These are the statements describing what students need to learn:
- understand and use the derivative of f (x) as the gradient of the tangent to the graph of y = f ( x) at a general point (x, y); the gradient of the tangent as a limit; interpretation as a rate of change, sketching the gradient function for a given curve, second derivatives, differentiation from first principles for small positive integer powers of x and for sin x and cos x. Understand and use the second derivative as the rate of change of gradient; connection to convex and concave sections of curves and points of inflection
- differentiate xn, for rational values of n, and related constant multiples, sums and differences. Differentiate ekx and akx, sin kx, cos kx, tan kx and related sums, differences and constant multiples. Understand and use the derivative of ln x
- apply differentiation to find gradients, tangents, normals, maxima, minima and points of inflection. Identify where functions are increasing or decreasing
- differentiate using the product rule, the quotient rule and the chain rule, including problems involving connected rates of change and inverse functions
- differentiate simple functions and relations defined implicitly or parametrically, for first derivative only
- construct simple differential equations in pure mathematics and in context, (contexts may include kinematics, population growth and modelling the relationship between price and demand)
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Can you get to the target number by multiplying together four different one digit numbers? Can you do it in three different ways? There are nine levels to this online challenge and a virtual Transum Trophy available for each level.
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The students numbered 1 to 8 should sit on the chairs so that no two consecutively numbered students sit next to each other. So far this activity has been accessed 53575 times and 662 Transum Trophies have been awarded for completing it.
