Course Syllabus

St. George's School

 Pre-Calculus Math 11

COURSE OUTLINE

2020-2021

THIS COURSE RELIES HEAVILY ON BOTH ALGEBRAIC AND GRAPHICAL METHODS: STUDENTS ARE REQUIRED TO HAVE A GRAPHICAL CALCULATOR. HOWEVER, this must not be capable of accessing the internet etc, nor can it have a “CAS” Computer Algebra System. A TI-84 or equivalent is sufficient.

The suggested timing below is approximate. There is some degree of flexibility by the teacher, in the time allocated to each topic, depending upon circumstances, but the program will be delivered broadly as indicated.

TERM 1        25 classes                                                                Specific Outcomes

 

Unit 1           Trigonometry                             9 classes                     M11,12, 13

Unit 2:          Quadratic Functions                  7 classes                     RF11, RF12

Unit 3:          Quadratic Equations                  10 classes                     RF9, 12, 13

 

TERM 2        25 classes

                    

Unit 4:          Financial Literacy                                 3 classes        FL6, FL7

Unit 5:          Radical Expressions and Equations   9 classes        AN23, AN24

Unit 6:          Rational Expressions and Equations 10 classes        AN25, AN26

Unit 7:          Arithmetic Sequences & Series           4 classes        RF9

 

TERM 3        26 classes

Unit 8:          Absolute Value functions                    6 classes        AN22, RF10

          Unit 9:          Systems of Equations                         6 classes        RF14

Unit 10:        Linear and Quadratic Inequalities       8 classes        RF15, RF16

         

This is a very tight curriculum, with very little opportunity for final review. Students must ensure that their recall and understanding of earlier material remains strong throughout the course.

 

 

 

Textbook Detail and Learning Outcomes.

Unit 1          Trigonometry                  (Chapter 2)                                     9 classes

Develop Trigonometric reasoning

M11    Demonstrate an understanding of angles in Standard Position (0 up to 360)

M12    Solve problems using the three primary trigonometric ratios (0 up to 360)

M13    Solve problems using the cosine law and sine law including the ambiguous case.

	Specific Outcome	Curriculum Focus	# of classes
2.1 Angles in standard position	M11	CAST, reference angle	1
2.2 Trigonometric ratios of any angle	M12	Special Angles, Terminal arm ratios, Solve problems involving CAST. Understand the graphs of Sine, Cosine and Tangent	2
2.3  The  Sine Law (incl Ambiguous case)	M13	Solving a triangle :minimum 3 pieces of info reqd. Proof of the sine law. Using the sine law. Ambiguous case + How it may occur	2
2.4  The Cosine Law	M13	SAS, modified Pythag. Derivation of proof. Solving problems, using both sine and cosine laws	2
Recap and Chapter test			2

           

Unit 2          Quadratic Functions       (Chapter 3)                                          7 classes

 

Develop algebraic and graphical reasoning through the study of quadratic functions and their graphs

RF11   Analyze quadratic functions in vertex form, and determine their characteristics

RF12   Analyze quadratic functions in regular form, to identify characteristics and solve problems

	Specific Outcome	Curriculum Focus	#  of cl classes
3.1 Vertex form	RF11	y= a(x-p)2+q. effect / role of a, p, q. vertex, max/ min direction of opening, symmetry	1
3.2 standard form	RF12	y = ax2+bx+c.Simple completing the Square.   Determine range, max/min, symmetry, intercepts	2
3.3 Completing the Square	RF12	Further work on completing the square. Converting between vertex and standard from. Solving problems	2
Recap and Chapter test			2

 

Unit 3          Quadratic equations       (Chapter 4)                                          10 classes

Factor polynomials, analyze quadratic functions, solve problems

RF9      Factor polynomial ‘quadratic’ expressions with rational coefficients

RF12   Analyze quadratic functions in regular form, to identify characteristics and solve problems

RF13   Solve problems that involve quadratic equations

 

	Specific Outcome	Curriculum Focus	# of classes
4.1       Graphical Solution of quadratic equations	RF12, RF13	Solve a quadratic equation by graphing. Explore the meaning of the intercepts, and the vertex	1
4.2 Factoring quadratic equations	RF9, RF12, RF13	Factoring, common factors, special products, How the solutions are linked to the factored form. Solving problems	2
4.3 Solving by completing the square	RF12, RF13	Completing the square. General procedure. Using it to solve problems	2
4.4 The quadratic formula	RF9, RF12, RF13	Develop and derive the formula. Significance of the discriminant. Nature of the roots. Problem-solving	2
Recap and Chapter test			2

 

Unit 4          Financial Literacy           (in - house worksheets)            4 classes

FL6      Understand and perform calculations involving compound interest, NPV, FV

using technology…for loans, mortgages and investments                                               

FL7      Understand the basics of buying and selling stocks and bonds. P/E, Yield     

                       

	Specific Outcome	Curriculum Focus	# of classes
9.3	FL6	Compound interest, Future value and annuities ( TVM Solver)	1
9.4	FL7	Stocks and Bonds	1
9.5	FL6	Financing Loans and Mortgages	1
Unit Assessment			1

 

 

 

Unit 5          Radical Expressions and Equations  (Chapter 5)                        9 classes

 

Develop algebraic reasoning and number sense. Solve problems involving operations on radicals, both numeric and algebraic.

