Mathematics subject knowledge enhancement course Developing Subject Knowledge - Quadratics

Don’t hesitate to mail (C.Bokhove@soton.ac.uk) or tweet me (@cb1601ej) A bit more about me

Candidates should be able to:

Quadratics - factorising

Useful representations …become tables a b sum prod 1 24 25 2 12 14 3 8 11 4 6 10

Quadratics – completing the square

Quadratics – graphical representation

Activity 1 – Linking forms Match the correct factorised form, completed square form, intercepts, and turning points to each of the seven graphs See Blackboard

Quadratics - the quadratic formula

Activity 2 – Proof sorter See http://nrich.maths.org/1394 and Blackboard

The discriminant The discriminant is the part of the quadratic formula which lies under the square root sign. Investigate the value of the discriminant and the graph of each of the following: What generalisations can you make?

Quadratics The discriminant no real roots 2 real roots 1(repeated) root

Quadratics - simultaneous equations Simultaneous equations can be used to find the point (if any) of intersection of a curve and a straight line. The most common method is to rearrange one of the equations, substitute it into the second, and solve the resulting equation formed. Solve the simultaneous equations Show that the same result can be achieved by two different methods Thinking of a graphical solution, and giving examples, explain how many roots would be possible for sets of such simultaneous equations.

Quadratics - other functions Sometimes equations which are not quadratic may be changed into quadratic equations by making a suitable substitution. Solve the equation: Let the equation can now be written as

Quadratics - other functions How could you solve: If we rearrange we can see: It is always important to check solutions to such equations. Replacing t with x2 has created additional roots which do not satisfy the original equation.

The parabella http://nrich.maths.org/785

What now? Additional readings: Look at the Peter Powers Party activity on Blackboard Read the article from Mathematics Teacher for a very interesting ‘collaborative planning’ session by three teachers. But now, Activity 3: Test your skills by making the quadratics practice exercises (on blackboard). Self-check with answers, and ask questions. (Every 10 minutes or so I’ll try to wrap up, and provide explanations if necessary)

Understanding and skills Activity 4 Log in to Integral and make a start on your subject knowledge by working through the Additional maths materials (Quadratics).  Once you are happy with the content of each section you can take the online multiple choice test. http://integralmaths.org/ (Another useful resource is on http://www.fi.uu.nl/dwo/soton/ . You can register, login, look at instruction but above all, practice, now with the opportunity to enter in-between steps.) Activity 5 Make a start on Developing Deep understanding in Algebra to hand in to me on 19th November.

Further resources Further resources can be found at: http://www.fi.uu.nl/dwo/soton/ http://www.purplemath.com/modules/quadform.htm http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut17_quad.htm http://www.youtube.com/watch?v=4dxF1V52glg