1. Starter – Try this exam question! C2 June 2012

2. Solutions – Swap and peer mark!

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

4. Differentiation – Part 2
AS Maths, Core 2

5. 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

6. 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

7. 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.

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

9. 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.

10. 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!

11. 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 

12. 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?