**Analysis of Official Marking scheme LCH Project maths Paper 1 2012 .**

Standards in freefall towards the bottom .The reasons for such a generous marking scheme are as follows .

(i)The extra 3,000 students who came up from Ordinary level who were there just for the 25 extra points (98% of those got the 25 extra points) and were not able for the papers.(ii)The exam was an experiment in full blown project maths and the experiment failed!

Note in 2013 there was little or no project maths on the leaving cert papers, is the SEC fighting back?

** **

**Question 1 (algebra) (25 marks) **

(a)Any attempt /any reasonable step 8 marks out of 15 (53%)

**Question 2 Number**

(a) 1 correct shaded region 11 marks out of 15 (73%)

(b)At least one correct (out of 6) 3 marks out of 5 (60%)

**Question 3 Complex numbers**

** **

(a) Any reasonable first step 14 marks out of 20 (70%)

(In pre project maths course 5 marks)

**Question 4 (induction/ series)**

(a)Any reasonable step 5 marks out of 10 50%

b)Any reasonable step 8 marks out of 15 (53%)

**Question 5 (functions /Calculus)**

** **

(a)Any reasonable step 5 marks out of 10 (50%)

(b)Any reasonable step 5 marks out of 15 (33%)

**Question 6**

(a)(i)(ii)(iii) (b)Any reasonable step17 marks out of 25 (68%)

**Question 7 **

(a) Any reasonable step 11 marks out of 15 (73%)

(b)Any reasonable first step 8 marks out of 15 (535)

(c) Any reasonable first step 3 marks out of 5 (60%)

(d) Any reasonable first step 7 marks out of 10 (70%)

(e or f) The two most difficult parts of the question any work of merit 3 marks out of 5 (60%)

In total 32 marks out of 50 (64% ) for “any reasonable first step”

**Question 8**

** **

(a) Any reasonable first step 7 marks out of 10 (70%)

(b) Any reasonable first step 6 marks out of 20. (30%)

(c) Any reasonable first step 3 marks out of 5 (60%)

(d)Any one correct entry (out 7) 3 marks out of 5 (60%)

(e)Correct answer no explanation 3 marks out of 5 (60%)

(f) Any reasonable first step 3 marks out of 5 (60%)

Total marks for any reasonable step 25 out of 50 ,(50%)

**Question 9**

** **

(a)(i)One correct entry 5 marks out of 10 (50%)

(a)(ii)Any correct relevant work 3 marks out of 5 (60%)

(b)(i,ii)Any relevant work 6 marks out of 10 (60%)

(c)(i,ii) Any relevant step 3 marks out of 5 (60%)

(d)Any relevant work 7 marks out of 10 (70%)

(e)(f) Any reasonable step 6 marks out of 10 (50%)

Total marks for” any relevant step” **30 marks out of 50 (60%)**

** **

**47% of the marks were awarded for Low partial credit **

**Analysis of Official Marking scheme LCH P maths Paper 2 2012 .**

**Question 1; Coordinate geometry of the Line**

** **

(a)Incomplete statement of method 9 marks out of 15 (60% )

(b)Any reasonable step 4 marks out of 10 ( 40% )

52% of the marks for any reasonable step!

**Question 2 Coordinate Geometry of the Circle**

(a,b,c,d) Any reasonable first step 15 out of 25 marks (60%)

**Question 3 Coordinate Geometry of Circle .**

** **

Any reasonable first step such as g = f 15 marks out of 25 (60%).

Writing centre as (r,r) 20 out of 25 marks (80%)

**Question 5 Probability/Statistics :**

** **

(a) Some relevant diagram 7 marks out of 20 (35%)

**Question 6 Geometry** :

(a) Any correct step 4 marks out of 10 (40%)

**Question 7 Statistics**

** **

(a(i)(ii)(iii) Incomplete or Partial Statement 11 marks out of 20 (55%)

(d) (i)(ii)(iii) Uses a relevant number 11 marks out of 25 (44%)

(e) One relevant step 7 marks out of 20 (35%)

**Question 8 Robotic Arm**

(a)(i)(ii)(iii) 55 marks out of 75 (73%) for Using Pythagoras and the Cosine Rule twice.

