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:
1. Divisibility
2. Series
3. 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

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