1.06i i) Understand and be able to use exponential growth C3 Algebra and (i) understand exponential growth and decay – and decay and use the exponential function in Functions (i) modelling. Examples may include the use of in continuous compound interest, radioactive decay, drug concentration decay and exponential growth as a model for population growth. Includes consideration of limitations and refinements of exponential models. 1.07 Differentiation 1.07a a) Understand and be able to use the derivative of as C1 Differentiation (a) understand the gradient of a curve at a point as the limit – the gradient of the tangent to the graph of at a (a) of the gradients of a suitable sequence of chords general point . 1.07b b) Understand and be able to use the gradient of the C1 Differentiation (a) understand the gradient of a curve at a point as the limit – tangent at a point where as: (a) & (b) of the gradients of a suitable sequence of chords 1. the limit of the gradient of a chord as tends to 2. a rate of change of with respect to . Learners should be able to use the notation to denote a rate of change of with respect to . (b) understand the ideas of a derived function and use the notations and Learners should be able to use the notations and and recognise their equivalence. 1.07c c) Understand and be able to sketch the gradient Sketching the gradient function for a given curve is new function for a given curve. content in the reformed specification.
1.06i i) Understand and be able to use exponential growth and decay and use the exponential function in modelling. Examples may include the use of in continuous compound interest, radioactive decay, drug concentration decay and exponential growth as a model for population growth. Includes consideration of limitations and refinements of exponential models. C3 – Algebra and Functions (i) (i) understand exponential growth and decay 1.07 Differentiation 1.07a a) Understand and be able to use the derivative of as the gradient of the tangent to the graph of at a general point . C1 – Differentiation (a) (a) understand the gradient of a curve at a point as the limit of the gradients of a suitable sequence of chords 1.07b b) Understand and be able to use the gradient of the tangent at a point where as: 1. the limit of the gradient of a chord as tends to 2. a rate of change of with respect to . Learners should be able to use the notation to denote a rate of change of with respect to . Learners should be able to use the notations and and recognise their equivalence. C1 – Differentiation (a) & (b) (a) understand the gradient of a curve at a point as the limit of the gradients of a suitable sequence of chords (b) understand the ideas of a derived function and use the notations and 1.07c c) Understand and be able to sketch the gradient function for a given curve. Sketching the gradient function for a given curve is new content in the reformed specification.