In the pre project maths exam this would have been worth 25 marks.

Note also the “low partial credit for part (a) was 27 marks out of 55 (49%)

**Getting the average mark for these questions for just turning up 47% That is 47 % of the marks for these questions were given for attempts and getting no correct answers.!**

This came from teachers at the meeting on Mon,who taught the relevant levels this year.This is a litany of errors,Typos ,topics no longer on the course being asked.In one case Q8 LH P2 the question as asked had a triangle that cannot be constructed!

**Junior Cert Foundation Level**

**Wording incorrect on Q12(c). The word “flavour” has been repeated. (Typing error on Q14 (b) was corrected prior to exam.)**

**Junior Cert Ordinary Level Paper 1**

- Nothing to note

**Junior Cert Ordinary Level Paper 1 – Pilot Schools**

**The wording of Q3(b) “difference” too vague, should be “monetary difference” or something similar**.The wording of Q4(a) “describe” too vague, what is actually required.- Q 8(b) contains the words eight/ate too many times, this comes across particularly badly when read by a reader. “Question 8b 8 people 8 …”
- Q13(c) The use of the word “got”, poor English.
- Q14 scaffolding may mislead some pupils as they may not be familiar with this particular method.
- More of paper 2 coming up on paper 1 and vice versa.

**Junior Cert Ordinary Level Paper 2 – all schools**

- Q1 and Q2 are very off putting to begin the paper with – suggest gentle marking. The diagrams in Q1 are quite complex and there is too much data in the table in Q2.
- The context provided in Q11 is set in a horizontal plane and yet the question asks about slopes. Asking slopes for the sake of asking rather than it being appropriate to the context.
- Q 9 constructing central symmetry is not on the course – the syllabus only has recognition of symmetry, not construction.

**Junior Cert Higher Level Paper 1**

- Wording on at start of question 6 “the rest of the site” was very confusing. The rest after what? Unable to answer the question if can’t understand this.
- Q3(b) contains unknowns on both sides of the inequality, syllabus has only a constant on one side. Part (ii) in particular is very “project maths” for an old syllabus question.
- The typing error in Q(c)(ii) was corrected prior to the start of the exam.
- Very long exam
- Q5(b)(ii) too difficult, also only one answer suitable.

**Junior Cert Higher Level Paper 1 – Pilot schools**

- Q1 table odd – difficult start to the exam.
- Q5 how will this be marked – need to be very flexible.
- Q14 is very long and difficult, Q15 is very straight forward. The recommended time doesn’t reflect this, will the balance of marks?

**Junior Cert Higher Level Paper 2**

- Q7(d) students needed to presume that everyone voted in all three of the elections or in none of the elections, but not in just one or two of them.
- Q2 Students need space to construct an unordered stem and leaf plot prior to ordering it. There is too much data here for it not to be presented in order anyhow. A back to back stem and leaf plot should have two keys.
- Q6(c)(i) students who “calculate” rather than “outline” shouldn’t be penalised, even if their calculations are incorrect.

** **

**Leaving Cert Applied**

- Research question 2: the students are asked to round to nearest €1. This produces an answer closer to 40 than 30, but the actual unrounded figure is closer to 30. What then is the answer to 2(b)?
- Generally, the lack of spacing on this paper is very intimidating.

**Leaving Cert Foundation Level Paper 1**

- Q8 Several levels of cross-referencing here to find a “number” that isn’t a “number” and isn’t labelled as a “number” in the table. If the student fails to understand the table then they cannot answer any of part (a). Part (b) used the word “return” to refer to both the outbound and the “return” flight. Students will be confused.
- Q9 If the students were unable to derive the two formulae then they could not answer any part of this question. When deriving formulae they should be encouraged to select their own notation; e.g. r for the number of rails. Instead, they were instructed to use x and y. Why? This is extremely confusing as the student will have to derive the formula (using r’s and p’s probably) and then “translate” it into x’s and y’s.
- Q10(a) the function notation is incorrect. “ ” has been omitted.
- Q1 use of calculator. Students should be able to use the calculator for all relevant operations but cubic roots would not be relevant to the foundation course.
- Q5 the nets of pyramids are not on the syllabus. Likewise, the surface area of a pyramid is not on the syllabus.
- Q6 is split into three parts (a), (b) and (c) each of which appears to be independent. However, students need their answer from (a) to answer (b). There is no “hence or otherwise …” type of statement to indicate this as would be normal in algebra questions.