AN23  Solve problems that involve operations on radical expressions

AN24  Solve problems that involve radical equations (limited to square roots)

 

	Specific Outcome	Curriculum Focus	# of classes
5.1 Working with radicals	AN23	Converting between mixed and entire radicals. Compare and order radicals. Be aware of restrictions in the radicand	2
5.2 Multiplying and dividing radical expressions	AN23	Multiple operations on radicals. Rationalizing the denominator. Simplifying, and equivalent forms. Solve problems involving radical expressions.	2
5.3  Radical equations	AN24	Set-up and solve problems that have radical expressions. Extraneous roots, Graphical solution methods	3
Recap and Chapter test			2

 

 

Unit 6          Rational Expressions and Equations (Chapter 6)                        10 classes

 

Determine equivalent forms of rational expressions. Perform operations on, and solve problems involving rational expressions

AN25  Determine equivalent forms of rational expressions (limited to at most trinomials in numerator or denominator)

AN26  Perform operations on, and solve problems that involve rational equations (limited to at most trinomials in numerator or denominator)

 

	Specific Outcome	Curriculum Focus	# of classes
6.1 Equivalent forms of Rational Expressions	AN25	Non-permissible values. Simplifying rational expressions Determining equivalent forms	1
6.2 Multiplying and dividing rational expressions	AN25, AN26	Thorough recap of how / why cancelling works in numeric fractions. Extension to rational expressions. Restrictions	2
6.3 Adding and subtracting rational expressions	AN25, AN26	Thorough recap of how / why + / - works in numeric fractions. Extension to rational expressions.	3
6.4 Rational Equations	AN26	Solve rational equations. Be aware of restrictions. Model and solve problems using a rational equation	2
Recap and Chapter test		Note. Aside from understanding the basic shape of f(x)=1/x, the focus is entirely on equations, not on their graphs (this is PC12)	2

 

 

Unit 7  Arithmetic Sequences and Series    ( Chapter 1)                             4 classes         

Develop algebraic and graphical reasoning through the study of relations

RF9      Analyze arithmetic sequences and series to solve problems

 

	Specific Outcome	Curriculum Focus	# of classes
1.1  Arithmetic Sequences	RF9	Derive rules for  general nth term, determine the values of a, tn, d  or n, and use them to solve	1
1.2 Arithmetic Sequences and Series	RF9	Derive the rule to find the sum of a series, determine the values to use in the formula. Solve problems	2
Chapter test			1

 

 

Unit 8          Absolute Value Functions       (Chapter 7)       6 classes

 

Demonstrate an understanding of the absolute value of real numbers

Graph analyze absolute value, to solve problems.

AN22  Demonstrate an understanding of Absolute value

RF10   Graph and analyze absolute value functions (limited to linear and quadratic) to solve problems

	Specific Outcome	Curriculum Focus
7.1  Absolute value	AN22	Absolute value, “distance between’, distance from zero. Compare and order absolute values	1
7.2  Absolute Value Functions	RF10	Graph and analyze absolute value functions. Sketch the graph of |f(x)|. Analyze domain, range, intercepts. Express the different segments as piecewise.	2
7.3  Absolute Value Equations	RF10	Solve an absolute value equation graphically, with or without technology. Solve algebraically, verify the solution. Understand why |f(x)|  < 0 has no solution	2
Chapter test		NOTE: working with manipulations of |f(x)| and f(|x|) now PC12	1

 

Unit 9          Systems of Equations  (Chapter 8)                                             6 classes 

 

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

RF14   Solve in multiple ways, problems that involve systems up to quadratic-quadratic in two variables

	Specific Outcome	Curriculum Focus	# of classes
8.1Solving graphically. Number of Solutions	RF14	Model a situation, determine and verify solutions. Explain the meaning of the intersection points	2
8.2 Solving algebraically	RF14	Model a situation. Relate the equations to the context. Determine and verify solutions algebraically. Solve problems explaining and choosing appropriate strategies	2
Recap and Chapter test			2

