Further mathematics workshop
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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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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


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


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.


  • 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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