Newfoundland and Labrador

1 Trigonometry

• Trigonometry

  • 1.T1 Demonstrate an understanding of angles in standard position [0° to 360°].

    • 1.T1.1 Sketch an angle in standard position, given the measure of the angle.

    • 1.T1.2 Determine the quadrant in which a given angle in standard position terminates.

      • Quadrants (11-O.1)
      • Graphs of angles II (11-O.3)

    • 1.T1.3 Determine the reference angle for an angle in standard position.

      • Reference angles (11-O.5)

    • 1.T1.4 Explain, using examples, how to determine the angles from 0° to 360° that have the same reference angle as a given angle.

    • 1.T1.5 Illustrate, using examples, that any angle from 90° to 360° is the reflection in the x-axis and/or the y-axis of its reference angle.

    • 1.T1.6 Draw an angle in standard position given any point P(x, y) on the terminal arm of the angle.

    • 1.T1.7 Illustrate, using examples, that the points P(x, y), P(-x, y), P(-x, -y) and P(x, -y) are points on the terminal arms of angles in standard position that have the same reference angle.

  • 1.T2 Solve problems, using the three primary trigonometric ratios for angles from 0° to 360° in standard position.

    • 1.T2.1 Determine, using the Pythagorean theorem, the distance from the origin to a point P(x, y) on the terminal arm of an angle.

    • 1.T2.2 Determine the value of sin θ, cos θ, or tan θ given any point P(x, y) on the terminal arm of angle θ.

      • Find trigonometric ratios using the unit circle (11-Q.4)

    • 1.T2.3 Determine the sign of a given trigonometric ratio for a given angle, without the use of technology, and explain.

    • 1.T2.4 Sketch a diagram to represent a problem.

    • 1.T2.5 Determine, without the use of technology, the value of sin θ, cos θ, or tan θ given any point P(x, y) on the terminal arm of angle θ, where θ = 0°, 90°, 180°, 270° or 360°.

    • 1.T2.6 Solve, for all values of θ, an equation of the form sin θ = a or cos θ = a, where –1 ≤ a ≤ 1, and an equation of the form tan θ = a, where a is a real number.

      • Inverses of sin, cos and tan (11-Q.8)
      • Solve trigonometric equations I (11-Q.10)
      • Solve trigonometric equations II (11-Q.11)

    • 1.T2.7 Determine the exact value of the sine, cosine or tangent of a given angle with a reference angle of 30°, 45°or 60°.

      • Sin, cos and tan of special angles (11-Q.5)

    • 1.T2.8 Describe patterns in and among the values of the sine, cosine and tangent ratios for angles from to 0° to 360°.

    • 1.T2.9 Solve a contextual problem, using trigonometric ratios.

      • Trigonometric ratios: sin, cos and tan (11-Q.1)
      • Trigonometric ratios in similar right triangles (11-Q.3)
      • 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)

  • 1.T3 Solve problems, using the cosine law and the sine law, including the ambiguous case.

    • 1.T3.1 Sketch a diagram to represent a problem that involves a triangle without a right angle.

    • 1.T3.2 Solve, using primary trigonometric ratios, a triangle that is not a right triangle.

      • 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)

    • 1.T3.3 Explain the steps in a given proof of the sine law and cosine law.

    • 1.T3.4 Sketch a diagram and solve a problem, using the sine law.

    • 1.T3.5 Describe and explain situations in which a problem may have no solution, one solution or two solutions.

    • 1.T3.6 Sketch a diagram and solve a problem, using the cosine law.

2 Quadratic Functions

• Relations and Functions

  • 2.RF3 Analyze quadratics of the form y = a(x - p)² + q, a ≠ 0, and determine the:

    • 2.RF3.a 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)

    • 2.RF3.b domain and range

    • 2.RF3.c direction of opening

      • Graph quadratic functions in vertex form (11-H.4)
      • Identify the direction a parabola opens (11-I.1)
      • Graph parabolas (11-I.6)

    • 2.RF3.d axis of symmetry

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

    • 2.RF3.e x- and y-intercepts.

      • Characteristics of quadratic functions (11-H.1)

    • 2.RF3.1 Explain why a function given in the form y = a(x - p)² + q is a quadratic function.

