Algebra and Functions |
Resource description |
SIMPLIFYING RATIONAL EXPRESSIONS |
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Simplifying by cancelling common factors |
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| 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 |
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| 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) | |
| Identify the range of a function given the function and it's domain | |
| 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. | |
| 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 |
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| 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 |
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| 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 |
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| 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 |
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| Exam question using dy/dx=dy/du x du/dx | |