Chapter 3 – Exponentials FORMULAE FROM THE FORMULA BOOKLET. KNOW HOW TO USE THESE AND KNOW WHICH ONES THAT ARE NOT IN THE BOOKLET. The Questions in this revision are taken from the book so you will be able to find the answers in there.

Chapter 3 Part A See example 1 & 2 I can do or I understand this vv v vv

Chapter 3 Part B KNOW THESE!!!! See examples 3 & 4 I can do or I understand this v v vv vv

Chapter 3 Part B See examples 5 See example 6 See example 7 I can do or I understand this vv vv vv vv vv vv vv vv

Chapter 3 Part S – This section is on how to handle fractional exponents/powers Know these. See example 8 See example 9 & 10 I can do or I understand this vv vv vv vv vv vv

Chapter 3 Part D – This section deals with expanding and factorising terms with exponents. Know how to do this!!! And remember or know how to do these expansions. See examples 11 & 12. 3D.1 Expansion See examples 13 & 14 – 3D.2 Factorisation See examples 15 & 16 I can do or I understand this v v v v v v v v v v v v v v v v v v v v v v

Chapter 3 Part E – This section is about solving for the unknown in the exponents If two exponentials are equal and have the same base then the exponents must be equal. See examples 17 & 18. Solve for x. Hint ensure both sides have the same base so that the exponents can be equated. See example 19. Hint Form a quadratic and solve for x. I can do or I understand this vv vv vv

Chapter 3 Part F – This section is similar to Chp 5 and what happens when add subtract multiply and divide various parts of the function by a constant. I can do or I understand this v This is one of the simplest exponentials. All exponentials of this form pass through (0,1). It is an asymptotic graph because as approaches negative infinity the graph approaches the -axis. So the -axis is an asymptote with equation y = 0. Below is what happens when you add, subtract, multiply or divide by a constant. Make sure you understand this. It is also in Chp 5 – Transformations. Use a graphics calculator or a graphing package (e.g. on the CD contents>demos>graph97 to explore what happens when you use different values for a, b, c & d.

Chapter 3 Part F See example 20 From the graph you can read of the value of x for a given value of y e.g. I can do or I understand this v v

Chapter 3 Part B I can do or I understand this v v This can be found in on the CD Contents>Demos>graph97

Chapter 3 Part G – This section looks at exponentially increasing graphs, growth, and exponentially decreasing graphs, decay. Many real life situations are modeled by by increasing exponential functions such as populations of animals, people and bacteria. IA idea – See World Record for Mouse Infestation. See example 21 I can do or I understand this

Chapter 3 Part G.1 See example 22 & 23 I can do or I understand this vv This can be found in on the CD Contents>Demos>graph99 v

Chapter 3 Part G.2 I can do or I understand this v v

Chapter 3 Part H – You will come across e in Mathematics, Science, Finance & all aspects of Engineering. What point do all the graphs go through on the y-axis? I can do or I understand this v v Where

Chapter 3 Part H I can do or I understand this v v Explore this. It can be found in on the CD Contents>Demos>graph103 v v

Chapter 3 Part H I can do or I understand this v v For more practice go to the review exercises 3A, 3B & 3C.