Landing Activities: Integrating factor

link to the activity here

Why does the "separation of variables" work with O.D.E. of the 1st order?

The full article here

Modelling curves using logarithms: worksheet

An activity-based worksheet

Jacob Bernoulli & logarithms

Learning Objectives

REVISE and APPLY

• laws of logarithms,
• equation of a straight line,
• finding the equation of a straight line by its gradient and the y- intercept

GET ABLE TO

• Identify if a given data set follows an exponential model
• Evaluate the constants within the model
• Reflect on the behavior of the model for very small or very large values
• Critique the appropriateness of the model

Assessment Objectives (OCR MEI spec)

1.1. construct and present mathematical arguments through the appropriate use of diagrams
Sketching graphs and deduce the values of constants

1.2. understand the mathematical language and set out in the context

2.1 recognise the underline mathematical structure in a situation

3.3 interpret the outputs of a mathematical model in the context of the original situation

3.4 understand that a mathematical model has limitations, can be improved. Evaluate if a model is adequate or appropriate.

Technology

Detailed guidelines for using the graphic calculator and/or GeoGebra applet have been incorporated in the worksheet.

Transferability of knowledge :

Cases where the acquired skills can be used in physics: radiation, measuring the capacity based on a capacitor's discharge current, finding drag coefficient by the kinematic quantities of a falling object.

Inspire-Motivate

"How can  0.0039-inch-thick paper get to be as thick as the Universe?"

Download here

toppling vs sliding 1

Multiplication of two complex numbers in their polar form: A geometrical proof

paradoxical proof by induction

Eubulides was one of Euclides students.Euclides is the "father" of geometry you have studied so far.
Well, Eubulides was pretty famous for his logical paradoxes one of which is :
"this statement is false".
Another example (modified) is the following paradoxical proof by induction :
 Every positive integer is a whole lot less than 1000000.

Proof: 
Base case. 1 is certainly a whole lot less than 1000000.

Induction step. 
If the positive integer k is a whole lot less  than  1000000, then certainly k+1 , which is just slightly bigger than  k, is still a whole lot less than  1000000.

Hence, by mathematical induction, the statement is true for all positive integers.
In particular, a billion is a whole lot less than a million.

What would you say?

Me Further Maths

I do not represent anyone but my enthusiasm.

Don' t blame anyone but me for the thoughts I share.

For me Further Maths is about   curiosity .  What if you  square a negative number.  Time for you to meet the complex numbers.

Further Maths is art: do you know that you can draw a heart by just writing equations? Just use polar coordinates.

For me, Further Maths sometimes is the whole truth which is out there and i want it all. You learned the "suvat" formulae but do they always apply? Why? When? What if? Let's meet mechanics to ask her all about it.

Further Maths is talking about symmetry and the way it explains various aspects of our world. Let you meet group theory to get to know why.

Further Maths is understanding the world of change, why it happens and how it works. Let you meet the differential equations.

Further Maths is being able to foresee the future based on a rather chaotic current and past data. Meet the random walk theory so that you do not walk at random.

Further Maths can :

• boost your reasoning,
• can make your A level maths and grades far more higher,
•  make science lessons even more charming.
• Widen your understanding in economy, business theory and marketing. 

Further maths open doors in universities.

They are not only for the very best achievers .

They are for all the curious ones, the dreamers and the sparkling minds .



Don't put yourself in a narrow frame. Think outside the box. 

Choose Further Maths.

Depy Makri
a maths teacher.