4,199 1 (ii) 10.67 87.16 1.76 1 (iii) 2.17 88.95 1.87 2 (i) 1.26 93.95 1.93 2 (ii) 0.64 93.83 2 (iii) 11.29 65.23 3.00 2.28 3 (a) 1.24 85.45 6.00 5.64 3 (b) 4.45 60.90 4.75 4 (i) 1.29 84.57 5.55 4 (ii) 24.10 34.77 1.78 5 (a) 0.88 79.07 2.75 5 (b) 0.69 66.37 7.00 6.04 6 (i) 1.48 83.50 1.82 6 (ii) 3.29 85.31 2.76 6 (iii) 4.72 64.35 5.11 7 (i) 8.72 75.21 4.00 7 (ii) 9.48 4.41 5.00 3.02 8 (a) 13.88 1.50 1.81 8 (b) 13.81 14.12 2.79

C2 Again, algebraic manipulation is often poor and candidates lose marks not for their lack of knowledge of a topic but because of poor algebra. Trigonometry is introduced in C2 and candidates need to read ranges carefully so that all answers are given and are in the required format. C2 lends itself very nicely to the testing of proofs and unless a proof is explicitly excluded then it may be asked, usually as a lead in to a question.

C2 Topic 1 is circles. The lack of knowledge of the 3 circle properties listed can prevent a candidate from starting a question. The 2018 question, Q2, was only testing the circle equation. In the trapezium rule, Q1, candidates need to be working to more than 3 sig. figs. so that the answer is correct. The rule is in the formulae booklet so there is no reason for them to misquote it.

C2  

Item Level Data C2 C2 Pure Summer 2018 Question % lowest % highest Mark Mean mark Total 1 4.49 55.95 6.00 4.74 4,365 2 (i) 4.51 76.72 4.00 3.49 2 (ii) 8.50 60.09 3.04 3 (a) 0.87 77.04 5.00 4.66 3 (b) 3.78 58.10 4 (i) 8.64 86.09 3.00 2.68 4 (ii) 7.79 37.64 4.54 5 (i) 2.54 80.27 3.60 5 (ii) 13.79 62.68 2.87 6 (i) 12.03 80.76 3.32 6 (ii) 10.03 50.61 4.52 7 (i) 12.85 66.58 2.24 7 (ii) 28.64 15.65 2.07 8 (a) 5.50 31.52 8.00 4.69 8 (b) 32.39 20.32 7.00 2.75

M1 2018

General comments on paper Paper allowed candidates to display their knowledge Level of difficulty of questions increased as paper progressed Within questions, parts became more difficult Some had difficulty with diagrams Still some untidy work which often led to errors in later working Need to read question carefully e.g Q3 (iii), Q4 (ii), Q5, Q7

General comments on diagrams Arrows should be included on forces to indicate their direction Reactions were sometimes placed in wrong places e.g Q3 and Q6 Weight should be marked as a vertical force on the diagram. It is fine to use components on the diagram but if they are incorrect then full marks for the diagram cannot be awarded. Both vertical weight and the components of weight may be on diagram {preferably components marked as dotted lines}

Q1 Impulse and momentum Less than half of the candidates gained full marks Lack of understanding that these are vector quantities Need to start with a positive direction and keep using it Common error not to know change of direction means change of sign on velocity In (ii) when a negative t value was found, often the negative disappeared rather than looking at the basic setup

Q2 Equations of motion, motion on plane, friction Generally well done. (i) very well done, (ii) well done and (iii) less well done - (ii) diagram – common errors No arrows on forces to show direction Vertical weight not marked but incorrect components of weight Some took R and μR to be vertical and horizontal - (iii) Method marks awarded to those who mixed up cos and sin components

Q3 Moments of parallel forces Only about 60% gained full marks on this question (i) Some had weight at pivot (i) Some had no reaction at pivot but had reactions at ends (ii) Most knew and could apply Principle of Moments to their situation (iii) Some did not give assumption about plank; gave assumptions related to people or pivot. Most correct answers were that the plank was rigid or did not bend. Few said plank was modelled as a rod.

