Functions (ME-F1, ME-F2)

5 dot points across 5 inquiry questions. Click any dot point for a focused answer with worked past exam questions where available.

How do parametric equations describe a curve, and how do we convert between parametric and Cartesian forms?

Sketch curves given parametrically, eliminate the parameter to obtain Cartesian equations, and use parametric form for circles, parabolas and lines

A focused answer to the HSC Maths Extension 1 dot point on parametric equations. Eliminating the parameter, sketching parametric curves, and standard parametrisations of lines, circles and parabolas, with worked examples.

13 min answer →

How do we divide one polynomial by another and use the remainder and factor theorems to find roots?

Apply the division algorithm for polynomials and use the remainder and factor theorems to identify and verify factors and roots

A focused answer to the HSC Maths Extension 1 dot point on polynomial division. The division algorithm, the remainder theorem, the factor theorem, and using these to factorise cubics and quartics, with worked examples.

15 min answer →

How does the multiplicity of a root affect the graph of a polynomial near that root?

Sketch polynomial functions using leading-term behaviour, intercepts and the multiplicity of each root

A focused answer to the HSC Maths Extension 1 dot point on graphing polynomials. End behaviour from the leading term, the role of root multiplicity (cross, touch, inflection), y-intercept and turning points, with worked sketches.

14 min answer →

How do we solve polynomial and rational inequalities using sign analysis?

Solve polynomial and rational inequalities by factoring and analysing the sign of each factor across critical values

A focused answer to the HSC Maths Extension 1 dot point on solving polynomial and rational inequalities. Sign tables, critical values, multiplicity behaviour, and the special care needed when a denominator is involved, with worked examples.

14 min answer →

How do the coefficients of a polynomial relate to the sum and product of its roots?

Use the relationships between roots and coefficients (Vieta's formulas) for polynomials of degree two, three and four

A focused answer to the HSC Maths Extension 1 dot point on the relationships between roots and coefficients. Sum and product of roots, sum of roots taken in pairs, and applications to building polynomials from given root conditions, with worked examples.

13 min answer →