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# STEP 3 Hyperbolic Functions

### Introduction

This module contains STEP 3 questions on Hyperbolic Functions.

Each STEP 3 module consists of 4 STEP questions, some topic notes and useful formulae, a "hints" sheet and a "solutions" booklet.

STEP questions are challenging, so don't worry if you get stuck. These STEP 3 modules assume that you have already begun to develop your problem-solving skills and approach to STEP questions by working on the Foundation modules and the STEP 2 modules.

### About this assignment

Hyperbolic functions are related to the Trigonometric functions, and they can be expressed rather nicely in terms of exponentials. They often appear in Calculus questions (such as Questions 1, 2 and 3 of this module).

Question 3 asks for a proof which can be done by induction. See Foundation Assignment 20 for an introduction to proof by induction. For Question 4 you need a little knowledge of complex numbers, i.e. $i^2=-1$, $\sqrt{-3}=i\sqrt{3}$ and $(a+bi)^2=a^2 - b^2 +2abi$.

Assignment PDF:
Topic Notes:
Solution:

## Useful Links

Underground Mathematics: Selected worked STEP questions

STEP Question database

University of Cambridge Mathematics Faculty: What do we look for?

University of Cambridge Mathematics Faculty: Information about STEP

University of Cambridge Admissions Office: Undergraduate course information for Mathematics

Stephen Siklos' "Advanced Problems in Mathematics" book (external link)

MEI: Worked solutions to STEP questions (external link)

OCR: Exam board information about STEP (external link)

AMSP (Advanced Maths Support programme): Support for University Admission Tests (external link)