Q4 Connected Particles First 3 parts very well done (iv) less well done with about 25% with correct answer In (ii), some gave answer 1.96 instead of g/5 as required In (iii) some used their wrong answer rather than the given correct one In (iv), only best about [25%] understood the setup. Many used acceleration = g and did not know how to use the 0.4 correctly

Q5 Variable acceleration Less than 50% correctly answered (i) and (ii) Some used equations of motion instead of calculus In (i), many integrated correctly but forgot about + c Some found c but not initial displacement In (ii) some did not understand v = 0 meant change of direction In (ii) some did not see how to combine the various displacements (iii) Very well done with over 80% getting full marks

Q6 Further Moments (i) Correct assumption usually given (ii) Around 35% got this correct Many had only vertical reaction at hinge Many had extra reaction at midpoint Some did not have vertical weight and used incorrect weight components (iii) Less than 50% were able to get the correct moments equation (iv) Only very best [< 20%] had 2 components of reaction which they combined correctly

Q7 Equations of motion (i) v – t graphs were well done but need to label axes (ii) Testing question – only very best [< 10%] with correct answer Some used v – t graphs; some used equations of motion Equations of motion were a generally more successful approach Clear work showing attempt to equate equations of motion for each person gained method marks Key was knowing how to deal with the 14.5m and the 9m travelled by Alan in first 0.5 seconds

Item level Data M1 M1 Mechanics Summer 2018 Question % lowest % highest Mark Mean mark Total 1 (i) 3.36 50.33 3.00 2.39 3,362 1 (ii) 13.62 39.29 2.00 1.26 2 (i) 3.81 89.56 2.79 2 (ii) 4.19 82.57 1.78 2 (iii) 1.96 64.60 6.00 4.96 3 (i) 10.32 61.12 1.51 3 (ii) 2.74 57.64 4.89 3 (iii) 48.51 51.49 1.00 0.51 4 (i) 1.10 92.62 1.92 4 (ii) 4.31 87.75 5.00 4.59 4 (iii) 5.21 82.66 1.77 4 (iv) 16.75 25.43 4.00 2.14 5 (i) 7.76 41.82 2.85 5 (ii) 22.87 44.29 3.09 5 (iii) 10.74 82.27 2.55 6 (i) 18.38 81.62 0.82 6 (ii) 10.26 35.37 1.25 6 (iii) 23.47 42.06 2.42 6 (iv) 17.73 17.64 2.32 7 (i) 3.54 70.73 2.60 7 (ii) 21.92 4.67 9.00 3.41

S1 2018

General Comments Paper was well attempted in general Questions increased in difficulty through the paper. Within questions, parts became harder Questions 1 – 4 were almost always done very well Questions 5 – 7 required more depth of understanding and were less well answered. Q7 was not well done – just over 25% had correct answer to (iv)

General comments on answers Mathematical notation often poor e.g dx omitted in integration. Very poor use of units in answers Accuracy not good. Answers not given to 3 sig. figs or work rounded too soon Most were able to answer within the allocated spaces with the possible exception of Q7

Q1 Binomial Well answered Few had difficulty with ‘at most’ meaning 0, 1, 2, 3 ‘at least 3’ meaning 3, 4, 5, ……… so 1 – P(0, 1, 2)

Mean and standard deviation  

Q3 Poisson More careful reading of question needed (i) well done (ii) some did not use P o (2 x 3.5) did not use P(X = 6) forgot to use 1 – (iii) not as well done. Some had same assumption stated twice or used number of misprints rather than rate of misprints or some quoted incorrect routine assumptions.

Q4 Discrete probability distribution Well answered apart from (ii) In (ii), many did not know that 1 was not a prime number and/or that 2 is a prime number.

