Leaving Cert Higher Level Maths Mock 2019 Paper 1 (DEB)

In This video I have done out the solutions in full for paper 1 of the 2019 maths mock from DEB. If you have any questions please ask. There may well be a mistake or two in there so if something doesn't look right then let me know!
Timecodes:
0:00 - Intro
0:42 - Question 1
15:00 - Question 2
25:26 - Question 3
33:45 - Question 4
44:35 - Question 5
1:00:27 - Question 6
1:10:36 - Question 7
1:25:47 - Question 8
1:48:05 - Question 9
Credits:
Kevin MacLeod: Carefree

[@QuantumNetwork]

Extremely helpful, thank you so much for such a hq video and thank you youtube algorithim recommending this!

[@SimpleScienceandMaths]

You are very welcome, I'm glad it helped!

[@SimpleScienceandMaths]

Small error in Q1(b), I calculated root2sin(2pi/3) as -root6/2, this of course should be positive root6/2. This results in the final answer having opposite signs for the real and imaginary parts. It is both - then + and + then -

[@SimpleScienceandMaths]

Time stamps for each question: Q1 - 0:42 Q6 - 1:00:27 Q2 - 15:00 Q7 - 1:10:36 Q3 - 25:26 Q8 - 1:25:47 Q4 - 33:45 Q9 - 1:48:05 Q5 - 44:35

[@seancullinane6875]

This is savage mate keep up the good up the work

[@SimpleScienceandMaths]

Thanks 👍

[@Sarah-qk2my]

You’re a lifesaver - has no clue where I was going wrong!

[@hamzajiile8611]

Very Helpful Thank you!!!Hope you continue posting them. as they are excellent in my opinion.

[@SimpleScienceandMaths]

Thanks, will do!

[@Alex-fp7wk]

Thank you. I watched this for the second time and I study along with you and this is great will you be doing 2020 mocks after they're done. Please do :)

[@SimpleScienceandMaths]

Thanks Alex, I'm glad it's helping you! If you can I would appreciate it if you could share the video on social media to help my channel reach more students like yourself, cheers!

[@markusrothm.d.2913]

Great video. Thanks for making it

[@SimpleScienceandMaths]

Glad it helped, thanks for watching!

[@aswell31]

one word: HELPFUL 💪🏻💪🏻

[@eoinbrennan3949]

Great work, really appreciate the time you took to do all of this. Need to ask about one thing though..........in question 9(iii) where it says "Hence show that a^3 = 16". How did you know that you needed to integrate at this point? There was nothing in the way the question was asked that would indicate(to me anyway)that you needed to integrate again?

[@SimpleScienceandMaths]

Hi Eoin, thanks for watching and for taking the time to ask a question. There is not much giving it away apart from the "hence" that's the big giveaway. In terms of why integrate again rather than using what we had from the last part it is asking to show something in terms of 'a' so we set our limits of integration in terms of 'a' instead of [-2,2] from the last part. Hope that helps somewhat

[@eoinbrennan3949]

@@SimpleScienceandMaths Thanks for the reply man

[@shanefoley6428]

Could you by any chance put up the solutions of the 2018 DEB maths papers for LC HL? I would really appreciate it.

[@SimpleScienceandMaths]

Hi Shane, Sorry but I won't be doing the 2018 paper!

[@dmeeley8326]

At 1:32:57 should it not be 15h over 16 rather than just 5h over 16 and r=45

[@alteredsanta6128]

Huh, good revision b4 the LC Maths ;) Thank you

[@SimpleScienceandMaths]

Glad I could help!

[@alteredsanta6128]

@@SimpleScienceandMaths sorry for questioning. But at 30:05. Could u briefly explain how do u choose which part to equal to a,b,c?

[@SimpleScienceandMaths]

@@alteredsanta6128 a is the coefficient of x^2, in this case (k-1), b is the coefficient of x, in this case (-6) and c is the constant(everything without an x), in this case k-1. This is the same as when you do the quadratic formula (-b formula) for a quadratic equation, we are just using the bit under the square root sign from that formula.

