British Columbia Curriculum 10 12

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1 Supported by independent evidence-based research practice. Follows provincial curricula Powerful reporting Student centred

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3 BC Content BC Apprenticeship Workplace BC Foundations Pre calculus BC Foundations of Mathematics BC Pre calculus BC Apprenticeship Workplace BC Foundations of Mathematics BC Apprenticeship Workplace BC Pre calculus 12 37

4 Mathletics the British Columbia Curriculum The education team at Mathletics is committed to providing a resource that is powerful, targeted most importantly, relevant to all students. Mathletics includes well over 1200 individual adaptive practice activities ebooks available for all grades. Our team of education publishers have created that specifically follow the British Columbia. You can be assured that students have access to relevant targeted content. Strs, sub-strs learning outcomes of the curriculum are supported with activities, each with pre post assessment. What s more, Mathletics contains an extensive library of ebooks for use on screen or as a printable resource that are also mapped to the requirements of the British Columbia Curriculum. This document outlines this mapping acts as a useful guide when using Mathletics in your school. Rene Burke CEO, 3P Learning Canada Engage Target Diagnose Assess Report Fluency Mobile 1 3P Learning

5 BC Apprenticeship Workplace 10 Str Outcome Outcome Description Activities ebooks Measurement BC.10.AW.M.1a Describing the relationships of the units for length, area, volume, capacity, mass temperature using SI units. Centimetres Metres Converting cm mm Kilometre Conversions Metres Kilometres Converting Units of Length Nautical Mile, Kilometre, Knot Measuring Length Operations with Length Converting Units of Area Perimeter: Composite Shapes Perimeter Circles Perimeter: Triangles Perimeter Perimeter of Shapes Perimeter: Squares Rectangles Area: Squares Rectangles Area: Triangles Area: Right Triangles Area: Circles 1 Area: Circles 2 Area: Quadrilaterals Volume: Prisms Volume: Pyramids Volume: Rectangular Prisms 1 Volume: Cylinders Surface Area: Rectangular Prisms Surface Area: Rectangular Pyramids Surface Area: Square Pyramids Surface Area: Spheres Surface Area: Cylinders Surface Area: Cones Nets Grams Kilograms Kilogram Conversions Grams Milligrams Converting Units of Mass Millilitres Litres Temperature Grade 7 Converting Units Grade 7 Area Perimeter Measuring Solids 3P Learning 2

6 BC Apprenticeship Workplace 10 Str Outcome Outcome Description Activities ebooks Measurement BC.10.AW.M.1b Applying strategies to convert SI units to imperial units. Centimetres Metres Converting cm mm Kilometre Conversions Metres Kilometres Converting Units of Length Nautical Mile, Kilometre, Knot Measuring Length Operations with Length Converting Units of Area Perimeter: Composite Shapes Perimeter Circles Perimeter: Triangles Perimeter Perimeter of Shapes Perimeter: Squares Rectangles Area: Squares Rectangles Area: Triangles Area: Right Triangles Area: Circles 1 Area: Circles 2 Area: Quadrilaterals Volume: Prisms Volume: Pyramids Volume: Rectangular Prisms 1 Volume: Cylinders Grams Kilograms Kilogram Conversions Grams Milligrams Converting Units of Mass Millilitres Litres Temperature 3 3P Learning

7 BC Apprenticeship Workplace 10 Str Outcome Outcome Description Activities ebooks Measurement BC.10.AW.M.2a Describing the relationships of the units for length, area, volume, capacity, mass temperature in Imperial units. Centimetres Metres Converting cm mm Kilometre Conversions Metres Kilometres Converting Units of Length Nautical Mile, Kilometre, Knot Measuring Length Converting Units of Area Operations with Length Perimeter: Composite Shapes Perimeter Circles Perimeter: Triangles Perimeter Perimeter of Shapes Perimeter: Squares Rectangles Area: Squares Rectangles Area: Triangles Area: Right Angled Triangles Area: Circles 1 Area: Circles 2 Area: Quadrilaterals Volume: Prisms Volume: Pyramids Volume: Rectangular Prisms 1 Volume: Cylinders Grams Kilograms Kilogram Conversions Grams Milligrams Converting Units of Mass Millilitres Litres Temperature 3P Learning 4

8 BC Apprenticeship Workplace 10 Str Outcome Outcome Description Activities ebooks Measurement BC.10.AW.M.2b Comparing the American British imperial units for capacity. Centimetres Metres Converting cm mm Kilometre Conversions Metres Kilometres Converting Units of Length Nautical Mile, Kilometre, Knot Measuring Length Converting Units of Area Operations with Length Perimeter: Composite Shapes Perimeter Circles Perimeter: Triangles Perimeter Perimeter of Shapes Perimeter: Squares Rectangles Area: Squares Rectangles Area: Triangles Area: Right Triangles Area: Circles 1 Area: Circles 2 Area: Quadrilaterals Volume: Prisms Volume: Pyramids Volume: Rectangular Prisms 1 Volume: Cylinders Grams Kilograms Kilogram Conversions Grams Milligrams Converting Units of Mass Millilitres Litres Temperature 5 3P Learning

9 BC Apprenticeship Workplace 10 Str Outcome Outcome Description Activities ebooks Measurement BC.10.AW.M.2c Applying strategies to convert imperial units to SI units. Centimetres Metres Converting cm mm Kilometre Conversions Metres Kilometres Converting Units of Length Nautical Mile, Kilometre, Knot Measuring Length Converting Units of Area Operations with Length Perimeter: Composite Shapes Perimeter Circles Perimeter: Triangles Perimeter Perimeter of Shapes Perimeter: Squares Rectangles Area: Squares Rectangles Area: Triangles Area: Right Triangles Area: Circles 1 Area: Circles 2 Area: Quadrilaterals Volume: Prisms Volume: Pyramids Volume: Rectangular Prisms 1 Volume: Cylinders Grams Kilograms Kilogram Conversions Grams Milligrams Converting Units of Mass Millilitres Litres Temperature 3P Learning 6

10 BC Apprenticeship Workplace 10 Str Outcome Outcome Description Activities ebooks Measurement BC.10.AW.M.3 Solve verify problems that involve SI imperial linear measurements, including decimal fractional measurements. Centimetres Metres Converting cm mm Kilometre Conversions Metres Kilometres Converting Units of Length Nautical Mile, Kilometre, Knot Measuring Length Converting Units of Area Operations with Length Perimeter: Composite Shapes Perimeter Circles Perimeter: Triangles Perimeter Perimeter of Shapes Perimeter: Squares Rectangles Area: Squares Rectangles Area: Triangles Area: Right Triangles Area: Circles 1 Area: Circles 2 Area: Quadrilaterals Volume: Prisms Volume: Pyramids Volume: Rectangular Prisms 1 Volume: Cylinders Grams Kilograms Kilogram Conversions Grams Milligrams Converting Units of Mass Millilitres Litres Temperature 7 3P Learning

11 BC Apprenticeship Workplace 10 Str Outcome Outcome Description Activities ebooks Measurement Geometry Geometry Geometry Geometry Geometry Geometry Number BC.10.AW.M.4 BC.10.AW.G.1 BC.10.AW.G.2 BC.10.AW.G.3 BC.10.AW.G.4 BC.10.AW.G.5 BC.10.AW.G.6 BC.10.AW.N.1 Solve problems that involve SI imperial area measurements of regular, composite irregular 2-D shapes 3-D objects, including decimal fractional measurements, verify the solutions. Analyze puzzles games that involve spatial reasoning, using problem-solving strategies. Demonstrate an understing of the Pythagorean theorem. Demonstrate an understing of similarity of convex polygons, including regular irregular polygons. Demonstrate an understing of primary trigonometric ratios (sine, cosine, tangent). Solve problems that involve parallel, perpendicular transversal lines, pairs of angles formed between them. Demonstrate an understing of angles, including acute, right, obtuse, straight reflex. Solve problems that involve unit pricing currency exchange, using proportional reasoning. Area: Squares Rectangles Area: Triangles Area: Right Angled Triangles Area: Circles 1 Area: Circles 2 Area: Quadrilaterals Volume: Composite Figures Volume: Prisms Volume: Pyramids Volume: Rectangular Prisms 1 Volume: Cylinders Nets Surface Area: Square Pyramids Surface Area: Cones Surface Area: Rectangular Pyramids Surface Area: Rectangular Prisms Pythagorean Theorem Pythagorean Triads Similar Figures Using Similar Triangles Similarity Proofs Similar Areas Volumes Sin A Cos A Tan A Elevation Depression Find Unknown Angles Find Unknown Sides Sides, Angles Diagonals Exterior Angles of a Triangle Equal, Complement or Supplement? Angles Parallel Lines Parallel Lines Measuring Angles Classifying Angles Best Buy Grade 7 Converting Units Grade 7 Area Perimeter Measuring Solids Grade 8 Pythagoras Theorem Similarity Congruence Trigonometry Grade 7 Angles Grade 7 Angles Decimals 3P Learning 8

12 BC Apprenticeship Workplace 10 Str Outcome Outcome Description Activities ebooks Number BC.10.AW.N.2 Demonstrate an understing of income, including wages, salary, contracts, commissions piecework. Wages Salaries Commission Piecework Royalties Budgeting Earning Money Algebra BC.10.AW.A.1 Solve problems that require the manipulation application of formulas related to perimeter, area, the Pythagorean theorem, primary trigonometric ratios income. Constructing Formulae Volume: Rearrange Formula Surface Area: Rearrange Formula Substitution in Formulae Real Formulae More Substitution in Formulae Measuring Solids 9 3P Learning

13 BC Foundations Pre-calculus 10 Str Outcome Outcome Description Activities ebooks Measurement Measurement BC.10.FP.M.1 BC.10.FP.M.2 Solve problems that involve linear measurement, using SI imperial units of measure, estimation strategies measurement strategies. Apply proportional reasoning to problems that involve conversions between SI imperial units of measure. Centimetres Metres Converting cm mm Kilometre Conversions Metres Kilometres Converting Units of Length Nautical Mile, Kilometre, Knot Measuring Length Operations with Length Perimeter: Composite Shapes Perimeter Circles Perimeter: Triangles Perimeter: Triangles 2 Perimeter Perimeter of Shapes Perimeter: Squares Rectangles 1 Grams Kilograms Kilogram Conversions Grams Milligrams Converting Units of Mass Millilitres Litres Temperature Centimetres Metres Converting cm mm Kilometre Conversions Metres Kilometres Converting Units of Length Nautical Mile, Kilometre, Knot Measuring Length Operations with Length Perimeter: Composite Shapes Perimeter Circles Perimeter: Triangles Perimeter: Triangles 2 Perimeter Perimeter of Shapes Perimeter: Squares Rectangles 1 Grams Kilograms Kilogram Conversions Grams Milligrams Converting Units of Mass Millilitres Litres Temperature Grade 7 Converting Units Grade 7 Area Perimeter Measuring Solids Grade 7 Converting Units Grade 7 Area Perimeter Measuring Solids Similarity Congruence 3P Learning 10

