There are a host of ways to find the first derivative on the CAS calculator and to solve calculus problems quickly. Sometimes I think exam writers are well behind what these calculators can do and fail to understand how trivial some problems have become.
Let's start with simple substitution into an equation:
a) Find y at x=3 for y = 2x^2 + 2x + 2
The "|" is important between the equation y = 2x^2 + 2x + 2 and x=3
Let's now find x if we know y. This is a little harder as we have to solve the equation.
b) Find x at y=14 for y = 2x^2 + 2x + 2
The easiest way to do this is to type 14 = 2x^2 + 2x + 2, highlight it using your stylus (this is important!) and then go
interactive->advanced->solve->ok
Note that it find both possible solutions (unlike using numsolve with the incorrect range specified)
Let's find the first derivative. For this use the 2D template in the soft keyboard
Go keyboard -> 2D -> Calc ->
c) Find the 1st derivative of y=2x^2 + 2x + 2
Note that I removed the "y=" this time. I differentiated the expression on purpose as it makes the next part easier.
Finding the 1st derivative/gradient/instantaneous rate of change at a point is also easy.
d) Find the 1st derivative of y = 2x^2 + 2x + 2 at x = 3
As you can see, it is a mix between c) and a)
Last but not least we can find a point for a particular gradient.
e) Find x at y' = 14 for y = 2x^2 + 2x + 2
To find y itself we could repeat a)
It's very much a case of thinking what you need and then finding it. As you can see it can all be done with one line on a CAS calculator, things that would take multiple steps on paper. TanLine is also a useful function that can be investigated and used to quickly find tangents.
Viola!
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Showing posts with label 3B MAT. Show all posts
Showing posts with label 3B MAT. Show all posts
Tuesday, April 3, 2012
Sunday, November 22, 2009
3B MAT/MAS course review
The 3B MAT course finished spot on 13 weeks (I used the remaining 6 weeks for revision and consolidation), which bodes well for the year 12 students moving into the course next year. The second semester is longer to cater for combined year 11/12 classes.
The 3B MAS course ran right down to the line finishing in 17 weeks and the vectors course was barely completed. It is quite full with Trig Identities and Vectors taking up large wads of time to do properly.
Some of my yr 11 3B MAS students are repeating 3B MAS in year 12 (with me again) and I need to lift the pace a little to make sure there is a little more revision time.
3B MAT exam
We used an external exam and the students were able to easily complete the project networks, correlation, linear programming, moving averages, optimisation and simple differentiation questions. Next year when teaching 3B MAT we will need to focus on interpreting graphs and their derivatives, conjectures and applications of differentiation. I'm happy with the two results over 80% (out of 10 students), but kicking myself that I missed one of the students that fell under 30%. I should have picked this one up sooner.
In particular I would find an alternate text to teach problem solving/conjectures with as the Saddler text is a little short on this topic.
In general I am pleased with their results (pat on the back guys) as I gave little in the way of exam tips (I didn't do the exam beforehand for fear of giving too much away!) and there was a 6-8% average increase across the class.
3B MAS exam
Urgh! The lack of revision showed, compared to the MAT paper. The exam also showed that working consistently through the year can work, with marks between the most gifted student and the conscientious student closing to just 3 marks in the calculator section. More work in vectors is required for the three students repeating next year to improve their C&D's to higher marks. They showed great improvement in the calculus sections of the test. With a bit more experience, they should be better able to identify what methods to apply to what questions. My results are skewed to the left with more C & D's than A & B's, but with 5 students, it would be a surprise to get a true bell curve (I would have liked it skewed more the other way!).
The MAS paper was a bit narrow compared to the MAT paper.. I would have liked to see more opportunity to show what they knew - rather than the imbalance of an overly large number of marks for questions that only an A or B student would be able to complete. Some questions were very misleading in their no. of marks compared to the actual work/knowledge required to complete them. Yet this is the price to pay for using external exams to judge how well the course is being delivered.
On to reports now!
The 3B MAS course ran right down to the line finishing in 17 weeks and the vectors course was barely completed. It is quite full with Trig Identities and Vectors taking up large wads of time to do properly.
Some of my yr 11 3B MAS students are repeating 3B MAS in year 12 (with me again) and I need to lift the pace a little to make sure there is a little more revision time.
3B MAT exam
We used an external exam and the students were able to easily complete the project networks, correlation, linear programming, moving averages, optimisation and simple differentiation questions. Next year when teaching 3B MAT we will need to focus on interpreting graphs and their derivatives, conjectures and applications of differentiation. I'm happy with the two results over 80% (out of 10 students), but kicking myself that I missed one of the students that fell under 30%. I should have picked this one up sooner.
In particular I would find an alternate text to teach problem solving/conjectures with as the Saddler text is a little short on this topic.
In general I am pleased with their results (pat on the back guys) as I gave little in the way of exam tips (I didn't do the exam beforehand for fear of giving too much away!) and there was a 6-8% average increase across the class.
3B MAS exam
Urgh! The lack of revision showed, compared to the MAT paper. The exam also showed that working consistently through the year can work, with marks between the most gifted student and the conscientious student closing to just 3 marks in the calculator section. More work in vectors is required for the three students repeating next year to improve their C&D's to higher marks. They showed great improvement in the calculus sections of the test. With a bit more experience, they should be better able to identify what methods to apply to what questions. My results are skewed to the left with more C & D's than A & B's, but with 5 students, it would be a surprise to get a true bell curve (I would have liked it skewed more the other way!).
The MAS paper was a bit narrow compared to the MAT paper.. I would have liked to see more opportunity to show what they knew - rather than the imbalance of an overly large number of marks for questions that only an A or B student would be able to complete. Some questions were very misleading in their no. of marks compared to the actual work/knowledge required to complete them. Yet this is the price to pay for using external exams to judge how well the course is being delivered.
On to reports now!
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