New Topic: Differentiation, MiA Higher Ch3

By the end of this topic you will:

• be familiar with the terminology associated with differentiation

• understand the principles of differentiation

• be able to derive the gradient formula of a given function

• be able to calculate the gradient of a tangent to a curve

• be able to use differentiation to solve optimisation problems

Filed under: Higher | Tagged: calculus, differentiation, Higher |

Mr H, on Wednesday 10 September, 2008 at 21:59 said:Thursday 11 September, Periods 2 & 3Introduction to Differentiation

Motion Graphs PPT & WS, calculate gradient of tangents using the normal.

Plot gradient function, derive link between curve and gradient function.

Derive differentaition from first principles if time.

Mr H, on Thursday 11 September, 2008 at 22:06 said:Completed powerpoint and activities, finished quicker than expected due to careers talk for half of 2nd period.

Did not look at first principles.

Mr H, on Thursday 11 September, 2008 at 22:07 said:Friday 12 September, Period 2Recap previous lesson. Complete some examples of finding gradient function.

First principles.

Mr H, on Monday 15 September, 2008 at 11:52 said:Most of class managed to follow proof of differentiation from first principles. Also looked briefly at gradient function of another graph and showed link between powers.

Mr H, on Monday 15 September, 2008 at 11:54 said:Monday 15 September, Period 6Functions starter. Recap work covered.

Basic differentiation, Ex2.

“Multiply by the power, subtract one from the power”

Practice using Show-Me boards before starting Ex2.

Mr H, on Tuesday 16 September, 2008 at 7:48 said:MA late to class due to meeting.

Class worked on starter.

Very quick recap then began Ex2.

Up to Q7 completed.

Mr H, on Tuesday 16 September, 2008 at 7:50 said:Tuesday 16 September, Period 1Differentiation questions on ‘Show-Me’ boards to start then complete Ex2.

See some pupils regarding Algebraic Functions HW while class working if possible.

Homework:Composite & Inverse FunctionsDue:Thursday 25 SeptemberMr H, on Tuesday 16 September, 2008 at 14:27 said:Discussed issues from Algebraic Functions HW.

Quickfire practice differentiating on show-me boards.

Most close to completing Ex2, remainder to be done at home for next lesson.

Mr H, on Tuesday 16 September, 2008 at 14:29 said:Wednesday 17 September, Period 6Indices revision, select examples from Ex3. Continue as class task if weak or set for homework depending on performance.

Move onto differentiating negative/fractional powers, Ex4A.

Mr H, on Wednesday 17 September, 2008 at 15:51 said:Straight Line starter ‘test’ revising weaker topics from the HW exercise. Poor perfoemance with m = tanx question. Most pupils admitted to not going over homework after returned. Alternative strategy needed.

Spent remainder of lesson recapping indices.

Mr H, on Wednesday 17 September, 2008 at 16:04 said:Thursday 18 September, Periods 2 & 3Finsih Indices revision then onto Ex4A and hopefully 4B during 2nd period.

Mr H, on Friday 19 September, 2008 at 8:07 said:After a starter and fairly thorough revision of indices only completed Ex4A up to Q10 by all, some further.

Mr H, on Friday 19 September, 2008 at 8:10 said:Friday 19 September, Period 2Go over some examples from end of Ex4A then onto Ex4B.

Mr H, on Friday 19 September, 2008 at 13:10 said:Most of Ex4B covered.

Mr H, on Monday 22 September, 2008 at 13:17 said:Monday 22 Spetember, Period 6Algebraic Functions revision questions to start.

Look at harder examples from Ex4B.

Main lesson – Tangents to curves Ex5A.

Mr H, on Monday 22 September, 2008 at 16:50 said:Response to revision questions still not good enough. Not enough pupils going over their homework and solutions and addressing issues.

Not sure what to try next to encourage greater responsibilty.

All tasks completed and Ex5A started (long ‘lecture’ regarding homework used up time)

Mr H, on Monday 22 September, 2008 at 16:52 said:Tuesday 23 September, Period 1Complete Tangents Ex5A and begin Ex5B.

Mr H, on Tuesday 23 September, 2008 at 10:46 said:Done

Mr H, on Wednesday 24 September, 2008 at 14:54 said:Thursday 25 September, Periods 2 & 3[School closed to pupils on Wednesday due to Unison industrial action]

Review topic to date and look ahead and elements still to cover.

Starter problems on quadratics, will need to be able to obtain function for quadratic from coordinates for Monday’s lesson.

Complete Ex5B and Sketching Derived Functions if time.

Homework due today.

Mr H, on Thursday 25 September, 2008 at 23:54 said:Spent some time on quadratics and discussing topic to date and to come.

Completed Ex5B. Will leave derived functions until later.

Mr H, on Friday 26 September, 2008 at 0:01 said:Friday 26 September, Period 2Displacement, Velocity & Acceleration

Practical exercise based on walking, obtain motion graph then determine velocity and acceleration.

Complete examples from Ex7.

Stop early to record videos of softball pitched across projector screen for Mondays lesson.

Rachael Bews, Rebecca Hodgson and Lynn Semple, on Wednesday 22 October, 2008 at 14:53 said:We need help…

We are really confused with the homework

Differention 2 is the worst and the gradient of the tangent

Please Help =]

Mr H, on Wednesday 22 October, 2008 at 20:19 said:It is a tough one but you can do it!

Here are some hints for each question that might help.

You need to reply with any specific bits if needed though.

Q1 (a)

Stationary points are points where the gradient is zero. So you need to differentiate the function to obtain the derivative (formula for gradient at any point, x, on the function). and find when it equals zero.

Q1 (b)

Decreasing = down = negative gradient

(Increasing = up = positive gradient)

In your working for part (a) you should have a nature table for your stationary points. Look at it to see where the gradient is negative and write down when it is.

Q2

Differentiate and find value of h'(t) when t = 3.

Q3

Look at the curve sketching examples in your jotter and the help sheet you had on the day I was away. (let me know if you don’t have it)

This question breaks down the curve sketching sum into three parts.

Q4

Firstly don’t be put off by the ‘v’ and ‘u’, they are just the same as using ‘y’ and ‘x’.

You must get the function ready to differentiate, i.e. rearrange the second fraction. (use indices and look at early Ex’s in class jotter)

Q5

This is an optimisation question. You have a couple of examples very similar in your class jotter.

This question is always in two stages, prove the formula (given) then differentiate the formula and find a maximum or minimum.

Check your jotter and see if you can follow an example with the equivalent to part (a).

Even if you can’t manage (a) you can still do (b) by differentiating the answer (given) and using stat-pts and a nature table to find the maximum.

Have another shot and use your class jotter. Every question has very, very similar copies in your jotter!

Get back to me to let me know how you got on and for more help [if needed 😉 ]