Unit 9          Linear and Quadratic Inequalities    (Chapter 9)                        8 classes

 

Solve problems that involve linear and quadratic inequalities in two variables, and quadratic inequalities in one variable

RF15   Solve problems that involve linear and quadratic inequalities in two variables

RF16   Solve problems that involve quadratic inequalities in one variable

	Specific Outcome	Curriculum Focus	# of classes
9.1 Solving linear inequalities in 2 variables	RF15	Is the boundary included? Dotted or solid line. Using test points to help find the solution ranges. Sketch the graph of a lin ineq. Solve problems involving linear inequalities.	2
9.2 Quadratic inequalities in 1 variable	RF16	Strategies for solving quadratic inequalities; graphing, case analysis, test points, sign analysis. Model and solve a problem by appropriate strategy, and interpret that solution in context.	2
9.3 Quadratic inequalities in 2 variables	RF15	Extend the strategy of 9.1 into quadratic inequality in 2 variables. Test points, sign analysis, boundary line, sketch the graph and feasible region. Model and solve problems, interpreting the solution range in context.	2
Recap and Chapter test			2

 

 

LEARNING OUTCOMES for Pre-Calculus 11 and Suggested Weightings

AN22  Demonstrate an understanding of Absolute value                                             2%

AN23  Solve problems that involve operations on radical expressions               8%

AN24  Solve problems that involve radical equations (limited to square roots) 4.5%

AN25  Determine equivalent forms of rational expressions (limited to at

most trinomials in numerator or denominator)                                                  4.5%

AN26  Perform operations on, and solve problems that involve rational equations (limited to at most trinomials in numerator or denominator)                                   8.5%

 

M11    Demonstrate an understanding of angles in Standard Position (0^o- 360^o)    2%

M12    Solve problems using the three primary trigonometric ratios (0^o- 360^o)       2.5%

M13    Solve problems using the cosine law and sine law including                                     5%

the ambiguous case.

 

RF9      Factor polynomial ‘quadratic’ expressions with rational coefficients                2.5%

RF10   Graph and analyze absolute value functions (limited to linear and                  4.5%

            quadratic) to solve problems

RF11   Analyze quadratic functions, in vertex form and determine their                4.5% characteristics.

RF12   Analyze quadratic functions in regular form, to identify                                     8%

characteristics and solve problems                                              

RF13   Solve problems that involve quadratic equations                                               8%

RF14   Solve in multiple ways, problems that involve systems up to

quadratic-quadratic equations in two variables                                                  3.5%

RF15   Solve problems that involve linear and quadratic inequalities in two variables                                                                                                                                               5.5%

RF16   Analyze arithmetic sequences and series to solve problems                                    6.5%

 

FL6   Understand and perform calculations involving compound interest, NPV, FV using technology…for loans, mortgages and investments                                           2.5%

FL7      Understand the basics of buying and selling stocks and bonds. P/E, Yield      1.5%

These weights total 84%

Assessment will be aligned against these Learning Outcomes and the following

Curricular Competencies:

CC1     Reasoning and Analysing                            4%

CC2     Understanding and Solving                        4%

CC3     Communicating and Representing           4%

CC4     Connecting and Reflecting                         4%

 

CURRICULUM COMPETENCIES:

These skills will be emphasized, embraced, valued, supported and encouraged throughout, and will be built into assessment where appropriate and relevant.

Reasoning and modelling

• Develop thinking strategies to solve puzzles and play games
• Explore, analyze, and apply mathematical ideas using reason, technology, and other tools
• Estimate reasonably and demonstrate fluent, flexible, and strategic thinking about number
• Model with mathematics in situational contexts
• Think creatively and with curiosity and wonder when exploring problems

 

Understanding and solving

• Develop, demonstrate, and apply mathematical understanding through play, story, inquiry, and problem solving
• Visualize to explore and illustrate mathematical concepts and relationships
• Apply flexible and strategic approaches to solve problems
• Solve problems with persistence and a positive disposition
• Engage in problem-solving experiences connected with place, story, cultural practices, and perspectives relevant to local First Peoples communities, the local community, and other cultures

 

Communicating and representing

• Explain and justify mathematical ideas and decisions in many ways
• Represent mathematical ideas in concrete, pictorial, and symbolic forms
• Use mathematical vocabulary and language to contribute to discussions in the classroom
• Take risks when offering ideas in classroom discourse

 

Connecting and reflecting

• Reflect on mathematical thinking
• Connect mathematical concepts with each other, other areas , and personal interests
• Use mistakes as opportunities to advance learning
• Incorporate First Peoples worldviews, perspectives, knowledge, and practices to make connections with mathematical concept