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LC HL Maths Paper 1 'controversy'

Treppen

So it's made it to the Joe Duffy show.

Can't say I'd disagree with any of the student's concerns.

I get the impression the SEC got confused with formative and summative assessment by trying to make the paper a 'teaching moment'.

I don't think the bell curve can be used to sort this one out.

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10000maniacs

It's disgrace that they could throw in a looper like that. Very unfair.

However, if I was doing my leaving cert with the internet available, which it wasn't in the 80's, I would have got a better marks because of the resources I could access.

All we had were those Folen's schoolbooks and these were crap especially for science and maths explanations.

Quantum Erasure

Was there any specific question that was particularly hard, or just the paper in general? Had a look at the paper but it's years since I did the leaving, so I wouldn't know with the new syllabus what's what..

Edit. It's available here, you'll have to click through a few options then choose paper one higher level EV for the English version

https://www.examinations.ie/exammaterialarchive/

Treppen

https://www.boards.ie/discussion/comment/120705408#Comment_120705408

I'm not sure if better resources would have made it any better. It seems to me (going by what students are saying) that the problem lay in trying to decipher exactly what the examiner was looking for.

Its like the exam designer was like the magician in the Seinfeld sketch. The whole point was to make the examiner feel clever.

https://youtu.be/jrRdq2pCjAM

10000maniacs

https://www.boards.ie/discussion/comment/120705612#Comment_120705612

Googling the answers is simple compared to what we had to do.

For example one of the questions was prove the square root of 2 was not a rational number.

I mean this proof was not in the Folen's textbook. You had to buy extra Answers books to get the proof.

But a second on Google would give you a simple proof. That's child's play compared to what you had to do before the internet.

This same theory could be applied to History, Geography, English, irish etc.

And ChatGBT would be an enormous help studying for English.

Not to mention those Second World War documentaries on the History Channel to put you bang in the centre of the topics without the abstractions and distractions of the Folen's school book writers. Re-read those Folen's books to see what I mean. Dreadful stuff. They probably covered the syllabus, but it was in a manner which sometimes confused the main points.

These History channels weren't available in the 80's either.

School kids have it on a plate these days.

derb12

That proof is in the folens book Active Maths. I gave it to my 5th years in their summer test and they weren’t pleased. It’s the only example of proof by contradiction on the course. I think that ever since they reduced the theorems in JC, more students just don’t get the idea of a mathematical proof.

10000maniacs

https://www.boards.ie/discussion/comment/120706130#Comment_120706130

If I remember correctly, our maths books in the 80's were called New Concise Maths Book 3A and 3B. or something like that.

The point I am making is the amount of time studying is reduced to a fraction of what it was by accessing the internet for answers to past questions and watching documentaries on the History channel.

You could certainly target a lot more A1 marks these days with a lot more ease and a lot less study.

I used to spend most of my study time retrieving relevant stuff in the 80's.

[Deleted User]

For the given quadratic equation, the discriminant should be equal to zero to have exactly one solution.

The discriminant (D) of a quadratic equation ax^2 + bx + c = 0 is given by:

D = b^2 - 4ac

In this case, the given quadratic equation is:

3x^2 - Mx + 3 = 0

Comparing with ax^2 + bx + c = 0, we get:

a = 3, b = -M, and c = 3

Therefore, the discriminant of the given equation is:

D = (-M)^2 - 4(3)(3) = M^2 - 36

For the given equation to have one solution, the discriminant should be zero. So, we have:

M^2 - 36 = 0

Solving for M, we get:

M = ±6

Therefore, the two values of M (belongs to the set of Z) for which the given equation has exactly one solution are M = 6 and M = -6.

Edit: the answer to Question A1 may or may not have been produced by ChatGBT. I think the students might have claimed to have a bad tummy bug and had to make frequent quick restroom visits to produce the answers 😉

[Deleted User]

https://www.boards.ie/discussion/comment/120706130#Comment_120706130

it’s the very basis for those studying computer science where part of it is inevitably going to be computational complexity with proofs galore.

amacca

https://www.boards.ie/discussion/comment/120706413#Comment_120706413

That would show initiative....a vital skill in the modern workforce.

[Deleted User]

https://www.boards.ie/discussion/comment/120706915#Comment_120706915

But you have to watch AI, I asked it to solve a taxation problem and it used an inappropriate recursion yielding a ridiculous result, it helps when you can track how it’s calculating, but AI can really help teach you maths, it’s one of its most practical uses. Also language constructs.