Continuous Probability distribution   Good answers came from students who had understanding

Q6 Normal Distribution Many coped well Often poor notation and/or understanding resulted in loss of marks Some seem not to understand relation between z value and area Some seemed to cope well by learning and applying formulae Some coped well by drawing the diagram and understanding the concept Many who used neither method, just muddled through and lost marks

Q7 Probability Poorly answered Needed insight and understanding Less than 40% had the correct answer in each part Key was to find p but many could not do this Those who used the Venn diagram fared best There were many long untidy and panicked attempts at this

Item level Data S1 S1 Statistics Summer 2018 Question % lowest % highest Mark Mean mark Total 1 (i) 1.92 96.25 3.00 2.92 2,398 1 (ii) 1.42 90.41 2.83 1 (iii) 2.00 88.78 2.80 2 (i) 1.46 79.86 5.00 4.49 2 (ii) 10.01 62.22 1.52 3 (i) 0.88 89.53 4.00 3.78 3 (ii) 4.05 67.76 4.08 3 (iii) 9.30 64.76 1.55 4 (i) 0.13 99.46 1.99 4 (ii) 26.81 69.60 1.43 4 (iii) 1.25 95.83 1.95 4 (iv) 1.33 90.78 3.83 5 (i) 43.66 49.21 1.06 5 (ii) 19.43 39.95 2.40 5 (iii) 30.86 40.08 1.09 5 (iv) 46.66 32.19 1.54 6 (i) 1.38 82.36 4.71 6 (ii) 2.54 86.03 3.67 6 (iii) 6.30 66.85 3.19 7 (i) 6.21 38.95 6.00 3.52 7 (ii) 61.55 38.45 1.00 0.38 7 (iii) 39.70 36.07 0.96 7 (iv) 35.36 26.86

C3 & C4  

C3 & C4 Rubric – full development of answers; answers only – 1 mark Timing – 75 marks in 90 minutes. Accuracy – 3 sig. figs. unless stated otherwise; working through questions should be to more than 3 sig. figs. Number of questions – can affect timing Formulae booklet – learn what is where, some not there Read question carefully – answer question asked Cancelled work – will not be marked

C3 & C4 Too many attempts Linked parts – (i) & (ii) are connected and answer from (i) can be used in answering (ii); (a) & (b) are not connected Algebra! Check – that all questions and parts have been answered and that no silly mistakes have been made Trial and improvement – not accepted Check that answers are sensible

C3 Q1(a) was very well answered. A few who split it up forgot 1 ‘side’. Those who drew a diagram were the most successful. The errors seen in (b) were mainly algebraic: an incorrect factorising or an incorrect solution to an equation. Q2 Simpson’s rule requires an odd number of x s. Those candidates who ignored the 0 had forgotten this. The formula is in the booklet. A very small number worked in degrees.

C3  

C3  

C3 Q6(a) A common mistake here was to take the 2 to the numerator when integrating the 3rd term. Some left it there and some brought it back down. Too many scripts were seen where the constant of integration was omitted. Part (b) differentiated well between candidates. Less able candidates failed to recognise that a ln was involved in the integration of the 2nd term. An exact answer was asked for here but candidates did not always give one.

C3   – 1). The left hand side of the graph was often missing as was a label on the asymptote. Candidates need to label the key axes values clearly.

Item level Data C3 C3 Pure Summer 2018 Question % lowest % highest Mark Mean mark Total 1 (a) 0.77 66.75 4.00 3.53 2,475 1 (b) 0.16 95.23 5.00 4.93 2 1.09 72.24 4.40 3 (a)i 0.53 84.48 3.73 3 (a)ii 37.05 62.95 1.00 0.63 3 (b)i 1.94 90.59 3.75 3 (b)ii 22.38 77.62 0.78 4 (i) 15.07 80.20 3.00 2.49 4 (ii) 92.53 3.83 4 (iii) 1.66 88.12 2.81 5 (a) 3.07 91.84 3.77 5 (b) 4.12 57.45 8.00 6.40 6 (a) 0.32 52.97 6 (b) 3.84 43.96 3.52 7 (a) 14.10 77.78 4.01 7 (b) 75.68 4.48 8 (a)i 10.87 69.33 3.13 8 (a)ii 4.20 35.03 2.65 8 (b) 39.56 7.84 0.93

C4 This paper differentiated well between candidates. Questions 7 and 8 differentiated well between the most able. Function notation continues to be done poorly as does implicit differentiation. The answer to Q7(i) was on the paper and many ‘creative’ responses were seen in order to get to this answer.

