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AC9M10A05: Year 10 Mathematics Content Descriptor – Algebra
AC9M10A05 Year 10 Mathematics

AC9M10A05 – 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

experiment with functions and relations using digital tools, making and testing conjectures and generalising emerging patterns

Elaborations

  • • applying the graphing zoom functionality of digital tools and systematically refining intervals to identify approximate location of points of intersection of the graphs of \(2\) functions, such as \(x^2=2^x\)
  • • applying a bisection algorithm to determine the approximate location of the horizontal axis intercepts of the graph of a quadratic function such as \(f(x)=2x^2-3x-7\)
  • • applying transformations to the graph of \(x^2+y^2=1\)
  • • identifying the coordinates of any points of intersection of the graph of a linear function with the graph of a quadratic function or a circle
  • • identifying intervals on the real number line over which a given quadratic function is positive or negative
  • • using a table of values to determine when an exponential growth or decay function exceeds or falls below a given value, such as monitoring the trend in value of a share price in a context of exponential growth or decay
  • • investigating how functions and relations serve as the mathematical underpinnings of machine learning, allowing data to be transformed, models to be defined and optimisation to occur

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.