Nova Scotia

12. Patterns

• 12.C4 demonstrate an understanding of patterns that are arithmetic, power, and geometric

  • Find terms of an arithmetic sequence (11-X.2)
  • Find terms of a geometric sequence (11-X.3)
  • Evaluate formulas for sequences (11-X.5)
  • Write a formula for an arithmetic sequence (11-X.6)
  • Write a formula for a geometric sequence (11-X.7)
  • Find terms of a sequence (12-W.1)

• 12.C5 determine and describe patterns and use them to solve problems

  • Evaluate formulas for sequences (11-X.5)

• 12.C6 explore, describe, and apply the Fibonacci sequence

• 12.C7 relate arithmetic patterns to linear relations

  • Complete a table and graph a linear function (10-L.12)

• 12.C21 create and analyze scatter plots, and determine the equations for the curves of best fit using appropriate technology

  • Outliers in scatter plots (12-AA.5)
  • Match correlation coefficients to scatter plots (12-AA.6)

12. Quadratics

• 12.A3 demonstrate an understanding of the role of irrational numbers in applications

  • Classify rational and irrational numbers (10-A.8)

• 12.B1 demonstrate an understanding of the relationships that exist between arithmetic and the operations used when solving equations

  • Solve a quadratic equation using square roots (12-C.5)
  • Solve a quadratic equation by factoring (12-C.6)
  • Solve a quadratic equation by completing the square (12-C.7)
  • Solve a quadratic equation using the quadratic formula (12-C.8)
  • Solve equations with sums and differences of cubes (12-D.11)
  • Solve equations using a quadratic pattern (12-D.13)

• 12.B3 apply the quadratic formula

  • Solve a quadratic equation using the quadratic formula (12-C.8)

• 12.B9 perform operations on algebraic expressions and equations

  • Solve a quadratic equation using square roots (12-C.5)
  • Solve a quadratic equation by factoring (12-C.6)
  • Solve a quadratic equation by completing the square (12-C.7)
  • Solve a quadratic equation using the quadratic formula (12-C.8)
  • Solve equations with sums and differences of cubes (12-D.11)
  • Solve equations using a quadratic pattern (12-D.13)

• 12.C1 model real-world phenomena using quadratic equations

• 12.C5 determine and describe patterns and use them to solve problems

• 12.C8 describe and translate between graphical, tabular, and written representations of quadratic relationships

  • Characteristics of quadratic functions (12-C.1)
  • Find the maximum or minimum value of a quadratic function (12-C.2)
  • Graph a quadratic function (12-C.3)
  • Match quadratic functions and graphs (12-C.4)

• 12.C12 describe and apply the characteristics of quadratic relationships

  • Characteristics of quadratic functions (12-C.1)
  • Find the maximum or minimum value of a quadratic function (12-C.2)

• 12.C14 determine and interpret x-intercepts of quadratic functions

  • Characteristics of quadratic functions (12-C.1)
  • Graph a quadratic function (12-C.3)
  • Match quadratic functions and graphs (12-C.4)
  • Solve a quadratic equation using square roots (12-C.5)
  • Solve a quadratic equation using the quadratic formula (12-C.8)

• 12.C21 create and analyze scatter plots and determine the equations for curves of best fit, using appropriate technology

• 12.C23 solve problems involving quadratic equations

  • Solve a quadratic equation using square roots (12-C.5)
  • Solve a quadratic equation by factoring (12-C.6)
  • Solve a quadratic equation by completing the square (12-C.7)
  • Solve a quadratic equation using the quadratic formula (12-C.8)

• 12.C29 analyze tables and graphs to distinguish between linear, quadratic, and exponential relationships

  • Identify linear, quadratic and exponential functions from graphs (10-S.1)
  • Identify linear, quadratic and exponential functions from tables (10-S.2)

• 12.E2 describe and apply symmetry

• 12.F3 use curve-fitting to determine the equations of quadratic relationships

• 12.F4 interpolate and extrapolate to predict and solve problems

12. Exponential Growth

• 12.A1 demonstrate an understanding of and apply zero and negative exponents

  • Negative exponents (10-B.3)

• 12.A2 develop, demonstrate an understanding of, and apply properties of exponents

