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:
  1. Linear Function
  2. Quadratic Function
  • Learn Proof by Induction methods for:
    1. Divisibility
    2. Series
    3. Inequality

See your textbook for full details all of these


  • 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 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. 5p

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)


  • 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 is the opposite of Differentiation


  1. How to use the rules of Integration (Log Tables Page 26)
  2. Find the area underneath a curve. (The Trapezoidal rule from the Ordinary level course could appear here with this)
  3. 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.


  • 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 5th & 6th Year (Leaving Certificate Students) and his Award Winning ACE Maths Solution Books for all students can be found via the below links:

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