Calculus

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It is really important that students understand what differentiation is. Always remember that a derivative is a rate of change. It is also the slope of the tangent to the curve.

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You need to know how to differentiate linear and quadratic functions from first principles

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The definition required for differentiation from first principles must be learnt off: ●

Be able to differentiate various functions and use the product, quotient and chain rules.

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Be able to deal with rates of change. Remember to use the area and volume formulae where necessary. Don’t forget to include units in your answer.

Example: A spherical balloon is being inflated at a rate of 50 cm3/s. Find the rate at which the radius is increasing when the radius of the balloon is 10cm. ● Be able to find the maxima and minima of curves. Use differentiation to sketch curves using turning points, intercepts, points of inflection, increasing and decreasing curves.

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Use differentiation to solve problems involving maxima and minima.

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Be able to sketch the slope function of a curve.

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Be able to find the slope of a tangent to a circle. This was added to the syllabus in recent years and has never been examined. It involves implicit differentiation.

Example: Find the slope of the tangent to the circle x2+ y2=100 at the point (8,6). At the point (8,6) ●

Integrate various functions

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Use integration to find the average value of a function over an interval

The average value of a function y = f(x) over an interval [a,b] is: Example: Find the average value of the function f(x )=3 x 2–2 x+1 on the interval [0,2]. ●

Determine areas of plane regions bounded by polynomial and exponential curves Example: Find the area between the curve y =4– x2 and the X-axis.