CHAPTER 7 Exponentials and logarithms (8 – Prior knowledge needed Chapter 1 Chapter 2 Chapter 3 Chapter 4 Technology Graph plotting software to draw the graphs . Use the log, of e and ln button on a calculator. Use spreadsheet software to calculate values of logarithms. Student Book One hour lessons Learning objectives Subject content references Topic links references 1 The function Use and manipulate expressions in F1 Know and use the function Links back to GCSE 7.1 – the form the variable x is an and its where a is positive Ex 7.1A Students learn the terms exponential index Draw and interpret graphs of the growth and exponential decay. The draw form graphs of the form and are made aware Use the to find approximate that there is a difference in the shape of solutions the graph when a < 1 and a > 1, they should understand this. Understand and use logarithms and 2 Logarithms F3 know and use the definition The skills learnt in 1.6 Laws 7.2 – their connection with indices of as the inverse of , where is of indices are used here Ex 7.2A Students start with the laws of logarithms Understand the proof of the laws of positive and Ex 7.2B logarithms in base 10 and the laws of logarithms are F4 understand and use the laws – linked to laws of indices with a proof for of logarithms each law. They work out basic logarithms in base 10 without a calculator. They then move onto using the laws for logarithms of any base and using the button on a calculator. Solve equations in the form 3 The equation F5 equations in the form 7.3 – Understand a proof of the formula Ex 7.3A Students solve equations of the form by to change the base of a logarithm taking the logarithms of both sides. The
CHAPTER 7 – Exponentials and logarithms (8 Prior knowledge needed Chapter 1 Chapter 2 Chapter 3 Chapter 4 Technology Graph plotting software to draw the graphs . Use the log, of e and ln button on a calculator. Use spreadsheet software to calculate values of logarithms. One hour lessons Learning objectives Subject content references Topic links Student Book references 1 The function Students learn the terms exponential growth and exponential decay. The draw graphs of the form and are made aware that there is a difference in the shape of the graph when a < 1 and a > 1, they should understand this. Use and manipulate expressions in the form the variable x is an index Draw and interpret graphs of the form Use the to find approximate solutions F1 – Know and use the function and its where a is positive Links back to GCSE 7.1 Ex 7.1A 2 Logarithms Students start with the laws of logarithms in base 10 and the laws of logarithms are linked to laws of indices with a proof for each law. They work out basic logarithms in base 10 without a calculator. They then move onto using the laws for logarithms of any base and using the button on a calculator. Understand and use logarithms and their connection with indices Understand the proof of the laws of logarithms F3 – know and use the definition of as the inverse of , where is positive and F4 – understand and use the laws of logarithms The skills learnt in 1.6 Laws of indices are used here 7.2 Ex 7.2A Ex 7.2B 3 The equation Students solve equations of the form by taking the logarithms of both sides. The Solve equations in the form Understand a proof of the formula to change the base of a logarithm F5 – equations in the form 7.3 Ex 7.3A
Collins%20A-level%20Maths%20SoW%20Year%201_final.docx