My Inquiry Year13-GO SOLO AS91587(3.6) Differentiation

My learners found SOLO  taxonomy very useful to understand the NCEA breakdown A/M/E.
We are almost halfway of the topic and planning to sit the mid topic test next week.



Here is the breakdown

Achievement Criteria	Explanatory Notes
Achievement Differentiate functions  and use derivatives to  solve problems. Multi structural-skills	·         Types of functions will be selected from: -      power -      exponential (base e only) -      logarithmic (base e only) -      trigonometric (including reciprocal functions). ·         Differentiation of functions may include the use of the chain  rule and product and quotient rules for expanded polynomials: -          chain rule with polynomials in expanded form such as i           (x2 + 5x)7 iii        7e2x iv        ln(2x + 7) v         sin5x -          product and quotient rules for combinations of straightforward  functions, at least one of which is in expanded polynomial form, such as i           x2. sinx ii         (2x3- 4).ex iii         2x   . Iv (x + 3) products, such as (3x2 –7)3(4x + 8) or                    v quotients, such as
	·         Problems may include: -        optimisation of a given function -        rates of change which may involve kinematics -        finding equations of normals and tangents -        locating maxima and minima of polynomial functions.
MERIT Demonstrate knowledge of advanced concepts and techniques of differentiation and solve differentiation problems. Relational - Explain,Relate, sketch,two steps, and modelling	·         Knowledge, concepts and techniques of differentiation will be selected  from the following types: -        sketching the graph of a derived function from a given graph -        differentiation of combinations of functions including: i         implicit differentiation such as x2+ 3y2 = 15 ii        parametric differentiation for first derivative only -        identifying features of given graphs involving a selection from: i         limits ii        differentiability iii       discontinuity iv       gradients v        concavity vi       turning points vii      points of inflection -        sketching graphs to demonstrate knowledge of the above features.

	·         Problems may involve: -        interpretation of features of graph -        modelling of a situation -        optimisation -        related rates of change, involving two directly related rates.
EXCELLENCE  Solve more complex differentiation problem(s). Extended Abstract- proof, establish a model	·         Problems may involve: -        establishing a model -        a proof -        testing the nature of turning points and verifying points of inflection -        related rates of change involving more than three related rates,  eg dh/dt = dh/dθ.dθ/dv.dv/dt -        the use of higher derivatives including parametric and implicit  differentiation techniques.