Content for Year 4
From Algebra
• Proving and using the quadratic formula
• Expressing the physical laws of falling bodies in terms of quadratic functions
From Analytic and Coordinate Geometry
• Defining polar coordinates
• Studying graphs of polar equations
• Expressing geometric transformations—translations, rotations, and reflections—in analytic terms
• Using matrices to represent geometric transformations
• Developing an analytic expression for projection onto a plane from a point perspective
• Representing a line in 3-space algebraically
From Precalculus
• Studying and using families of functions from several perspectives:
—through their algebraic representations
—in relationship to their graphs
—as tables of values
—in terms of real-world situations they describe
• Studying the effect of changing parameters on functions in a given family
• Working with asymptotes of rational functions
• Working with the algebra of functions, including composition and inverse functions
• Defining the least-squares approximation and using a calculator’s regression facility to do curve-fitting
From Trigonometry
• Extending the right-triangle trigonometric functions to circular functions
• Using trigonometric functions to work with polar coordinates
• Defining radian measure
• Graphing the sine and cosine functions and variations of these functions
• Working with inverse trigonometric functions
• Developing and using various trigonometric formulas, including
—the Pythagorean identity
—formulas for the sine and cosine of a sum of angles
—the law of sines and the law of cosines
From Probability and Statistics
• Using the binomial distribution to model a polling situation
• Distinguishing between sampling with replacement and sampling without replacement
• Understanding the central limit theorem as a statement about approximating a binomial distribution by a normal distribution
• Using area estimates to understand and use a normal distribution table
• Extending the concepts of mean and standard deviation from sets of data to probability distributions
• Developing formulas for mean and standard deviation for binomial sampling situations
• Using the normal approximation for binomial sampling to assess the significance of poll results
• Working with the concepts of confidence interval, confidence level, and margin of error
• Understanding the relationship between poll size and margin of error
From Programming
• Using loops
• Writing and interpreting programs
• Using graphics facilities on a calculator to create programs involving animation
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