Newfoundland and Labrador

A Algebra and Number

• A.1 Develop algebraic reasoning and number sense.

  • A.1.1 Demonstrate an understanding of the absolute value of real numbers.

    • Absolute value and opposites (10-A.11)

  • A.1.2 Solve problems that involve operations on radicals and radical expressions with numerical and variable radicands.

    • Roots of integers (11-K.1)
    • Roots of rational numbers (11-K.2)
    • Find roots using a calculator (11-K.3)
    • Nth roots (11-K.4)
    • Simplify radical expressions with variables I (11-K.5)
    • Simplify radical expressions with variables II (11-K.6)
    • Multiply radical expressions (11-K.7)
    • Divide radical expressions (11-K.8)
    • Add and subtract radical expressions (11-K.9)
    • Simplify radical expressions using the distributive property (11-K.10)
    • Simplify radical expressions using conjugates (11-K.11)

  • A.1.3 Solve problems that involve radical equations (limited to square roots).

    • Solve radical equations (11-K.13)

  • A.1.4 Determine equivalent forms of rational expressions (limited to numerators and denominators that are monomials, binomials or trinomials).

    • Simplify rational expressions (11-M.4)

  • A.1.5 Perform operations on rational expressions (limited to numerators and denominators that are monomials, binomials or trinomials).

    • Multiply and divide rational expressions (11-M.5)
    • Add and subtract rational expressions (11-M.6)

  • A.1.6 Solve problems that involve rational equations (limited to numerators and denominators that are monomials, binomials or trinomials).

    • Solve rational equations (11-M.7)

T Trigonometry

• T.1 Develop trigonometric reasoning.

  • T.1.1 Demonstrate an understanding of angles in standard position [0° to 360°].

    • Graphs of angles II (11-O.3)
    • Coterminal angles (11-O.4)
    • Reference angles (11-O.5)

  • T.1.2 Solve problems, using the three primary trigonometric ratios for angles from 0° to 360° in standard position.

    • Trigonometric ratios: sin, cos and tan (11-Q.1)
    • Trigonometric ratios in similar right triangles (11-Q.3)
    • Find trigonometric ratios using the unit circle (11-Q.4)
    • Sin, cos and tan of special angles (11-Q.5)
    • Find trigonometric functions using a calculator (11-Q.7)
    • Trigonometric ratios: find a side length (11-Q.12)
    • Trigonometric ratios: find an angle measure (11-Q.13)
    • Solve a right triangle (11-Q.14)
    • Area of a triangle: sine formula (11-Q.18)

  • T.1.3 Solve problems, using the cosine law and sine law, including the ambiguous case.

    • Law of Sines (11-Q.15)
    • Law of Cosines (11-Q.16)
    • Solve a triangle (11-Q.17)
    • Area of a triangle: Law of Sines (11-Q.19)

R Relations and Functions

• R.1 Develop algebraic and graphical reasoning through the study of relations.

  • R.1.1 Factor polynomial expressions of the form:

    • R.1.1.1 ax² + bx + c, a does not equal 0, where a, b and c are rational numbers.

      • Factor quadratics with leading coefficient 1 (10-P.3)
      • Factor quadratics with other leading coefficients (10-P.4)
      • Factor quadratics using algebra tiles (10-P.5)
      • Factor quadratics (11-G.2)
      • Solve a quadratic equation by factoring (11-H.8)

    • R.1.1.2 a²x² – b²y², a does not equal 0, b does not equal 0, where a, b and c are rational numbers.

    • R.1.1.3 a(f(x))² + b(f(x)) + c, a does not equal 0, where a, b and c are rational numbers.

      • Factor using a quadratic pattern (11-G.4)

    • R.1.1.4 a²(f(x))² – b²(g(y))², a does not equal 0, b does not equal 0, where a, b and c are rational numbers.

  • R.1.2 Graph and analyze absolute value functions (limited to linear and quadratic functions) to solve problems.