14 BC Foundations Pre-calculus 10 Str Outcome Outcome Description Activities ebooks Measurement Measurement Algebra Number Algebra Number BC.10.FP.M.3 BC.10.FP.M.4 BC.10.FP.AN.1 BC.10.FP.AN.2 Solve problems, using SI imperial units, that involve the surface area volume of 3-D objects, including right cones, right cylinders, right prisms, right pyramids spheres. Develop apply the primary trigonometric ratios (sine, cosine, tangent) to solve problems that involve right triangles. Demonstrate an understing of factors of whole numbers by determining the prime factors, greatest common factor, least common multiple, square root cube root. Demonstrate an understing of irrational numbers by representing, identifying simplifying irrational numbers, ordering irrational numbers. Surface Area: Rectangular Prisms Surface Area: Cuboids Surface Area: Cylinders Surface Area: Triangular Prisms Surface Area: Square Pyramids Surface Area: Spheres Surface Area: Cones Surface Area: Rearrange Formula Surface Area: Rectangular Pyramids Volume: Rectangular Prisms 1 Volume: Cuboid 1 Converting Volume Volume: Rectangular Prisms 2 Volume: Cuboid 2 Volume: Cylinders Volume: Triangular Prisms Volume: Triangular Prisms 1 Volume: Composite Figures Volume: Prisms Volume: Pyramids Volume: Cones Volume: Spheres Sin A Cos A Tan A Find Unknown Angles Find Unknown Sides Elevation Depression Pythagoras Theorem Hypotenuse of a Right Triangle Using Similar Triangles Using SImilar Trinales 1 Greatest Common Factor Factors Multiples Least Common Multiple Irrational Numbers Simplifying Irrational Numbers Adding Subtracting Irrational Numbers Multiplying Irrational Numbers Exping Irrational Number Expressions Dividing Irrational Numbers Exping Binomial Irrational Numbers Grade 7 Converting Units Grade 7 Area Perimeter Measuring Solids Similarity Congruence Trigonometry Grade 7 Whole Numbers Grade10 Irrational Numbers Exponents 11 3P Learning

15 BC Foundations Pre-calculus 10 Str Outcome Outcome Description Activities ebooks Algebra Number Algebra Number Algebra Number BC.10.FP.AN.3 BC.10.FP.AN.4 BC.10.FP.AN.5 BC.10.FP.RF.1 BC.10.FP.RF.2 Demonstrate an understing of powers with integral rational exponents. Demonstrate an understing of the multiplication of polynomial expressions (limited to monomials, binomials trinomials), concretely, pictorially symbolically. Demonstrate an understing of common factors trinomial factoring, concretely, pictorially symbolically. Interpret explain the relationships among data, graphs situations. Demonstrate an understing of relations functions. Exponents Properties of Exponents Exponent Notation Negative Exponents Multiplication Division with Exponents Multiplication with Exponents Integer Exponents Exping Binomial Products Special Binomial Products Exping with Negatives Exping Brackets Factoring Expressions Factoring with Exponents Factoring with Negatives Factoring Factoring Quadratics 1 Factoring Quadratics 2 Factoring Fractions 1 Factoring Fractions 2 Highest Common Algebraic Factor Pattern Rules Tables Function Rules Tables Graphing from a Table of Values Graphing from a Table of Values 2 Ordered Pairs Pattern Rules Tables Function Rules Tables Graphing from a Table of Values Graphing from a Table of Values 2 Ordered Pairs Exponents Irrational Numbers Exponents Grade 8 Exping Factorising Grade 8 Simplifying Algebra Simplifying Algebra Factorising Quadratic Equations Grade 8 Linear hips Grade 8 Straight Lines Linear hips Straight Lines Parabolas Simple Non Linear Graphs Grade 8 Linear hips Grade 8 Straight Lines Linear hips Straight Lines Parabolas Simple Non Linear Graphs 3P Learning 12

16 BC Foundations Pre-calculus 10 Str Outcome Outcome Description Activities ebooks BC.10.FP.RF.3 Demonstrate an understing of slope with respect to rise run, line segments lines, rate of change, parallel lines perpendicular lines. Slope of a Line y=ax Gradients for Real Gradient Are they Parallel? Are they Perpendicular? Grade 8 Linear hips Grade 8 Straight Lines Linear hips Straight Lines BC.10.FP.RF.4 Describe represent linear relations, using words, ordered pairs, tables of values, graphs equations. Equation from Point Gradient Equation from Two Points Equation of a Line 1 Equation of a Line 2 Equation of a Line 3 Grade 8 Linear hips Grade 8 Straight Lines Linear hips Straight Lines BC.10.FP.RF.5 Determine the characteristics of the graphs of linear relations, including the intercepts, slope, domain range. Intercepts Gradient Slope of a Line Domain Range Grade 8 Linear hips Grade 8 Straight Lines Linear hips Straight Lines BC.10.FP.RF.6 Relate linear relations expressed in slope intercept form, general form, slope point form to their graphs. General Form of a Line Equation from Point Gradient Equation from Two Points Which Straight Line? Grade 8 Linear hips Grade 8 Straight Lines Linear hips Straight Lines BC.10.FP.RF.7 Determine the equation of a linear relation, given a graph, a point the slope, two points, a point the equation of a parallel or perpendicular line to solve problems. General Form of a Line Equation from Point Gradient Equation from Two Points Are they Parallel? Are they Perpendicular? Which Straight Line? Grade 8 Linear hips Grade 8 Straight Lines Linear hips Straight Lines BC.10.FP.RF.8 Represent a linear function, using function notation. Function Notation 1 BC.10.FP.RF.9 Solve problems that involve systems of linear equations in two variables, graphically algebraically. Simultaneous Equations 1 Simultaneous Equations 2 Simultaneous Linear Equations Equations Inequalities 13 3P Learning

17 BC Foundations of Mathematics 11 Str Outcome Outcome Description Activities ebooks Measurement BC.F11.A1 Measurement BC.F11.A2 Measurement BC.F11.A3 Geometry BC.F11.B1 Geometry BC.F11.B2 Geometry BC.F11.B3 Solve problems that involve the application of rates. Solve problems that involve scale diagrams, using proportional reasoning. Demonstrate an understing of the relationships among scale factors, areas, surface areas volumes of similar 2-D shapes 3-D objects. Derive proofs that involve the properties of angles triangles. Solve problems that involve the properties of angles triangles. Solve problems that involve the cosine law the sine law, including the ambiguous case. Travel Graphs Rates Word Problems Rates Average Speed Distance Travelled Converting Rates Rates Calculations Similarity Proofs Using Similar Triangles Similar Figures Scale Measurement Scale Factor Floor Plans Elevations Similar Areas Volumes Equal, Complement, or Supplement? Parallel Lines Angle Sum of a Quadrilateral Angle Sum of a Triangle Exterior Angles of a Triangle Interior Exterior Angles Parallel Lines Ratio of Intercepts Equal, Complement, or Supplement? Angle Sum of a Triangle Exterior Angles of a Triangle Sin A Cos A Sine Rule 1 Sine Rule 2 Cosine Rule 1 Cosine Rule 2 Area Rule 1 Area Rule 2 Area Problems Find Unknown Angles Find Unknown Sides Bearings Decimals Similarity Congruence Measuring Solids Grade 7 Angles Polygons Angles Grade 7 Angles Polygons Angles Non Right Angled Triangles 3P Learning 14

18 BC Foundations of Mathematics 11 Str Outcome Outcome Description Activities ebooks Logical Reasoning Logical Reasoning Statistics Statistics BC.F11.C1 BC.F11.C2 BC.F11.D1 BC.F11.D2 BC.F11.E1 BC.F11.E2 Analyze prove conjectures, using inductive deductive reasoning, to solve problems. Analyze puzzles games that involve spatial reasoning, using problemsolving strategies. Demonstrate an understing of normal distribution, including: stard deviation z-scores. Interpret statistical data, using confidence intervals, confidence levels margin of error. Model solve problems that involve systems of linear inequalities in two variables. Demonstrate an understing of the characteristics of quadratic functions, including vertex, intercepts, domain range axis of symmetry. Calculating Stard Deviation Interpreting Stard Deviation Equivalent z-scores Calculating z-scores Comparing z-scores Normal Distribution Calculating Stard Deviation Interpreting Stard Deviation Equivalent z-scores Calculating z-scores Comparing z-scores Intersecting Linear Regions Linear Regions Simultaneous Equations 1 Simultaneous Equations 2 Simultaneous Equations 3 Quadratic Equations 1 Quadratic Equations 2 Quadratic Formula Grouping in Pairs Factoring Quadratics 1 Factoring Quadratics 2 Completing the Square Vertex of a Parabola Domain Domain Range Parabolas Marbles Parabolas Rectangles Quadratic Inequalities The Discriminant Graphing Parabolas Roots of the Quadratic Equation Reducible to Quadratics Quadratic Equations Parabolas 15 3P Learning