    • 2.RF3.2 Compare the graphs of a set of functions of the form y = ax² to the graph of y = x² , and generalize, using inductive reasoning, a rule about the effect of a.

    • 2.RF3.3 Compare the graphs of a set of functions of the form y = (x - p)² to the graph of y = x² , and generalize, using inductive reasoning, a rule about the effect of p.

    • 2.RF3.4 Compare the graphs of a set of functions of the form y = x² + q to the graph of y = x², and generalize, using inductive reasoning, a rule about the effect of q.

    • 2.RF3.5 Determine the coordinates of the vertex for a quadratic function of the form y = a(x - p)² + q, and verify with or without technology.

      • 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)

    • 2.RF3.6 Generalize, using inductive reasoning, a rule for determining the coordinates of the vertex for quadratic functions of the form y = a(x - p)² + q.

    • 2.RF3.7 Sketch the graph of y = a(x - p)² + q, using transformations, and identify the vertex, domain and range, direction of opening, axis of symmetry and x- and y-intercepts.

      • Graph quadratic functions in vertex form (11-H.4)

    • 2.RF3.8 Explain, using examples, how the values of a and q may be used to determine whether a quadratic function has zero, one or two x-intercepts.

    • 2.RF3.9 Write a quadratic function in the form y = a(x - p)² + q for a given graph or a set of characteristics of a graph.

      • Find a quadratic function (11-H.3)
      • Write equations of parabolas in vertex form from graphs (11-I.4)
      • Write equations of parabolas in vertex form using properties (11-I.5)

  • 2.RF4 Analyze quadratic functions of the form y = ax² + bx + c, a ≠ 0 to identify characteristics of the corresponding graph, including:

    • 2.RF4.a vertex

      • Characteristics of quadratic functions (11-H.1)
      • Graph quadratic functions in vertex form (11-H.4)

    • 2.RF4.b domain and range

    • 2.RF4.c direction of opening

      • Graph quadratic functions in vertex form (11-H.4)
      • Identify the direction a parabola opens (11-I.1)
      • Graph parabolas (11-I.6)

    • 2.RF4.d axis of symmetry

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

    • 2.RF4.e x- and y-intercepts

      • Characteristics of quadratic functions (11-H.1)

    • 2.RF4.1 Determine the characteristics of a quadratic function given in the form y = ax² + bx + c, and explain the strategy used.

      • Characteristics of quadratic functions (11-H.1)

    • 2.RF4.2 Sketch the graph of a quadratic function given in the form y = ax² + bx + c .

      • Graph quadratic functions in vertex form (11-H.4)

    • 2.RF4.3 Explain the reasoning for the process of completing the square as shown in a given example.

      • Complete the square (11-H.9)

    • 2.RF4.4 Write a quadratic function given in the form y = ax² + bx + c as a quadratic function in the form y = a(x - p)² + q by completing the square.

    • 2.RF4.5 Identify, explain and correct errors in an example of completing the square.

    • 2.RF4.6 Verify, with or without technology, that a quadratic function in the form y = ax² + bx + c represents the same function as a given quadratic function in the form y = a(x - p)² + q.

    • 2.RF4.7 Write a quadratic function that models a given situation, and explain any assumptions made.

    • 2.RF4.8 Solve a problem, with or without technology, by analyzing a quadratic function.

      • 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)

  • 2.RF1 Factor polynomial expressions of the form:

    • 2.RF1.a ax² + bx + c, a ≠ 0

      • Factor quadratics (11-G.2)
      • Factor quadratics using algebra tiles (11-G.3)

    • 2.RF1.b a² x² - b² y² , a ≠ 0, b ≠ 0

      • Factor quadratics: special cases (10-P.6)

    • 2.RF1.c a(f(x))² + b(f(x)) + c, a ≠ 0

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

    • 2.RF1.d a² (f(x))² - b² (g(y))² , a ≠ 0, b ≠ 0

  • 2.RF10 Analyze geometric sequences and series to solve problems.

    • 2.RF10.1 Identify assumptions made when identifying a geometric sequence or series.

    • 2.RF10.2 Provide and justify an example of a geometric sequence.

      • Classify formulas and sequences (11-X.1)

    • 2.RF10.3 Determine a rule for finding the general term of a geometric sequence.

