- Mathematics Extension 1
- Year 11
Polynomials
approx. 8 hrs
5 topics
17 concepts
Attain proficiency in Polynomials to optimise your academic results.
approx. 8 hrs
5 topics
17 concepts
Attain proficiency in Polynomials to optimise your academic results.
We help students in Year 11 Mathematics Extension 1 learn the essential skills associated with Polynomials as specified in the NSW Mathematics syllabus. In this program, we teach students extensive algebraic skills to enable them to manipulate polynomials to find rational factors, and fully factorise any given polynomial. In addition, we show students how to sketch polynomials using rational factors.
This learning program is made up of the following 5 topics, broken down into 17 concepts.
Division of polynomials
Add and subtract polynomials and multiply polynomials by linear expressions
Identify a polynomial expression and describe the key features using appropriate terminology
State the degree of a polynomial after adding, subtracting, multiplying or dividing of one or more polynomials
Applications of the remainder or factor theorem
Use given data to find the roots of a polynomial
Equating coefficients of a polynomial
Verify the remainder theorem and use it to find factors
Use the factor theorem and long division to find all zeroes of a polynomial
Graph and identify key features of graphs of power functions including turning point form
Sketch polynomials with degree no more than four by using the leading term, the roots and the x- and y-intercepts
Determine the effect of single, double and triple roots of a polynomial equation on the shape of the graph
Root-coefficient relationships for cubic equations
Root-coefficient relationships for quartic equations
Approximate solutions of equations using Newton's method
Approximate solutions of equations through an iterative process
Approximate solutions of equations by halving the interval
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