19 BC Pre-calculus 11 Str Outcome Outcome Description Activities ebooks Algebra Number Algebra Number Algebra Number Algebra Number Algebra Number Algebra Number BC.P11.A1 BC.P11.A2 BC.P11.A3 BC.P11.A4 BC.P11.A5 BC.P11.A6 Trigonometry BC.P11.B1 Trigonometry BC.P11.B2 Demonstrate an understing of the absolute value of real numbers. Solve problems that involve operations on Irrational Numbers Irrational Number expressions with numerical variable radics. Solve problems that involve Irrational Number equations (limited to square roots). Determine equivalent forms of rational expressions (limited to numerators denominators that are monomials, binomials or trinomials). Perform operations on rational expressions (limited to numerators denominators that are monomials, binomials or trinomials). Solve problems that involve rational equations (limited to numerators denominators that are monomials, binomials or trinomials). Demonstrate an understing of angles in stard position [0 to 360 ]. Solve problems, using the three primary trigonometric ratios for angles from 0 to 360 in stard position. Absolute Value Inequalities Absolute Value Expressions Absolute Value Absolute Value Equations Simplifying Irrational Numbers Multiplying Irrational Numbers Dividing Irrational Numbers Exping Irrational Number Expressions Exping Binomial Irrational Numbers Rationalising the Denominator Special Binomial Products Domain Equations with Square Roots Equations with Cube Roots Domain Algebraic Fractions 2 Exp then Simplify Simplifying Expressions Simplifying Binomial Expressions Special Binomial Products Factoring Fractions 1 Domain Algebraic Fractions 1 Algebraic Fractions 2 Algebraic Fractions 3 Factoring Fractions 2 Simplifying Binomial Expressions Domain Equations with Fractions Equations with Fractions 2 Measuring Angles Equal, Complement, or Supplement? Which Quadrant? Transformations: Coordinate Plane Pythagoras Theorem Distance Between Two Points Sign of the Angle Sin A Cos A Tan A Find Unknown Angles Find Unknown Sides Trigonometry Problems 1 Trigonometry Problems 2 Exact Trigonometric Ratios Sine Cosine Curves Elevation Depression Irrational Numbers Exponents Factorising Equations Inequalities Angles Polygons Trigonometry Non Right Angled Triangles Trigonometryic hips 3P Learning 16

20 BC Pre-calculus 11 Str Outcome Outcome Description Activities ebooks Trigonometry BC.P11.B3 BC.P11.C1 BC.P11.C2 BC.P11.C3 BC.P11.C4 Solve problems, using the cosine law sine law, including the ambiguous case. Factor polynomial expressions of the form: ax² + bx + c, a 0 a²x² - b²y², a 0, b 0. a(f(x))² + b(f(x)) + c, a 0 a²(f(x))² - b²(g(y))², a 0, b 0. where a, b c are rational numbers. Graph analyze absolute value functions (limited to linear quadratic functions) to solve problems. Analyze quadratic functions of the form y=a(x - p)² + q determine the: vertex domain range direction of opening axis of symmetry x- y-intercepts. Analyze quadratic functions of the form y=ax² + bx + c to identify characteristics of the corresponding graph, including: vertex domain range direction of opening axis of symmetry x- y-intercepts to solve problems. Sine Rule 1 Sine Rule 2 Cosine Rule 1 Cosine Rule 2 Area Rule 1 Area Rule 2 Highest Common Algebraic Factor Factoring Quadratics 1 Factoring Quadratics 2 Grouping in Pairs Completing the Square Completing the Square 2 Polynomial Long Division Polynomial Factor Theorem Equations Reducible to Quadratics Piecemeal Domain Absolute Value Graphs Absolute Value Expressions Absolute Value Equations Graphing Parabolas Vertex of a Parabola The Discriminant Roots of the Quadratic Sum Product of Roots Equations Reducible to Quadratics Parabolas Marbles Parabolas Rectangles Graphing Parabolas The Discriminant Roots of the Quadratic Sum Product of Roots Completing the Square Completing the Square 2 Non Right Angled Triangles Quadratic Equations Parabolas Polynomials Grade 11 Continuity Quadratic Equations Parabolas Quadratic Equations Parabolas 17 3P Learning

21 BC Pre-calculus 11 Str Outcome Outcome Description Activities ebooks BC.P11.C5 BC.P11.C6 BC.P11.C7 BC.P11.C8 BC.P11.C9 BC.P11.C10 BC.P11.C11 Solve problems that involve quadratic equations. Solve, algebraically graphically, problems that involve systems of linearquadratic quadratic-quadratic equations in two variables. Solve problems that involve linear quadratic inequalities in two variables. Solve problems that involve quadratic inequalities in one variable. Analyze arithmetic sequences series to solve problems. Analyze geometric sequences series to solve problems. Graph analyze reciprocal functions (limited to the reciprocal of linear quadratic functions). Factoring Quadratics 1 Factoring Quadratics 2 Grouping in Pairs Quadratic Equations 1 Quadratic Equations 2 Completing the Square Completing the Square 2 Quadratic Formula Graphing Parabolas Sum Product of Roots Roots of the Quadratic The Discriminant Breakeven Point Linear Modelling Solve Systems by Graphing Simultaneous Linear Equations Simultaneous Equations 1 Simultaneous Equations 2 Simultaneous Equations 3 Intersecting Linear Regions Intersecting Non Linear Regions Graphing Inequalities 1 Graphing Inequalities 2 Linear Regions Non Linear Regions Quadratic Inequalities Find the Pattern Rule Sigma Notation 1 Sigma Notation 2 Terms: Arithmetic Progressions Pattern Rules Tables Sum: Arithmetic Progressions Sum: Geometric Progressions Limiting Sum Sigma Notation 1 Sigma Notation 2 Terms: Geometric Progressions 1 Terms: Geometric Progressions 2 Graphing Hyperbolas Quadratic Equations Parabolas Equations Inequalities Grade 11 Sequence Series - Arithmetic Grade 11 Sequence Series - Geometric Simple Non Linear Graphs 3P Learning 18

22 BC Apprenticeship Workplace 11 Str Outcome Outcome Description Activities ebooks Measurement Measurement Geometry BC.AW.11.A1 BC.AW.11.A2 BC.AW.11.B1 Solve problems that involve SI imperial units in surface area measurements verify the solutions. Solve problems that involve SI imperial units in volume capacity measurements. Solve problems that involve two three right triangles. Geometry BC.AW.11.B2 Solve problems that involve scale. Geometry BC.AW.11.B3 Geometry BC.AW.11.B4 Model draw 3-D objects their views. Draw describe exploded views, component parts scale diagrams of simple 3-D objects. Surface Area: Rectangular Prisms Surface Area: Cylinders Surface Area: Cones Surface Area: Square Pyramids Surface Area: Rectangular Pyramids Surface Area: Spheres Surface Area: Rearrange Formula Error in Measurement Millilitres Litres Litre Conversions Capacity Word Problems Converting Volume Volume: Rectangular Prisms 1 Volume: Rectangular Prisms 2 Volume: Cylinders Volume: Triangular Prisms Volume: Pyramids Volume: Cones Volume: Prisms Volume: Shperes Volume: Composite Figures Volume: Rearrange Formula Similar Areas Volume Similar Figures Similarity Proofs Using Similar Triangles Elevation Depression Trigonometry Problems 1 Trigonometry Problems 2 Scale Factor Scale Measurement Similar Figures Similarity Proofs Nets Elevations Floor Plans Nets Elevations Floor Plans Measuring Solids Measuring Solids Trigonometry Similarity Congruence 19 3P Learning

23 BC Apprenticeship Workplace 11 Str Outcome Outcome Description Activities ebooks Number BC.AW.11.C1 Number BC.AW.11.C2 Number BC.AW.11.C3 Number BC.AW.11.C4 Number BC.AW.11.C5 Algebra BC.AW.11.D1 Analyze puzzles games that involve numerical reasoning, using problem-solving strategies. Solve problems that involve personal budgets. Demonstrate an understing of compound interest. Demonstrate an understing of financial institution services used to access manage finances. Demonstrate an understing of credit options, including: credit cards loans. Solve problems that require the manipulation application of formulas related to: volume capacity surface area slope rate of change simple interest finance charges. Budgeting Wages Salaries Commission Working Overtime Reading from a Bill Calculating Income Tax Purchase Options Deductions Tax Instalments Calculating Dividends Credit Card Repayments Shares Simple Interest Compound Interest Compound Interest by Formula Depreciation Declining Balance Depreciation Present Future Value Tables Future Value of Investments 1 Future Value of Investments 2 Simple Interest Compound Interest Compound Interest by Formula Depreciation Straight Line Depreciation Declining Balance Depreciation Simple Interest Compound Interest Compound Interest by Formula Depreciation Declining Balance Depreciation Comparing Loans Comparing Home Loans Credit Card Repayments Simple Substitution Real Formulae Find the Mistake Checking Solutions Substitution in Formulae Earning Money Interest Depreciation " Interest Depreciation" Interest Depreciation Equations Inequaities Measuring Solids 3P Learning 20

24 BC Apprenticeship Workplace 11 Str Outcome Outcome Description Activities ebooks Algebra Algebra Statistics BC.AW.11.D2 BC.AW.11.D3 BC.AW.11.E1 Demonstrate an understing of slope: as rise over run as rate of change by solving problems. Solve problems by applying proportional reasoning unit analysis. Solve problems that involve creating interpreting graphs, including: bar graphs histograms line graphs circle graphs. Which Straight Line? Gradients for Real Horizontal Vertical Lines Slope of a Line Gradient Tan y=ax Equation of a Line 1 Gradients for Real Rates Calculations Rate Word Problems Similar Areas Volumes Using Similar Triangles Tally Charts Divided Bar Graphs Histogram or Polygon? Travel Graphs Bar Graphs 1 Line Graphs: Interpretation Divided Bar Graphs Creating a Sector Graph Frequency Histograms Cumulative Frequency Histogram Dot Plots Step Graphs Travel Graphs Grade 8 Linear hips Grade 8 Straight Lines Linear hips Straight Lines Under Review Data Interpreting Data 21 3P Learning

