New Topic: Further Calculus, MiA Unit 3 Ch2
By the end of this topic you will be able to:
• differentiate and integrate functions involving brackets
• differentiate and integrate trig functions
• apply these skills to solve problems
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Filed under: Higher | Tagged: calculus, chain rule, differentiation, integration |
Wednesday 23 February, periods 5 & 6
Starter leading into sketching derived functions for y = sin x and y = cos x.
Define the rule for differentiating sin x and cos x then p221 Ex2A Q1-4, 7,9,11,12.
By second period progress to Ex2B, work through a selection from Q1-4 with class then class fill in gaps.
Aim to cover Q1-4, 6, 8-10 minimum.
Homework Due: Vectors and prelim paper
Work covered as detailed above.
Need to revise exact values and using CAST rule – class will be tested on Friday on this.
Thursday 24 February, period 2
Chain Rule Ex3A
By expanding and differentiating squared and cubed brackets develop a rule for taking a short-cut from original function to derived function, i.e. Chain Rule.
(click to enlarge)
Examples will cover Q1-3 so begin at Q4
As above but only a few beyond Q8
Friday 25 February, period 5
Exact values test, e.g. sin240, cos 3π/4, etc
Ex3B chain rule involving more algebraic manipulation before and after differentiation step.
Exact values better than expected, those who did not so well had not revised.
Most reached Q8 in textbook.
Will come back and cover Q10 as part of topic review.
Monday 28 February, period 1
Short exact values starter.
Using Chain Rule with trig functions Ex 4A
Recap of chain rule with polynomials and differentiating sin/cos.
Selection of examples from Q1-7 then aim to complete remainder within period.
Up to Q10 covered
Tuesday 1 March, period 4
Recap chain rule for ‘brackets’ and trig and develop rule for integrating brackets.
Aim to complete Ex5
Most around Q8-10
Ex to be completed for tomorrow
Wednesday 2 March, periods 5 & 6
Period 5: Integrating Trig Functions, Ex6 and definite integrals Ex7 – selected examples from both ex’s
Period 6: Go over questions from 2010 prelim paper class found most challenging.
Also discuss main issues from Vectors HW
Ex6 Q1(a) to 11(a) & Q15 completed.
Then Ex7 Q1-4 by all, some further on
Spent period 6 discussing Vectors HW and Q23 & 24 from prelim homework.
Homework: Further Calculus
Due: Wednesday 9 March
Thursday 3 March, period 2
Class to work on areas from topic that they feel they need more practice on or complete Chapter Review Ex.
While class working I’ll try and see 3/4 pupils for their progress report interview.
Done