← Maths Standard 2 syllabus

NSWMaths Standard 2

Year 12: Algebra

6 dot points across 6 inquiry questions. Click any dot point for a focused answer with worked past exam questions where available.

How are linear cost and revenue functions used to model break-even points and profit?

Model practical problems with linear cost and revenue functions and find the break-even point
A focused answer to the HSC Maths Standard 2 dot point on linear modelling and break-even analysis. Fixed and variable costs, revenue functions, profit equations, and graphical or algebraic break-even points with worked Australian small-business examples.
8 min answer →

How do we decide whether a real situation is best modelled by a linear, quadratic, exponential or reciprocal function?

Compare linear and non-linear models of real-world data and select the most appropriate model
A focused answer to the HSC Maths Standard 2 dot point on selecting an appropriate model. Identifying the shape of data from a table or scatterplot, the difference between constant, proportional, multiplicative and inversely proportional change, and worked Australian examples for choosing the right model.
7 min answer →

How are exponential functions used to model growth, decay and compound processes in the real world?

Model practical problems with exponential functions of the form $y = a b^x$ and interpret growth, decay and asymptotes
A focused answer to the HSC Maths Standard 2 dot point on exponential modelling. Growth and decay, the base $b$ and rate, asymptotes, and applications including compound interest, population growth, radioactive decay and depreciation with worked examples.
8 min answer →

How are quadratic functions used to model real-world situations such as projectile motion and maximum revenue?

Model practical situations with quadratic functions and find maximum or minimum values, intercepts and zeros
A focused answer to the HSC Maths Standard 2 dot point on quadratic models. Standard form, finding the vertex, intercepts and zeros, and applying quadratics to projectile motion, maximum revenue and area problems with worked examples.
8 min answer →

How are reciprocal functions used to model inverse variation, and what does the graph look like?

Model practical problems involving reciprocal functions and inverse variation of the form $y = \frac{k}{x}$
A focused answer to the HSC Maths Standard 2 dot point on reciprocal functions and inverse variation. Finding the constant of proportionality, graphing $y = k/x$ , identifying asymptotes, and applying to speed-time, pressure-volume and household budget problems with worked examples.
7 min answer →

How are simultaneous linear equations solved algebraically and graphically, and how are they used to model practical situations?

Solve a pair of simultaneous linear equations graphically and algebraically, and use simultaneous equations to model practical situations
A focused answer to the HSC Maths Standard 2 dot point on simultaneous linear equations. Algebraic solution by substitution and elimination, graphical solution by intersection of lines, and modelling break-even and comparison problems with worked Australian examples.
8 min answer →