Mathematics

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Algebra

Understanding dependency relationships

Understanding and manipulating algebraic expressions

Understanding dependency relationships

Student constructs knowledge with teacher guidance.

Student applies knowledge by the end of the school year.

 

Student reinvests knowledge.

Elementary

Secondary
Cycle
One
Cycle
Two
  1. Relations, functions and inverses
6 1 2 3 4 5
  1. Identifies patterns in various situations and in various forms
             
  1. Analyzes situations using different registers (types) of representation
       
  1. Represents a situation generally using a graph
         
  1. Chooses the dependent variable and the independent variable
           
  1. Recognizes relations, functions and inverses
           
  1. Describes, in the functions under study, the role of
    1. multiplicative parameters
            CST
  TS
  S
    1. additive parameters
            CST
  TS
  S
  1. Performs operations on functions (including composition)
    Note : In TS, operations on functions can be approached intuitively as of Secondary IV. In Secondary V, they are studied using concrete situations.
            CST
  TS
  S
  1. Analyzing situations using real functions1
6 1 2 3 4 5  
    Note : Statements 1 to 9 apply to the functions listed below.
  1. Models a situation verbally, algebraically, graphically, using a table of values or a scatter plot
  2. Finds the rule of a function or its inverse, depending on the context
  3. Represents and interprets the inverse
  4. Interprets parameters (multiplicative or additive) and describes the effect of changing their value, if necessary
  5. Describes the properties of real functions: domain, range, interval within which the function is increasing or decreasing, sign, extrema, x-intercept and y-intercept
    Note : In Secondary III, students are informally introduced to the study of properties, always in relation to a context. In CST, students use a graphical representation to describe the context.
  6. Determines values or data by solving equations and inequalities
  7. Interpolates and extrapolates data, if applicable
  8. Compares situations or graphical representations
  9. Makes decisions, if necessary, depending on the context
    1. Polynomial functions of degree 0 or 1
           
    1. Second-degree polynomial functions
      1. f(x) = ax2
          CST
  TS
    S
      1. f(x) = (bx)2 ou f(x) = a(bx)2
            CST
  TS
    S
      1. f(x) = ax2+ bx + c, f(x) = a(b(xh))2 + k, f(x) = a(xx1)(xx2)
            CST
  TS
  S
    1. Square root functions
      1. f(x) = a
        Note : This function is introduced in connection with the second-degree function as inverse (relation expressed as two square root functions).
            CST
  TS
    S
      1. f(x) = a  + k
            CST
  TS
  S
    1. Rational functions
      1. f(x) =  or xy = k, k
           
      1. f(x) = a  + k and f(x) =
            CST
  TS
  S
    1. Exponential functions
      1. f(x) = acx
          CST
    TS
    S
      1. f(x) = acbx
        Note : In CST, students are able to manipulate this type of function, but are not required to determine the rule.
            CST
  TS
    S
      1. f(x) = acb(xh) + k
        Note : The study of these functions should focus on bases 2, 10 and e.
            CST
  TS
  S
    1. Logarithmic functions
      1. f(x) = a logc bx
        Note : This function is introduced in connection with exponential functions (as an inverse).
            CST
  TS
    S
      1. f(x) = a logc b(x – h) + k
        Note : The study of these functions should focus on bases 2, 10 and e.
            CST
  TS
  S
    1. Piecewise functions
      Note : In Secondary III, students are introduced to this type of function informally.
        CST
  TS
  S
    1. Absolute value functions : f(x) = a|b(xh)| + k
      Note : In TS, this function is treated mainly as a piecewise function.
            CST
    TS
  S
    1. Step functions
           
    1. Greatest integer functions
      1. f(x) = a[bx]
            CST
  TS
    S
      1. f(x) = a[b(xh)] + k
            CST
  TS
  S
    1. Functions
      1. Modelling periodic occurences (e.g. natural phenomena such as tides or sound, medical or electrical phenomena)
        Note : The analysis is based on a graphical representation. In this context, students are not required to determine the rule.
          CST
  TS
  S
      1. sinusoidal : f(x) = a sin b(x – h) + k,
        f
        (x) = a cos b(x – h) + k
            CST
  TS
  S
      1. tangent : f(x) = a tan b(x – h) + k
            CST
  TS
  S
1.  Functions are introduced using contexts adapted to Secondary III and the various options, with or without the use of technological tools.

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