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Further Mathematics WorkshopPowerPoint Presentation

Further Mathematics Workshop

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### Further Mathematics Workshop

Stowupland High School

8th November 2005

See next slide for details of how the lesson on curve sketching was organised

- Lesson followed the slides in this presentation
- “Role play” involved the students in a warm up exercise where they modelled, using their arms, the graphs
- Syllabus specification and key words were then covered with explanation
- Sketching the function (slide 7 ) was a teacher led explanation
- Card matching activity used resource sheets that accompany this lesson
- Students were then given the handout with the opportunity to make their own notes against the six card matching graphs, explaining to themselves how the key features were identified
- Final activity was in pairs working on the questions at the end of the handout

x = 0

y = x

y = -x

x = -y

y = x2

y = - x2

x = y2

y = x3

y = -x3

y = sin x

y = cos x

y = tan x

y = sin2x + cos2x

Role PlayMore role play……

G y = x

M y = 2x

G y = x2

M y = 2x2

G y = x2

M y = (x-1)2

G y = 1/x, x < 0

M y = 1/x, x > 0

G y = 1/x2, x < 0

M y = 1/x2, x < 0

this time in pairs! One person to be George and the other person Mildred.George to always stand in front of Mildred.

- CURVE SKETCHING
- Treatment and sketching of graphs of rational functions.
- FP1C1
- Be able to sketch the graph of y=f(x) obtaining information about symmetry, asymptotes parallel to the axes, intercepts with the co-ordinate axes, behaviour near x=0 and for numerically large x.
- Be able to ascertain the direction from which a curve approaches an asymptote.
- Be able to use a curve to solve an inequality.

Key words

- Rational function
- A function which can be expressed as N(x)/D(x) where N(x) and D(x) are both polynomials and D(x) is not the zero polynomial.

- Polynomial
- F(x) = a0+a1x+a2x2+a3x3+…..+anxn

- Asymptote
- a straight line towards which a curve approaches but ever meet

- Sketch
- show axis intersections, asymptotes, and behaviour of the graph either side of any asymptote.

Sketch the graph y = (3-x)/(2-x)(4-x)

- check where graph crosses axes.
- look for vertical asymptotes.
- find behaviour as x approaches infinity.
- consider approach towards asymptotes.
- check with Autograph or graphical calculator

Card matching activity

- match the six graphs with the six equations
Graph A…..Eqn R

Graph B…..Eqn W

Graph C…..Eqn P

Graph D…..Eqn T

Graph E…..Eqn Q

Graph F…..Eqn S

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