  • Exponents with integer bases (10-B.1)
  • Exponents with decimal and fractional bases (10-B.2)
  • Negative exponents (10-B.3)
  • Multiplication with exponents (10-B.4)
  • Division with exponents (10-B.5)
  • Multiplication and division with exponents (10-B.6)
  • Power rule (10-B.7)
  • Evaluate expressions using properties of exponents (10-B.8)
  • Identify equivalent expressions involving exponents (10-B.9)

• 12.A8 demonstrate an understanding of the exponential growth of compound interest

  • Compound interest: word problems (12-G.12)

• 12.B5 demonstrate an understanding of and apply compound interest

  • Compound interest: word problems (12-G.12)

• 12.B6 determine the amount and present value of annuities

• 12.C5 determine and describe patterns and use them to solve problems

• 12.C11 describe and translate between graphical, tabular, and written representations of exponential relationships

  • Match exponential functions and graphs (12-G.3)

• 12.C13 describe and apply the characteristics of exponential relationships

  • Domain and range of exponential and logarithmic functions (12-G.1)
  • Match exponential functions and graphs (12-G.3)
  • Identify linear and exponential functions (12-G.8)
  • Exponential functions over unit intervals (12-G.9)
  • Describe linear and exponential growth and decay (12-G.10)

• 12.C21 create and analyze scatter plots and determine the equations for curves of best fit, using appropriate technology

  • Outliers in scatter plots (12-AA.5)
  • Match correlation coefficients to scatter plots (12-AA.6)

• 12.C25 solve problems involving exponential equations

  • Solve exponential equations by rewriting the base (12-G.4)
  • Solve exponential equations using common logarithms (12-G.5)

• 12.C26 solve problems that require the application of compound interest

  • Compound interest: word problems (12-G.12)
  • Continuously compounded interest: word problems (12-G.13)

• 12.C29 analyze tables and graphs to distinguish between linear, quadratic, and exponential relationships

  • Identify linear, quadratic and exponential functions from graphs (10-S.1)
  • Identify linear, quadratic and exponential functions from tables (10-S.2)

• 12.F2 use curve-fitting to determine the equations of exponential relationships

• 12.F4 interpolate and extrapolate to predict and solve problems

12. Circle Geometry

• 12.D2 determine midpoints and the lengths of line segments using coordinate geometry

  • Midpoints (10-F.2)
  • Distance between two points (10-F.3)

• 12.E1 perform geometric constructions and analyze the properties of the resulting figures

  • Construct an angle bisector (10-X.1)
  • Construct a congruent angle (10-X.2)

• 12.E2 describe and apply symmetry

• 12.E5 apply inductive reasoning to make conjectures in geometric situations

• 12.E6 explore, make conjectures about, and apply centres of circles

  • Find properties of circles (12-Q.4)
  • Write equations of circles in standard form (12-Q.5)
  • Graph circles (12-Q.6)

• 12.E7 investigate and make and prove conjectures associated with chord properties of circles

• 12.E8 investigate and make and prove conjectures associated with angle relationships in circles

• 12.E10 present informal deductive arguments

12. Probability

• 12.A6 develop an understanding of factorial notation and apply it to calculating permutations and combinations

• 12.B7 calculate probabilities to solve problems

  • Calculate probabilities of events (12-Y.2)
  • Find probabilities using two-way frequency tables (12-Y.5)

• 12.B8 determine probabilities using permutations and combinations

  • Find probabilities using combinations and permutations (12-Y.4)

• 12.G1 develop and apply simulations to solve problems

• 12.G2 demonstrate an understanding that determining probability requires the quantifying of outcomes

  • Introduction to probability (12-Y.1)
  • Calculate probabilities of events (12-Y.2)

• 12.G3 demonstrate an understanding of the Fundamental Counting Principle and apply it to calculate probabilities of dependent and independent events

  • Counting principle (11-Y.4)

• 12.G4 apply area diagrams and tree diagrams to interpret and determine probabilities of dependent and independent events

• 12.G6 demonstrate an understanding of the difference between probability and odds

• 12.G7 distinguish between situations that involve combinations and permutations

  • Find probabilities using combinations and permutations (12-Y.4)

• 12.G8 develop and apply formulas to evaluate permutations and combinations

  • Combinations and permutations (12-Y.3)
  • Find probabilities using combinations and permutations (12-Y.4)