This resource has handwritten notes for the first topic of the new Analysis and Approaches HL course, for first exams in 2021. This has the 9 subtopics that are included in SL, plus an additional 7 subtopics for HL. There will also be significant overlap with the A&I Topic 1. I wrote and sold notes for the current IB courses, which have been fairly successful, so I am in the process of writing notes for the new courses, from scratch. My hope is that if you like this resource, please ‘follow’ my shop, so you will be notified when the remainder of the notes become available over the next few months. Please let me know if you have any feedback or improvements that could be made. This topic (algebra) includes: 1.1 - Standard Form/Scientific Notation 1.2 - Arithmetic Sequences 1.3 - Geometric Sequences 1.4 - Compound Interest 1.5 - Exponents and Logs Intro 1.6 - Simple Deductive Proofs 1.7 - More Logarithms 1.8 - Infinite Geometric Series 1.9 - Binomial Theorem 1.10 - Combinatorics [AHL] 1.11 - Partial Fractions [AHL] 1.12 - Intro to Complex Numbers [AHL] 1.13 - Other Complex Forms [AHL] 1.14 - Roots, De Moivre’s Thm. [AHL] 1.15 - More Proof Types [AHL] 1.16 - Solving Systems of 3 Eqs. [AHL]

A full 75 marks test that should be completed in 1 hour 30 minutes. It replicates the actual test that A-level Further Maths students (Edexcel) will have to take. This test will help develop a student’s time management skills and improve their knowledge on complex numbers.

This is a Core Pure 1 predicted paper using old FP1-FP3 exam questions and using the topic tests released by Edexcel to help with your revision. This paper is built on the advanced information released by Edexcel but is merely a prediction. You should ensure you are confident with all aspects of the course including topics not mentioned on the advanced information.

Introduction

This contains a complete set of 250 flahscards covering Pure, Decision and Stats modules. Made using @https://apps.ankiweb.net/

Example and Exercise with brief solutions

Powerpoint presentation on the Taylor and Maclaurin's series for Further Maths 1 for Edexcel specification.

A ‘Teach Further Maths’ Resource 57 Slides To find the cube roots of unity. To illustrate these cube roots on an Argand Diagram. To solve problems relating to the cube roots of unity. To find the nth roots of unity. To illustrate these nth roots on an Argand Diagram. To find the nth roots of any number.

40 slide Powerpoint for Advanced Higher Maths Unit 2: Complex Numbers. There is a brief revision of the basics of Complex numbers followed by a series of questions. The 24 questions (many of them multi-part) require the construction of Argand Diagrams, use of the quadratic formula, polynomial long division, and simultaneous equations. There are fully worked solutions (including diagrams) for complex number topics relating to: Equating Real and Imaginary Parts; Finding square, cube, fourth, fifth and sixth roots of complex numbers (including unity) and plotting them on an Argand diagram; Verifying and finding roots of complex number polynomials; Expanding and simplifying complex numbers using the Binomial Theorem and De Moivre’s Theorem; Interpreting geometrically loci in the complex plane; Conversions between polar and rectangular forms; Complex Conjugates; Exponential Form; Trigonometric identities, substitutions and simplification. The questions are grouped in approximate order of difficulty and to match the usual order of progress through this topic. *Animated workings come up line by line on mouse clicks.*

These two lessons introduce students to the modulus argument format for writing complex number.

A 1 hour test with worked solutions on complex numbers covering the Edexcel A level further maths. It will also likely have the content for other further maths boards too. The test contains questions on: Forms of complex numbers (a+bi, modulus and argument, exponential) Properties of complex numbers (modulus and argument) Solving polynomials with complex roots Argand diagram Loci Integrating with De Moivre’s Theorem Geometric problem solving with roots of unity Complex series sums

A ‘Teach Further Maths’ Resource 43 Slides To recall how to multiply and divide complex numbers in Modulus-Argument form. To understand DeMoivre’s Theorem. To use DeMoivre’s Theorem to find powers of complex numbers. To use DeMoivre’s Theorem to establish trigonometric identities.