Algebra and Functions 
Resource description 
SIMPLIFYING RATIONAL EXPRESSIONS 

Simplifying by cancelling common factors 

Self marking spreadsheet revising factorising and simplifying  
Simplify by cancelling common factors  
Cancel common factors then multiply and divide  
Add and subtract algebraic fractions  
Self marking spreadsheet adding and subtracting algebraic fractions  
Self marking spreadsheet adding and subtracting algebraic fractions  
Exam questions  
PROPERTIES OF FUNCTIONS, DOMAIN AND RANGE,COMPOSITE AND INVERSE FUNCTIONS 

Identify properties of graphs such as 11,1many,many1,odd, even,periodic  
Put each function into the correct range section on the answer sheet (answer sheet below)  
Identify the range of a function given the function and it's domain  
Using the functions e(x)=2x1,f(x)=4x, g(x)=x+5,h(x)=x^2, i(x)=3x+1 find comosite functions.  
Finding gf(x)  
Substituting into functions and finding composite functions  
Finding fg(x) and gf(x)  
Finding ff(x) and gg(x)  
Finding the inverse of one, two and three stage functions  
Finding inverse functions and state domain of the function  
Deciding whether inverse functions are true or false  
A mixture of rational, composite and inverse function exam questions  
MODULUS FUNCTIONS 

Self marking worksheet for students to calculate the modulus of functions  
Excel activity to investigate linear, quadratic, cubic and trigonometric modulus functons  
Excel activity to compare functions like y=x+2, y=mod(x+2) and y=mod(x)+2  
Self marking worksheet for students to sketch graphs and solve equations involving modulus functions  
TRIGONOMETRY 

Powerpoint reviewing C2 trigonometric identities  
Powerpoint introducing and proving simple C3 trig identities and proofs  
Solve equation involving cosec  
Solve equation involving tan and sec  
Proof using cosec and sec  
Proof using cosec2 and sec2  
Further proofs with cosec and cot  
Proof involving difference of 2 squares  
Proof involving definitions and fractions with trigonometry  
Explanation and example  
Worked exam question  
All the identities on one page.  
AS Guru test on the identities  
EXPONENTIALS AND LOGARITHMS 

Starter activity covering prior knowledge of logs  
AS Guru revision/research  
Worksheet with links to websites to research key concepts  
Solve equations using knowledge and properties of logs  
Solve equations using knowledge and properties of logs  
Loop problem finding the inverse of exponential and natural log functions  
DIFFERENTIATION 

Exam question using dy/dx=dy/du x du/dx  