      • Write a formula for a geometric sequence (11-X.7)

    • 2.RF10.4 Determine t?, r, n or t? in a problem that involves a geometric sequence.

      • Find terms of a geometric sequence (11-X.3)

    • 2.RF10.5 Determine a rule for finding the sum of n terms of a geometric series.

    • 2.RF10.6 Determine t?, r, n or S? in a problem that involves a geometric series.

      • Find the sum of a finite arithmetic or geometric series (11-X.12)
      • Partial sums of geometric series (11-X.15)

    • 2.RF10.7 Solve a problem that involves a geometric sequence or series.

      • Find terms of a geometric sequence (11-X.3)
      • Write a formula for a geometric sequence (11-X.7)
      • Find the sum of a finite arithmetic or geometric series (11-X.12)
      • Partial sums of geometric series (11-X.15)

    • 2.RF10.8 Determine if a given a geometric series is convergent or divergent.

      • Convergent and divergent geometric series (11-X.17)

    • 2.RF10.9 Generalize, using inductive reasoning, a rule for determining the sum of an infinite geometric series.

3 Quadratic Equations

• Relations and Functions

  • 3.RF1 Factor polynomial expressions of the form:

    • 3.RF1.a ax² + bx + c, a ≠ 0

      • Factor quadratics (11-G.2)
      • Factor quadratics using algebra tiles (11-G.3)
      • Solve a quadratic equation by factoring (11-H.8)

    • 3.RF1.b a²x² - b²y², a ≠ 0, b ≠ 0

      • Factor quadratics: special cases (10-P.6)

    • 3.RF1.c a(f(x))² + b(f(x)) + c, a ≠ 0

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

    • 3.RF1.d a²(f(x))² - b²(g(y))², a ≠ 0, b ≠ 0

    • 3.RF1.1 Factor a given polynomial expression that requires the identification of common factors.

      • Factor monomials (11-G.1)
      • Factor quadratics (11-G.2)
      • Factor using a quadratic pattern (11-G.4)

    • 3.RF1.2 Factor a given polynomial expression of the form:

      • 3.RF1.2.a ax² + bx + c, a ≠ 0

        • Factor quadratics (11-G.2)
        • Factor quadratics using algebra tiles (11-G.3)
        • Solve a quadratic equation by factoring (11-H.8)

      • 3.RF1.2.b a²x² - b²y², a ≠ 0, b ≠ 0

        • Factor quadratics: special cases (10-P.6)

    • 3.RF1.3 Determine whether a given binomial is a factor for a given polynomial expression, and explain why or why not.

    • 3.RF1.4 Factor a given polynomial expression that has a quadratic pattern, including:

      • 3.RF1.4.a a(f (x))² + b(f(x)) + c, a ≠ 0

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

      • 3.RF1.4.b a²(f (x))² - b²(g(y))², a ≠ 0, b ≠ 0

  • 3.RF5 Solve problems that involve quadratic equations.

    • 3.RF5.1 Explain, using examples, the relationship among the roots of a quadratic equation, the zeros of the corresponding quadratic function and the x-intercepts of the graph of the quadratic function.

    • 3.RF5.2 Solve a quadratic equation of the form ax² + bx + c = 0 by using strategies such as:

      • 3.RF5.2.a determining square roots

        • Solve a quadratic equation using square roots (11-H.6)

      • 3.RF5.2.b factoring

        • Factor quadratics (11-G.2)
        • Factor quadratics using algebra tiles (11-G.3)
        • Solve a quadratic equation by factoring (11-H.8)

      • 3.RF5.2.c completing the square

        • Complete the square (11-H.9)

      • 3.RF5.2.d applying the quadratic formula

        • Solve a quadratic equation using the quadratic formula (11-H.11)

      • 3.RF5.2.e graphing its corresponding function.

    • 3.RF5.3 Derive the quadratic formula, using deductive reasoning.

    • 3.RF5.4 Identify and correct errors in a solution to a quadratic equation.

    • 3.RF5.5 Select a method for solving a quadratic equation, justify the choice, and verify the solution.

    • 3.RF5.6 Explain, using examples, how the discriminant may be used to determine whether a quadratic equation has two, one, or no real (i.e., imaginary) roots; and relate the number of zeros to the graph of the corresponding quadratic function.

