Computation and properties of derivatives (2.3.10 – 2.3.15) estimate numerically the value of a derivative for simple power functions Topic 2.3: examine examples of variable rates of change of non-linear functions Weeks 24–26 Introduction to establish the formula for non-negative integers expanding or by (9 hours) differential factorising calculus understand the concept of the derivative as a function identify and use linearity properties of the derivative calculate derivatives of polynomials Applications of derivatives and anti-derivatives (2.3.16 – 2.3.22) determine instantaneous rates of change determine the slope of a tangent and the equation of the tangent construct and interpret position-time graphs with velocity as the slope of the tangent Topic 2.3: recognise velocity as the first derivative of displacement with respect to Weeks 26–29 Introduction to time (12 hours) differential sketch curves associated with simple polynomials, determine stationary calculus points, and local and global maxima and minima, and examine behaviour as and solve optimisation problems arising in a variety of contexts involving polynomials on finite interval domains calculate anti-derivatives of polynomial functions Week 29–30 Revision and end of course assessment
Weeks 24–26 (9 hours) Topic 2.3: Introduction to differential calculus Computation and properties of derivatives (2.3.10 – 2.3.15) estimate numerically the value of a derivative for simple power functions examine examples of variable rates of change of non-linear functions establish the formula for non-negative integers expanding or by factorising understand the concept of the derivative as a function identify and use linearity properties of the derivative calculate derivatives of polynomials Weeks 26–29 (12 hours) Topic 2.3: Introduction to differential calculus Applications of derivatives and anti-derivatives (2.3.16 – 2.3.22) determine instantaneous rates of change determine the slope of a tangent and the equation of the tangent construct and interpret position-time graphs with velocity as the slope of the tangent recognise velocity as the first derivative of displacement with respect to time sketch curves associated with simple polynomials, determine stationary points, and local and global maxima and minima, and examine behaviour as and solve optimisation problems arising in a variety of contexts involving polynomials on finite interval domains calculate anti-derivatives of polynomial functions Week 29–30 Revision and end of course assessment