  • R.1.3 Analyze quadratic functions of the form y = a(x – p)² + q and determine the:

    • R.1.3.1 vertex

      • Characteristics of quadratic functions (11-H.1)
      • Graph quadratic functions in vertex form (11-H.4)
      • Find the vertex of a parabola (11-I.2)
      • Write equations of parabolas in vertex form from graphs (11-I.4)
      • Write equations of parabolas in vertex form using properties (11-I.5)
      • Graph parabolas (11-I.6)

    • R.1.3.2 domain and range

      • Graph parabolas (11-I.6)

    • R.1.3.3 direction of opening

      • Identify the direction a parabola opens (11-I.1)

    • R.1.3.4 axis of symmetry

      • Find the axis of symmetry of a parabola (11-I.3)

    • R.1.3.5 x- and y-intercepts.

      • Factor quadratics (11-G.2)
      • Find a quadratic function (11-H.3)
      • Solve a quadratic equation using the zero product property (11-H.7)
      • Solve a quadratic equation by factoring (11-H.8)

  • R.1.4 Analyze quadratic functions of the form y = ax² + bx + c to identify characteristics of the corresponding graph, including:

    • R.1.4.1 vertex to solve problems.

      • Characteristics of quadratic functions (11-H.1)
      • Graph quadratic functions in vertex form (11-H.4)
      • Find the vertex of a parabola (11-I.2)

    • R.1.4.2 domain and range to solve problems.

    • R.1.4.3 direction of opening to solve problems.

      • Identify the direction a parabola opens (11-I.1)

    • R.1.4.4 axis of symmetry to solve problems.

      • Characteristics of quadratic functions (11-H.1)
      • Find the axis of symmetry of a parabola (11-I.3)

    • R.1.4.5 x- and y-intercepts to solve problems.

      • Characteristics of quadratic functions (11-H.1)
      • Find a quadratic function (11-H.3)
      • Solve a quadratic equation using the zero product property (11-H.7)
      • Solve a quadratic equation by factoring (11-H.8)

  • R.1.5 Solve problems that involve quadratic equations.

    • Solve a quadratic equation using square roots (11-H.6)
    • Solve a quadratic equation using the zero product property (11-H.7)
    • Solve a quadratic equation by factoring (11-H.8)
    • Complete the square (11-H.9)
    • Solve a quadratic equation using the quadratic formula (11-H.11)
    • Using the discriminant (11-H.12)

  • R.1.6 Solve, algebraically and graphically, problems that involve systems of linear-quadratic and quadratic-quadratic equations in two variables.

    • Solve a nonlinear system of equations (11-E.12)

  • R.1.7 Solve problems that involve linear and quadratic inequalities in two variables.

    • Graph a linear inequality in the coordinate plane (11-C.2)
    • Write a linear inequality: word problems (11-C.4)
    • Is (x, y) a solution to the system of inequalities? (11-F.1)
    • Find the vertices of a solution set (11-F.3)
    • Linear programming (11-F.4)

  • R.1.8 Solve problems that involve quadratic inequalities in one variable.

    • Graph solutions to quadratic inequalities (11-C.9)
    • Solve quadratic inequalities (11-C.10)

  • R.1.9 Analyze arithmetic sequences and series to solve problems.

    • Classify formulas and sequences (11-X.1)
    • Find terms of an arithmetic sequence (11-X.2)
    • Evaluate formulas for sequences (11-X.5)
    • Write a formula for an arithmetic sequence (11-X.6)
    • Sequences: mixed review (11-X.9)
    • Introduction to sigma notation (11-X.10)
    • Identify arithmetic and geometric series (11-X.11)
    • Find the sum of a finite arithmetic or geometric series (11-X.12)
    • Partial sums of arithmetic series (11-X.14)
    • Partial sums: mixed review (11-X.16)

  • R.1.10 Analyze geometric sequences and series to solve problems.

    • Classify formulas and sequences (11-X.1)
    • Find terms of a geometric sequence (11-X.3)
    • Evaluate formulas for sequences (11-X.5)
    • Write a formula for a geometric sequence (11-X.7)
    • Sequences: mixed review (11-X.9)
    • Introduction to sigma notation (11-X.10)
    • Identify arithmetic and geometric series (11-X.11)
    • Find the sum of a finite arithmetic or geometric series (11-X.12)
    • Partial sums of geometric series (11-X.15)
    • Partial sums: mixed review (11-X.16)
    • Convergent and divergent geometric series (11-X.17)
    • Find the value of an infinite geometric series (11-X.18)

  • R.1.11 Graph and analyze reciprocal functions (limited to the reciprocal of linear and quadratic functions).

    • Rational functions: asymptotes and excluded values (11-M.1)