Section
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Content
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Suggested Problems
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Section 1.1
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- Cartesian Plane
- Coordinates
- x coordinate; abscissa
- y coordinate; ordinate
- Quadrants
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Section 1.2
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- Distance Formula
- Applications
- Determine whether three points form the vertices of a right triange
- Determine whether three points are co-linear
- Determine whether four points form the vertices of a parallelogram
- Determine whether four points form the vertices of a rhombus
- Determine whether four points form the vertices of a rectangle
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Page 9: 5, 9, 15, 19, 23, 25
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Section 1.3
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- Point of Division Formulas
- Mid-point Formula
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Page 18: 3, 9, 15, 21, 23
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Section 1.4
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- Inclination and Slope
- Slope formula
- Special Cases
- Slope of a horizontal line
- Slope of a vertical line
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Section 1.5
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- Parallel and Perpendicular Lines
- Criteria for two non-vertical lines to be parallel
- Criteria for two lines to be parallel if one of them is a vertical line
- Criteria for two non-vertical lines to be perpendicular
- Slopes are negative reciprocals
- Criteria for two lines to be perpendicular if one of them is a vertical line
- Applications
- Determine whether three points form the vertices of a right triange
- Determine whether three points are co-linear
- Determine whether four points form the vertices of a parallelogram
- Determine whether four points form the vertices of a rhombus
- Determine whether four points form the vertices of a rectangle
- Determine whether two lines are parallel, co-incident, perpendicular or none of the above
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Page 28: 1, 3, 5, 11, 15, 19, 25, 30
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Section 1.6
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- Angle from One Line to Another
- Formula for the tangent of the angle between two non-vertical lines
- Given two non-vertical lines find the slope of the line which bisects the angle between the two lines
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Page 35: 3, 9, 17
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Section 1.7
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- Graphs of Equations
- Points of Intersections of Graphs of Equations
- Function
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Page 42: 3, 6, 9, 13, 17, 21, 25, 31
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Section 2.1
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- Directed Line Segment
- Vector
- Geometric definition of the sum of two vectors
- Parallelogram law for sum of two vectors
- Geometric definition of the difference of two vectors
- Length of a vector
- Geometric definition of a scalar multiple of a vector
- Theorem 2.2 Algebraic properties of sum, difference and scalar multiples of vectors
- Geometric definition of a unit vectors
- Standard basis vectors
- Theorem 2.3 Every vector can be written (as a unique) sum of scalar multiples of the standard basis vectors
- Algebraic rule for the sum of two vectors (in terms of components)
- Algebraic rule for the scalar multiple of a vector (in terms of components)
- Algebraic rule for the length of a vector
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Page 60: 1, 3, 23, 25, 39, 41
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Section 2.2
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- Dot Product
- Theorem 2.6 Algebraic properties of dot product
- Angle between two non-zero vectors
- Theorem 2.7 Relationship between dot product and the angle between two vectors
- Theorem 2.8 Two non-zero vectors are perpendicular if and only if their dot product is zero
- Projection of a vector u onto a vector v
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Page 69: 1, 9, 13, 17, 21, 29
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