Content for Year 3
From Algebra
• Solving quadratic equations by factoring
• Studying the number of roots of a quadratic equation and relating this number to the graph of the associated quadratic function
• Using the method of completing the square to analyze the graphs of quadratic equations and to solve quadratic equations
• Working with exponential and logarithmic functions:
—describing their graphs
—understanding the relationship between logarithms and exponents
—finding that the derivative of an exponential function is proportional to the value of the function
—developing general laws of exponents
—understanding the meaning and significance of e
—approximating data by an exponential function
• Developing and using the elimination method for solving systems of linear equations in up to four variables
• Extending the concepts of dependent, inconsistent, and independent systems of linear equations to more than two variables
• Working with matrices:
—developing the operations of matrix addition and multiplication in the context of applied problems
—understanding the use of matrices in representing systems of linear equations
—developing the concepts of identity element and inverse in the context of matrices
—understanding the use of matrices and matrix inverses to solve systems of linear equations
—relating existence of matrix inverses to uniqueness of solution of corresponding systems of linear equations
—using calculators to multiply and invert matrices and to solve systems of linear equations
• Extending concepts of linear programming to problems with several variables
From Analytic and Coordinate Geometry
• Defining slope and understanding its relationship to rate of change and to equations for straight lines
• Developing equations for straight lines from two points and from point-slope information
• Developing and applying various formulas from coordinate geometry, including
—the distance formula
—the midpoint formula
—the equation of a circle with arbitrary center and radius
• Finding the distance from a point to a line
• Developing and working with equations of planes in three-dimensional coordinate geometry
From Precalculus
• Understanding and using inverse functions
• Understanding the meaning of the derivative of a function at a point and its relationship to instantaneous rate of change
• Approximating the value of a derivative at a given point
From Geometry
• Developing the relationship of the area and circumference of a circle to its radius
• Understanding the definition and significance of p
• Using regular polygons to approximate the area and circumference of a circle
• Discovering and justifying locus descriptions of various geometric entities, such as perpendicular bisectors and angle bisectors
• Developing properties of parallel lines
• Studying the possible intersections of lines and planes in 3-space
From Trigonometry
• Applying right triangle trigonometry to real-world situations
From Probability and Statistics
• Developing and applying principles for finding the probability for a sequence of events
• Developing methods for the systematic listing of possibilities for complex problems
• Developing the meaning of combinatorial and permutation coefficients in the context of real-world situations, and understanding the distinction between combinations and permutations
• Developing principles for computing combinatorial and permutation coefficients
• Understanding and using Pascal’s triangle
• Developing and applying the binomial distribution
From Logic
• Using “if and only if” in describing sets of points fitting given criteria
• Defining and using the concept of the converse of a statement