25 BC Foundations of Mathematics 12 Str Outcome Outcome Description Activities ebooks Financial Mathematics BC.12.F.A1.1 Financial Mathematics BC.12.F.A1.2 Financial Mathematics BC.12.F.A1.3 Financial Mathematics BC.12.F.A1.4 Financial Mathematics BC.12.F.A1.5 Financial Mathematics BC.12.F.A1.6 Financial Mathematics BC.12.F.A1.7 Financial Mathematics BC.12.F.A1.8 Financial Mathematics BC.12.F.A2.1 Explain the advantages disadvantages of compound interest simple interest. Identify situations that involve compound interest. Graph compare, in a given situation, the total interest paid or earned for different compounding periods. Determine, given the principal, interest rate number of compounding periods, the total interest of a loan. Graph describe the effects of changing the value of one of the variables in a situation that involves compound interest. Determine, using technology, the total cost of a loan under a variety of conditions; e.g., different amortization periods, interest rates, compounding periods terms. Compare explain, using technology, different credit options that involve compound interest, including bank store credit cards special promotions. Solve a contextual problem that involves compound interest. Identify describe examples of assets that appreciate or depreciate. Simple Interest Compound Interest Compound Interest by Formula Depreciation Comparing Home Loans Declining Balance Depreciation Future Value of Investments 1 Future Value of Investments 2 Inflation Depreciation Comparing Home Loans Declining Balance Depreciation Future Value of Investments 1 Future Value of Investments 2 Inflation Depreciation Comparing Home Loans Declining Balance Depreciation Future Value of Investments 1 Future Value of Investments 2 Inflation Depreciation Comparing Home Loans Declining Balance Depreciation Future Value of Investments 1 Future Value of Investments 2 Inflation Depreciation Comparing Home Loans Declining Balance Depreciation Future Value of Investments 1 Future Value of Investments 2 Inflation Depreciation Comparing Home Loans Declining Balance Depreciation Future Value of Investments 1 Future Value of Investments 2 Inflation Interest Depreciation Interest Depreciation Interest Depreciation Interest Depreciation Interest Depreciation Interest Depreciation Interest Depreciation 3P Learning 22

26 BC Foundations of Mathematics 12 Str Outcome Outcome Description Activities ebooks Financial Mathematics BC.12.F.A2.2 Financial Mathematics BC.12.F.A2.3 Financial Mathematics BC.12.F.A2.4 Financial Mathematics BC.12.F.A2.5 Financial Mathematics BC.12.F.A3.1 Financial Mathematics BC.12.F.A3.2 Financial Mathematics BC.12.F.A3.3 Financial Mathematics BC.12.F.A3.4 Financial Mathematics BC.12.F.A3.5 Financial Mathematics BC.12.F.A3.6 Financial Mathematics BC.12.F.A P Learning Compare, using examples, renting, leasing buying. Justify, for a specific set of circumstances, if renting, buying or leasing would be advantageous. Solve a problem involving renting, leasing or buying that requires the manipulation of a formula. Solve, using technology, a contextual problem that involves cost-benefit analysis. Determine compare the strengths weaknesses of two or more portfolios. Determine, using technology, the total value of an investment when there are regular contributions to the principal. Graph compare the total value of an investment with without regular contributions. Apply the Rule of 72 to solve investment problems, explain the limitations of the rule. Determine, using technology, possible investment strategies to achieve a financial goal. Explain the advantages disadvantages of long-term short-term investment options. Explain, using examples, why smaller investments over a longer term may be better than larger investments over a shorter term. Best Buy Successive Discounts Future Value of an Annuity Future Value of an Annuity Compound Interest Compound Interest by Formula Depreciation Comparing Home Loans Declining Balance Depreciation Future Value of Investments 1 Future Value of Investments 2 Inflation Future Value of an Annuity Depreciation Comparing Home Loans Declining Balance Depreciation Future Value of Investments 1 Future Value of Investments 2 Inflation Future Value of an Annuity Depreciation Comparing Home Loans Declining Balance Depreciation Future Value of Investments 1 Future Value of Investments 2 Future Value of an Annuity Earning Money

27 BC Foundations of Mathematics 12 Str Outcome Outcome Description Activities ebooks Financial Mathematics BC.12.F.A3.8 Logical Reasoning Logical Reasoning Logical Reasoning Logical Reasoning Logical Reasoning BC.12.F.B1.1 BC.12.F.B1.2 BC.12.F.B1.3 BC.12.F.B2.1 BC.12.F.B2.2 Solve an investment problem. Determine, explain verify a strategy to solve a puzzle or to win a game; e.g., - guess check - look for a pattern - make a systematic list - draw or model - eliminate possibilities - simplify the original problem - work backward - develop alternative approaches. Identify correct errors in a solution to a puzzle or in a strategy for winning a game. Create a variation on a puzzle or a game, describe a strategy for solving the puzzle or winning the game. Provide examples of the empty set, disjoint sets, subsets universal sets in context, explain the reasoning. Organize information such as collected data number properties, using graphic organizers, explain the reasoning. Depreciation Comparing Home Loans Declining Balance Depreciation Future Value of Investments 1 Future Value of Investments 2 Inflation Future Value of an Annuity Sector Graph Calculations Creating a Sector Graph Frequency Histograms Histograms Cumulative Frequency Histogram Cumulative Frequency Table Dot Plots Caroll Diagram Stem Leaf Introduction Double Stem Leaf Plots Correlation Circle Graphs Sector Graph Calculations Divided Bar Graphs Data Interpreting Data 3P Learning 24

28 BC Foundations of Mathematics 12 Str Outcome Outcome Description Activities ebooks Logical Reasoning Logical Reasoning Logical Reasoning Logical Reasoning Logical Reasoning Logical Reasoning Logical Reasoning Logical Reasoning Logical Reasoning Logical Reasoning Logical Reasoning Logical Reasoning 25 3P Learning BC.12.F.B2.3 BC.12.F.B2.4 BC.12.F.B2.5 BC.12.F.B2.6 BC.12.F.B2.7 BC.12.F.B3.1 BC.12.F.B3.2 BC.12.F.B3.3 BC.12.F.B3.4 BC.12.F.B3.5 BC.12.F.B3.6 BC.12.F.B3.7 BC.12.F.C1.1 BC.12.F.C1.2 Explain what a specified region in a Venn diagram represents, using connecting words (, or, not) or set notation. Determine the elements in the complement, the intersection or the union of two sets. Explain how set theory is used in applications such as Internet searches, database queries, data analysis, games puzzles. Identify correct errors in a given solution to a problem that involves sets. Solve a contextual problem that involves sets, record the solution, using set notation. Analyze an if-then statement, make a conclusion, explain the reasoning. Make justify a decision, using what if? questions, in contexts such as probability, finance, sports, games or puzzles, with or without technology. Determine the converse, inverse contrapositive of an if-then statement; determine its veracity;, if it is false, provide a counterexample. Demonstrate, using examples, that the veracity of any statement does not imply the veracity of its converse or inverse. Demonstrate, using examples, that the veracity of any statement does imply the veracity of its contrapositive. Identify describe contexts in which a biconditional statement can be justified. Analyze summarize, using a graphic organizer such as a truth table or Venn diagram, the possible results of given logical arguments that involve biconditional, converse, inverse or contrapositive statements. Provide examples of statements of probability odds found in fields such as media, biology, sports, medicine, sociology psychology. Explain, using examples, the relationship between odds (part-part) probability (part-whole). Venn Diagrams - 'And' 'Or' Venn Diagrams Scale Simple Data Interpreting Data

29 BC Foundations of Mathematics 12 Str Outcome Outcome Description Activities ebooks BC.12.F.C1.3 BC.12.F.C1.4 BC.12.F.C1.5 BC.12.F.C1.6 BC.12.F.C2.1 BC.12.F.C2.2 BC.12.F.C2.3 BC.12.F.C2.4 BC.12.F.C2.5 BC.12.F.C2.6 BC.12.F.C3.1 BC.12.F.C3.2 BC.12.F.C3.3 BC.12.F.C3.4 BC.12.F.C4.1 Express odds as a probability vice versa. Determine the probability of, or the odds for against, an outcome in a situation. Explain, using examples, how decisions may be based on probability or odds on subjective judgments. Find the Complementary Events With Replacement Without Replacement Dice Coins Solve a contextual problem that involves odds or probability. Classify events as mutually exclusive or non mutually exclusive, explain the Complementary Events reasoning. Determine if two events are complementary, explain the reasoning. Represent, using set notation or graphic organizers, mutually exclusive (including - 'And' 'Or' complementary) non mutually exclusive events. Solve a contextual problem that involves the probability of mutually exclusive or non mutually exclusive events. Solve a contextual problem that involves the probability of Complementary Events, complementary events. Create solve a problem that involves mutually exclusive or non - 'And' 'Or' mutually exclusive events. Compare, using examples, dependent independent events. Complementary Events Determine the probability of an event, With Replacement given the occurrence of a previous Without Replacement event. Dice Coins - 'And' 'Or' Determine the probability of two dependent or two independent events. Create solve a contextual problem that involves determining the probability of dependent or independent events. Represent solve counting problems, Tree Diagrams using a graphic organizer. 3P Learning 26

30 BC Foundations of Mathematics 12 Str Outcome Outcome Description Activities ebooks BC.12.F.C4.2 BC.12.F.C4.3 BC.12.F.C4.4 BC.12.F.C5.1 BC.12.F.C5.2 BC.12.F.C5.3 Generalize the fundamental counting principle, using inductive reasoning. Identify explain assumptions made in solving a counting problem. Solve a contextual counting problem, using the fundamental counting principle, explain the reasoning. Represent the number of arrangements of n elements taken n at a time, using factorial notation. Determine, with or without technology, the value of a factorial. Simplify a numeric or algebraic fraction containing factorials in both the numerator denominator. BC.12.F.C5.4 Solve an equation that involves factorials. BC.12.F.C5.5 BC.12.F.C5.6 BC.12.F.C5.7 BC.12.F.C5.8 BC.12.F.C5.9 BC.12.F.D1.3 BC.12.F.D1.5 BC.12.F.D1.6 Determine the number of permutations of n elements taken r at a time. Determine the number of permutations of n elements taken n at a time where some elements are not distinct. Explain, using examples, the effect on the total number of permutations of n elements when two or more elements are identical. Generalize strategies for determining the number of permutations of n elements taken r at a time. Solve a contextual problem that involves probability permutations. Match equations in a given set to their corresponding graphs. Interpret the graph of a polynomial function that models a situation, explain the reasoning. Solve, using technology, a contextual problem that involves data that is best represented by graphs of polynomial functions, explain the reasoning. Counting Techniques 1 Counting Techniques 2 Counting Principle Counting Techniques 1 Counting Techniques 2 Counting Principle Combinations Permutations Combinations Permutations Combinations Permutations Permutations Permutations Permutations Permutations Permutations Identifying Graphs Graphing Parabolas Graphing Exponentials Exponential or Log Graph? Graphing Cubics Parabolas Rectangles Parabolas Marbles Parabolas Rectangles Parabolas Marbles Simple Nonlinear Graphs 27 3P Learning

