# Joe’s Jotter: What Maths You Should know for Higher Level Paper 1 2023

Paper 1 usually contains Algebra, Complex numbers, Functions and graphs, Indices and Logs, Financial Maths, Numbers, Proof by induction.

__What do you need to learn off for Paper 1?__

- Prove that Root 2 is irrational
- Construct Root 2 and Root 3
- Derive the amortisation formula
- Derive De-Moivres theorem
- Derive Sum to Infinity of a Geometric Series
- Use differentiation from first principles method on a:

- Linear Function
- Quadratic Function

- Learn Proof by Induction methods for:
- Divisibility
- Series
- Inequality

*See your textbook for full details all of these*

__Algebra__

- This is the most important topic on the course, and it is very hard to score well unless you know it. It is a massive part of Paper 1 and Paper 2, but more so Paper 1
- Know solving, simplifying terms, multiplying terms, dividing terms, quadratic equations, inequalities, simultaneous equations, modulus equations etc…

__Logs__

- Logs seem to be appearing more lately -> Know how to use the basic rules of logs from page 21 of your log tables (LT) – These are well worth practicing finding out when to use which rule.. do some basic examples from your book to get started here.
- Logs appear when you get an unknown as a power (5 to the power of p and we are trying to solve for p) e.g. 5
^{p}

__Complex Numbers__

- Multiplying and dividing complex numbers is really important
- Convert a complex number into polar form
- De-Moivres theory is always worth learning

__Proof by Induction__

- You need to practice this technique and just know what the three basic steps are here
- Prove true for n=1, Assume true for n=k and prove is true for n=k+1

__Sequences and Series (Patterns)__

- This could be a number pattern or a picture pattern
- You will need to be able to predict future patterns and come up with a formula to describe the pattern presented
- Big Emphasis on the formula’s here for the Arithmetic sequence and the Geometric Sequence – Page 22 of the Log tables
- The Sum to infinity of a geometric series is a popular question
- The best way to prepare for this question is to practice past exam questions..

__Calculus (Differentiation and Integration)__

__Differentiation__

- Diff (80%) Integ (20%) That 20% integration comes up every year so it’s worth knowing
- Differentiation appears on Section A, but can also appear with functions on Section B
- ‘Max’/’Min’ or similar words used – Differentiate the function…let equal to zero and solve
- Practice Product, Quotient, and chain rules here from log tables
- Again you could be asked to differentiate a trig function (sin, cos, or tan). Page 26 of the Log tables will help you here. Indices links in here.
- Rates of change…Rate is always something over dt as it’s how an object changes over time e.g. of this might be how an area change over time da/dt…
- Again practice past questions here…

- ‘Slope of a line or a tangent’ also means differentiation. This can appear on either paper…
- Can appear on Paper 2

__Integration__

- Integration is the opposite of Differentiation

Know..

- How to use the rules of Integration (Log Tables Page 26)
- Find the area underneath a curve. (The Trapezoidal rule from the Ordinary level course could appear here with this)
- Find the average value of a function [Learn this formula – Not in LT]

__Financial Maths__

- Students get a little hung up on this topic given it is only one section of many in P1..
- There is way more in the books than is needed in my opinion
- Know how to deal with Taking out money (Loans) and Depositing money
- Know how to use your Sn Formula from P22 of log Tables
- Know how to use your Amortisation Formula from P31 of log tables

Question types include…

- A person needs to have 100,000 in an account by 2050.. Work back, how much should he deposit in his account each month. These are a bit trickier than the loan questions
- Use the amortisation formula to calculate equal payments on a loan. i.e. how much I have to pay back each month? These payments are always the same each month. You need to able to derive the proof of this formula also
- Know how to convert between monthly rate ‘i’ & the Annual rate (APR) & vice versa.

__Functions__

- This involves a link between Algebra and graphs.
- This often appears on Section B and is what I call ‘Equations representing reality’.
- g. The amount of fish in a lake or the path taken by a basketball in motion
- e can be popular here..
- You need to be able to recognise a graph of a function and also answer questions on it
- Trig functions can appear here even though Trig is mainly a Paper 2 topic

More details about Joe’s Maths Tuition Classes for September 2023 for 5^{th} & 6^{th} Year (Leaving Certificate Students) and his Award Winning ACE Maths Solution Books for all students can be found via the below links:

**ACE Maths Classes: **acesolutionbooks.com/ace-maths-tuition

**ACE Maths Solution Books:** acesolutionbooks.com/ace-solution-books-package/

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