C4  

C4  

C4 Q6 Markers needed to watch for ‘creative solutions’ in this question as the correct answer would appear after incorrect working. As the answer to (i) was given, candidates, if they picked up this answer and did not proceed with their incorrect answer, usually did quite well in (ii). A number did not evaluate the gradient, they simply substituted the gradient in terms of x and y into a straight line equation.

C4 Q7 As the answer to (i) was on the paper, most candidates gained the 1 mark in (ii). Differential equations are always difficult for less able candidates to solve. They have problems in separating the variables and doing the integration. ‘c’ was seldom omitted which was pleasing. The manipulation of the logs proved too difficult for many.

C4  

Item level Data C4 C4 Pure Summer 2018 Question % lowest % highest Mark Mean mark Total 1 0.97 84.13 5 4.67 2,482 2 (i) 4.43 55.00 3.00 2.37 2 (ii) 20.63 64.75 4.00 2.92 3 (i) 36.70 63.30 1.00 0.63 3 (ii) 4.19 43.76 3.21 3 (iii) 2.82 77.20 3.51 4 (i) 13.30 60.11 2.25 4 (ii) 1.49 81.51 5.00 4.54 1.61 33.28 9.00 6.70 6 (i) 4.51 82.92 7.00 6.28 6 (ii) 67.69 3.37 7 (i) 6.97 30.86 6.87 7 (ii) 10.52 89.48 0.89 8 (a) 7.86 25.54 6.00 2.99 8 (b)i 0.77 91.62 2.00 1.91 8 (b)ii 3.30 26.03 8.00 4.23

M2 This paper was well answered by most. This is an examination paper that is not in booklet form so candidates need to read the questions carefully and answer the question that is asked. They also need to check that they have answered all parts of every question. In questions 3 and 6 candidates were told to take g to be 10. This is simply to make the calculations easier. However, if they used 9.8 they were not penalised. Using 10 is not acceptable in the other questions.

M2 Q1 Candidates answered this question very well. However, some lost marks by failing to find the speed in (i) and/or failing to give an exact answer in (ii). In (ii) candidates needed to show, either on a diagram or in words, where the angle was. Candidates could have lost 4 easy marks when answering this question.

M2 In Q2, parts (ii) and (iii), too many candidates did not use the methods that they were asked to use, energy in (ii) and work-energy in (iii). Too many candidates seemed unsure of what the work-energy equation was. They had the correct terms but not on the correct side of the equation. (Signs on the terms were wrong). When answering (iii) a fair number gave the resistive force as their answer.

M2 Q3 was well answered. Some candidates forgot to change the direction of the resistive force when answering (iii). Q4 It is amazing that, if an answer is on the question paper then no matter how wrong the working is, the correct answer will appear. The majority did derive the equation correctly. However, the separation of the variables was not always well done with the kv2 and the g being split up. The – 1/2k was sometimes left out of the term.

M2 Q5 The trick to these questions is, as you know, to resolve vertically and horizontally. Those who did this scored well. Those who resolved along the plane and at right angles to it usually forgot to think about the acceleration towards the centre. Q6 These are the questions that require a candidate to get the set-up clear in their mind before they start. If they then make two lists, in this case for B and for C, based on this set-up they usually are successful in answering the question. If they do not understand the set-up then few marks can be gained. A number of candidates used vectors, usually with great success. Using 10 here did made the work simpler.

