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Mathematics / Year 10 / Algebra
Curriculum content descriptions
solve linear inequalities and simultaneous linear equations in 2 variables; interpret solutions graphically and communicate solutions in terms of the situation (AC9M10A02)
Elaborations
- investigating situations involving linear equations in context, such as multiple quotes for a job, or profit and loss; solving the equations graphically, giving solutions in everyday language, such as “break-even point” or “point to change providers” for the job
- describing the solution of simultaneous equations within the context of the situation
- graphing regions corresponding to inequalities in the Cartesian plane; for example, graphing \(2x+3y<24\) and verifying using a test point such as (\(0, 0\))
- identifying all the combinations of trips to the movies, each costing \(\$12\), and ice-skating sessions, each costing \(\$21\), as the integer solutions for an entertainment budget of up to \(\$150\) for the school holidays; expressing algebraically as \(12m+21s\leq150\)
- testing when a circle of a specified radius has a corresponding area greater than a given value, or whether a point satisfies an inequality; for example, whether the point (\(3, 5\)) satisfies \(2y
- investigating the strategies inherent in First Nations Australian children’s instructive games; for example, Weme from the Warlpiri Peoples of central Australia, and their connection to strategies to solve simultaneous linear equations in \(2\) variables
General capabilities
ScOT terms
Critical thinking, Linear equations, Simultaneous equations, Function graphs, Inequations