 Algebra and Functions Resource description SIMPLIFYING RATIONAL EXPRESSIONS Simplifying by cancelling common factors Factorise and simplify algebraic fractions Self marking spreadsheet revising factorising and simplifying Simplify by cancelling common factors Cancel common factors then multiply and divide Add and subtract algebraic fractions Algebraic fractions 1 Self marking spreadsheet adding and subtracting algebraic fractions Algebraic fractions 2 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 1-1,1-many,many-1,odd, even,periodic Put each function into the correct range section on the answer sheet (answer sheet below) Tarsia Range of a Function activity -Sheet 2 Domain and Range of functions (bbc.co.uk/asguru) Identify the range of a function given the function and it's domain Composite Function Loop Cards Using the functions e(x)=2x-1,f(x)=4x, g(x)=x+5,h(x)=x^2, i(x)=3x+1 find comosite functions. Composite Functions Activity (bbc.co.uk/asguru) Finding gf(x) Composite Functions Multiple Choice Test (bbc.co.uk/asguru) Substituting into functions and finding composite functions Composite Functions Questions (mathsnet.net) Finding fg(x) and gf(x) Composite Functions Questions (mathsnet.net) 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 Inverse Functions True or False (mathsnet.net) Deciding whether inverse functions are true or false A mixture of rational, composite and inverse function exam questions MODULUS FUNCTIONS Calculating the modulus Self marking worksheet for students to calculate the modulus of functions Modulus functions Excel activity to investigate linear, quadratic, cubic and trigonometric modulus functons Comparing modulus functions Excel activity to compare functions like y=x+2, y=mod(x+2) and y=mod(x)+2 Solving modulus equations Self marking worksheet for students to sketch graphs and solve equations involving modulus functions TRIGONOMETRY Trig identities starter Powerpoint reviewing C2 trigonometric identities Secant, Cosecant, Cotangent Powerpoint introducing and proving simple C3 trig identities and proofs Solve equation involving cosec Tan and sec exam question (mathsnet.net) Solve equation involving tan and sec Proof using cosec and sec Proof (mathsnet.net) Proof using cosec2 and sec2 Proof (mathsnet.net) Further proofs with cosec and cot Proof (mathsnet.net) Proof involving difference of 2 squares Proof (mathsnet.net) Proof involving definitions and fractions with trigonometry Explanation and example acosǾ+bsinǾ exam question (mathsnet.net) Worked exam question The identities (mathsnet.net) All the identities on one page. The identities test (asguru) AS Guru test on the identities EXPONENTIALS AND LOGARITHMS Tarsia log dominoes (C2 revision) 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 with exponentials & logs (mathsnet.net) Solve equations using knowledge and properties of logs Loop problem finding the inverse of exponential and natural log functions DIFFERENTIATION Chain rule exam question (mathsnet.net) Exam question using dy/dx=dy/du x du/dx