[Deleted User]

ChatGPT to calculate if I can safely take off in my hired Cessna 172 under specified conditions:

Problem: A Cessna 172 with maximum permitted loading & within c of g envelope is taking off from a wet grass runway of rising gradient 1/20, there are 30 foot trees at end of runway 18 which is 600 metres, wind vector is 15 knots at 200 degrees. Elevation 400 feet, temperature at sea level 25C. What is the predicted take-off run and clearance over trees?

Answer: To calculate the predicted take-off run and clearance over trees, we need to perform the following steps:

Step 1: Calculate the density altitude

Step 2: Calculate the take-off distance

Step 3: Calculate the height above the trees

Step 1: Calculate the density altitude

Density altitude is the pressure altitude corrected for non-standard temperature. It is calculated using the following formula:

Density Altitude = Pressure Altitude + [120 x (OAT - ISA)]

where OAT is the outside air temperature and ISA is the standard temperature for the given altitude.

Pressure altitude can be calculated using the following formula:

Pressure Altitude = (1013.25 - (QNH x 0.02953)) x 30

where QNH is the local altimeter setting in inches of mercury.

In this case, the elevation is 400 feet, so the pressure altitude is:

Pressure Altitude = (1013.25 - (29.92 x 0.02953)) x 30 = 425 feet

The standard temperature for 400 feet is 15.5C. Therefore, ISA = 15.5C.

The temperature at sea level is 25C. Therefore, the outside air temperature is:

OAT = 25C - (1.98C x 0.4) = 24.21C

Substituting these values into the density altitude formula:

Density Altitude = 425 + [120 x (24.21 - 15.5)] = 1,926 feet

Step 2: Calculate the take-off distance

The take-off distance can be calculated using the following formula:

Take-off Distance = Ground Roll + 50% of Total Distance to Clear 50-foot Obstacle

where Ground Roll is the distance covered from brake release to lift-off, and Total Distance to Clear 50-foot Obstacle is the total distance required to clear a 50-foot obstacle at the end of the runway.

Ground Roll can be calculated using the following formula:

Ground Roll = 1.15 x (Take-off Speed)² / (2 x (g x (µ - (g x sin(θ)))))

where Take-off Speed is the speed at which the aircraft lifts off the ground, g is the acceleration due to gravity (32.2 ft/s²), µ is the coefficient of friction between the tires and the runway, and θ is the angle of the runway gradient.

Take-off Speed can be calculated using the following formula:

Take-off Speed = 1.2 x Stall Speed

where Stall Speed is the speed at which the aircraft stalls in the take-off configuration.

Stall Speed can be calculated using the following formula:

Stall Speed = √(2 x W / (ρ x S x CLmax))

where W is the weight of the aircraft, ρ is the air density, S is the wing area, and CLmax is the maximum lift coefficient.

Assuming maximum permitted loading, the weight of the aircraft is 2,550 lbs.

The wing area of a Cessna 172 is 174.5 ft².

The maximum lift coefficient of a Cessna 172 is 1.5.

The air density can be calculated using the following formula:

ρ = (P / (R x T))

where P is the pressure, R is the gas constant for air (1716 ft²/s²/°R), and T is the temperature in Rankine (°R).

The pressure can be calculated using the following formula:

P = QNH x 3386.39

where QNH is the local altimeter setting in hectopascals.

In this case, the altimeter setting is not given, so we will assume it to be 1013.25 hPa.

Substituting these values into the air density formula:

ρ = (1013.25 x 3386.39) / (1716 x (459.67 + 24.21)) = 0.00218 slug/ft³

Substituting these values into the Stall Speed formula:

Stall Speed = √(2 x 2550 / (0.00218 x 174.5 x 1.5)) = 52.5 knots

Substituting these values into the Take-off Speed formula:

Take-off Speed = 1.2 x 52.5 = 63 knots

Assuming a coefficient of friction of 0.6, the ground roll can be calculated as follows:

Ground Roll = 1.15 x (63)² / (2 x (32.2 x (0.6 - (32.2 x sin(1/20))))) = 1,080 feet

Total Distance to Clear 50-foot Obstacle can be calculated using the following formula:

Total Distance to Clear 50-foot Obstacle = (1.2 x Take-off Speed x (TOD + 50)) + (TOD x tan(θ))

where TOD is the height of the obstacle above the runway, and θ is the angle of climb at the obstacle.