      • Using the discriminant (11-H.12)

    • 3.RF5.7 Solve a problem by:

      • 3.RF5.7.a analyzing a quadratic equation

        • 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)

      • 3.RF5.7.b determining and analyzing a quadratic equation.

4 Radical Expressions and Equations

• Algebra and Number

  • 4.AN2 Solve problems that involve operations on radicals and radical expressions with numerical and variable radicands.

    • 4.AN2.1 Compare and order radical expressions with numerical radicands in a given set.

    • 4.AN2.2 Express an entire radical with a numerical radicand as a mixed radical.

      • Simplify radical expressions (10-D.1)

    • 4.AN2.3 Express a mixed radical with a numerical radicand as an entire radical.

    • 4.AN2.4 Explain, using examples, that (-x)² = x² , √x² = |x| and √x² ≠ ±x ; e.g., √9 ≠ ±3 .

    • 4.AN2.5 Identify the values of the variable for which a given radical expression is defined.

    • 4.AN2.6 Express an entire radical with a variable radicand as a mixed radical.

      • Nth roots (11-K.4)
      • Simplify radical expressions with variables I (11-K.5)
      • Simplify radical expressions with variables II (11-K.6)

    • 4.AN2.7 Express a mixed radical with a variable radicand as a entire radical.

    • 4.AN2.8 Perform one or more operations to simplify radical expressions with numerical or variable radicands.

      • 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)

    • 4.AN2.9 Rationalize the denominator of a rational expression with monomial or binomial denominators.

      • Simplify radical expressions using conjugates (11-K.11)

    • 4.AN2.10 Describe the relationship between rationalizing a binomial denominator of a rational expression and the product of the factors of a difference of squares expression.

  • 4.AN3 Solve problems that involve radical equations (limited to square roots with non-negative radicands).

    • 4.AN3.1 Determine any restrictions on values for the variable in a radical equation.

      • Domain and range of radical functions (11-K.12)

    • 4.AN3.2 Determine the roots of a radical equation algebraically, and explain the process used to solve the equation.

      • Solve radical equations (11-K.13)

    • 4.AN3.3 Verify, by substitution, that the values determined in solving a radical equation algebraically are roots of the equation.

    • 4.AN3.4 Explain why some roots determined in solving a radical equation algebraically are extraneous.

    • 4.AN3.5 Solve problems by modeling a situation using a radical equation.

      • Solve radical equations (11-K.13)

5 Rational Expressions and Equations

• Algebra and Number

  • 5.AN4 Determine equivalent forms of rational expressions (limited to numerators and denominators that are monomials, binomials or trinomials).

    • 5.AN4.1 Explain why a given value is non-permissible for a given rational expression.

    • 5.AN4.2 Determine the non-permissible values for a rational expression.

    • 5.AN4.3 Compare the strategies for writing equivalent forms of rational expressions to the strategies for writing equivalent forms of rational numbers.

    • 5.AN4.4 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.

      • Simplify rational expressions (11-M.4)

    • 5.AN4.5 Simplify a rational expression.

      • Simplify rational expressions (11-M.4)

    • 5.AN4.6 Explain why the nonpermissible values of a given rational expression and its simplified form are the same.

    • 5.AN4.7 Identify and correct errors in a given simplification of a rational expression, and explain the reasoning.

  • 5.AN5 Perform operations on rational expressions (limited to numerators and denominators that are monomials, binomials or trinomials.

    • 5.AN5.1 Compare the strategies for performing a given operation on rational expressions to the strategies for performing the same operation on rational numbers.

    • 5.AN5.2 Determine the non-permissible values when performing operations on rational expressions.

    • 5.AN5.3 Determine, in simplified form, the product or quotient of rational expressions.

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

    • 5.AN5.4 Determine, in simplified form, the sum or difference of rational expressions with the same denominator.

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

    • 5.AN5.5 Determine, in simplified form, the sum or difference of rational expressions in which the denominators are not the same and which may or may not contain common factors.

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

    • 5.AN5.6 Simplify an expression that involves two or more operations on rational expressions.

      • Simplify rational expressions (11-M.4)

  • 5.AN6 Solve problems that involve rational equations (limited to numerators and denominators that are monomials, binomials or trinomials).

