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I should be able to:
Ordinary Level
– find first and second derivatives of linear, quadratic and cubic functions by rule
– associate derivatives with slopes and tangent lines
– apply differentiation to
• rates of change
• maxima and minima
• curve sketching
Higher Level
– differentiate linear and quadratic functions from first principles
– differentiate the following functions: • polynomial • exponential • trigonometric • rational powers • inverse functions • logarithms
– find the derivatives of sums, differences, products, quotients and compositions of functions of the above form
– apply the differentiation of above functions to solve problems
– use differentiation to find the slope of a tangent to a circle
– recognise integration as the reverse process of differentiation
– use integration to find the average value of a function over an interval
– integrate sums, differences and constant multiples of functions of the form
• x^a where a ∈ Q
• a^x where a ∈ R, a>0
• Sin ax where a ∈ R
• Cos ax where a ∈ R
– determine areas of plane regions bounded by polynomial and exponential curves
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