**Leaving Cert Foundation Level Paper 2**

- Q2 the language of blood types is very off putting. The majority of the population should be R+ not R- as implied in the table.

**Leaving Cert Ordinary Level Paper 1**

- Q2. Trapezoidal rule was expected on paper 2, not paper 1.
- Q6(h) What is the problem with the graph? Is it that 2011 hasn’t been plotted? Or that the data appears to be continuous? Students will not pick up on continuity.

**Leaving Cert Ordinary Level Paper 1 (Project Maths phase 3)**

- Q9 switched between “daily income” and “revenue” – confusing.
**Q5(b) and (c) are not on the OL****syllabus**. Recommend all marks are allocated to part (a). Students could in theory have multiplied out rather than use the product rule but this level of expansion is also outside the syllabus.

**Leaving Cert Ordinary Level Paper 2 (Project Maths phase 1)**

- Q2(b) too wordy.
- Query if Q2(c) is on the syllabus
- Q5(a) is not clear about which dimensions are required. If the students have “only” to write the dimensions it implies that they only have to include the two given in the question. If they were expected to “calculate” the third dimension then this should have been explained in the question.
**Q6A(b) constructions of transformations are not on the syllabus.****Q7 room should have been included for the unordered stem and leaf plot. Students will make loads of silly mistakes simply because they haven’t the space.****Q7(c) is flawed. The inter-quartile range requires the number of data items to divide into quarters neatly, these don’t.**- Q7(d) the word “List” has been used implying that repeated numbers should not be listed twice, but that is not clear in the question.
**Q8 sometimes the students were told “correct to nearest …” and sometimes they were not told. Estimates and exact answers should both be acceptable**.

**Leaving Cert Higher Level Paper 1**

- Only issue will be time.
- Q1(b) students should have been asked to write the polar form first and then plot. Plotting first will mean some students will plot an approximation. This should not be penalised.
**Q4(b) Students not told whether the payments are to be made at the beginning or the end of the month**. Students shouldn’t be penalised for not stating an assumption, or for making an incorrect assumption- Q6(a)(b) too easy
- Q5(g) likely to separate out the A1 students

**Leaving Cert Higher Level Paper 1 (Project Maths phase 3)**

- Q9(a) too basic for HL.
**Only integration was in 6b (integration of Sine) which is not on the course.**

**Leaving Cert Higher Level Paper 2 (Project Maths phase 1)**

- Q9(a) diagram right angle was difficult to see.
**Q8(a) was faulty for two reasons. Firstly the wording is wrong: the ship did not turn through an angle of 124° at all. It turned -56° or 56° in a clockwise direction. Secondly the numbers given are incompatible: 80Sin36 is not equal to 110Sin20. The same question on the Irish language paper did not include the 36° in the diagram, which might have been correct. However, these students were told that their diagram was wrong and they should use the English paper as their guide. Students spent a lot of time on this question trying to figure out where they were going wrong. This didn’t just impact on part (a) but on the whole of question 8 and question 9. We would strongly recommend extremely generous marking on both Q8 and Q9.****Q8 and Q9 were split into 3 parts (a), (b), (c). Students were unclear as to whether or not these parts were connected.**

** **

**Question 1** Statistics : Much more straightforward than 2012 but parts a and b are basically the same thing.

**Question2** robability this was all over the place not difficult dame as q1 2012 P2 but this time you were given the numbers.Most students did not know what a Bernoulli trial was.

**Question 3:**The line .typical old course question most should be happy .

Suggested solutions (a) -1.5,(b)2x-3y-14=0,(c)(-2,-6)

**Question4**:The Circle: Would have suited most people part (c) would have tested weaker students

Suggested solutions(a) x^2+y^2=100,(b) (x-4)^2+(y-3)^2 =25 (c) (8,0)

**Question 5**: Area/Volume Odd question lots of space most should be happy ,part c may challenge some students.

Suggested solutions(a) Lenght of rectangle 62.83mm,(b)4500Pi(c)900Pi.

