It is difficult to hack into the mind of the people who make out the Leaving Cert Maths exam.
One thing is for certain though: They are obsessed with Sequences & Series!
Every year since 2013, Sequences & Series has appeared on multiple occasions (see Tip #7) in both Paper 1 and Paper 2.
This is both good news (see Tip #1) and bad news (see Tip #2) for anyone preparing for the Leaving Cert.
The key is to use this information to your advantage...(see Tip #3).
This blog post highlights a few top tips that should help you prepare for Sequences & Series.
NOTE: Skip to the end of the post to see the Youtube solution to the WORST ANSWERED question in Paper 1 in 2022!
Link to Module and Worksheet Preview
Download the worksheet (which corresponds to eLearning Modules (for students) and Powerpoint (for teachers).
The module can be found here: https://www.tacitmaths.ie/sequencesseries
Tips when Revising Sequences & Series
Tip 1: The GOOD NEWS...there's not much to it!
Worksheet: Pg 2-3
Powerpoint: Page 3 - 6
A Seq. & Series question comes up every year.
In most cases, you are either dealing with an Arithmetic Sequence or Series, or a Geometric Sequence or Series.
Once you have a IDENTIFIED which one you are dealing with, a lot of the time it's just a matter of using the relevant formula correctly. Sounds good right??
2. The BAD NEWS...It comes up everywhere and anywhere.
One of the reasons that Seq. & Series questions are so popular, is they can be inserted anywhere, in combination with any topic.
LC 2022: With the Exponential Function
LC 2020: With Complex Numbers (see example)
LC 2018: With the Factor Theorem
LC 2018 (Paper 2): With the Area & Volume.
And of course, every time Financial Maths appears in the Leaving Cert, it is technically just an application of Sequences & Series!
3. TOP TIP: Use Tip #2 above to your advantage...
Sequences & Series is an excellent tool to maximise the effectiveness of your study time.
Imagine the scenario:
It's two weeks before the LC exam. You don't know what to revise next. What do you do?
Well, if you spend a few hours just doing Seq. & Series exam questions, you are not only covering a topic that is almost certain to come up, but also you are covering all of the other topics mentioned above in Tip #2!
4. What are the key features of an Arithmetic/Geometric sequence?
Worksheet: Page 4
Powerpoint: Page 7 - 10
OK, we're getting a bit technical here.
In LC 2022 the WORST ANSWERED question in Paper 1 was Q5(b), which contained an Arithmetic sequence.
Have a look at the image here.
If students simply appreciated that in an Arithmetic Sequence, the difference between any two terms is the same, then that was the basis of solving that problem!
Another example would be 2018 Q2, which contained a Geometric Sequence.
Note: The Youtube solution to the question above is found at the end of this page. Why not try it out, and see would you have made the same mistake!
5. NON - Arithmetic/Geometric Sequences
OK, OK, I exaggerated slightly in Tip #1.
Very often you will get sequences that are NOT Arithmetic or Geometric (See 2022 Q4 (a) or 2020 Q7).
The key thing here is do NOT ATTEMPT to use a formula for these.
These are all about problem solving.
The only real way to master these properly is through practice.
6. INFINITE Geometric Series
Worksheet: Pg 5
Powerpoint: Page 13-19
It's something that even the greatest minds find it difficult to get their head's around.
How can it be possible to add up an infinite amount of terms in a sequence?
(HINT: Is r < 1 or is r >1...?)
The good news is that the formula is very simple.
The challenge is looking for key words that indicate you are dealing with and Infinite series.
Words like "indefinitely" , "limit" , "infinitely" etc. often can indicate that it's the Infinite Geometric Series you are dealing with.
7. How/When they appear in the Leaving Cert
Prepare for a long list here.
In general, Sequences & Series questions tend to come up in Paper 1, but they frequently appear in Paper 2 also.
They can come up on their own, or as mentioned in Tip #2, combined with other topics.
They can come up as 25 Mark (Part A) or full 50 Mark (Part B) questions.
NOTE: NOT included in this list is Financial Maths, even though it is technically an application of Geometric Series.
Here is a list of when and how Financial Maths has appeared over the last 7 years of the Leaving Cert:
LC 2022: Q4 (Part A, combined with Exponential Functions)
LC 2022: Q5 (Part B)
LC 2021: Q4 (Part A)
LC 2020: Q2 (Part A, combined with Complex Numbers)
LC 2020: Q7 (Part B)
LC 2019: Q7 (Part B)
LC 2018: Q2 (Part A combined with the Factor Theorem)
LC 2018: Q5 (Part A)
LC 2018: Q9 (Part B)
LC 2018: Q7 PAPER 2 (Part B, combined with Area & Volume)
LC 2017: Q4 (Part A)
LC 2016: Q9 (Part B)
BONUS: LC 2022 Q4 Paper 1
How would you have faired with this question in 2022?
Try out the question here first, and then see where the marks were going from the video below.