AC9M10A02 Year 10 Mathematics

AC9M10A02 – Year 10 Mathematics: null

Strand

Algebra

Substrand

Algebra

This Content Descriptor from Year 10 Mathematics provides the specific knowledge and skills students should learn. Use it to plan lessons, create learning sequences, and design assessments that align with the Australian Curriculum v9.

Content Descriptor

solve linear inequalities and simultaneous linear equations in 2 variables; interpret solutions graphically and communicate solutions in terms of the situation

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

Achievement Standard This Supports

This Content Descriptor contributes to the following Achievement Standard:

Year 10 ASMATY10

Year 10 Mathematics Achievement Standard

By the end of Year 10, students recognise the effect of approximations of real numbers in repeated calculations. They use mathematical modelling to solve problems involving growth and decay in financial and other applied situations, applying linear, quadratic and exponential functions as appropriate, and solve related equations, numerically and graphically. Students make and test conjectures involving functions and relations using digital tools. They solve problems involving simultaneous linear equations and linear inequalities in 2 variables graphically and justify solutions. Students interpret and use logarithmic scales representing small or large quantities or change in applied contexts. They solve measurement problems involving surface area and volume of composite objects. Students apply Pythagoras’ theorem and trigonometry to solve practical problems involving right-angled triangles. They identify the impact of measurement errors on the accuracy of results. Students use mathematical modelling to solve practical problems involving proportion and scaling, evaluating and modifying models, and reporting assumptions, methods and findings. They use deductive reasoning, theorems and algorithms to solve spatial problems. Students interpret networks used to represent practical situations and describe connectedness. They plan and conduct statistical investigations involving bivariate data. Students represent the distribution of data involving 2 variables, using tables and scatter plots, and comment on possible association. They analyse inferences and conclusions in the media, noting potential sources of bias. Students compare the distribution of continuous numerical data, using various displays, and discuss distributions in terms of centre, spread, shape and outliers. They apply conditional probability to solve problems involving compound events. Students design and conduct simulations involving conditional probability, using digital tools.