Saskatchewan Grade 11 Pre-Calculus 2010
Introduction
Saskatchewan's Grade 11 Pre-Calculus 2010 curriculum provides students with mathematical preparation for post-secondary programs requiring calculus. The course develops mathematical thinking, problem-solving skills, and conceptual understanding that form the foundation for advanced mathematics study. This curriculum emphasizes mathematical reasoning, communication, and connections between different mathematical concepts and their applications in various fields including science, engineering, and technology.
Throughout the course, students engage in mathematical investigations that develop their ability to think critically and communicate mathematical ideas effectively. The curriculum encourages students to make connections between mathematical concepts and their applications in real-world contexts.
Functions and Relations
Understanding Functions
Functions form a central concept in mathematics. In this unit, students explore:
- The definition and representation of functions using multiple representations (algebraic, graphical, numerical, verbal)
- Domain and range of functions and their significance
- Function notation and evaluation of functions
- Operations on functions (addition, subtraction, multiplication, division, and composition)
- Inverse functions and their properties
- Transformations of functions (translations, reflections, stretches, and compressions)
Types of Functions
Students study several important types of functions:
- Linear functions and their characteristics (slope, intercepts, rate of change)
- Quadratic functions and multiple forms (vertex form, standard form, factored form)
- Absolute value functions and their properties
- Square root functions and their characteristics
- Rational functions, including identification of asymptotes
- Exponential functions and logarithmic functions as their inverses
Algebra and Number
This unit focuses on developing algebraic skills and understanding number concepts:
- Factoring polynomial expressions using multiple methods
- Solving polynomial equations by factoring
- Simplifying rational expressions
- Solving rational equations
- Operations with radicals and irrational numbers
- Understanding complex numbers and performing operations with them
- Solving systems of equations using multiple methods
Trigonometry
Trigonometry explores the relationships between angles and sides of triangles:
- Angular measurement in degrees and radians, and conversion between the two
- Trigonometric ratios (sine, cosine, tangent, cosecant, secant, cotangent)
- Applying trigonometric ratios to solve right triangles
- The unit circle and trigonometric functions of any angle
- Graphing trigonometric functions with transformations
- Trigonometric identities and their applications
- Solving trigonometric equations
- Applications of trigonometry in real-world contexts
Geometry and Spatial Reasoning
This unit develops geometric thinking skills and covers:
- Properties of triangles, quadrilaterals, and other polygons
- Circle geometry including properties of chords, tangents, secants, and arcs
- Properties of three-dimensional figures
- Geometric proofs using various reasoning methods
- Coordinate geometry including distance, midpoint, and equations
- Transformations of geometric figures and their properties
Statistics
The statistics component introduces students to data analysis:
- Collection of data and various sampling methods
- Organization and representation of data using multiple formats
- Measures of central tendency and interpretation
- Measures of dispersion and what they indicate about data
- Analysis of data and interpretation of results
- Probability concepts and calculations for various events
- Expected value in probability contexts
Mathematical Processes
Throughout the curriculum, students develop key mathematical processes:
- Problem-solving using multiple strategies
- Mathematical reasoning and proof (inductive and deductive)
- Communication of mathematical ideas clearly
- Connections between mathematical concepts and to other disciplines
- Multiple representations of mathematical concepts
- Appropriate use of technology to enhance understanding
Assessment Approaches
Assessment in the Saskatchewan Grade 11 Pre-Calculus curriculum evaluates students' understanding and application of mathematical concepts:
- Concept-focused quizzes and tests
- Skill-reinforcing assignments and homework
- Contextual projects and investigations
- Collaborative problem-solving activities
- Portfolio assessments showing growth over time
- Comprehensive examinations
Evaluation focuses on conceptual understanding, application, communication, and problem-solving abilities rather than rote memorization. The assessment design aims to provide meaningful feedback that guides student learning and measures achievement of curriculum outcomes.
Grade 12 Introduction To Calculus And Grade 12 Advanced Mathematics Manitoba Curriculum Fr...
Pre Calculus 11 Course Outline For Grade 11 Mathematics and Reference File Download Link