Year 10 Bomaderry High School Mathematics program 2006
Topic: 17
Curve sketching and polynomials
Report outcome(s)
Recognise, describe and sketch polynomials
Syllabus Ref
Stage 5.3 Program
Suggested time:
2 weeks
Knowledge and skills
Reg
PAS5.3.7
Recognising polynomial expressions and using the terms degree, leading term,
leading coefficient, constant tern and monic polynomial appropriately
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PAS5.3.7
Using the notation P(x) for polynomials and P(c) to indicate the value of P(x)
at x = c.
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Adding and subtracting polynomials and multiplying polynomials by linear
expressions
Dividing polynomials by linear expressions to find the quotient and remainder,
expressing the polynomial as the product of the linear expression and another
polynomial plus a remainder eg. P(x) = (x – a) Q(x) + R(x)
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PAS5.3.7
Verifying the remainder theorem and using it to find factors of polynomials
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PAS5.3.7
Using the factor theorem to factorise certain polynomials completely, and to find
all zeros
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PAS5.3.7
Recognising linear, quadratic and cubic expressions as examples of polynomials
and sketch the graphs of quadratic, cubic and quartic polynomials by factorising
and finding the zeros
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PAS5.3.7
Determining the significance of single, double and triple roots of the polynomial
equation on the shape of the curve
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PAS5.3.7
Using the leading term, the roots of the equation and the x and y intercepts to
sketch polynomials
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All students learn about:
PAS5.3.7
PAS5.3.7
Topic 17 Curve sketching and polynomials
Page 1 of 2
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Year 10 Bomaderry High School Mathematics program 2006
Textbook references
Signpost Advanced 10 Chapter 13
Stage 5.3 Program
Resources
Technology
Graphic calculators
Language Coefficient, cubic, decreasing, degree, dividend, divisor, factor, graph, horizontally,
increasing, intercept, monic, negative, polynomial, positive, quotient, remainder, sketch, vertically, zeros
Suggested activities - Working mathematically
Students learn to:
 Determine the importance of the sign of the leading term of the polynomial on the behaviour of
the curve as x  
 Use a graphics calculator to sketch polynomials of odd or even degree and investigate the
relationship between the number of zeros and the degree of the polynomial
 Describe the key features of a polynomial so the graph of the polynomial can be drawn from the
description
 Discuss the similarities and differences between the graphs of two polynomials such as
y  x 3  x 2  x and y  x 3  x 2  x  1
Assessment strategies used:
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Class topic test
Assignment
Bookwork
Practical work
Short questions
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Other
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Teacher evaluation of topic
How did the unit ‘rate’ in
these areas ?
Time allocated for topic
Student mastery
Suitability of resources
Variety of teaching modes
Appropriate technology used
Literacy strategies used
Teacher comments
Date commenced:
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Head Teacher signature:
Topic 17 Curve sketching and polynomials
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