    • 5.AN6.1 Determine the non-permissible values for the variable in a rational equation.

    • 5.AN6.2 Determine the solution to a rational equation algebraically, and explain the strategy used to solve the equation.

      • Solve rational equations (11-M.7)

    • 5.AN6.3 Explain why a value obtained in solving a rational equation may not be a solution of the equation.

    • 5.AN6.4 Solve problems by modeling a situation using a rational equation.

6 Absolute Value and Reciprocal Functions

• Algebra and Number

  • 6.AN1 Demonstrate an understanding of the absolute value of real numbers.

    • 6.AN1.1 Determine the distance of two real numbers of the form ±a, a ∈ R , from 0 on a number line, and relate this to the absolute value of a (a).

    • 6.AN1.2 Determine the absolute value of a positive or negative real number.

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

    • 6.AN1.3 Explain, using examples, how distance between two points on a number line can be expressed in terms of absolute value.

    • 6.AN1.4 Determine the absolute value of a numerical expression.

    • 6.AN1.5 Compare and order the absolute values of real numbers in a given set.

• Relations and Functions

  • 6.RF2 Graph and analyze absolute value functions (limited to linear and quadratic functions) to solve problems.

    • 6.RF2.1 Create a table of values for y = |f(x)|, given a table of values for y = f(x).

    • 6.RF2.2 Sketch the graph of y = |f(x)|; state the intercepts, domain and range; and explain the strategy used.

    • 6.RF2.3 Generalize a rule for writing absolute value functions in piecewise notation.

    • 6.RF2.4 Solve an absolute value equation graphically, with or without technology.

    • 6.RF2.5 Solve, algebraically, an equation with a single absolute value, and verify the solution.

      • Solve absolute value equations (11-B.4)

    • 6.RF2.6 Explain why the absolute value equation |f(x)|< 0 has no solution.

    • 6.RF2.7 Determine and correct errors in a solution to an absolute value equation.

    • 6.RF2.8 Solve a problem that involves an absolute value function.

      • Graph solutions to absolute value equations (11-B.5)

  • 6.RF11 Graph and analyze reciprocal functions (limited to the reciprocal of linear and quadratic functions).

    • 6.RF11.1 Compare the graph of y= 1/f(x) to the graph of y = f(x).

    • 6.RF11.2 Identify, given a function f(x), values of x for which y = 1/f(x) will have vertical asymptotes; and describe their relationship to the non-permissible values of the related rational expression.

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

    • 6.RF11.3 Graph, with or without technology, y = 1/f(x), given y = f(x) as a function or a graph, and explain the strategies used.

    • 6.RF11.4 Graph, with or without technology, y= f(x) given y = 1/f(x) as a function or a graph, and explain the strategies used.

7 Systems of Equations

• Relations and Functions

  • 7.RF6 Solve, algebraically and graphically, problems that involve systems of linear-quadratic and quadratic-quadratic equations in two variables.

    • 7.RF6.1 Explain the meaning of the points of intersection of a system of linear-quadratic or quadratic-quadratic equations.

    • 7.RF6.2 Explain, using examples, why a system of linear-quadratic or quadratic-quadratic equations may have zero, one, two or an infinite number of solutions.

    • 7.RF6.3 Determine and verify the solution(s) of a system of linear-quadratic or quadratic-quadratic equations graphically, with and without technology.

    • 7.RF6.4 Determine and verify the real solution(s) of a system of linear-quadratic or quadratic-quadratic equations algebraically.

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

    • 7.RF6.5 Model a situation, using a system of linear-quadratic or quadratic-quadratic equations.

    • 7.RF6.6 Relate a system of linear-quadratic or quadratic-quadratic equations to the context of a given problem.

    • 7.RF6.7 Solve a problem that involves a system of linear-quadratic or quadratic-quadratic equations, and explain the strategy used.

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

8 Linear and Quadratic Inequalities

• Relations and Functions

  • 8.RF7 Solve problems that involve linear and quadratic inequalities in two variables.

    • 8.RF7.1 Explain, using examples, how test points can be used to determine the solution region that satisfies a linear inequality.

    • 8.RF7.2 Explain, using examples, when a solid or broken line should be used in the solution for a linear inequality.

