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

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