Assuming a height of 30 feet for the trees, and an angle of climb of 6 degrees (10% gradient), the Total Distance to Clear 50-foot Obstacle can be calculated as follows:

Total Distance to Clear 50-foot Obstacle = (1.2 x 63 x (30 + 50)) + (30 x tan(6)) = 1,508 feet

Substituting these values into the Take-off Distance formula:

Take-off Distance = 1,080 + 0.5 x 1,508 = 1,848 feet

Step 3: Calculate the height above the trees

The height above the trees at the end of the runway can be calculated using the following formula:

Height Above Obstacle = (TOD / Total Distance to Clear 50-foot Obstacle) x Ground Run

Substituting the values calculated above:

Height Above Obstacle = (30 / 1,508) x 1,080 = 21.5 feet

Therefore, the predicted take-off run is 1,848 feet and the clearance over trees is 21.5 feet.

As a one time trained pilot under these conditions I have decided the clearance over the trees is insufficient, so I must recalculate and inform my passengers they can’t all come on the trip. Back in the 80s when I was flying this was a pen and paper exercise.

am_zarathustra

https://www.boards.ie/discussion/comment/120706193#Comment_120706193

Main issue with the maths paper 1 was the level of abstraction required. There is always a bit, separates your H1s from you H2s so necessary. They'd normally be the last part of the question, so your "normal" students can still start the question and show what they know.

Having sat the old course and taught the new one I'd say they both offer challenges but a pre project maths paper would be even easier for Chatgpt to solve, high level of algebra required and things like matrices. But on the other hand if you could do it, you could do it. No messing about. You might have (and probable most students realized after) been able to do all the maths on that paper but not have understood what they were asking. The factors long q was mad easy but not if it was brand new info and you are sitting in your LC.....fun puzzle but not when your gambling a college course.

Totally agree about proofs, keep them a JC if you want them at LC or just get rid of them. And take Complex Numbers out too. If you want abstraction taught you need to shorten the course.

Treppen

Is the 'prove root 2 isn't rational' outlined in the specification ? .. or just a general 'knowledge of rational numbers' requirement?

am_zarathustra

https://www.boards.ie/discussion/comment/120707742#Comment_120707742

Ah yeah, that's not a weird one at all. A good student wouldn't be thrown, you'd know that and induction (DeMoivres), deriving amortisation (there or thereabout the financial maths qs) ect Proof and construction of root 2 are both on the course. The paper had mad stuff, that wasn't one of them.

Now I hate proofs myself. Induction is grand but a lot of them are rote learning and that has no place on a HL maths paper. My main issue is not abstraction either. Lovely to teach, really important for real world problem solving. But I'd need more time, the course is just too long to get to that depth.

My daughter thought the paper was ok. She had studied the root 2 proof and done some sample questions on it so she was happy to see it and did that first to settle herself. She was also happy with the financial maths.

Furze99

As far as I can judge, the focus of LC teachers and grinds people as well these days, is to show students how to maximise their marking on any given paper. They focus on what will come up, how the question will be phrased and how it will be marked.

All logical of course but it's the difference between teaching the syllabus of a subject and teaching how to maximise marks in that subject.

Not the same thing and isn't that what happened here - the SEC threw a bit of a curve ball to test students ability at maths and their understanding of the syllabus.

No harm in this at all, to address grade inflation of last decade and so.

Treppen

What exactly was the nub of the problem then. Like which questions were the 'unfair' ones?

Jaffa3000

Also wondering which ones were the unfair ones. Theres definitely some tricky questions on there that require you to know what you're doing with the derivatives, integrals etc. but with the choice it seems alright to me

Montage of Feck

There really should be media silence on the reporting of exams while they are in progress. It seems to get worse every year with hyperbolic nonsense about hard papers.

As long as the paper is the same for everyone what's the issue. Isn't the point of it to grade people according to their ability of the given subject.

am_zarathustra

https://www.boards.ie/discussion/comment/120711042#Comment_120711042

Nothing really, like it was just hard.....a paper essentially where the ratio of hard to regular questions was larger than normal. If an exam is hard for everyone then it's curved, happened a few times in college, I think the hysteria around the LC gives them expectations and the grind colleges and courses give "guarantees". There's a serious element of raw ability in maths at that level that no grinds will fix.

I'd agree with the above, too. Teach the syllabus, try and make it applicable to the world and a few weeks of exam prep at the end. Cramming for exams all the time and worrying doesn't give anyone a love for maths or an understanding of it's use.

Feisar

https://www.boards.ie/discussion/comment/120711762#Comment_120711762

All lofty ideals however that's not the name of the game, maximizing points is what it's about. It's the classic, don't hate the player, hate the game situation.

am_zarathustra

https://www.boards.ie/discussion/comment/120716361#Comment_120716361

I think paper 1 was designed to show that cramming for exams by rote without understanding might be a poor approach if this style of paper is the new normal. Even at ordinary there was a nice bit of actual thinking required.

