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ACER Certificate in Mathematics

The ACER Certificate in Mathematics assesses mathematical and numeracy skills across all strands of the curriculum:

  • Number and algebra
  • Measurement and geometry
  • Statistics and probability

The assessment tasks provide information about students’ mathematical knowledge, as well as their ability to apply their knowledge and reasoning skills to solve everyday problems. The tests contain questions of increasing difficulty.

Students who achieve the ACER Certificate in Mathematics will demonstrate the following skills.

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Level 1

Students who achieve the ACER Certificate in Mathematics Level 1 demonstrate mathematical and numeracy skills. Number and Algebra, Measurement and Geometry, Statistics and Probability are assessed. The assessment tasks provide information about students' mathematical knowledge, as well as their ability to apply their knowledge and reasoning skills to solve everyday problems.

Number and algebra:

  • Use addition, subtraction, multiplication and division in questions and problems
  • Recognise and use fractions e.g. on a number line
  • Continue number patterns and find missing numbers in number patterns

Measurement and geometry

  • Tell time and solve problems with time
  • Measure distance and length
  • Recognise and name shapes
  • Find area and perimeter
  • Identify symmetry

Statistics and probability

  • Reading and understand different tables and graphs
  • Use and understand simple probability
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Level 2

Students who achieve the ACER Certificate in Mathematics Level 2 demonstrate mathematical and numeracy skills. Number and Algebra, Measurement and Geometry, Statistics and Probability are assessed. The assessment tasks provide information about students' mathematical knowledge, as well as their ability to apply their knowledge and reasoning skills to solve everyday problems.

Number and algebra

  • Use multiplication and division in multi-step problems
  • Use fractions in calculations or on number lines
  • Add and subtract decimals
  • Continue number patterns including those with decimals, fractions and shapes

Measurement and geometry

  • Tell time and convert between 12 and 24-hour time
  • Read and use timetables
  • Find perimeter and area of shapes
  • Find volume of objects
  • Identify cross-sections
  • Read maps and find the distance between two locations on a map
  • Find and identify angles
  • Reflect or rotate shapes

Statistics and probability

  • Read and understand different tables and graphs including column graphs and pie charts
  • Use and find probability for objects such as dice and spinners

Level 3

Students who achieve the ACER Certificate in Mathematics Level 3 demonstrate mathematical and numeracy skills. Number and Algebra, Measurement and Geometry, Statistics and Probability are assessed. The assessment tasks provide information about students' mathematical knowledge, as well as their ability to apply their knowledge and reasoning skills to solve everyday problems.

Number and algebra

  • Use negative numbers in calculations
  • Solve one and two-step problems
  • Convert between fractions, decimals and percentages
  • Use fractions, decimals and percentages in calculations
  • Interpret distance-time (line) graphs
  • Identify a number pattern that is extended
  • Use proportions and ratios when solving problems

Measurement and geometry

  • Read and interpret timetables
  • Find the area of compound shapes
  • Convert between units of measurement
  • Identify key features of 3D objects such as faces, edges and vertices
  • Match 3D shapes and their nets
  • Identify and give coordinates of a point

Statistics and probability

  • Read and understand tables and graphs including two-way tables
  • Calculate the mean, median, mode and range
  • Use and find probability for a range of different activities
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Level 4

Students who achieve the ACER Certificate in Mathematics Level 4 demonstrate the ability to apply knowledge and skills in problem solving situations, which sometimes may be unfamiliar. Understanding a range of different content areas may be required to answer a question. The content areas included are:

Number and algebra

  • The use and application of real numbers, including index laws and scientific notation
  • Calculation of simple and compound interest, and financial applications
  • Graph, solve and use linear and quadratic equations and inequalities
  • Use algebraic fractions in problems

Measurement and geometry

  • Calculate and use surface area and volume of various 3D shapes to solve problems
  • Solve problems involving scale factors, similarity or congruence
  • Use and apply Pythagoras theorem
  • Use and apply trigonometric ratios

Statistics and probability

  • Calculate and interpret probabilities for a range of different situations
  • Calculate and interpret statistical data including measures of centre (such as mean and median) and measures of spread (such as range and interquartile range)
  • Construct and interpret a range of plots and graphs

Level 5

Students who achieve the ACER Certificate in Mathematics Level 5 demonstrate the ability to apply knowledge and skills in problem solving situations, which sometimes may be unfamiliar. Understanding a range of different content areas may be required to answer a question. The content areas included are:

Number and algebra

  • The use and application of real numbers
  • Calculation of simple and compound interest, and financial applications
  • Graph, solve and use linear and quadratic equations and inequalities
  • Use algebraic fractions in problems
  • Use algebraic and graphical representations of a variety of relations including linear, exponential, quadratic and other simple conics

Measurement and geometry

  • Calculate and use surface area and volume of various 3D shapes to solve problems
  • Solve problems involving scale factors, similarity or congruence
  • Use and apply Pythagoras theorem
  • Use and apply trigonometric ratios
  • Solve problems involving logic and the use of geometrical reasoning and proof

Statistics and probability

  • Calculate and interpret probabilities for a range of different situations
  • Calculate and interpret statistical data including measures of centre (such as mean and median) and measures of spread (such as interquartile range)
  • Construct, interpret and analyse a range of plots and graphs, including univariate and bivariate data sets
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