    • 8.RF7.3 Sketch, with or without technology, the graph of a linear inequality.

      • Graph a linear inequality in one variable (11-C.1)
      • Graph a linear inequality in the coordinate plane (11-C.2)
      • Graph solutions to linear inequalities (11-C.6)

    • 8.RF7.4 Solve a problem that involves a linear inequality.

      • Write a linear inequality: word problems (11-C.4)
      • Solve linear inequalities (11-C.5)

    • 8.RF7.5 Explain, using examples, how test points can be used to determine the solution region that satisfies a quadratic inequality.

    • 8.RF7.6 Explain, using examples, when a solid or broken line should be used in the solution for a quadratic inequality.

    • 8.RF7.7 Sketch, with or without technology, the graph of a quadratic inequality.

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

    • 8.RF7.8 Solve a problem that involves a quadratic inequality.

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

  • 8.RF8 Solve problems that involve quadratic inequalities in one variable.

    • 8.RF8.1 Determine the solution of a quadratic inequality in one variable, using strategies such as case analysis, graphing, roots and test points, or sign analysis; and explain the strategy used.

      • Solve quadratic inequalities (11-C.10)

    • 8.RF8.2 Represent and solve a problem that involves a quadratic inequality in one variable.

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

    • 8.RF8.3 Interpret the solution to a problem that involves a quadratic inequality in one variable.

9 Sequences and Series

• Relations and Functions

  • 9.RF9 Analyze arithmetic sequences and series to solve problems.

    • 9.RF9.1 Identify the assumption(s) made when defining an arithmetic sequence or series.

    • 9.RF9.2 Provide and justify an example of an arithmetic sequence.

      • Classify formulas and sequences (11-X.1)

    • 9.RF9.3 Determine a rule for finding the general term of an arithmetic sequence.

      • Write a formula for an arithmetic sequence (11-X.6)

    • 9.RF9.4 Determine t?, d, n, or t? in a problem that involves an arithmetic sequence.

      • Find terms of an arithmetic sequence (11-X.2)
      • Find terms of a recursive sequence (11-X.4)

    • 9.RF9.5 Solve a problem that involves an arithmetic sequence or series.

      • Find terms of an arithmetic sequence (11-X.2)
      • Write a formula for an arithmetic sequence (11-X.6)
      • Find the sum of a finite arithmetic or geometric series (11-X.12)
      • Partial sums of arithmetic series (11-X.14)

    • 9.RF9.6 Describe the relationship between arithmetic sequences and linear functions.

    • 9.RF9.7 Determine a rule for finding the sum of n terms of an arithmetic series.

    • 9.RF9.8 Determine t?, d, n, or S? in a problem that involves an arithmetic series.

      • Find the sum of a finite arithmetic or geometric series (11-X.12)
      • Partial sums of arithmetic series (11-X.14)

  • 9.RF10 Analyze geometric sequences and series to solve problems.

    • 9.RF10.1 Identify assumptions made when identifying a geometric sequence or series

    • 9.RF10.2 Provide and justify an example of a geometric sequence.

      • Classify formulas and sequences (11-X.1)

    • 9.RF10.3 Determine a rule for finding the general term of a geometric sequence.

      • Write a formula for a geometric sequence (11-X.7)

    • 9.RF10.4 Determine t¹, r, n or t? in a problem that involves a geometric sequence.

      • Find terms of a geometric sequence (11-X.3)

    • 9.RF10.5 Determine a rule for finding the sum of n terms of a geometric series.

    • 9.RF10.6 Determine t?, r, n or S? in a problem that involves a geometric series.

      • Find the sum of a finite arithmetic or geometric series (11-X.12)
      • Partial sums of geometric series (11-X.15)

    • 9.RF10.7 Solve a problem that involves a geometric sequence or series.

      • Find terms of a geometric sequence (11-X.3)
      • Write a formula for a geometric sequence (11-X.7)
      • Find the sum of a finite arithmetic or geometric series (11-X.12)
      • Partial sums of geometric series (11-X.15)

    • 9.RF10.8 Determine if a given a geometric series is convergent or divergent.

      • Convergent and divergent geometric series (11-X.17)

    • 9.RF10.9 Generalize, using inductive reasoning, a rule for determining the sum of an infinite geometric series.