[@alteredsanta6128]

@@SimpleScienceandMaths ohh yeah. Sound! Thank Youu )

[@SimpleScienceandMaths]

@@alteredsanta6128 no problem!

[@tomatrix7525]

Hi, is Q8 iv wrong by any chance? By setting it equal to 0 you are in fact minimising the growth.

[@ronan5115]

Regarding Q8 b iii How did you multiply by 199N and -1. It does give you the answer but are you allowed to do that?

[@SimpleScienceandMaths]

Hi Ronan, it's the chain rule where the 199 and -1 are coming from. Differentiate ln199N and you get (1/199N) x (199), differentiate ln(20000-N) and you get (1/(20000-N) )x (-1) If you need further explanation let me know.

[@alba4565]

@ 19:18 would there be an easy way to get those factors as 725 is a big number and also @ 37:28 how would you work that out without wasting time

[@SimpleScienceandMaths]

You can use your calculator to find 725 as a product of it's prime factors. Then the factors you choose will be a product of those, there will still be a bit of trial and error

[@alba4565]

Thanks for this it really helps

[@SimpleScienceandMaths]

You're welcome!

[@kelvinadigun254]

Can anyone explain where he got -1 for the u of n in question 4 part (b) (i) just a little confused

[@SimpleScienceandMaths]

Which part exactly are you referring to? The u of 2 was calculated as -1 and this was subbed into the next part U(3)=(-1)^2(-1), the second -1 there was calculated in the previous step

[@alfazulu714]

In Q1 (a)(i), can you explain how you got to 24-3k+i(4k-32)=0 please. I understand all the rest except how you got there. This is all new to me so would appreciate some help. Thanks

[@SimpleScienceandMaths]

Hi Anthony sorry for the late reply, I was away on holidays! To get to the line you have above I multiplied out the first two sets of brackets, multiplied the next set by the -k and then simplified everything down till I got what is above. If you haven't yet done complex numbers in class you need to know that i^2 = -1, so anywhere there is an i^2 replace it with -1. Try to do it out yourself and if you're still stuck email me with your attempt and I'll help you further. my email is [e-mail]

[@eoghangallagher1030]

Would q8 b(ii) not be 100

[@SimpleScienceandMaths]

Great question and you could probably make that argument alright but I think the 100 is when the infection first appears i.e. when it is first detected at t=0, N=100. But you can still go back in time from this to say t=-1 (1 day before the infection was detected) and there would be some number of infections in the town which are undetected. The marking scheme gave it as 0

[@cathalkeenan8]

Im sitting a mock tommorow, i only know some chapters like co ordinate geometry of circle, trig, differentiation, complex numbers (some) and by no means everything. im not in 6th yr, any tips?

[@SimpleScienceandMaths]

Sorry for not getting back before the mock, how did it go?

[@gman_origin9620]

Hey im a bit confused for q1 (i). Im not sure how you seperated the the real part.

[@SimpleScienceandMaths]

use algebra and factorising to separate everything that doesnt have an i in it

[@davidduggan3328]

Any last minute advice before I sit paper one today?

[@SimpleScienceandMaths]

If you're looking at a differentiation question and have no idea what to do just differentiate the function, then solve =0 if it's looking for a point, if something mentions rates of change or something similar then differentiate. For everything else if you've no idea then choose the MOST RELAVENT (not a random) formula from your log tables and give it a go! most of all stick to your timing so you don't run out of time. Best of luck!

[@Ethaliano]

In Q7, a iii, why do you not sub in that Y value into the A formula, to find the area?

[@SimpleScienceandMaths]

Sorry, I must have forgot to do the last step! Of course you need to sub that back in to find the actual area! Surprised nobody noticed that before you....

