SACE Stage 1 Mathematics – Trigonometry, Counting and Statistics

2.1 Cosine and sine Rules
2.2 Circular Measure and Radian Measure
2.3 Trigonometric functions
2.4 Counting
2.5 Discrete and continuous Random Data
2.6 Samples and Statistical Measures
2.7 Normal Distributions


The study of trigonometry enables students to expand their mathematical modelling into contexts such as construction, design, navigation, and surveying by using periodic functions. The variation in demand for electricity throughout the day, the seasonal variations in climate, and the cycles within the economy are examples of periodic phenomena. Understanding how to model these phenomena, students predict trends in them.

Students extend their understanding of trigonometry into non-right-angled triangles. They learn about one particular family of periodic functions by introducing the basic trigonometric functions, beginning with considering the unit circle using degrees. Radian measure of angles is introduced, the graphs of the trigonometric functions are examined, and their applications in a range of settings are explored. More complex trigonometric functions are explored in SACE Stage 1 Mathematics – Vectors in the Plane and Further Trigonometry.

Counting and Statistics

The study of inferential statistics begins in this unit with the introduction to counting techniques and the use of combinations for counting the number of selections from a group. An exploration of distributions and measures of spread, extending students’ knowledge of the measures of central tendency in statistics, provides background for the study of inferential statistics in Stage 2 Mathematical Methods.

Source – Subject Outline, South Australian Certificate of Education 2023

SACE Stage 1 Mathematics Courses

SACE Stage 1 Mathematics Syllabus

Course Content

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Trigonometric Identities

Radian Measure
Trigonometric Graphs
Counting Techniques
Continuous Random Variables
Discrete Random Variables
Exploring Data
Normal Distribution
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Course Includes

  • 52 Lessons
  • 325 Topics
  • 75 Quizzes