**Question 6A**: Geometry /Construction pretty basic .

**Question 6B** Ignored by most students but there is a lovely way of doing this by breaking the diagram into the three triangles APC,BQA, and BCR.

**Question7**: Statistics Another dreadful question spread over 4 pages by the time you got to the end of this you had lost the will to live!Students had to flick back and forth to check the data.

Suggested solutions (c)Median 50,inter quartile range 5,(d) mean 78333,(dii)68-89(e)4,556,000(f)27792

**Question 8**:Trigonometry : Nice question but spread over 4 pages! They asked the entire trig syllabus.Most students should have got some marks.

Suggested solutions: (a) 60 degrees (ii)389.7 (iii)82.6% (iv) 30km(v)Equilateral triangle.(b)188Km (iii)90degrees(iv)45 minutes(c)(i)25.98km(ii)17.32Km

Overall verdict :Most students happy but something will have to be done about big questions spreading over 4 pages.

**The 24 Pilot schools asked to answer question on Topics not on the course !**

Paper 1 Friday 7th June LOrd Project maths Phase 3.

Pilot School students were surprised to discover that they were been asked to answer questions on Differential Calculus which are no longer on their course.In fact they are not part ofOrd Level strand 5 functions and Calculus which was examined for the first time in 2012.

In Paper 1 question 5 (a) Students were asked to differentiate a product **but the product rule is no longer on the Ord Level Syllubus**. In question 5(c) on the same paper they were asked to differentiate a **quotient but the quotient rule is no longer on the Ord level course**. Mistakes like this are unforgivable you would think that those setting the exam would know what was on the course.

This was a 25 mark question 2/3 of which was not on the course.

Meanwhile on the Higher (Question 5 Paper 1) paper students were asked to find the area between a sine graph and the x axis using Integration** but finding areas under sine curves by Integration are not on the course** !

This rendered pats c and d of this question invalid .

Verdict easier than the samples or 2012/2o11 papers

Question 1 Probability .Nice question But lots of rote learning.

Question:2 Normal distribution very predictable part b may have caused problems.

Suggested solutions (a)0.9452,(ii)0.08904

Question : 3 The Line very basic just about Ord level standard.

Suggested solutions (a)l,l,h,m,k and l (b)30 degrees

Question ;;4 The circle Not a bad question similar to old course

Suggested solutions b(i)-7/5,-4/5 b() 4x+3y+8 = 0

Question:5 Trigonometry ;Again very basic question ,similiar had been asked before on Ord level.

suggested solutions (b)49,131,(c)7

Question6 :Geometry More rote learning ,Construction of the Orthocentre for a triangle with an obtuse angle was expected.

Question 6B :Geometry .(a)Very basic junior Ord level.

Question7:Probability/Statistics; not a bad question far too much information.

suggested solutions 0.231,0.238,not independent ,(e)0.7 is outside confidence interval. No new margin of error is 0.2236,(f) 0.88.

Question 8:The question with the impossible triangle.

suggested solutions (a)(i) 37.62KM or 47.02km (ii)193.93km or 168.35

Question 9 ;Trigonometry /Geometry Looked much worse than it actually was . It ran out of ideas before the end.

(a) k =4/2 ,.(b)P =2piR1.(ii)8pi c(iii)9pi(d) Show the figure TCRS has 4 right angles.

Answers shortly.

Teachers have discovered that the triangle given in question 8 paper 2 has too much information in it .

The dimensions of triangle HRP are given as follows /HR/=80km,/RP/=110KM the /<HRP = 124′/ and /<RHP =36′/

It follows that the 3rd angle is 20′ .

(a)i asks to find the perpendicular height of the triangle which is 80 sin 36 = 47.02 or 110sin 20 = 37.62 not exactly equal .

(a)iiThey asked you to find /HP/. Using the area of a triangle method you get /HP)=193.92km which is strange as it fails the triangular inequality rule /a/</b/+/c/.

If you use the cosine rule you get /HP/=168.35km .

But the story does not end here.On the Irish version of the paper the angle of 36′ was omitted in the diagram but the Irish speaking schools were contacted by the SEC to sort out this error.But if the SEC told the Irish speaking schools to insert the 36′ it means they were not aware of the error that the triangle with these measurements was impossible.