31 BC Foundations of Mathematics 12 Str Outcome Outcome Description Activities ebooks BC.12.F.D2.1 BC.12.F.D2.2 BC.12.F.D2.3 BC.12.F.D2.4 BC.12.F.D2.5 BC.12.F.D2.6 BC.12.F.D3.1 BC.12.F.D3.2 BC.12.F.D3.3 BC.12.F.D3.4 BC.12.F.D3.5 Describe, orally in written form, the characteristics of exponential or logarithmic functions by analyzing their graphs. Describe, orally in written form, the characteristics of exponential or logarithmic functions by analyzing their equations. Match equations in a given set to their corresponding graphs. Graph data determine the exponential or logarithmic function that best approximates the data. Interpret the graph of an exponential or logarithmic function that models a situation, explain the reasoning. Solve, using technology, a contextual problem that involves data that is best represented by graphs of exponential or logarithmic functions, explain the reasoning. Describe, orally in written form, the characteristics of sinusoidal functions by analyzing their graphs. Describe, orally in written form, the characteristics of sinusoidal functions by analyzing their equations. Match equations in a given set to their corresponding graphs. Graph data determine the sinusoidal function that best approximates the data. Interpret the graph of a sinusoidal function that models a situation, explain the reasoning. Exponential or Log Graph? Exponential Equations Equations with Logs Exponential Growth Decay Graphing Exponentials Exponential Equations Equations with Logs Exponential Growth Decay Graphing Exponentials Exponential or Log Graph? Non Linear Graphs Identifying Graphs Graphing Parabolas Graphing Cubics Function Notation 1 Function Notation 2 Function Notation 3 Odd Even Horizontal Vertical Change Logarithms Exponential Power Graphs Logarithms Exponential Power Graphs Simple Nonlinear Graphs Logarithms Exponential Power Graphs Exponential Growth Decay Exponential Growth Decay Sine Cosine Curves Period Amplitude Sine Cosine Curves Period Amplitude Sine Cosine Curves 3P Learning 28

32 BC Foundations of Mathematics 12 Str Outcome Outcome Description Activities Mathematics Research Project Mathematics Research Project Mathematics Research Project Mathematics Research Project Mathematics Research Project BC.12.F.D3.6 BC.12.F.E1.1 BC.12.F.E1.2 BC.12.F.E1.3 BC.12.F.E1.4 BC.12.F.E1.5 Solve, using technology, a contextual problem that involves data that is best represented by graphs of sinusoidal functions, explain the reasoning. Collect primary or secondary data (statistical or informational) related to the topic. Assess the accuracy, reliability relevance of the primary or secondary data collected by: - identifying examples of bias points of view - identifying describing the data collection methods - determining if the data is relevant - determining if the data is consistent with information obtained from other sources on the same topic. Interpret data, using statistical methods if applicable. Identify controversial issues, if any, present multiple sides of the issues with supporting data. Organize present the research project, with or without technology. Line Graphs: Interpretation Divided Bar Graphs Sector Graph Calculations Circle Graphs Frequency Histograms Cumulative Frequency Histogram Cumulative Frequency Table Box--Whisker Plots 1 Box--Whisker Plots 2 Dot Plots Caroll Diagram Stem Leaf Introduction Calculating Interquartile Range Mean Median Mode Data Extremes Range Mean from Frequency Table Mode from Frequency Table Median from Frequency Table Median Cumulative Frequency Correlation ebooks Under review Under review Under review Interpreting Data Under review Under review 29 3P Learning

33 BC Apprenticeship Workplace 12 Str Outcome Outcome Description Activities ebooks Measurement BC.12.AW.A1.1 Measurement BC.12.AW.A1.2 Measurement BC.12.AW.A1.3 Measurement BC.12.AW.A1.4 Measurement BC.12.AW.A1.5 Measurement BC.12.AW.A1.6 Measurement BC.12.AW.A1.7 Measurement BC.12.AW.A1.8 Measurement BC.12.AW.A1.9 Geometry BC.12.AW.B1.1 Geometry BC.12.AW.B1.2 Geometry BC.12.AW.B2.1 Explain why, in a given context, a certain degree of precision is required. Explain why, in a given context, a certain degree of accuracy is required. Explain, using examples, the difference between precision accuracy. Compare the degree of accuracy of two given instruments used to measure the same attribute. Relate the degree of accuracy to the uncertainty of a given measure. Analyze precision accuracy in a contextual problem. Calculate maximum minimum values, using a given degree of tolerance in context. Describe, using examples, the limitations of measuring instruments used in a specific trade or industry; e.g., tape measure versus Vernier caliper. Solve a problem that involves precision, accuracy or tolerance. Identify describe the use of the sine law cosine law in construction, industrial, commercial artistic applications. Solve a problem, using the sine law or cosine law, when a diagram is given. Describe illustrate properties of triangles, including isosceles equilateral. Error in Measurement Percentage Error Error in Measurement Percentage Error Sine Rule 1 Sine Rule 2 Cosine Rule 1 Cosine Rule 2 Triangles: Acute, Right, Obtuse Plane Figure Theorems Nets Hypotenuse of a Right Triangle Pythagoras Theorem Pythagorean Triads Angle Sum of a Triangle Exterior Angles of a Triangle Non Right Angled Triangles Polygons Angles 3P Learning 30

34 BC Apprenticeship Workplace 12 Str Outcome Outcome Description Activities ebooks Geometry BC.12.AW.B2.2 Geometry BC.12.AW.B2.3 Geometry BC.12.AW.B2.4 Geometry BC.12.AW.B2.5 Geometry BC.12.AW.B2.6 Geometry BC.12.AW.B3.1 Geometry BC.12.AW.B3.2 Geometry BC.12.AW.B3.3 Geometry BC.12.AW.B3.4 Geometry BC.12.AW.B3.5 Geometry BC.12.AW.B3.6 Geometry BC.12.AW.B3.7 Geometry BC.12.AW.B P Learning Describe illustrate properties of quadrilaterals in terms of angle measures, side lengths, diagonal lengths angles of intersection. Describe illustrate properties of regular polygons. Explain, using examples, why a given property does or does not apply to certain polygons. Identify explain an application of the properties of polygons in construction, industrial, commercial, domestic artistic contexts. Solve a contextual problem that involves the application of the properties of polygons. Identify a single transformation that was performed, given the original 2-D shape or 3-D object its image. Draw the image of a 2-D shape that results from a given single transformation. Draw the image of a 2-D shape that results from a given combination of successive transformations. Create, analyze describe designs, using translations, rotations reflections in all four quadrants of a coordinate grid. Identify describe applications of transformations in construction, industrial, commercial, domestic artistic contexts. Explain the relationship between reflections lines or planes of symmetry. Determine explain whether a given image is a dilation of another given shape, using the concept of similarity. Draw, with or without technology, a dilation image for a given 2-D shape or 3-D object, explain how the original 2-D shape or 3-D object its image are proportional. Plane Figure Theorems Angle Sum of a Quadrilateral Area: Quadrilaterals Interior Exterior Angles Plane Figure Theorems Plane Figure Theorems Transformations Transformations: Coordinate Plane Rotations: Coordinate Plane Transformations Transformations: Coordinate Plane Rotations: Coordinate Plane Rotations: Coordinate Plane Transformations: Coordinate Plane Rotational Symmetry Symmetry or Not? Congruent Triangles Using Similar Triangles Similar Figures Scale Factor Similarity Proofs Polygons Angles Polygons Angles Polygons Angles Polygons Angles Similarity Congruence

35 BC Apprenticeship Workplace 12 Str Outcome Outcome Description Activities ebooks Geometry BC.12.AW.B3.9 Number BC.12.AW.C1.1 Number BC.12.AW.C1.2 Number BC.12.AW.C1.3 Number BC.12.AW.C2.1 Number Number Number BC.12.AW.C2.2 BC.12.AW.C2.3 BC.12.AW.C3.1 Number BC.12.AW.C3.2 Number BC.12.AW.C3.3 Number BC.12.AW.C3.4 Number BC.12.AW.C3.5 Solve a contextual problem that involves transformations. Determine, explain verify a strategy to solve a puzzle or to win a game; e.g., - guess check - look for a pattern - make a systematic list - draw or model - eliminate possibilities - simplify the original problem - work backward - develop alternative approaches. Identify correct errors in a solution to a puzzle or in a strategy for winning a game. Create a variation on a puzzle or a game, describe a strategy for solving the puzzle or winning the game. Describe explain various options for buying, leasing leasing to buy a Purchase Options vehicle. Solve, with or without technology, problems that involve the purchase, lease or lease to purchase of a vehicle. Justify a decision related to buying, leasing or leasing to buy a vehicle, based on factors such as personal finances, intended use, maintenance, warranties, mileage insurance. Calculating Income Tax Budgeting Graphs from Bills Identify expenses in operating a small Deductions Tax business, such as a hot dog st. Installments Reading from a Bill GST (also called VAT) Special Allowances Identify feasible small business options for a given community. Generate options that might improve the profitability of a small business. Determine the break-even point for a small business. Explain factors, such as seasonal variations hours of operation, that might impact the profitability of a small business. Breakeven Point 3P Learning 32

36 BC Apprenticeship Workplace 12 Str Outcome Outcome Description Activities ebooks Algebra Algebra Algebra Algebra Algebra Algebra Algebra Algebra BC.12.AW.D1.1 BC.12.AW.D1.2 BC.12.AW.D1.3 BC.12.AW.D1.4 BC.12.AW.D1.5 BC.12.AW.D1.6 BC.12.AW.D1.7 BC.12.AW.D1.8 Identify describe the characteristics of a linear relation represented in a graph, table of values, number pattern or equation. Sort a set of graphs, tables of values, number patterns /or equations into linear nonlinear relations. Write an equation for a given context, including direct or partial variation. Create a table of values for a given equation of a linear relation. Sketch the graph for a given table of values. Explain why the points should or should not be connected on the graph for a context. Create, with or without technology, a graph to represent a data set, including scatterplots. Describe the trends in the graph of a data set, including scatterplots. Table of Values Find the Pattern Rule Pattern Rules Tables Function Rules Tables Graphing from a Table of Values Reading Values from a Line Determining a Rule for a Line Which Straight Line? Modelling Linear hips y=ax Direct Variation Determining a Rule for a Line Pattern Rules Tables Function Rules Tables Graphing from a Table of Values Graphing from a Table of Values 2 Graphing from a Table of Values Graphing from a Table of Values 2 Non Linear Graphs Correlation Line Graphs: Interpretation Grade 8 Linear Grade 8 Straight Lines Linear Coordinate Geometry Straight Lines Grade 8 Linear Grade 8 Straight Lines Linear Coordinate Geometry Straight Lines Grade 8 Linear Grade 8 Straight Lines Linear Coordinate Geometry Straight Lines Grade 8 Linear Grade 8 Straight Lines Linear Coordinate Geometry Straight Lines Grade 8 Linear Grade 8 Straight Lines Linear Coordinate Geometry Straight Lines 33 3P Learning