[@Ethaliano]

@@SimpleScienceandMaths Haha no worries :)

[@1_Quest_1]

for question 2a, can you just square all the numbers individually? Like (root2x-1)^2 + (rootx-1)^2 = 5^2

[@SimpleScienceandMaths]

No you can't do them individually, you must square each side. Try it with 3+4=7, squaring each individually would give 9+16=49, which is not true

[@1_Quest_1]

ah got it, thank you very much :)

[@GarlitoMc]

Regarding Q1 (ii), I think it's important to clarify that complex roots exist as conjugate pairs ONLY when the ALL COEFFICIENTS of the complex polynomial are all REAL!

[@SimpleScienceandMaths]

This is true and it came up in a question in 2016. If you have a polynomial with complex coefficients then the roots will not be in conjugate pairs. In this case there are several ways to solve for the roots including the quadratic formula if it is a quadratic. Thanks for your input on this! Hope paper 1 went well for you!

[@dorar4468]

for Q1 part a, (2 - i ) to the power of 3 was turned into ( 2 - 1 )(4 - 4i + i sq). I understand that in the second bracket you square the first and last, but where did you get -4i in the middle? The rule for difference in cubes is to just multiply the two numbers together, not double it. Please let me know what i'm not getting, thanks!

[@SimpleScienceandMaths]

It's not the difference of 2 cubes, you are cubing the expression.

[@ryanb1468]

In question 2 (a) on the on the 6th line why is it a positive 100 when multiplying by -1?

[@ryanb1468]

My bad stupid me! Great video keep it up🤠

[@SimpleScienceandMaths]

@@ryanb1468 😎

[@ryanb1468]

Simple Science and Maths had my fifth year summer exam and there was a question for 30% of the entire test and our teacher barely ran over it 🤦‍♂️ Really not fair to be honest 😂

[@SimpleScienceandMaths]

@@ryanb1468 That's what it'll be like in the LC, you'll most likely see a couple of questions asked in a way you've not seen before!,

[@diegobrule]

In question 8 (b) (iv) it says find the number of people infected when the disease is spreading most rapidly. You say to let dN/dt=0 to find this, but wouldn't dN/dt be the infection rate as it is the rate of change of people infected, and if you let it =0 it would be when the infection is spreading the slowest? (And the point at where most people are infected), wouldn't you need to let d2N/dt2 =0 to maximise the rate of change?

[@SimpleScienceandMaths]

In this tge first derivative tells us that there is a turning point in the graph i.e. a local max or local min. Letting this =0 and solving gives us the x value of the max/min. Since we only get one value and the question asks for the point of local max I assumed this to be the local max. The second derivative test tells us the nature of the turning point, find the second derivative and sub in 20000, you will get an answer of -4 which is less than 0 and therefore a local max. In summary: 1st derivative =0 local max/min 2nd derivative 0 local min In this case only one value for 1st derivative so assumed to be the local max. Hope that helps

[@alexclifford1896]

Surely for the trapazoid question any answer is right as it for part (a) since they don't give you H, all they said is it's split evenly so used H as 2 and got 8. Am I missing something or can I do that.

[@SimpleScienceandMaths]

Unfortunately you can't do that. You have to use your own knowledge and understanding to realise that letting H=2 would be too inaccurate. This is higher level maths so we can't take short cuts! H=1 would be the largest allowed in this question but you could have let H= 0.5 although it creates more work... H=1 would be standard unless otherwise told.

[@alexclifford1896]

@@SimpleScienceandMaths thank you

[@DrSanjayKeshri]

Great video

[@SimpleScienceandMaths]

Thank you

[@GarlitoMc]

Regarding part (i), there is no need to solve for k twice! There is only one value of k.

[@SimpleScienceandMaths]

Yes that's true! no harm in doing both though because if you get two different answers then you will know that you did something wrong and you can recheck your work.