F1 2018

General Comments Paper was accessible Allowed candidates to demonstrate their knowledge Poor presentation was a problem Work was cramped and/or untidy Work cancelled before replacement was in place Poor transfer from one line to the next Diagrams not clearly labelled e.g see Q3 and Q5 Need to read questions carefully

Q1 Eigenvectors and Eigenvalues Well answered In (iii) some did not write down both equations from the matrix expansion Read carefully to know when unit eigenvector is requested

Q2 Group theory (i) Well done (ii) Not well answered Some included reflections Some drew diagrams but did not define the symmetries in words (iii) Well done by those who had (ii) correct In (iv), some did not give the isomorphism clearly In (v), explanations were of a variable quality

Q3 Circle (i) and (ii) were standard questions and were well answered (iii) Those who drew a clear diagram did well since symmetry was indicated on the diagram If a poor or no diagram, algebraic methods were tried and were long, complicated and error prone

Q4 (a) Transformations (i) usually well answered but ……. In (ii) some multiplied the matrices together in the wrong order Some solved the simultaneous equations by substitution when elimination would have been shorter and easier Some candidates assumed all points on the line were invariant

Q4(b) Poorly answered in general Need to remember rotation description needs direction and centre of rotation Of those who recognised rotation, many got the wrong angle (ii) Mixed response Some considered combinations of rotations Some multiplied A by itself until the correct answer appeared

Q5 Complex numbers (a) (i) Routine question but there were many errors in the denominator (b) (i) and (ii) usually well done Poorly labelled diagrams with radius unclear and/or direction of line not marked, caused loss of marks (iii) a clear diagram in (ii) usually led to an easy solution here Use of algebraic methods usually meant question was not completed

Q6 (a) Matrices and equations (a) (i) well done (ii) Some thought these matrices could not be multiplied Most understood what the commutative law meant

Q6(b) Matrices and systems of equations (i) Generally well answered A few did not seem to know that determinant was not equal to zero (ii) Solving these simultaneous equations caused problems. Many did not see that with already one equation in 2 unknowns, only one other equation was needed (iii) Well done

F2 2108

General Comments Candidates performed well Most marks were evenly spaced in range 40 – 75 25 candidates scored 70+ raw marks Algebra was generally pleasing Presentation generally good Only Q5(ii) and Q7(i) caused difficulty across most centres

Q1 General solution of a trig equation Some solved by Double Angle formula as intended Some used sin(A – B) A few missed one solution

Q2 Series Summation (i) and (ii) very well done (iii) sometimes correct answer by a variety of deductions

Q3 Partial Fractions Very well done

Q4 Maclaurin Expansion  

Q5 Ellipse (i) Many did not pick up gradient of tangent from its given equation (ii) the concept of locus seems to be beyond many candidates Some could not correctly write down the correct midpoint

Q6 Proof by Induction Most made a good attempt at this question Most know the correct structure of the proof method Algebra sometimes was not up to standard to complete the question Some took initial value as n = 1 rather than n = 0

Q7 Complex Numbers Parts (ii), (iii) and (iv) used a familiar technique and were well done Answers to (i) were generally not good. Only a few candidates were able to answer this correctly.

Q8 2nd order differential questions (i) (a) Most could start this and wrote down the correct Auxilliary equation but were then unable to correctly solve this and so stopped. In (b) many were unable to do this correctly; possibly (a) put them off (ii) was well answered Some centres used the Particular Integral as y = ax2 + c rather than y = ax2 + bx + c This made the algebra more difficult.

F3 The syllabus for this module is challenging but candidates taking the paper are able and had been well prepared. Algebraic manipulation often causes problems for even these very good students. The algebra on this paper was not as complicated as in previous years but too many mistakes were still made. Questions 5(i) and 8(ii) proved to be the most difficult with many failing to recognise that they had to use R sin(θ + α) in Q6.

F3 Q1 Most candidates used the scalar triple product accurately. Q2 Candidates should have explained why the negative root disappeared in part (i) not just ignored it. Q3 Here a minority of candidates used the vector triple product and then found a common point rather than the solution in the mark scheme. Overall a well answered question.

F3 Q4 The only problem in this question was in tidying the algebra to get the answer on the paper. Q5 (i) The least well done question on the paper. Candidates needed to know to split the tann x into tan2 x and tann - 2 x as nothing else would lead to the correct solution. The only problem in (ii) was an inability to find and evaluate I1 = ln Isec xI.