37 BC Apprenticeship Workplace 12 Str Outcome Outcome Description Activities ebooks Algebra BC.12.AW.D1.9 Algebra Algebra Algebra Algebra Statistics BC.12.AW.D1.10 BC.12.AW.D1.11 BC.12.AW.D1.12 BC.12.AW.D1.13 BC.12.AW.E1.1 Statistics BC.12.AW.E1.2 Statistics BC.12.AW.E1.3 Statistics BC.12.AW.E1.4 Statistics BC.12.AW.E1.5 Sort a set of scatterplots according to the trends represented (linear, nonlinear or no trend). Solve a contextual problem that requires interpolation or extrapolation of information. Relate slope rate of change to linear relations. Match given contexts with their corresponding graphs, explain the reasoning. Solve a contextual problem that involves the application of a formula for a linear relation. Explain, using examples, the advantages disadvantages of each measure of central tendency. Determine the mean, median mode for a set of data. Identify correct errors in a calculation of a measure of central tendency. Identify the outlier(s) in a set of data. Explain the effect of outliers on mean, median mode. Correlation Modelling Linear hips y=ax Direct Variation Determining a Rule for a Line Gradient Gradients for Real Which Straight Line? Horizontal Vertical Lines Which Straight Line? Modelling Linear hips Gradients for Real Mean Median Mode Mean from Frequency Table Median from Frequency Table Median Cumulative Frequency Grade 8 Linear Grade 8 Straight Lines Linear Coordinate Geometry Straight Lines Grade 8 Linear Grade 8 Straight Lines Linear Coordinate Geometry Straight Lines Grade 8 Linear Grade 8 Straight Lines Linear Coordinate Geometry Straight Lines Data Data Data 3P Learning 34

38 BC Apprenticeship Workplace 12 Str Outcome Outcome Description Activities ebooks Statistics BC.12.AW.E1.6 Statistics BC.12.AW.E1.7 Statistics BC.12.AW.E1.8 Statistics BC.12.AW.E1.9 Statistics BC.12.AW.E1.10 Statistics BC.12.AW.E2.1 Statistics BC.12.AW.E2.2 Statistics BC.12.AW.E2.3 Statistics BC.12.AW.E2.4 Statistics BC.12.AW.E2.5 BC.12.AW.F1.1 Calculate the trimmed mean for a set of data, justify the removal of the outliers. Explain, using examples such as course marks, why some data in a set would be given a greater weighting in determining the mean. Calculate the mean of a set of numbers after allowing the data to have different weightings (weighted mean). Explain, using examples from print other media, how measures of central tendency outliers are used to provide different interpretations of data. Solve a contextual problem that involves measures of central tendency. Explain, using examples, percentile ranks in a context. Explain decisions based on a given percentile rank. Explain, using examples, the difference between percent percentile rank. Explain the relationship between median percentile. Solve a contextual problem that involves percentiles. Describe explain the applications of probability; e.g., medication, warranties, insurance, lotteries, weather prediction, 100- year flood, failure of a design, failure of a product, vehicle recalls, approximation of area. Calculating Interquartile Range Box--Whisker Plots 1 Box--Whisker Plots 2 Box--Whisker Plots 1 Box--Whisker Plots 2 Interpreting Data Interpreting Data 35 3P Learning

39 BC Apprenticeship Workplace 12 Str Outcome Outcome Description Activities ebooks BC.12.AW.F1.2 BC.12.AW.F1.3 BC.12.AW.F1.4 BC.12.AW.F1.5 BC.12.AW.F1.6 BC.12.AW.F1.7 Calculate the probability of an event based on a data set; e.g., determine the probability of a romly chosen light bulb being defective. Express a given probability as a fraction, decimal percent in a statement. Explain the difference between odds probability. Determine the probability of an event, given the odds for or against. Explain, using examples, how decisions may be based on a combination of theoretical probability calculations, experimental results subjective judgements. Solve a contextual problem that involves a given probability. Fair Games Possible Outcomes Simple Complementary Events With Replacement Without Replacement Dice Coins Tables Two-way Table Relative Frequency Venn Diagrams Possible Outcomes Simple Complementary Events With Replacement Without Replacement Dice Coins Tables Two-way Table Relative Frequency Venn Diagrams Possible Outcomes Simple Complementary Events With Replacement Without Replacement Dice Coins Tables Two-way Table Relative Frequency Venn Diagrams 3P Learning 36

40 BC Pre-calculus 12 Str Outcome Outcome Description Activities ebooks Trigonometry BC.12.P.A1.1 Trigonometry BC.12.P.A1.2 Trigonometry BC.12.P.A1.3 Trigonometry BC.12.P.A1.4 Trigonometry BC.12.P.A1.5 Trigonometry BC.12.P.A1.6 Trigonometry BC.12.P.A1.7 Trigonometry BC.12.P.A1.8 Trigonometry BC.12.P.A1.9 Trigonometry BC.12.P.A2.1 Trigonometry BC.12.P.A2.2 Sketch, in stard position, an angle (positive or negative) when the measure is given in degrees. Describe the relationship among different systems of angle measurement, with emphasis on radians degrees. Sketch, in stard position, an angle with a measure of 1 radian. Sketch, in stard position, an angle with a measure expressed in the form kπ radians, where k-q. Express the measure of an angle in radians (exact value or decimal approximation), given its measure in degrees. Express the measure of an angle in degrees, given its measure in radians (exact value or decimal approximation). Determine the measures, in degrees or radians, of all angles in a given domain that are coterminal with a given angle in stard position. Determine the general form of the measures, in degrees or radians, of all angles that are coterminal with a given angle in stard position. Explain the relationship between the radian measure of an angle in stard position the length of the arc cut on a circle of radius r, solve problems based upon that relationship. Derive the equation of the unit circle from the Pythagorean theorem. Describe the six trigonometric ratios, using a point P (x, y) that is the intersection of the terminal arm of an angle the unit circle. Converting Radians Degrees Converting Radians Degrees Converting Radians Degrees Unit Circle Reductions Trig Equations 1 Trig Equations 2 Trig Equations 3 Trigonometric Intercepts Unit Circle Reductions Trig Equations 1 Trig Equations 2 Trig Equations 3 Trig Equations 4 Length of an Arc Sin A Cos A Tan A Trigonometry Grade 12 Trigonometry Polar Coordinates Trigonometry Grade 12 Trigonometry Polar Coordinates Trigonometry Grade 12 Trigonometry Polar Coordinates Trigonometry Grade 12 Trigonometry Polar Coordinates Trigonometry Grade 12 Trigonometry Polar Coordinates Trigonometry Grade 12 Trigonometry Polar Coordinates Trigonometry Trigonometric hips Grade 12 Trigonometry Polar Coordinates Trigonometry Trigonometric hips Grade 12 Trigonometry Polar Coordinates Grade 12 Trigonometry Polar Coordinates Circle Graphs Trigonometry Trigonometric hips Grade 12 Trigonometry Polar Coordinates 37 3P Learning

41 BC Pre-calculus 12 Str Outcome Outcome Description Activities ebooks Trigonometry BC.12.P.A2.3 Trigonometry BC.12.P.A3.1 Trigonometry BC.12.P.A3.2 Trigonometry BC.12.P.A3.3 Trigonometry BC.12.P.A3.4 Trigonometry BC.12.P.A3.5 Trigonometry BC.12.P.A3.6 Trigonometry BC.12.P.A3.7 Trigonometry BC.12.P.A3.8 Generalize the equation of a circle with centre (0, 0) radius r. Determine, with technology, the approximate value of a trigonometric ratio for any angle with a measure expressed in either degrees or radians. Determine, using a unit circle or reference triangle, the exact value of a trigonometric ratio for angles expressed in degrees that are multiples of 0, 30, 45, 60 or 90, or for angles expressed in radians that are multiples of 0, π/6, π/4, π/3 or π/2, explain the strategy. Determine, with or without technology, the measures, in degrees or radians, of the angles in a specified domain, given the value of a trigonometric ratio. Explain how to determine the exact values of the six trigonometric ratios, given the coordinates of a point on the terminal arm of an angle in stard position. Determine the measures of the angles in a specified domain in degrees or radians, given a point on the terminal arm of an angle in stard position. Determine the exact values of the other trigonometric ratios, given the value of one trigonometric ratio in a specified domain. Sketch a diagram to represent a problem that involves trigonometric ratios. Solve a problem, using trigonometric ratios. Graphing Circles Centre Radius 1 Centre Radius 2 Exact Trigonometric Ratios Sign of the Angle Exact Trigonometric Ratios Exact Trigonometric Ratios Sign of the Angle Which Quadrant? Circle Graphs Trigonometry Trigonometric hips Trigonometry Trigonometric hips Trigonometry Trigonometric hips Trigonometry Trigonometric hips Trigonometry Trigonometric hips Trigonometry Trigonometric hips Trigonometry Trigonometric hips Trigonometry Trigonometric hips 3P Learning 38

