All Junior Cert Mathematics posts
• #### What was todays Paper 1 VampireBlue1234

Was it just me or was maths not great??

1. #### folieapanic

I'm awful at maths and I scraped a 51% in the mocks but I didn't think it was the worst.

That being said, I couldn't even attempt Question 6, and I left quite early (I think it was around 20 to 4) so I could have done awful and I'm just delusional after it :')

2. #### VampireBlue1234

Yea there was some tricky questions alright.. ahh. Lets hope Paper 2 is better!

3. #### Curley-Holmes

thank god, i thought i was the only one. HL? right

4. #### Christy

The amount of letters that were in it 😭

5. #### Dazzla16

As you might expect, Paper 1 HL was easy for me. I understand that not everyone shares my opinion. However, I did enjoy answering questions 3(b) and 14(d), as it required a bit of thought. Looking forward to Paper 2!

6. #### Atom

@Dazzla16, what answers did you get for 14(d) and 3(b)? I've been looking over the questions and I think I got 3(b) when looking over the paper last night (41200, let me know what you got) but I couldn't get theast question. I got a nice and neat 90 percent in my pre and I thought the exam was great, only had issues on those questions and 1(c).

7. #### timone

14d involved a sequence of numbers called the fibanacci numbers

8. #### Dazzla16

@Atom I got the same answer for question 3(b), in fact, this was the workings that I posted on another discussion page:

Here's how you work it out:

Gross income: x

Gross tax:

€33800 . 20% = €6760 (I used the full stop as a multiplication sign so you wont be confused by it and the variable 'x')

(x - €33800) . 40% = 2/5(x - €33800) = 2/5x - €13520

Total Gross tax: €6760 + 2/5x - €13520 = 2/5x - €6760

Tax credit: €3300

Net tax (tax payable): 2/5x - €6760 - €3300 = 2/5x - €10060

Net income: €34780

We know that: Gross income - Net tax = Net income

So: x - (2/5x - €10060) = €34780

5x - (2x - €50300) = €173900 (Multiplied both sides by 5)

5x - 2x + €50300 = €173900 (Remember: double negatives gives you a positive)

3x = €123600

x = €41200

Therefore: the Gross income was €41200.

For 1(c), the answer was: (A U C). The question was testing if you knew the distributive property within sets. In that specific question, it was showing that the union of sets is distributive over intersection.

For 14(d), this is how I explained it in the exam:

When Taylor tries to reach the 100th step by starting by going up 1 step, she will have 99 steps remaining after starting with 1 step. That means she will have T99 ways of getting to the 100th step if she starts by going up 1 step. When Taylor tries to reach the 100th step by starting by going up 2 steps, she will have 98 steps remaining after starting with 2 steps. That means she will have T98 ways of getting to the 100th step if she starts by going up 2 steps. When you combine the amount of ways of getting to the 100th step when starting with 1 step (T99) and the amount of ways of getting to the 100th step when starting with 2 steps (T98), you will get the total amount of ways of getting to the 100th step (T100). Therefore: T100 = T99 + T98. The previous questions give you a hint that there is some kind of pattern. In question 14(c)(i) you are practically listing all the ways of getting to the 4th step, except you add "1 +" to the start of all of them. In question 14(c)(ii) you are practically listing all the ways of getting to the 3rd step, except you add "2 +" to the start of all of them. You then have to realise that T5 = T4 + T3, and for that sequence, this is always true: Tn = (Tn-1) + (Tn-2).

9. #### GymnastMusician3

I thought it was pretty easy compared to the mocks. I was finished at half 3 but still waited until half 4

10. #### Dazzla16

@timone slight correction, it's the Fibonacci numbers. The sequence of Fibonacci numbers were found by Italian mathematician Leonardo Bonacci. He was also a person who popularised the Middle-Eastern (Hindu-Arabic, to be specific) numerical system, where the number 0 was introduced to the Western world.

11. #### Cathy20155

I was really puzzled by 8b where you had to fill in values for the inequality. What was the answer? And also I think I got 3b, 4c,14d and 12ai wrong. Could I still get an a

12. #### Dazzla16

@Cathy20155 you could put in any real number in one of the blanks for question 8(b), as long as you put the exact same number in the other blank. You might now realise that, for example, there is only one possible value of x when 3≤x≤3, x ∈ R.

