Specification Clarification

Please see below. My comments are added in blue, the red is which year this relates to, and the black is verbatim from Pearson. My suspicion is that these points are being clarified as the exams have been written, and these have been flagged!

A level Mathematics

Pure Mathematics

Y12 and Y13 Proof: it is a requirement of the criteria that students should be able to tackle proofs in “unfamiliar” cases so there may be questions to address this; however, there is no exhaustive list available (there are examples in textbooks and units tests). The examiners are well aware of the potential difficulty of this for students and will be carefully choosing examples, possibly with a suitable “lead in” if appropriate, so that the question is accessible for the target level. Proof is definitely something they hated in both Y12 and Y13, so this should be reassuring for the pupils. I have a feeling proof will come us, particularly by contradiction, since it’s new.

Y13 Concave and convex functions: examiners will accept either "less than" or "less than or equal to" inequalities or intervals expressed in any standard manner; (3, 8) or [3, 8] are fine too. We discussed and sought clarification on this at the time, but again, good to know they’re sticking by what they said.

Y13 Increasing and decreasing functions: examiners will accept either "greater than or equal to zero" or "greater than zero" for these definitions in the examinations. An increasing function is one where f'(x) > 0 is the one in the SAMs mark scheme but examiners would be instructed to accept either. As above.

Y13 Factor formulae: students would not be asked to integrate functions like sin 5x cos 2x. Students do not need to know factor formulae (even though they are included in the formulae booklet). I had wondered why it was in the formula book, but again, good to know it won’t be in there

Y13 The vector product is not required for Pure Mathematics since, as it says in the specification, it appears in the Further Mathematics specification. Some centres are teaching both units and then, of course, the vector product could be used but the examiners would be aware of this and will be making sure that this “extra knowledge” does not give them an advantage over students who have just covered Core Pure Mathematics 1. I think this is a non-issue, to be honest. As with the old course, Further Mathematicians are free to use this content in normal maths.

Y13 Parametric equations: students will be expected to integrate where curves are defined parametrically - you can find details here. Not an issue, our textbooks had the extra content which was emailed about and should have been covered at the time.

Mechanics

Y12 and Y13 Significant figures: the rubric on the examination papers says that "unless otherwise stated, whenever a value of g is required, take g = 9.8 m s–2 and give your answer to either 2 significant figures or 3 significant figures." However, examiners penalise more than 3 significant figures (only once in any given question). Please emphasise this to students, it would be such a stupid reason to lose marks.

Y13 Hinges: questions on hinges are expected as a simple application of the ideas of resolving and taking moments. The online version of the ActiveLearn student book has been revised to include a couple of questions, but I believe the teacher book hasn't been as yet . (You can find examples of hinge questions in the legacy M2 papers which can be found on the maths emporium.) I can’t see any evidence of these extra questions. The challenge question in the textbook for the Ch7 Mixed Ex on p158 was a hinge Q anyway. Please see attached for three examples that I’ve found from the old M2 books, for which I have completed a model solution. I will also run a PD session on this on Sunday lunchtime in F4, as our next departmental meeting is not for nearly a month and will be too late.

Statistics

Y13 The criteria states that students should be able to use their calculators to find probabilities from a normal distribution but does not state that they should also be able to "work backwards" to find a z-value. Calculators which have the facility to find probabilities can also do the reverse calculation, but we have included the normal tables in case they are needed (perhaps by students who don't know how to use the calculator). The textbook uses the tables, though, of course, using a calculator is perfectly acceptable as well. This to me seems to be covering their back for the fact that they haven’t amended examples or solution banks to reflect the improved calculators. Z values only really need to be found when you have an unknown s.dev and/or mean, but if you’ve used Dr Frost, you will have taught it like this anyway.

Y13 p-values are mentioned in section 5.1 of the A Level specification and also crop up in AS. They are the probability associated with a hypothesis test and many calculators will give them automatically.

If p-values are required in connection with testing a correlation coefficient, then they would have to be given in the question. However, since students are expected to be able to calculate probabilities connected with a binomial distribution or a normal distribution, then in effect they could be asked to calculate these.

For example, using a binomial distribution to test H0: p = 0.32 vs H1: p > 0.32 with an observed value of 11 and a sample of 22 using a 5% significance level we would expect students to use the model X ~B(22, 0.32) and calculate P(X > 11) = 0.06026. This is the p-value which students would compare with 0.05 and conclude that the test was not significant or there is insufficient evidence to reject H0. The specification would allow us to ask the candidates for the p-value in this case too (AS paragraph 5.1)

This is further clarification on the issue we raised with Pearson at the time. We should hopefully have delivered the extra content at the time (also reattached).

Y12 and Y13 Large data set: students will not be expected to know conversion units such as knots to mph. They will be expected to know what units the various variables are measured in, rough positions of the locations (for example Camborne is near the coast, Heathrow is not) and of course where the international locations are. Students should also be familiar with the notation tr, n/a etc. There is no definitive list of things they should know; the criteria is merely that students should be “familiar” with the large data set. We should aim to complete a whole lesson on the large data set alone, here is the link to all of the large data set resources N:\MATHS\Key Stage 5\19. Large Data Set. The OUP ones are particularly good, but you won’t be able to do them all in the time that we have.

A level Further Mathematics

Core Pure Mathematics

Y12 and Y13 Proof by induction is part of the prescribed DfE content. Criteria did not intend that the list in the specification be exhaustive but the intention is that candidates be able to use the method of proof by induction and apply it to construct proofs (rather than 'rote learn' a few types of proofs).

Y12 and Y13 Recurrence relations: We have had a number of queries about question 6 in the Core Pure Maths 1 mock paper and in particular whether or not questions involving recurrence relationships would be included in the examination. The chief examiner has responded that the list in the specification is not exhaustive and so such questions may be set. The question on the mock paper is there specifically to illustrate the type of question that might occur (there are plenty of examples in past FP1 papers which are available on the emporium). Alex, recurrence relations seemed to have been taken out of the textbook for proof by induction, yet one appeared in the mock. We definitely need to go through an example or two with the kids.

Y12 and Y13 Vector equation of the line of intersection of two planes: part (d) of question 7 on the Core Pure Maths 1 mock paper was set as problem-solving question as required by the assessment objectives for the new A levels, but does not require any knowledge beyond the specification. Candidates could have been asked to find two points common to the planes and hence find a vector equation of the line (though this would not have been problem solving, since examiners would be telling students how to do it). Examiners wanted to include this type of question on the mock examination to further exemplify problem-solving questions.

Further Statistics

Y13 The use of the Central Limit Theorem does not expect the use of a continuity correction.

Decision Mathematics

Y13 There are two methods in common usage for completing Floyd’s algorithm. Examiners are aware that most resources show only one of these methods and not all resources follow the same method. An example can be found on the emporium here that illustrates the difference between the two methods. In exam questions either method will be accepted as follows:

• when students are asked to complete the algorithm in full, they can use either method

• when we give a partially completed version of the algorithm and students have to finish it, we will ensure that the part we complete is the same using either method and therefore that students can continue with it using either method.