42 BC Pre-calculus 12 Str Outcome Outcome Description Activities ebooks Trigonometry BC.12.P.A4.1 Trigonometry BC.12.P.A4.2 Trigonometry BC.12.P.A4.3 Trigonometry BC.12.P.A4.4 Trigonometry BC.12.P.A4.5 Trigonometry BC.12.P.A4.6 Trigonometry BC.12.P.A4.7 Trigonometry BC.12.P.A4.8 Trigonometry BC.12.P.A4.9 Trigonometry BC.12.P.A4.10 Trigonometry BC.12.P.A4.11 Sketch, with or without technology, the graph of y=sin x, y=cos x or y=tan x. Determine the characteristics (amplitude, asymptotes, domain, period, range zeros) of the graph of y=sin x, y=cos x or y=tan x. Determine how varying the value of a affects the graphs of y=a sin x y=a cos x. Determine how varying the value of d affects the graphs of y=sin x + d y=cos x + d. Determine how varying the value of c affects the graphs of y=sin (x + c) y=cos (x + c). Determine how varying the value of b affects the graphs of y=sin (bx) y=cos (bx) Sketch, without technology, graphs of the form y=a sin b(x c) + d or y=a cos b(x c) + d, using transformations, explain the strategies. Determine the characteristics (amplitude, asymptotes, domain, period, phase shift, range zeros) of the graph of a trigonometric function of the form y=a sin b(x c) + d or y=a cos b(x c) + d. Determine the values of a, b, c d for functions of the form y=a sin b(x c) + d or y=a cos b(x c) + d that correspond to a given graph, write the equation of the function. Determine a trigonometric function that models a situation to solve a problem. Explain how the characteristics of the graph of a trigonometric function relate to the conditions in a problem situation. Sine Cosine Curves Period Amplitude Trig Graphs in Radians Period Amplitude Sine Cosine Curves Sine Cosine Curves Period Amplitude Sine Cosine Curves Period Amplitude Trig Graphs in Radians Period Amplitude Trig Graphs in Radians Period Amplitude Trigonometry Trigonometric hips 39 3P Learning

43 BC Pre-calculus 12 Str Outcome Outcome Description Activities ebooks Trigonometry BC.12.P.A4.12 Trigonometry BC.12.P.A5.1 Trigonometry BC.12.P.A5.2 Trigonometry BC.12.P.A5.3 Trigonometry BC.12.P.A5.4 Trigonometry BC.12.P.A5.5 Trigonometry BC.12.P.A5.6 Trigonometry BC.12.P.A6.1 Trigonometry BC.12.P.A6.2 Trigonometry BC.12.P.A6.3 Trigonometry BC.12.P.A6.4 Solve a problem by analyzing the graph of a trigonometric function. Verify, with or without technology, that a given value is a solution to a trigonometric equation. Determine, algebraically, the solution of a trigonometric equation, stating the solution in exact form when possible. Determine, using technology, the approximate solution of a trigonometric equation in a restricted domain. Relate the general solution of a trigonometric equation to the zeros of the corresponding trigonometric function (restricted to sine cosine functions). Determine, using technology, the general solution of a given trigonometric equation. Identify correct errors in a solution for a trigonometric equation. Explain the difference between a trigonometric identity a trigonometric equation. Verify a trigonometric identity numerically for a given value in either degrees or radians. Explain why verifying that the two sides of a trigonometric identity are equal for given values is insufficient to conclude that the identity is valid. Determine, graphically, the potential validity of a trigonometric identity, using technology. Trigonometric Intercepts Trig Graphs in Radians Period Amplitude Sine Cosine Curves Trig Equations 1 Trig Equations 2 Trig Equations 3 Trig Equations 4 Trigonometry Problems 1 Trigonometry Problems 2 Trig Equations 1 Trig Equations 2 Trig Equations 3 Trig Equations 4 Trig Equations 1 Trig Equations 2 Trig Equations 3 Trig Equations 4 Trigonometric Intercepts Trigonometry Trigonometric hips Trigonometry Trigonometric hips 3P Learning 40

44 BC Pre-calculus 12 Str Outcome Outcome Description Activities ebooks Trigonometry Trigonometry Trigonometry BC.12.P.A6.5 BC.12.P.A6.6 BC.12.P.A6.7 BC.12.P.B1.1 BC.12.P.B1.2 BC.12.P.B1.3 BC.12.P.B1.4 BC.12.P.B1.5 BC.12.P.B1.6 BC.12.P.B1.7 BC.12.P.B1.8 BC.12.P.B1.9 BC.12.P.B2.1 BC.12.P.B2.2 Determine the non-permissible values of a trigonometric identity. Prove, algebraically, that a trigonometric identity is valid. Determine, using the sum, difference double-angle identities, the exact value of Double Angles a trigonometric ratio. Sketch the graph of a function that is the sum, difference, product or quotient of two functions, given their graphs. Write the equation of a function that is the sum, difference, product or quotient of two or more functions, given their equations. Determine the domain range of Domain a function that is the sum, difference, product or quotient of two functions. Domain Range Write a function h(x) as the sum, difference, product or quotient of two or more functions. Determine the value of the composition Composition of of functions when evaluated at a point, 1 including: f(f(a)), f(g(a)), g(f(a)). Determine, given the equations of two functions f(x) g(x), the equation of the Composition of composite function: f(f(x)), f(g(x)), g(f(x)) 1 explain any restrictions. Sketch, given the equations of two functions f(x) g(x), the graph of the composite function: f(f(x)), f(g(x)), g(f(x)). Write a function h(x) as the composition of Composition of two or more functions. 1 Write a function h(x) by combining two or more functions through operations on, compositions of, functions. Compare the graphs of a set of functions of the form y k=f(x) to the graph of y=f(x), generalize, using inductive reasoning, a rule about the effect of k. Compare the graphs of a set of functions of the form y=f(x - h) to the graph of y=f(x), generalize, using inductive reasoning, a rule about the effect of h. 41 3P Learning

45 BC Pre-calculus 12 Str Outcome Outcome Description Activities ebooks BC.12.P.B2.3 BC.12.P.B2.4 BC.12.P.B2.5 BC.12.P.B3.1 BC.12.P.B3.2 BC.12.P.B3.3 BC.12.P.B3.4 BC.12.P.B3.5 BC.12.P.B4.1 Compare the graphs of a set of functions of the form y - k=f(x - h) to the graph of y=f(x), generalize, using inductive reasoning, a rule about the effects of h k. Sketch the graph of y - k=f(x), y=f(x - h) or y - k=f(x - h) for given values of h k, given a sketch of the function y=f(x), where the equation of y=f(x) is not given. Write the equation of a function whose graph is a vertical /or horizontal translation of the graph of the function y=f(x). Compare the graphs of a set of functions of the form y=af(x) to the graph of y=f(x), generalize, using inductive reasoning, a rule about the effect of a. Compare the graphs of a set of functions of the form y=f(bx) to the graph of y=f(x), generalize, using inductive reasoning, a rule about the effect of b. Compare the graphs of a set of functions of the form y=af(bx) to the graph of y=f(x), generalize, using inductive reasoning, a rule about the effects of a b. Sketch the graph of y=af(x), y=f(bx) or y=af(bx) for given values of a b, given a sketch of the function y=f(x), where the equation of y=f(x) is not given. Write the equation of a function, given its graph which is a vertical /or horizontal stretch of the graph of the function y=f(x). Sketch the graph of the function y - k=af(b(x - h)) for given values of a, b, h k, given the graph of the function y=f(x), where the equation of y=f(x) is not given. Parabolas 3P Learning 42

46 BC Pre-calculus 12 Str Outcome Outcome Description Activities ebooks BC.12.P.B4.2 BC.12.P.B5.1 BC.12.P.B5.2 BC.12.P.B5.3 BC.12.P.B5.4 BC.12.P.B5.5 BC.12.P.B6.1 BC.12.P.B6.2 BC.12.P.B6.3 BC.12.P.B6.4 Write the equation of a function, given its graph which is a translation / or stretch of the graph of the function y=f(x). Generalize the relationship between the coordinates of an ordered pair the coordinates of the corresponding ordered pair that results from a reflection through the x-axis, the y-axis or the line y=x. Sketch the reflection of the graph of a function y=f(x) through the x-axis, the y-axis or the line y=x, given the graph of the function y=f(x), where the equation of y=f(x) is not given. Generalize, using inductive reasoning, explain rules for the reflection of the graph of the function y=f(x) through the x-axis, the y-axis or the line y=x. Sketch the graphs of the functions y= f(x), y=f( x) x= f(y), given the graph of the function y=f(x), where the equation of y=f(x) is not given. Write the equation of a function, given its graph which is a reflection of the graph of the function y=f(x) through the x-axis, the y-axis or the line y=x. Explain how the graph of the line y=x, can be used to sketch the inverse of a relation. Explain how the transformation (x, y)=> (y, x) can be used to sketch the inverse of a relation. Sketch the graph of the inverse relation, given the graph of a relation. Determine if a relation its inverse are functions. Transformations: Coordinate Plane Inverse functions Graphing Inverse Inverse Trigonometric Graph Inverse Trig Inverse functions Graphing Inverse Inverse Trigonometric Graph Inverse Trig Inverse functions Graphing Inverse Inverse Trigonometric Graph Inverse Trig Inverse functions Graphing Inverse Inverse Trigonometric Graph Inverse Trig Inverse functions Graphing Inverse Inverse Trigonometric Graph Inverse Trig Inverse functions Graphing Inverse Inverse Trigonometric Graph Inverse Trig 43 3P Learning

47 BC Pre-calculus 12 Str Outcome Outcome Description Activities ebooks BC.12.P.B6.5 BC.12.P.B6.6 BC.12.P.B6.7 BC.12.P.B6.8 BC.12.P.B7.1 BC.12.P.B7.2 BC.12.P.B7.3 BC.12.P.B7.4 BC.12.P.B8.1 Determine restrictions on the domain of a function in order for its inverse to be a function. Determine the equation sketch the graph of the inverse relation, given the equation of a linear or quadratic relation. Explain the relationship between the domains ranges of a relation its inverse. Determine, algebraically or graphically, if two functions are inverses of each other. Explain the relationship between logarithms exponents. Express a logarithmic expression as an exponential expression vice versa. Determine, without technology, the exact value of a logarithm, such as log 2 (8). Estimate the value of a logarithm, using benchmarks, explain the reasoning; e.g. since log 2 (8)= 3 log 2 (16)= 4, log 2 9 is approximately equal to 3.1. Develop generalize the laws for logarithms, using numeric examples exponent laws. Inverse functions Graphing Inverse Inverse Trigonometric Graph Inverse Trig Inverse functions Graphing Inverse Inverse Trigonometric Graph Inverse Trig Log Base e Graphing Exponentials Exponential or Log Graph? Log Laws Change of Base Equations with Logs Log Laws Logarithms Logarithms Logarithms Logarithms Exponents Logarithms BC.12.P.B8.2 Derive each law of logarithms. Logarithms BC.12.P.B8.3 BC.12.P.B8.4 Determine, using the laws of logarithms, an equivalent expression for a logarithmic expression. Determine, with technology, the approximate value of a logarithmic expression, such as log 2 (9). Log Laws Logarithms Logarithms 3P Learning 44