And lots of teachers teach a joy of the subject, amazing how much and interested and engaged student will retain. Win win

Treppen

Yes I've yet to read or hear of any reports of what exactly was the issue. So essentially it was just a difficult exam.

It's a simple fact that you can't have a certain amount achieving H1s just by doing the past papers, the bell curve for 20,000 students odd should be pretty bell shaped. Maybe it's about time they start rewarding exceptional students appropriately by not giving everyone the trophy.

As a follow on they need to start looking at other subjects discussed here before where there's an abnormal amount of H1s (I won't start a subject wars by making them 😁, but you know who you are).

It comes up every year in Music with prodigious performers just losing out on the H1 by exceptional all rounders (in written paper also ). You know that 1 exceptional student in your class, but it seems with enough grinds it's up for grabs with a larger number of students.

It must be stressed however that H2 is good enough to study maths in college. There seems to be the notion that unless you get the H1 your no good. Some students come back to maths in later life and can be quite good given another chance.

am_zarathustra

https://www.boards.ie/discussion/comment/120718759#Comment_120718759

I think had the department not explicitly said the paper this year would be similar to the last few years there would have been less outcry. This is a fair criticism as it was a large departure from the explicit questions we've seen in recent times. If they had just stated "its back to normal HL standard" this would have warned off the very weak students assuming they were getting the very approachable questions from the last couple of years. But I can't see anything on the appear that you couldn't do if you understood the concept.

A valid criticism might be the language makes it difficult for kids who have English as a second language. Maybe more care could have been taken with the phrasing.

Newbie20

As a Maths teacher I thought the reaction to it was a bit over the top. There was plenty there that even the weaker student should have got. There was one part of a long question with factors of 12 that a primary school student could do.

Now I should clarify that while I usually have a 6th year class I didn’t have one this year so maybe I would have felt more sympathy if I was directly involved.

I think the crux of the problem is that ever since the bonus points came in there has been a large enough cohort of students doing Higher Level Maths despite clearly being out of their depth. And these students sometimes get by in the LC (and sometimes done) by regurgitating the questions from previous exams papers but if you change the appearance of a question even slightly, they can’t deal with it. These students are putting themselves under ferocious pressure to pass the exam to get 25 extra points. But as I always point out to them, they have probably lost that 25 points on other subjects by the extra time invested in Maths.

Newbie20

https://www.boards.ie/discussion/comment/120718759#Comment_120718759

I agree, I have a serious issue with certain subjects getting crazy amounts of higher grades while they’re like hens teeth then in other. In the new JC it’s even worse. Surely the bell curve should apply across all subjects with similar enough percentages of the higher grades in each?

am_zarathustra

https://www.boards.ie/discussion/comment/120719552#Comment_120719552

100% agree and a decent cohort staying at HL til the end and spending large amounts of time studying concepts by rote that a real HL student will just get which damages their overall understanding.

The grind culture around it is out of control too. It's an uneven playing field. I don't think anyone in my class in school would have said they were a sure A1 but plenty of students say it now ........based on people they are paying saying they are capable. Even the level of algebraic manipation required for a HL student is often not there.

They can push HL maths all they want but they need to be realistic about how many students are actually capable.......and want to do the work required.

I'd love to see the course trimmed a little too, so you could really drill into the calculas and stats, like there is so much there and for the real HL students its lovely but you don't always have the time to get stuck in which would really separate the wheat from the chaffe.

Treppen

Is it time to get rid of the bonus points then!

It's creating enormous stress in our school, where, despite advice to move down, students are only moving down at the last moment after 2 years of complete stress and grinds, when they could devote their time better to other subjects and easily gotten a decent ordinary level grade.

It's patently unfair to other subjects and students too.

Has anyone in the department done a review and asked what exactly the 25 bonus has achieved?

If they want STEM maybe look after the supply of physics, chemistry, comp. sci. and applied maths teachers. That's where the numbers studying are relatively low compared to maths.

rainbowtrout

https://www.boards.ie/discussion/comment/120706130#Comment_120706130

Had this argument with a guy giving JC Maths inservice a number of years ago. He commented that students sitting LC Maths were consistently poor at geometry. I pointed out that they're going to be crap at geometry if you don't make them learn the theorems and be able to prove them. Given that they don't have to be able to do most of it at JC anymore, why would they be any good at it for LC?

amacca

https://www.boards.ie/discussion/comment/120731458#Comment_120731458

I'd imagine that went down well!