For 4(c), this is how you work it out:

f(k) = k

3k + 5 = k (as f(x) = 3x + 5)

2k = -5

k = -2.5

For 12(a)(i) it was the difference of two squares, so once you realise that, it's easy to factorise:

n^2 - 1

(n)^2 - (1)^2

(n + 1)(n - 1)

For the other questions, simply look at my previous posts in this discussion page to get the answers.

13. #### Cathy20155

I said 0 is that right?

14. #### Dazzla16

@Cathy20155 if you put 0 in both blanks in question 8(b), then you are correct.

15. #### Cathy20155

Yay!! Ok thank you. It seems to me you could have got 100% by how much you know. With what I got wrong (above) could I still get an a, taking into account a hard marking scheme

16. #### Dazzla16

Thanks! I feel some people are surprised by the fact that I'm only a Junior Cert student doing their exams this year.

17. #### Rburke96

i found the paper super easy! i finished in an hour but the arithmitic part (b) caught me off guard. i got it in the end though! (41,200)

18. #### granners

same RBurke96. did anyone find the paper really easy timing wise, because i did most of it in an hour

19. #### No_Name_Nick

@Dazzla16 Thanks. Now I realise that my answers for 12(a)(i) and 8(b) were right. I was a bit iffy about my answers on those.

This might be my best maths exam since first year.

20. #### Isabelle3b

For 8(b) if you put 1 in both boxes is that wrong?

21. #### No_Name_Nick

Also @ Dazzla, for 14(d) I wrote that T4=T3+T2 and T3=T2+T1, so that kinda means that each T number is gotten by adding the two before it. At least that's how I explained it.

22. #### hamzamughees

Have you ever noticed that the differences between Fibonacci numbers are neither linear, nor quadratic, not even exponential. In fact, If you calculate the difference between a sequence of Fibonacci numbers, you will always get Fibonacci numbers.

23. #### VampireBlue1234

Is that even on the Junior Cert course?

24. #### hamzamughees

Alright maybe not

25. #### hamzamughees

But now we are all moving in to leaving cert. So its good to know.

26. #### granners

I only knew the Fibonacci sequence cuz it was in the da Vinci code :D

hamzahugees, ya I realised it in the exam after trying to draw the graph and it just didn't add up as either linear, quadratic or exponential

27. #### 5678

what was the answer to the inequality question? I know people are saying two of the same number but that's not really an inequality if theyre the same?

28. #### VampireBlue1234

Hahaha wish I had watched it!

29. #### hamzamughees

I wrote x as an answer to that.

30. #### 5678

I think it was a misprint like supposed to say N not R

31. #### granners

I wasn't sure were they asking about the inequality above or just one in general for that question

32. #### 5678

I think it was in general but its not possible for x to be part of the set of real numbers and be only one value unless you use the same number on both sides which seems wrong

33. #### 1234567

I found the paper surprisingly easy.. Am I the only person who thinks this???☺️ I know paper2 will be harder but in general I'm happy

34. #### hamzamughees

Yeah, but the question asked only one possible value, out of the millions we could have written any number, so if you wrote, x is greater than or equal to x and smaller than or equal to x, than x could be any one possible value, that means that the inequality, refers to only one possible value.

35. #### Isabelle3b

so if you wrote the same number in both boxes it was right?

36. #### 5678

yeah I know like it has to be the same number I just think they didn't mean to write R or something cos an inequality cant be the same number

37. #### hamzamughees

No, I think you write x on both side, not a number, just x.

38. #### VampireBlue1234

I think paper 2 will be great:] Looking back on paper one it was actually grand. Do ye think therums will come up?Everyones saying 14.

39. #### hamzamughees

well 19 has no chance of coming up, because it has come up two times, in 2014 and 2012, but i would say there is a fifty fifty chance of it coming up because it came up in 2012 and 2014, so looking at that, it should come up in 2016, not 2015, but I still recommend learning them off, here is a file that you could use to practice your theorems. I would recommend learning 14, first.

40. #### Cathy20155

My grind said that paper 2 will crucify us because they need to make a distinction between a and b/c students. I'm terrified