Analyzing situations using analytic geometry 

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 
 Locating

6 
1 
2 
3 
4 
5 
 Locates objects/numbers on an axis, based on the types of numbers studied
Note : In Secondary Cycle One, students locate positive or negative numbers written in decimal or fractional notation.








 Locates points in a Cartesian plane, based on the types of numbers studied (x and ycoordinates of a point)








 Straight lines and halfplanes

6 
1 
2 
3 
4 
5 

 Uses the concept of change to


 calculate the distance between two points
Note : In Secondary III, students are introduced to the concept of distance between two points while studying the Pythagorean relation. In Secondary IV, the distance between two parallel lines or from a point to a line or segment is studied using concepts and processes associated with distance and equations systems.








 determine the coordinates of a point of division using a given ratio (including the coordinates of a midpoint)
Note : In S, students can also determine the coordinates of a point of division using the product of a vector and a scalar.







CST 


TS 


S 
 calculate and interpret a slope
Note : In Secondary III, students are introduced informally to the concept of slope while studying the rate of change of functions (degree 0 and 1).








 Determines the relative position of two straight lines using their respective slope (intersecting at one point, perpendicular, nonintersecting parallel or coincident)
Note : In Secondary III, students are introduced to the concept of relative position between two lines when comparing the rate of change and graphs of functions (degree 0 and 1). The same is true for solving systems of linear equations in two variables.








 Models, with or without technological tools, a situation involving


 straight lines: graphically and algebraically
Note : In Secondary III, students are introduced informally to the concept of lines when they study functions of degree 0 and 1. The different forms of equations of a line (standard, general and symmetric) are explored in the various options. The symmetric form of the equation of a line is not covered in CST; it is optional in TS and compulsory in S. The general form of the equation of a line is optional in CST.








 a halfplane: graphically and algebraically








 parallel lines and perpendicular lines








 Determines the equation of a line using the slope and a point or using two points
Note : The general form of the equation of a line is optional in CST.








 Determines the equation of a line parallel or perpendicular to another
Note : The general form of the equation of a line is optional in CST.








 Geometric transformations

6 
1 
2 
3 
4 
5 

 Identifies, through observation, the characteristics of geometric transformations in the Cartesian plane: translations, rotations centred at the origin, reflections with respect to the xaxis and
yaxis, dilatations centred at the origin, scaling (expansions and contractions)







CST 


TS 


S 
 Defines algebraically the rule for a geometric transformation
Note : In TS, students may also use a matrix to define a geometric transformation.







CST 


TS 


S 
 Constructs, in the Cartesian plane, the image of a figure using a transformation rule
Note :In TS, students also determine the vertices of an image using a matrix.







CST 


TS 


S 
 Anticipates the effect of a geometric transformation on a figure







CST 


TS 


S 
 Geometric loci

6 
1 
2 
3 
4 
5 

 Describes, represents and constructs geometric loci in the Euclidian and Cartesian planes, with or without technological tools
Note : In S, the study of geometric loci is limited to conics.







CST 


TS 


S 
 Analyzes and models situations involving geometric loci in the in the Euclidian and Cartesian planes
Note : In TS, geometric loci also include plane loci, i.e. geometric loci involving lines or circles only. In S, the study of geometric loci is limited to conics.







CST 


TS 


S 
 Analyzes and models situations using conics
 describing the elements of a conic: radius, axes, directrix, vertices, foci, asymptotes, regions
 graphing a conic and its internal and external region
 constructing the rule of a conic based on its definition
 finding the rule (standard form) of a conic and its internal and external region
 validating and interpreting the solution, if necessary


 parabola centred at the origin and resulting from a translation







CST 


TS 


S 
 circle, ellipse and hyperbola centred at the origin







CST 


TS 


S 
 circle, ellipse and hyperbola resulting from a translation







CST 


TS 


S 
 Determines the coordinates of points of intersection between


 a line and a conic
Note : In TS, this is associated with solving systems involving the functional models under study and entails mostly graphical solutions (with or without the use of technological tools).







CST 


TS 


S 
 two conics (a parabola and a conic)







CST 


TS 


S 
 Standard unit circle

6 
1 
2 
3 
4 
5 

 Establishes the relationship between trigonometric ratios and the standard unit circle (trigonometric ratios and lines)







CST 


TS 


S 
 Determines the coordinates of points associated with significant angles using metric relations in right triangles (Pythagorean relation, properties of angles: 30°, 45°, 60°)







CST 


TS 


S 
 Analyzes and uses periodicity and symmetry to determine coordinates of points associated with significant angles in the standard unit circle







CST 


TS 


S 
 Proves Pythagorean identities







CST 


TS 


S 