Starter – Try this exam question! C2 June 2012

Solutions – Swap and peer mark!

Solutions – Swap and peer mark! write “marked by _______” give them a total out of 10 write some sort of positive feedback 

Differentiation – Part 2 AS Maths, Core 2

Learning Objectives To be able to apply and teach all the rules and processes of differentiation from Core 1 to include indices that are negative or are fractions. This involves: the process of working out the 1st and 2nd derivative finding the gradient of a curve at a given point determining if a function is increasing or decreasing on a given interval finding stationary points determining the nature of a stationary point (minimum or maximum) writing equations of tangents and normal

On mini whiteboards! Steps: Can you write an algorithm for creating the equation of a tangent to a curve at a given point (assume you’re given the original curve’s equation and the x-coordinate of the point)? Steps: 1. Find the y-coordinate of the point by substituting the given x-coordinate into the original equation and solving for y. 2. Find the gradient function of the curve by differentiation (dy/dx). 3. Find the gradient of the tangent by substituting the x-coordinate into dy/dx. 4. Use m and (x, y) to write an equation in the form

On mini-whiteboards! How does your algorithm change if you’re asked to write an equation of the normal to a curve at a given point instead? We need to find the opposite reciprocal gradient instead. dy/dx will give us m and we will need to use 1/m when writing our normal equation.

Example 1 – C2 June 2014 When The gradient of the normal at point P is

Since our tangent is parallel to the line the gradient of the tangent must also be -12. Next, we need to find a point (x, y). To do this, we’ll set the gradient -12 equal to our gradient function dy/dx and solve for x. Substitute x = 1/2 into original to find y. The tangent occurs at pt. (1/2, 6) Use m and (x, y) to write an equation of the tangent.

Dates will be announced on next slide! Speed dating activity! You have approximately 10 – 12 minutes to work out your given question individually. GO! Find someone who has the same colour card as you and verify your answers. I’ll give you a mark scheme to help, but make sure you understand your question enough to teach it to someone else in a moment without using a mark scheme. Fill in your speed dating card Dates will be announced on next slide!

Date one: 6pm Date two: 7pm Date three: 8pm Date four: 9pm Get ready, get set, go….. Date one: 6pm Date two: 7pm Date three: 8pm Date four: 9pm Return home 

Plenary – Summarise Is this easier than before? Are you improving? How do I work out the nature of stationary points? How do I differentiate with negative or fractional powers? Can you recall how to write the equation of a tangent to a curve at a given point? What are the steps for finding the gradient of a curve at a given point? How can I tell if a function is increasing or decreasing at a given point? How do I work out the stationary points of a curve? Can you recall how to write the equation for a normal to a curve at a given point?