Newfoundland and Labrador

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Skills available for Newfoundland and Labrador grade 12 math curriculum

Objectives are in black and IXL math skills are in dark green. Hold your mouse over the name of a skill to view a sample question. Click on the name of a skill to practise that skill.

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Set Theory

  • Develop logical reasoning.

    • 12.LR1 Analyze puzzles and games that involve numerical and logical reasoning, using problem solving strategies.

      • 12.LR1.1 Determine, explain and verify a strategy to solve a puzzle or to win a game; e.g.,

        • 12.LR1.1.a guess and check

        • 12.LR1.1.b look for a pattern

        • 12.LR1.1.c make a systematic list

        • 12.LR1.1.d draw or model

        • 12.LR1.1.e eliminate possibilities

        • 12.LR1.1.f simplify the original problem

        • 12.LR1.1.g work backward

        • 12.LR1.1.h develop alternative approaches.

      • 12.LR1.2 Identify and correct errors in a solution to a puzzle or in a strategy for winning a game.

      • 12.LR1.3 Create a variation on a puzzle or a game, and describe a strategy for solving the puzzle or winning the game.

    • 12.LR2 Solve problems that involve the application of set theory.

      • 12.LR2.1 Provide examples of the empty set, disjoint sets, subsets and universal sets in context, and explain the reasoning.

      • 12.LR2.2 Organize information such as collected data and number properties, using graphic organizers, and explain the reasoning.

      • 12.LR2.3 Explain what a specified region in a Venn diagram represents, using connecting words (and, or, not) or set notation.

      • 12.LR2.4 Determine the elements in the complement, the intersection or the union of two sets.

      • 12.LR2.5 Solve a contextual problem that involves sets, and record the solution, using set notation.

      • 12.LR2.6 Identify and correct errors in a solution to a problem that involves sets.

      • 12.LR2.7 Explain how set theory is used in applications such as Internet searches, database queries, data analysis, games and puzzles.

Counting Methods

  • Develop critical thinking skills related to uncertainty.

    • 12.P4 Solve problems that involve the fundamental counting principle.

      • 12.P4.1 Represent and solve counting problems, using a graphic organizer.

      • 12.P4.2 Generalize, using inductive reasoning, the Fundamental Counting Principle.

      • 12.P4.3 Identify and explain assumptions made in solving a counting problem.

      • 12.P4.4 Solve a contextual counting problem, using the Fundamental Counting Principle, and explain the reasoning.

    • 12.P5 Solve problems that involve permutations.

      • 12.P5.1 Represent the number of arrangements of n elements taken n at a time, using factorial notation.

      • 12.P5.2 Determine, with or without technology, the value of a factorial.

      • 12.P5.3 Simplify a numeric or an algebraic fraction that contains factorials in both the numerator and the denominator.

      • 12.P5.4 Solve an equation that involves factorials.

      • 12.P5.5 Determine the number of permutations of n elements taken r at a time.

      • 12.P5.6 Generalize strategies for determining the number of permutations of n elements taken r at a time.

      • 12.P5.7 Determine the number of permutations of n elements taken n at a time where some elements are not distinct.

      • 12.P5.8 Explain, using examples, the effect on the total number of permutations of n elements when two or more elements are identical.

      • 12.P5.9 Solve a contextual problem that involves probability and permutations.

    • 12.P6 Solve problems that involve combinations.

    • 12.LR1 Analyze puzzles and games that involve numerical and logical reasoning, using problem solving strategies.

Probability

  • Develop critical thinking skills related to uncertainty.

    • 12.P1 Interpret and assess the validity of odds and probability statements.

      • 12.P1.1 Provide examples of statements of probability and odds found in fields such as media, biology, sports, medicine, sociology and psychology.

      • 12.P1.2 Explain, using examples, the relationship between odds (part-part) and probability (part-whole).

      • 12.P1.3 Determine the probability of, or the odds for and against, an outcome in a situation.

      • 12.P1.4 Express odds as a probability and vice versa.

      • 12.P1.5 Solve a contextual problem that involves odds or probability.

      • 12.P1.6 Explain, using examples, how decisions may be based on probability or odds and on subjective judgments.

    • 12.P2 Solve problems that involve the probability of mutually exclusive and non-mutually exclusive events.

      • 12.P2.1 Classify events as mutually exclusive or non–mutually exclusive, and explain the reasoning.

      • 12.P2.2 Determine if two events are complementary, and explain the reasoning.

      • 12.P2.3 Represent, using set notation or graphic organizers, mutually exclusive (including complementary) and nonmutually exclusive events.

      • 12.P2.4 Solve a contextual problem that involves the probability of mutually exclusive (including complementary) or non-mutually exclusive events.