[@asfahsabrie6207]

@@SimpleScienceandMaths hey sir am finding it Difficult to solve for K after multiplying am not getting a simple equation like urs any help plzz😭

[@jackosullivan8323]

Question 8 b (iv) they are looking for the no of people infected when the RATE of infection is greatest. This occurs at the point of inflection. So would u not let the second derivative equal to zero? Ur answer 20000 is the max no of people affected and at this time the slope is zero. This is actually when it is spreading least rapidly

[@SimpleScienceandMaths]

Yes I think you are right! If you read part iii it says that dN/dt is the 'rate at which the infection is increasing'. So in order to find the max of this we would differentiate and let equal to zero (which would be the second derivative=0). Remember that this is a mock paper and often the questions are ambiguous and the marking schemes not 100%....I used the solution from the marking scheme which I don't have to hand at the moment but I'll have another look at the question during the week to confirm the correct solution.

[@gionnybanana9613]

bro what is q5

[@Alex-fp7wk]

Man, just watching this gives me so much anxiety. Jc was so easy but this makes me question if I am able for higher level

[@SimpleScienceandMaths]

How did you get on in the JC?

[@Alex-fp7wk]

@@SimpleScienceandMaths I got a h2 for jc . But for my end of 5th year exam I got 47%

[@chickpeas100]

Alex thats honestly good

[@TheSpaceman332211]

It seems the difference between ordinary and honours level leaving cert maths is substantial.

[@SimpleScienceandMaths]

It sure is!

[@darraghosullivan7567]

32:00

[@tomwhelan7447]

What does DEB stand for?

[@SimpleScienceandMaths]

Dublin Examinations Board

[@harrya9205]

What year group is this for?

[@SimpleScienceandMaths]

5th and 6th year higher level

[@harrya9205]

@@SimpleScienceandMaths Thank you

[@wise588]

Should I do higher level maths if I got a D in ordinary level maths for the JC 😂 would grinds help?

[@SimpleScienceandMaths]

In general those who get a D in the jc find hl maths in the lc very difficult. If you need to resort to grinds from the start then it will be a struggle. My advice would be to try out hl if you want and work hard at it. If you are serious about doing hl then do a jchl maths paper1 and paper 2 every week over the summer before you start 5th year.

[@davidpower7568]

Here I’m doing jc higher level and when I saw the first question my heart dropped

[@SimpleScienceandMaths]

😂 panic over! Best of luck in the JC!

[@davidpower7568]

Simple Science and Maths thank you

[@nikithalnikithal8182]

Godfather

[@jeremiahduru5912]

Do the Junior Certificate Higher Level Mock Paper next pls

[@SimpleScienceandMaths]

I'll see if I can get to it over the Easter break.

[@jeremiahduru5912]

@@SimpleScienceandMaths Alright thank you so much because I'd really like to correct my mock paper before the Junior Certificate

[@SimpleScienceandMaths]

@@jeremiahduru5912 do you know what company your mock came from because there's several different papers

[@jeremiahduru5912]

@@SimpleScienceandMaths it is definitely not the DEB mock paper and I'm not too sure the exact company it's from but it should be based on the Active Maths 2 book but anyway I'll try get back to you tomorrow about it

[@SimpleScienceandMaths]

Great thanks, even if you can give me the wording of the first question I might be able to figure out which paper it is

[@charlottegibson9776]

i cant fail ordinary maths again i cant

[@SimpleScienceandMaths]

I would focus on algebra and trigonometry especially word problems

[@charlottegibson9776]

@@SimpleScienceandMaths thank you

[@Jason-jy6js]

How big is your brain?

[@SimpleScienceandMaths]

Average to regular, bordering on medium???

[@Jason-jy6js]

@@SimpleScienceandMaths nice, thanks for the vids

[@SimpleScienceandMaths]

@@Jason-jy6js you're welcome

[@tiernanomahoney8826]

I'm 6th class

[@SimpleScienceandMaths]

Great, did you understand any of this?

[@tiernanomahoney8826]

@@SimpleScienceandMaths a small bit I always get 10 in my sigma T which is the most I could do at the moment

[@nicekerr7367]

ur so cute

[@JasonBrown-ub6be]

Great stuff except you got somewhat lazy when it came to question 9, taking shortcuts which made it difficult to understand

[@SimpleScienceandMaths]

Sorry about that, even maths teachers get tired after more than 2 hours! It actually took more than 3 hours to film and the same again to edit and upload.