AlbertaGrade 11
AB Grade 11 Mathematics 20-1 Curriculum
Video lessons and practice for every Mathematics 20-1 topic. Aligned to what Alberta schools teach in Grade 11. Get help with homework anytime.
AB Grade 11 Mathematics 20-1 Curriculum | StudyPugHelp
LO_ID | Learning Outcome-Skills & Procedures | StudyPug Topic |
|---|---|---|
AB.SO.20-1.1 | Demonstrate an understanding of the absolute value of real numbers: Determine the distance of two real numbers from 0 on a number line and relate to absolute value; Determine the absolute value of positive and negative real numbers; Explain how distance between points on a number line relates to absolute value; Determine the absolute value of numerical expressions; Compare and order absolute values of real numbers |
AB.SO.20-1.2 | Solve problems that involve operations on radicals and radical expressions with numerical and variable radicands: Compare and order radical expressions with numerical radicands; Express entire radicals as mixed radicals and vice versa; Perform operations to simplify radical expressions; Rationalize denominators of rational expressions; Identify values for which radical expressions are defined; Solve problems involving radical expressions |
AB.SO.20-1.3 | Solve problems that involve radical equations (limited to square roots): Determine restrictions on variables in radical equations; Solve radical equations algebraically; Verify solutions by substitution; Explain why some algebraically determined roots are extraneous; Solve problems by modeling situations using radical equations |
AB.SO.20-1.4 | Determine equivalent forms of rational expressions (limited to numerators and denominators that are monomials, binomials or trinomials): Compare strategies for rational expressions to those for rational numbers; Explain non-permissible values for rational expressions; Determine equivalent rational expressions by multiplying numerator and denominator; Simplify rational expressions; Explain why non-permissible values remain the same after simplification; Identify and correct errors in simplification of rational expressions |
AB.SO.20-1.5 | Perform operations on rational expressions (limited to numerators and denominators that are monomials, binomials or trinomials): Compare strategies for operations on rational expressions to those on rational numbers; Determine non-permissible values when performing operations; Determine sums and differences of rational expressions; Determine products and quotients of rational expressions; Simplify expressions involving multiple operations on rational expressions |
AB.SO.20-1.6 | Solve problems that involve rational equations (limited to numerators and denominators that are monomials, binomials or trinomials): Determine non-permissible values for variables in rational equations; Solve rational equations algebraically; Explain why some algebraically determined values may not be solutions; Solve problems by modeling situations using rational equations |
AB.SO.20-1.7 | Demonstrate an understanding of angles in standard position 0° to 360°: Sketch angles in standard position; Determine reference angles for angles in standard position; Explain how to determine angles from 0° to 360° with the same reference angle; Illustrate reflection of reference angles in x-axis and y-axis; Determine quadrants for angles in standard position; Draw angles given points on terminal arms; Illustrate points on terminal sides with same reference angle |
AB.SO.20-1.8 | Solve problems, using the three primary trigonometric ratios for angles from 0° to 360° in standard position: Determine distance from origin to points using Pythagorean theorem or distance formula; Calculate trigonometric ratios given points on terminal arms; Determine signs of trigonometric ratios for given angles; Solve trigonometric equations; Determine exact values of trigonometric ratios for special angles; Describe patterns in trigonometric ratio values; Sketch diagrams to represent problems; Solve contextual problems using trigonometric ratios |
AB.SO.20-1.9 | Solve problems, using the cosine law and sine law, including the ambiguous case: Sketch diagrams for non-right triangle problems; Solve non-right triangles using primary trigonometric ratios; Explain steps in proofs of sine and cosine laws; Solve problems using cosine and sine laws; Describe situations with no solution, one solution, or two solutions |
AB.SO.20-1.10 | Factor polynomial expressions of various forms: Factor expressions requiring identification of common factors; Determine if binomials are factors of polynomial expressions; Factor quadratic expressions and expressions with quadratic patterns |
AB.SO.20-1.12 | Analyze quadratic functions of the form y = a(x - p)² + q and determine their characteristics: Explain why given functions are quadratic; Compare graphs of quadratic functions to y = x²; Generalize rules about effects of a, p, and q on quadratic function graphs; Determine vertex coordinates for quadratic functions; Sketch graphs of quadratic functions using transformations; Explain how a and q affect x-intercepts of quadratic functions; Write quadratic functions for given graphs or characteristics |
AB.SO.20-1.13 | Analyze quadratic functions of the form y = ax² + bx + c to identify characteristics of the corresponding graph: Explain the process of completing the square; Convert quadratic functions between y = ax² + bx + c and y = a(x - p)² + q forms; Identify and correct errors in completing the square; Determine characteristics of quadratic functions in y = ax² + bx + c form; Sketch graphs of quadratic functions in y = ax² + bx + c form; Verify equivalence of different forms of quadratic functions; Write quadratic functions to model situations; Solve problems by analyzing quadratic functions |