      • 12.P2.5 Create and solve a problem that involves mutually exclusive or non-mutually exclusive events.

    • 12.P3 Solve problems that involve the probability of two events.

Rational Expressions and Equations

  • Develop algebraic and graphical reasoning through the study of relations.

    • 12.RF1 Demonstrate equivalent forms of rational expressions (limited to numerators and denominators that are monomials and binomials).

      • 12.RF1.1 Explain why a given value is non-permissible for a given rational expression.

      • 12.RF1.2 Determine the non-permissible values for a rational expression.

      • 12.RF1.3 Compare the strategies for writing equivalent forms of rational expressions to the strategies for writing equivalent forms of rational numbers.

      • 12.RF1.4 Determine a rational expression that is equivalent to a given rational expression by multiplying the numerator and denominator by the same factor (limited to a monomial or a binomial), and state the non-permissible values of the equivalent rational expression.

      • 12.RF1.5 Simplify a rational expression.

      • 12.RF1.6 Explain why the non-permissible values of a given rational expression and its simplified ed form are the same.

      • 12.RF1.7 Identify and correct errors in a given simplification of a rational expression, and explain the reasoning.

    • 12.RF2 Perform operations on rational expressions (limited to numerators and denominators that are monomials and binomials).

      • 12.RF2.1 Compare the strategies for performing a given operation on rational expressions to the strategies for performing the same operation on rational numbers.

      • 12.RF2.2 Determine the non-permissible values when performing operations on rational expressions.

      • 12.RF2.3 Determine, in simplified form, the product or quotient of rational expressions.

      • 12.RF2.4 Determine, in simplified form, the sum or difference of rational expressions that have the same denominator.

      • 12.RF2.5 Determine, in simplified form, the sum or difference of two rational expressions that have different denominators.

    • 12.RF3 Solve problems that involve rational equations (limited to numerators and denominators that are monomials and binomials).

      • 12.RF3.1 Determine the non-permissible values for the variable in a rational equation.

      • 12.RF3.2 Determine the solution to a rational equation algebraically, and explain the strategy used to solve the equation.

      • 12.RF3.3 Explain why a value obtained in solving a rational equation may not be a solution of the equation.

      • 12.RF3.4 Solve a contextual problem that involves a rational equation.

    • 12.LR1 Analyze puzzles and games that involve numerical and logical reasoning, using problem solving strategies.

Polynomial Functions

  • Develop algebraic and graphical reasoning through the study of relations.

Exponential Functions

Logarithmic Functions

Sinusoidal Functions

  • Develop algebraic and graphical reasoning through the study of relations.

    • 12.RF8 Represent data using sinusoidal functions to solve problems.

      • 12.RF8.1 Demonstrate an understanding of angles expressed in degrees and radians.

      • 12.RF8.2 Describe, orally and in written form, the characteristics of a sinusoidal function by analyzing its graph.

      • 12.RF8.3 Interpret the graph of a sinusoidal function that models a situation, and explain the reasoning.

      • 12.RF8.4 Describe, orally and in written form, the characteristics of a sinusoidal function by analyzing its equation.

      • 12.RF8.5 Match equations in a given set to their corresponding graphs.

      • 12.RF8.6 Graph data, and determine the sinusoidal function that best approximates the data.

      • 12.RF8.7 Solve, using technology, a contextual problem that involves data that is best represented by graphs of sinusoidal functions, and explain the reasoning.

Financial Mathematics: Borrowing Money

  • Develop number sense in financial applications.

    • 12.F1 Solve problems that involve compound interest in financial decision making.

      • 12.F1.1 Explain the advantages and disadvantages of compound interest and simple interest.

      • 12.F1.2 Identify situations that involve compound interest.

      • 12.F1.3 Solve a contextual problem that involves compound interest.

      • 12.F1.4 Compare, in a given situation, the total interest paid or earned for different compounding periods.

      • 12.F1.5 Determine the total interest of a loan given the principal, interest rate and number of compounding periods.

      • 12.F1.6 Determine, using technology, the total cost of a loan under a variety of conditions; e.g., different amortization periods, interest rates, compounding periods and terms.

      • 12.F1.7 Determine, using technology, the unknown variable in compound interest loan situations.

      • 12.F1.8 Compare and explain, using technology, different credit options that involve compound interest, including bank and store credit cards and special promotions.

    • 12.F2 Analyze costs and benefits of renting, leasing and buying.

      • 12.F2.1 Identify and describe examples of assets that appreciate or depreciate.

      • 12.F2.2 Compare, using examples, renting, leasing and buying.

      • 12.F2.3 Justify, for a specific set of circumstances, if renting, buying or leasing would be advantageous.

      • 12.F2.4 Solve, using technology, a contextual problem that involves cost-and-benefit analysis.