Sinéad Vaughan PhD Study

Resource 1: Gradient as a tangent to a graph at a point

Key learning

  • The gradient of a curve at a given point is defined as the gradient of the tangent to the curve at that point.
  • The gradient function shows the rate of change of one variable with respect to another.

Requisite prior knowledge

  • Finding the gradient of a straight line

Open GeoGebra Book: Gradient as a tangent to a graph at a point

What next?

  • Gradient of chords
  • Differentiation from first principles
  • If f(x) = xn then f'(x) =nxn-1
  • If y = xn then dy/dx =nxn-1
  • If f(x) = axn then f'(x) =naxn-1
  • If y = axn then dy/dx =naxn-1
  • Fluency practice
  • Resource 2: Sketching the gradient function of a curve (GeoGebra)

Resource 2: Sketching the gradient function of a curve

Key learning

  • Sketching the gradient function of a curve
  • Identifying what happens when the value of the gradient of the tangent is zero

Requisite prior knowledge

  • Finding the gradient of a straight line
  • •Exploring the gradient of a curve using GeoGebra

Open GeoGebra book: Sketching the gradient function of a curve

What next?

  • Finding stationary points algebraically using differentiation
  • Fluency practice
  • Finding gradients, tangents and normals
  • Resource 3: Differentiation from First Principles
  • Resource 4: Determining where a function is increasing and decreasing (GeoGebra)

Resource 3: Differentiation from First Principles

Key learning

  • Explore an algebraic approach to finding the gradient of a curve

Requisite prior knowledge

  • Finding the gradient of a straight line – GCSE / Year 12 Coordinate Geometry

Open GeoGebra book: Differentiation from First Principles

What next?

  • Fluency practice
  • Finding gradients, tangents and normals
  • Resource 4: Determining where a function is increasing and decreasing (GeoGebra)

Resource 4: Determining where a function is increasing and decreasing

Key learning

  • Determine where a function is increasing and decreasing

Requisite prior knowledge

  • Sketching the gradient function of a curve
  • Identifying stationary points

Open GeoGebra book: Determining where a function is increasing and decreasing

What next?

  • Determining where functions are increasing and decreasing algebraically using differentiation
  • Fluency practice
  • Classifying stationary points
  • Resource 5: Modelling with Differentiation (GeoGebra)

Resource 5: Modelling with differentiation

Key learning

  • Model real-life situations that involve rates of change, and optimise using differentiation

Requisite prior learning

  • Sketching the gradient function of a curve
  • Identifying stationary points
  • Classifying stationary points
  • Knowledge of formulae for area, volume and surface area for various 2D and 3D shapes

Open GeoGebra book: Modelling with differentiation

What next?

  • Fluency practice
  • Chapter review
  • Topic assessment, including exam-style questions