Principled Maths

Y1 Pure, Chapter 14:

Exponentials & logarithms

Y1 Pure Chp14 KO.pdf

Knowledge organiser

Edexcel AS level - P1 Ch14 - Exponentials _ Logs.pdf

Textbook chapter

Y1 Pure Chp14 Solutions.pdf

PMT solutions

Use of Technology

https://sites.google.com/view/mathematics-videos-geogebra/home/a-level-year-1/14-exponentials-and-logarithms

Y1 Pure 14.1

Exponential functions

Intro: function a^x

Intro: asymptotes

Examples of sketching functions of the form a^x

+F1:04-05

Examples of sketching

y = a^x + b

Sketching y = 2^(x - 1) + 3

+F1:09-10

Examples of sketching

y = a^(x+b) + c

Sketching further exponentials

+F1-13 ( maximise (20/x)^x )

Y1 Pure 14.2

y = e^x

Introducing e via compound interest

+F2-01 (another way of deriving e)

Sketching y = e^x

+F1:18-19

Examples of transforming

y = e^x

Sketching y = e^(x - 3) - 6

+F1:21-23

The gradient of e^(kx)

+G2-06 (differentiate)

Examples of gradient functions of e^kx

+F2-04

EXTENSION:

e as an infinite series

Y1 Pure 14.3

Exponential modelling

Modelling: microbiologist problem

Modelling: insect problem

Growth & decay: long-term behaviour

+F7-02 (examples)

Y1 Pure 14.4

Logarithms

Intro: logarithms

Converting between exponential and logarithmic form

Logarithmic graphs

Sketching

y = log_2(x) and y = log_3(x)

+F3:05-06

Examples of sketching

y = log_b(x+a)

Examples of sketching

y = log_b(x+a) + c

Sketching y = log_4(x - 2) + 5

+F3:09-11

Y1 Pure 14.5

Laws of logarithms

Intro: laws of logarithms

Using the laws

Writing in the form log_b(k)

Writing as a single logarithm

Laws of logs: examples

Laws of logs: tougher problem

Laws of logs: proof example

Y1 Pure 14.6

Solving equations using logs

Solve 2^x = 5

+F5:02-03

Taking logs of both sides

+F5:06-08

EXTENSION: changing base

Solve 6^x = 7^(x+1)

+F5:10-12

Spotting hidden quadratics

+F5-18,20-21 (solving)

Dealing with

3^(x+2) and 4^(2x+1)

Solve log_2(x) = 3

+F5:28-31

+F7-07

Y1 Pure 14.7

Working with natural logs (ln)

Intro: natural logarithm ln(x)

Sketching y = ln(x - 4)

+F3:15-16

Sketching y = ln(x - 5) + 2

+F3:18-19

Laws of Logs: in terms of ln(x)

+F4:09-13

Solve e^x = 5

+F5:23-24

Hidden quadratics in terms of e

+f5-26

Solve ln(x) = 3

+F5:33-35

Growth & decay: the cup of water problem

Growth & decay: the metal ball problem

Growth & decay: the rabbits problem

Growth & decay: the dosage problem

Y1 Pure 14.8

Logs and non-linear data

Reduction to linear form: the basic idea

Reducing y = ax^n to linear form

Straight line to curve, example 1

Reducing y = kb^x to linear form

Straight line to curve, example 2

The whole process, example 1

The whole process, example 2

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