Logarithmic functions
Chapter 40 of 34 strong
RESTS ONConvert exactly between negative or rational powers and reciprocal radical forms, and evaluate constructions whose required roots are exactCH 2Form a function's maximal real domain by excluding zeros of denominators, requiring radicands to be non-negative, requiring denominator radicands to be positive, and intersecting all component restrictionsCH 2Simplify products, quotients and powers with a common positive base by adding, subtracting or multiplying exponents as appropriate, without applying an index law across addition or subtractionCH 7RoundingCH 1State the order of magnitude of a number and interpret changes in ordersFOUNDATIONSMultiplication and divisionCH 9Signed numbersCH 3Decimal place valueFOUNDATIONSSolve a one-step linear equationCH 7Solve equations with unknowns on both sides by collecting them onto one sideCH 1Solve a one-variable linear inequation, reversing the order relation exactly when multiplication or division by a negative value occursCH 3Identify a repeated subexpression, replace it with a temporary variable, solve the resulting quadratic and substitute backCH 1Rearrange to zero, factorise, apply the null factor law and solve the resulting linear equationsCH 1Multiply and divide fractionsCH 1Obtain the domain and range of a relation represented by ordered pairs, a table, a rule or described graph data, preserving set membership and open or closed endpointsCH 2Classify a relation as one-to-one, many-to-one, one-to-many or many-to-many from repeated inputs and outputs or from horizontal- and vertical-line evidenceCH 2Read a transformed rule in normalised form and name its horizontal and vertical translations, axis reflections and reciprocal horizontal or direct vertical dilation factorsCH 2Apply or undo a sequence of transformations in a stated order, with dilations and reflections acting before translations in the normalised parameter formCH 2Determine the exact coefficient carriers of a simple function or relation from enough point, feature or image information, and verify the resulting rule at every supplied conditionCH 2Construct the inverse of a relation by interchanging every ordered pair, hence interchanging domain and range, and map graph points through reflection in y=xCH 3Decide whether the inverse of a function is also a function by testing whether the original is one-to-one, and choose a valid monotone domain restriction when neededCH 3Identify endpoints or central points, domain, range, orientation and correspondence for square-root and cube-root functions and their simple transformationsCH 2Solve equations with the unknown inside a fraction by clearing the denominator firstCH 9Percentage change as a multiplierFOUNDATIONSBuild a table of values from a formula by independent substitutionFOUNDATIONSDecide whether a given transformation linearises a data setFOUNDATIONSSolve a pair of simultaneous linear equations for the shared (x, y)CH 1Translate a described situation into a linear equation in one unknownCH 6
Logarithms and their laws
Rewriting logarithmic expressions
Logarithmic scales
Exponential and logarithmic equations
Logarithmic graphs and rules
Logarithmic models