F3  

M3 2018

General comments Paper was very well done Most gained very good marks and there were very few weak responses Candidates were able to gain marks from almost every question Candidates need to read questions carefully e.g Q 3, 4, 5 Most testing question parts were Q2(ii), Q3 and Q6(iii)

Q1 Centre of Mass Well done by most Some could not find position of centre of mass of the triangle

Q2 Simple Harmonic Motion (i) well done by most It was surprising to see some candidates work from the given position and not state the tension in BQ = 0 Strange to see errors made in working and yet the final 2 lines were written down correctly This question could also have been done using energy methods

Q3 Relative velocity Well done by those using velocity diagrams Those using i, j vector method usually struggled Need to read questions carefully and give answers in form requested In (i) some did not give the bearing In (ii) some gave time taken and not the actual time Using sine or cosine rule, most were able to solve the triangle but did not always remember that the ambiguous case gave 2 possible solutions Usually if (i) was well answered, so too was (ii)

Q4 Centre of Mass of system of particles Most knew the method well But many slipped up finding distances from the axes Again, need to read questions carefully In (ii), many found length of GM but did not continue to find AG

Q5 Vectors and Work-energy (i) well done (ii) some used F2 only instead of F1 + F2. Need to read carefully

Q6 Work energy (i) and (ii) were well done (iii) Those who chose Q as zero level often had problems Some omitted Work Done against friction Some used Work Done by friction

M4 2018

General Comments Questions well answered by most candidates Almost half of candidates scored 60 or more raw marks Paper was very accessible so most candidates were able to gain some marks from each question Solution of inequalities posed a problem for many Q3(i), Q6, (i), (iii) Most simply solved as an equation and assumed the inequality as required

Q1 Frameworks Well done Two main methods seen assuming all forces were tensions trying to decide direction for each force on diagram Those taking all as tensions were more successful In (iii), some did a lot of unnecessary work by not having a strategy for their solution

Q2 Centre of mass Integration usually done well Notation often poor in the integration In (iii), there seemed to be some lack of understanding since some used the coordinates of the centre of mass rather than distances from the axes

Q3 Motion in a Vertical Circle (i) Well done in general (ii) Some had problems including the T and then setting T = 0

Q4 Dimensions Some used units and not dimensions Quite a few candidates verified the given formula rather than showing the formula was of the form given

Q5 System of forces, couples Question well done For some, marking dimensions and distances on the same diagram caused some confusion

Q6 Elastic collisions Main problem was dealing with the changes of direction Also difficulty dealing with the inequalities Two ways tried Some kept one direction as positive for all collisions Some tried to decide what the directions would be each time Those who kept one direction as positive usually fared better (iii) This needed a lot of thought and understanding to get the correct range

S4 The examiner for this module commented on how well prepared candidates had been for this paper. He commented on the excellent teaching and learning and how confidently candidates had tackled the questions. However, candidates did not always work to the required accuracy nor set their work out in a logical way. This can lead to marks being lost.

S4 Q1 was extremely well answered. Q2 Here a small number of candidates ran into difficulty when finding the summary statistics. They did not seem comfortable with using a calculator in two-variable statistics mode. Q3 posed no difficulty for candidates. Q4 This was a 2 tail test. Candidates need to read the wording of the question carefully to see if a 1 tail or 2 tail test is required. It is usual in a paired t-test to take the initial value from the final value to find the change. Here, as it was a 2 tail test, it did not matter. If it had been a 1 tail test, it would have.

S4 Q5 The best answered question on the paper. A few did have difficulty when combining variances. Q6 There was an improvement in the quality of the answers to this question. In the conclusion, candidates should have ‘we do not reject the Null Hypothesis’ rather than ’we accept the Null Hypothesis’.

S4 Q7 Some candidates seemed to have been taught two methods of answering this question. A number mixed up the two methods and so failed to gain full marks. Q8 Candidates do not appear to like questions of this type. They need to read the question very carefully to see exactly what is being asked of them. Too many discussed questionnaire design or how to take a random sample. This was disappointing. Most of the best answers were short and to the point. 6 marks would indicate 6 factors.

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ALCAB document

ALCAB document

Use of Calculators JCQ guidelines