AB.SO.20-1.14 | Solve problems that involve quadratic equations: Explain relationships among roots, zeros, and x-intercepts of quadratic functions; Derive the quadratic formula; Solve quadratic equations using various strategies; Select and justify methods for solving quadratic equations; Use the discriminant to determine the nature of roots; Identify and correct errors in quadratic equation solutions; Solve problems involving quadratic equations |
AB.SO.20-1.15 | Solve, algebraically and graphically, problems that involve systems of linear-quadratic and quadratic-quadratic equations in two variables: Model situations using systems of equations; Relate systems of equations to problem contexts; Solve systems graphically using technology; Solve systems algebraically; Explain the meaning of intersection points; Explain why systems may have zero, one, two, or infinite solutions; Solve problems involving systems of equations |
AB.SO.20-1.16 | Solve problems that involve linear and quadratic inequalities in two variables: Explain use of test points to determine solution regions; Explain when to use solid or broken lines in inequality solutions; Sketch graphs of linear and quadratic inequalities; Solve problems involving linear and quadratic inequalities |
AB.SO.20-1.17 | Solve problems that involve quadratic inequalities in one variable: Determine solutions to quadratic inequalities using various strategies; Represent and solve problems involving quadratic inequalities; Interpret solutions to quadratic inequality problems |
AB.SO.20-1.18 | Analyze arithmetic sequences and series to solve problems: Identify assumptions in arithmetic sequences and series; Provide examples of arithmetic sequences; Derive rules for general terms of arithmetic sequences; Describe relationships between arithmetic sequences and linear functions; Determine various elements of arithmetic sequences and series; Derive sum formulas for arithmetic series; Solve problems involving arithmetic sequences and series |
AB.SO.20-1.19 | Analyze geometric sequences and series to solve problems: Identify assumptions in geometric sequences and series; Provide examples of geometric sequences; Derive rules for general terms of geometric sequences; Determine various elements of geometric sequences and series; Derive sum formulas for geometric series; Generalize rules for infinite geometric series; Explain convergence and divergence of geometric series; Solve problems involving geometric sequences and series |
AB.SO.20-1.20 | Graph and analyze reciprocal functions (limited to the reciprocal of linear and quadratic functions): Compare graphs of reciprocal functions to their corresponding functions; Identify characteristics of reciprocal function graphs; Explain the relationship between non-permissible values and vertical asymptotes; Graph reciprocal functions with and without technology; Graph original functions given their reciprocal functions |
Alberta Grade 11 Mathematics 20-1 Overview
Mathematics 20-1 is Alberta's Grade 11 pre-calculus pathway, designed for students planning to take Math 30-1 and pursue post-secondary programs in science, engineering, or business. The course covers a wide range of topics that build algebraic reasoning, graphical analysis, and problem-solving skills.
Key Topics in Mathematics 20-1
- Absolute Value and Radicals: Students explore absolute value of real numbers, simplify radical expressions, rationalize denominators, and solve radical equations.
- Rational Expressions and Equations: Students simplify rational expressions, identify non-permissible values, and solve rational equations algebraically.
- Trigonometry: Topics include angles in standard position, reference angles, trigonometric ratios for all quadrants, the sine law, cosine law, and solving non-right triangles.
- Quadratic Functions and Equations: Students analyze and graph quadratic functions using transformations, complete the square, apply the quadratic formula, and use the discriminant.
- Systems of Equations and Inequalities: Students solve linear-quadratic systems graphically and algebraically, and solve linear and quadratic inequalities.
- Sequences and Series: Arithmetic and geometric sequences and series are explored, including infinite geometric series and convergence.
- Reciprocal Functions: Students graph reciprocal functions, identify vertical asymptotes, and connect them to their original functions.
How StudyPug Supports Mathematics 20-1 Students
StudyPug provides video lessons and practice problems for every Mathematics 20-1 topic listed in the Alberta curriculum. Students can watch a lesson before a test, revisit a concept they missed in class, or work ahead at their own pace. Every lesson is broken into short segments that are easy to pause and replay.
Parents looking for Grade 11 math help in Alberta will find that StudyPug covers all the topics their child needs, from factoring and quadratics to trigonometry and series. Students can practice problems, check their work with step-by-step solutions, and build confidence before exams.
Preparing for Math 30-1
Mathematics 20-1 is the direct prerequisite for Math 30-1, which includes the Alberta diploma exam. A strong foundation in quadratic functions, trigonometry, and rational expressions in Grade 11 makes the transition to Grade 12 significantly smoother. StudyPug helps students fill gaps early so they are fully prepared when diploma exam preparation begins.