48 BC Pre-calculus 12 Str Outcome Outcome Description Activities ebooks BC.12.P.B9.1 BC.12.P.B9.2 BC.12.P.B9.3 BC.12.P.B9.4 BC.12.P.B9.5 BC.12.P.B9.6 BC.12.P.B9.7 BC.12.P.B10.1 BC.12.P.B10.2 Sketch, with or without technology, a graph of an exponential function of the form y=a^x, a > 0. Identify the characteristics of the graph of an exponential function of the form y=a^x, a > 0, including the domain, range, horizontal asymptote intercepts, explain the significance of the horizontal asymptote. Sketch the graph of an exponential function by applying a set of transformations to the graph of y=a^x, a > 0, state the characteristics of the graph. Sketch, with or without technology, the graph of a logarithmic function of the form y=log 2 (x), a > 1. Identify the characteristics of the graph of a logarithmic function of the form y=log 2 (x), a > 1, including the domain, range, vertical asymptote intercepts, explain the significance of the vertical asymptote. Sketch the graph of a logarithmic function by applying a set of transformations to the graph of y=log 2 (x), a > 1, state the characteristics of the graph. Demonstrate, graphically, that a logarithmic function an exponential function with the same base are inverses of each other. Determine the solution of an exponential equation in which the bases are powers of one another. Determine the solution of an exponential equation in which the bases are not powers of one another, using a variety of strategies. Graphing Exponentials Exponential or Log Graph? Graphing Exponentials Exponential or Log Graph? Exponential or Log Graph? Logarithms Exponential Power Graphs Simple Nonlinear Graphs Logarithms Exponential Power Graphs Simple Nonlinear Graphs Logarithms Exponential Power Graphs Simple Nonlinear Graphs Logarithms Exponential Power Graphs Simple Nonlinear Graphs Logarithms Exponential Power Graphs Simple Nonlinear Graphs Logarithms Exponential Power Graphs Simple Nonlinear Graphs Logarithms Exponential Power Graphs Simple Nonlinear Graphs Logarithms Logarithms 45 3P Learning

49 BC Pre-calculus 12 Str Outcome Outcome Description Activities ebooks BC.12.P.B10.3 BC.12.P.B10.4 BC.12.P.B10.5 BC.12.P.B10.6 BC.12.P.B10.7 BC.12.P.B10.8 BC.12.P.B11.1 BC.12.P.B11.2 BC.12.P.B11.3 BC.12.P.B11.4 Determine the solution of a logarithmic equation, verify the solution. Explain why a value obtained in solving a logarithmic equation may be extraneous. Solve a problem that involves exponential growth or decay. Solve a problem that involves the application of exponential equations to loans, mortgages investments. Solve a problem that involves logarithmic scales, such as the Richter scale the ph scale. Solve a problem by modelling a situation with an exponential or a logarithmic equation. Explain how long division of a polynomial expression by a binomial expression of the form x a, x Є I, is related to synthetic division. Divide a polynomial expression by a binomial expression of the form x a, x Є I, using long division or synthetic division. Explain the relationship between the linear factors of a polynomial expression the zeros of the corresponding polynomial function. Explain the relationship between the remainder when a polynomial expression is divided by x a, x Є I, the value of the polynomial expression at x=a (remainder theorem). Log Laws Change of Base Equations with Logs Exponential Growth Decay Exponential Growth Decay Compound Interest Compound Interest by Formula Future Value of Investments 1 Future Value of Investments 2 Exponential Growth Decay Compound Interest Compound Interest by Formula Future Value of Investments 1 Future Value of Investments 2 Polynomial Long Division Polynomial Factor Theorem Logarithms Polynomials Polynomials Polynomials 3P Learning 46

50 BC Pre-calculus 12 Str Outcome Outcome Description Activities ebooks BC.12.P.B11.5 BC.12.P.B12.1 BC.12.P.B12.2 BC.12.P.B12.3 BC.12.P.B12.4 BC.12.P.B12.5 BC.12.P.B12.6 BC.12.P.B12.7 BC.12.P.B13.1 BC.12.P.B13.2 BC.12.P.B13.3 BC.12.P.B13.4 Explain apply the factor theorem to express a polynomial expression as a product of factors. Identify the polynomial functions in a set of functions, explain the reasoning. Explain the role of the constant term leading coefficient in the equation of a polynomial function with respect to the graph of the function. Generalize rules for graphing polynomial functions of odd or even degree. Explain the relationship between: y the zeros of a polynomial function, y the roots of the corresponding polynomial equation, y the x-intercepts of the graph of the polynomial function. Explain how the multiplicity of a zero of a polynomial function affects the graph. Sketch, with or without technology, the graph of a polynomial function. Solve a problem by modelling a given situation with a polynomial function analyzing the graph of the function. Sketch the graph of the function y= x, using a table of values, state the domain range. Sketch the graph of the function y k=a* (b(x - h)) by applying transformations to the graph of the function y= x, state the domain range. Sketch the graph of the function y= (f(x)), given the graph of the function y=f(x), explain the strategies used. Compare the domain range of the function y= (f(x)), to the domain range of the function y=f(x), explain why the domains ranges may differ. Polynomial Factor Theorem Odd Even Polynomial Factor Theorem Grade Graphing Parabolas Graphing Cubics Parabolas Marbles Parabolas Rectangles Domain Domain Range Domain Domain Range Polynomials Polynomials Polynomials Sketching Polynomials Polynomials Sketching Polynomials 10 Polynomials Sketching Polynomials Polynomials Sketching Polynomials Polynomials Sketching Polynomials 47 3P Learning

51 BC Pre-calculus 12 Str Outcome Outcome Description Activities ebooks Permutations, Combinations Binomial Theorem Permutations, Combinations Binomial Theorem Permutations, Combinations Binomial Theorem Permutations, Combinations Binomial Theorem Permutations, Combinations Binomial Theorem BC.12.P.B13.5 BC.12.P.B13.6 BC.12.P.B14.1 BC.12.P.B14.2 BC.12.P.B14.3 BC.12.P.B14.4 BC.12.P.B14.5 BC.12.P.B14.6 BC.12.P.B14.7 BC.12.P.C1.1 BC.12.P.C1.2 BC.12.P.C1.3 BC.12.P.C2.1 BC.12.P.C2.2 Describe the relationship between the roots of a radical equation the x-intercepts of the graph of the corresponding radical function. Determine, graphically, an approximate solution of a radical equation. Graph, with or without technology, a rational function. Analyze the graphs of a set of rational functions to identify common characteristics. Explain the behaviour of the graph of a rational function for values of the variable near a non-permissible value. Determine if the graph of a rational function will have an asymptote or a hole for a non-permissible value. Match a set of rational functions to their graphs, explain the reasoning. Describe the relationship between the roots of a rational equation the x-intercepts of the graph of the corresponding rational function. Determine, graphically, an approximate solution of a rational equation. Count the total number of possible choices that can be made, using graphic organizers such as lists tree diagrams. Explain, using examples, why the total number of possible choices is found by multiplying rather than adding the number of ways the individual choices can be made. Solve a simple counting problem by applying the fundamental counting principle. Count, using graphic organizers such as lists tree diagrams, the number of ways of arranging the elements of a set in a row. Determine, in factorial notation, the number of permutations of n different elements taken n at a time to solve a problem. Domain Domain Range How many Combinations? Counting Techniques 1 Counting Techniques 2 How many Combinations? Counting Techniques 1 Counting Techniques 2 How many Combinations? Permutations 3P Learning 48

52 BC Pre-calculus 12 Str Outcome Outcome Description Activities ebooks Permutations, Combinations Binomial Theorem Permutations, Combinations Binomial Theorem Permutations, Combinations Binomial Theorem Permutations, Combinations Binomial Theorem Permutations, Combinations Binomial Theorem Permutations, Combinations Binomial Theorem Permutations, Combinations Binomial Theorem Permutations, Combinations Binomial Theorem Permutations, Combinations Binomial Theorem Permutations, Combinations Binomial Theorem Permutations, Combinations Binomial Theorem Permutations, Combinations Binomial Theorem BC.12.P.C2.3 BC.12.P.C2.4 BC.12.P.C2.5 BC.12.P.C2.6 BC.12.P.C3.1 BC.12.P.C3.2 BC.12.P.C3.3 BC.12.P.C3.4 BC.12.P.C3.5 BC.12.P.C3.6 BC.12.P.C4.1 BC.12.P.C4.2 Determine, using a variety of strategies, the number of permutations of n different elements taken r at a time to solve a problem. Explain why n must be greater than or equal to r in the notation n Pr. Solve an equation that involves n Pr notation, such as n P2=30. Explain, using examples, the effect on the total number of permutations when two or more elements are identical. Explain, using examples, the difference between a permutation a combination. Determine the number of ways that a subset of k elements can be selected from a set of n different elements. Determine the number of combinations of n different elements taken r at a time to solve a problem. Explain why n must be greater than or equal to r in the notation n Cr. Explain, using examples, why there exists symmetry about r n - r in n Cr. (both notations). Solve an equation that involves n Cr notation, such as n C2=15 (both notations). Explain the patterns found in the exped form of (x + y) n, n 4 n Є N, by multiplying n factors of (x + y). Explain how to determine the subsequent row in Pascal s triangle, given any row. Permutations Permutations Permutations Permutations Combinations Permutations Combinations Permutations Combinations Combinations Combinations Combinations Pascal s Triangle, Expansion Pascal s Triangle, Expansion Grade 12 Binomials Pascal's Triangle 49 3P Learning

53 BC Pre-calculus 12 Str Outcome Outcome Description Activities ebooks Permutations, Combinations Binomial Theorem Permutations, Combinations Binomial Theorem Permutations, Combinations Binomial Theorem Permutations, Combinations Binomial Theorem BC.12.P.C4.3 BC.12.P.C4.4 BC.12.P.C4.5 BC.12.P.C4.6 Relate the coefficients of the terms in the expansion of (x + y) n to the (n + 1) row in Pascal s triangle. Explain, using examples, how the coefficients of the terms in the expansion of (x + y) n are determined by combinations. Exp, using the binomial theorem, (x + y) n. Determine a specific term in the expansion of (x + y) n. Pascal s Triangle, Expansion Pascal s Triangle, Expansion Pascal s Triangle, Expansion Pascal s Triangle, Expansion 3P Learning 50

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