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Further Mathematics Workshop

Further Mathematics Workshop. Stowupland High School 8 th November 2005 See next slide for details of how the lesson on curve sketching was organised. Lesson followed the slides in this presentation

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Further Mathematics Workshop

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  1. Further Mathematics Workshop Stowupland High School 8th November 2005 See next slide for details of how the lesson on curve sketching was organised

  2. 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

  3. y = 0 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 Play

  4. More 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.

  5. 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.

  6. 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.

  7. 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

  8. 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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