The following is an extract from a post on Twitter by Minister Sherlock concerning the 2012 marking scheme .

“*Marking of the exams:*

*Standards do not radically vary year on year for large cohorts of students. When new*

*knowledge and skill sets are being tested the standard required is difficult to tie down in the first year.*

**Editors Comments :2012 was in fact the 3rd year project maths was examined.**

*This is particularly the case with Project Maths where candidates are developing new skills*

*and more are sitting the exam at higher level. These candidates cannot be treated unfairly*

*compared to previous candidates.*

*The exam papers and marking schemes for Project Maths are new. For this reason, some latitude is required in the development and implementation of the marking scheme. This is fully in line with international practice in large scale public exams like the Leaving Certificate.Last year, the number of candidates who got an A1 was 345, compared to 486 in 2011*.

**Editors comments** **The A1 % rate in 2012 was 3.2% : The A1 Rate in 2011 was 5.9%:The A1 % rate in 2010 was 7.5% and in 2009 the A1% rate was 6.9%! Project maths has reduced the numbers getting A1 by 50% .**

*This does not suggest that the exam has been “dumbed down”. In contrast, 256*

*candidates were awarded an EFNG grade in 2012 compared to 246 in 2011. Whilst any*

*increase in EFGN grades is not desirable, a difference of 10 candidates is in no way*

*dramatic.*

**Editors comments :The failure rate in 2012 was 2.3% (lowest ever)Pre Project maths the failure rate was about 4%! Project maths has reduced the failure rate by 40% !**

*The State Examinations Commission (SEC) is satisfied that the marking schemes used in*

*the marking of the 2012 Project Maths examinations were fully appropriate and fit for*

*purpose. The development and finalisation of these schemes followed the normal*

*practices and procedures which apply across all exams delivered by the SEC in the early*

*years of a new syllabus”.*

There is only one different question on this paper in comparison to the regular paper.

Question 9: Functions/Calculus:Parts a,b very easy ,c,d,e,f may have caused some difficulty but if teachers had practiced this type of question there should not have any problems.

Verdict : about the same level of difficulty as the regular paper.

Question1:**Complex Numbers** . Nice question provided students were familiar with modulus .Nothing new here.

Question 2: **Algebra/Area** .Trapezoid rule a bit of a surprise but the table will get most marks even if student uses the table function on the calculator.

Question 3: **Number :**Parts a,b, just use your calculator (foundation level ML) ,(c) will have troubled some students.

Question 4: **Compound Interest /Money**; Just use your Calculator (ML says a half decent 1st year could have done this question.

Question 5: **Patterns/sequences**:Same question as the flowers on the sample .Weaker students will have struggled with some parts of this question.

Question **6: Patterns /Number;** Identical to question 5; Probably more difficult than Q5 as it had more parts.

Question 7:**Calculus (old course);**Part c will have troubled some students ,although not difficult it is based on the old Q8 which mant students tend to avoid.

Question 8;**Calculus Old Course** : Part b (max and min plus graph )Students would normally be given a domain (none given here) this may have upset some students.Part c was expected identical tom old course.

Verdict : Nice paper ,easier than the mocks , the worry would be Q5,Q6, depending how they are marked.

The big difference is the style of questions very similar to the old course ,very much to the point , very little English .Very little in context questions.This looks like that project maths in it’s original format is dead !

There were 3 different questions on this paper in comparison to the regular paper .

Question 5** : Functions/Calculus**.Given 4 graphs and asked to identify the graphs of the first and 2nd derivatives.This is a recycled question from the old course .Based on the fact if you differentiate a quadratic you get a line if you differentiate a line you get a constant.Very,Very,Very easy should have taken 2-3 minutes.

Question 6:**Functions/Calculus/Area** :The trapezoid rule not expected on H paper but again very basic.

Question 8: **Functions/Calculus**;Identical to Sample infact practically the same question !On the sample it was a snowball here it is a raindrop. 50 marks for very little .The Calculus on the regular paper was more difficult .

Verdict : The Project maths paper for the Pilot schools was easier than the paper used by the regolar schools.