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

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

Mr H, on Wednesday 8 September, 2010 at 21:03 said:Thursday 9 September, period 2Introduction to Differentiation

How can we determine the gradient of a curve?

Beginning with linear travel graphs we will look at the parabolic path of a basketball to try and answer this question.

Mr H, on Thursday 9 September, 2010 at 22:10 said:Friday 10 September, period 5Differentiation from First Principles

Mr H, on Sunday 12 September, 2010 at 21:31 said:Monday 13 September, period 1Starter: Find the equation of the parabola below

Recap ‘first principles’ lesson then use to differentiate some basic functions,

e.g. f(x) = 3x, f(x) = x²

Consolidate mental rule “Multiply by the power, take one from the power” – practice differentiating polynomial functions.

Introduce practical experiment which will be carried out on Tuesday – calculating the gravitational constant.

Mr H, on Monday 13 September, 2010 at 10:28 said:There are times when we need to work faster.

More of the class need to review a days work more often to allow us to progress effectively lesson to lesson.

Too much time spent going over work covered on Friday.

Practical lesson described, starter completed but not as much time as planned spent practicing finding derivatives.

Class are to be prepared for practical lesson by ensuring they can find the equation of a parabola from its graph.

Mr H, on Monday 13 September, 2010 at 10:28 said:Tuesday 14 September, period 4Practical experiment:

Use a digital camera and softball to capture video of parabolic flight of a ball.

Use Windows Movie Maker on laptops to freeze frame the videos and estimate height of ball for each frame (frame rate 4/100 sec)

Plot on graph pa[er and determine equation of the parabola.

Final task is to deduce how to determine an experimental value for the gravitational constant.

Mr H, on Tuesday 14 September, 2010 at 16:09 said:Best results were RS & DM with g = -9.6 m/s²

Most results came in between -8 and -12.

Variations were due to experimental error estimating position of the ball. Some pairs tried different values for a point on the curve and obtained different g values.

Well done folks!

Mr H, on Tuesday 14 September, 2010 at 23:07 said:Wednesday 15 September, periods 5 & 6Complete any unfinished gravity calculations. Recap by working through a class example.

Practice differentiating various class created functions.

Mr H, on Thursday 16 September, 2010 at 23:18 said:Thursday 16 September, period 2Discuss Composite Functions homework.

Revise and practice working with indices.

In particular negative and fractional indices.

Homework:Trig FunctionsDue:Thursday 23 SeptemberMr H, on Thursday 16 September, 2010 at 23:21 said:Friday 17 September, period 5Further practice differentiating functions.

Focus on those with negative, fractional powers and with ‘sorting out’ to do before and after the differentiation step.

Use selection from MiA p64-65 E4A & B

cameron, on Sunday 19 September, 2010 at 11:57 said:is the homework the differentiation one? i cant remember and there are too many there to know what the homework is

Mr H, on Sunday 19 September, 2010 at 14:57 said:Hi Cameron, no it’s the Trig Functions homework.

We have a lot more on differentiation to do yet.

Let me know if you have problems completing it.

Mr H, on Sunday 19 September, 2010 at 14:56 said:Monday 20 September, period 1Differentiation Functions Ex4B

Continue to focus on negative/fractional indices and arranging function before and after differentiation step.

Mr H, on Monday 20 September, 2010 at 21:06 said:Tuesday 21 September, period 4&Tangents to curves

Start Ex5A

Mr H, on Tuesday 21 September, 2010 at 22:18 said:Wednesday 22 September, periods 5 & 6Continue working on tangents to curves

Complete Ex5A and Q1-4 from Ex5B

Period 6 – Stationary Points Ex2

Mr H, on Wednesday 22 September, 2010 at 15:35 said:Thursday 23 September, period 2Curve Sketching

Start with a quadratic example and sketch using roots and line of symmetry, repeat by completing the square then finally by stationary points.

Cubic example then start Ex3

Mr H, on Thursday 23 September, 2010 at 23:30 said:Friday 24 September, period 5Continue to practice full curve sketching sum.

Aim for at least three completed in period.

Mr H, on Saturday 25 September, 2010 at 11:11 said:Worked solutions to Curve Sketching questions 9-11:

Maths in Action p75 Q9

Maths in Action p75 Q10

Maths in Action p74 Q11

Use these to check your solutions after you have tried them!

Mr H, on Sunday 26 September, 2010 at 21:20 said:Monday 27 September, period 1Check curve sketching examples completed at home.

Optimisation Ex5A

Cover Q1,5,6 as worked examples

Reminder about homework procedures.

Ask class to bring in tin can from kitchen cupboards for Tuesday’s lesson.

Mr H, on Monday 27 September, 2010 at 11:39 said:Assembly cut into class time so only one full worked example completed.

Mr H, on Monday 27 September, 2010 at 11:39 said:Tuesday 28 September, period 4Applying optimisation to solve practical problem.

“Are the tins in our kitchen cupboards the most efficient construction?”

Use optimisation to deduce whether the tins use the optimal amount of metal.

Mr H, on Wednesday 29 September, 2010 at 13:09 said:Only practice examples completed (fish tank)

Mr H, on Wednesday 29 September, 2010 at 13:09 said:Wednesday 29 September, periods 5 & 6Period 5

Applying optimisation to solve practical problem.

“Are the tins in our kitchen cupboards the most efficient construction?”

Use optimisation to deduce whether the tins use the optimal amount of metal.

Period 6

Introduction to Recurrence Relations

Ex1-3 selected examples