Download Math 30P Course Outline

Math 30 Pure
COURSE OUTLINE
Textbook: MathPower 12 + Handouts Provided
Course Work = 50%
Diploma Final Exam = 50%
1. Transformations
9 classes
Stretches
• vertical and horizontal stretches
• stretches about other lines
• stretches and the zeros of a function
Reflections
• vertical and horizontal reflections
• combining stretches and reflections
• the inverse of a function
Translations
• vertical and horizontal translations
Combining Transformations
• the algebra of transformations
• graphing transformations
• describing transformations
The Reciprocal of a Function
2. Exponents
and
Logarithms
14 classes
The Exponential Function
• definition and terminology related to exponential functions
• graphing the exponential function
• transformations of the exponential function
Exponential Regression
• exponential growth
• exponential decay
The Logarithmic Function
• definition and terminology related to logarithmic functions
• graph and analyze the logarithmic function with and without technology
• converting between exponetial and logarithmic forms
• common logarithms
• the laws of logarithms
• solve exponential and logarithmic equations
• change of base law
• applications and problem solving
LTCHS M30P Course Outline Sept2011
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3. Geometric
Sequences
and Series
8 classes
Geometric Sequences
• definition and terminology related to geometric sequences
• the general term of a geometric sequence
• relationship to exponential functions
• applications and problem solving
Geometric Series
• definition and terminology related to geometric series
• sigma notation
• finite geometric series
• applications and problem solving
4. Trigonometry I
12 classes
Trig Theory
• rotation angles, coterminal angles, principal angle
• the primary and reciprocal trig ratios
• reference angles
• exact ratios
Degree and Radian Measure for Angles
• conversion between radians and degrees
• arc length of a circle
The Unit Circle
• the CAST rule
• special triangle relationships - exact values
Graphing Trig Functions
• graphing the basic sine, cosine, and tan functions with and without
technology
• understand the characteristics of the primary trig functions – amplitude,
vertical translation, period, phase shift, range, max/min values
• understand, interpret, and analyze the primary trig functions
• transformations as they apply to the primary trig functions
• graphs and terminology related to the
reciprocal trig functions
• use the sine curve to represent and
solve related problems
• develop and apply sine regression
models which represent periodic
data with and without technology
LTCHS M30P Course Outline Sept2011
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5. Trigonometry II
8 classes
Trig Identities
• verify trig identities numerically, algebraically and graphically
• understand and apply the various trig identities to
simplify and verify trig expressions and equations
Solve Trig Equations (0 ≤ θ < 2π)
• solve trig equations graphically and algebraically: linear,
quadratic, multiple angle, double function equations
• relate graphs and solutions to trig equations
• determine general solutions
6. Conics
8 classes
The Geometry of Conics
• definitions and terminology related to conics
• slicing the cone – the geometric model
• classify conics according to shape and according to the vertex angle
• recognize degenerate conics
The Algebra of Conics
• classify conics according to AC rules
• general form Ax2 + Cy2 + Dx + Ey + F = 0
• standard form - study the effects of changing various parameters: h, k, a, b
• transformations as they relate to conics
• convert between general and standard forms
• terminology - center, vertex, domain, range, intercepts, asymptotes
• sketch conics from the equation, given key points, or a transformation
• write the equation when given key points or a transformation
7. Combinatorics
and Probability
14 classes
The Fundamental Counting Principle
• construct and interpret tree diagrams
• understand and apply the fundamental counting principle
• dealing with various restrictions
• factorial notation
Linear Permutations
• definition and terminology related to permutations
• permuting a part of a set
• permutations involving various restrictions
• distinguishable permutations
Combinations
• definition and terminology related to combinations
• combinations involving various restrictions
The Algebra of Factorial Notation
• simplifying algebraic expressions involving perms and combs
• solving algebraic equations involving perms and combs
LTCHS M30P Course Outline Sept2011
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Pathway Problems
• solve simple pathway problems
• solve compound two-dimensional pathway problems with a given diagram
• solve two-dimensional pathway problems without a given diagram
• solve three-dimensional pathway problems
The Binomial Theorem
• definition and terminology related to the binomial theorem
• relationship to combinations
• expanding binomials of various degrees
• understand and apply patterns as they relate to the binomial theorem
Probability
• determine probability by using the fundamental counting principle
where order is important and where order is not important
• determine the probability of one event in which permutations or
combinations are involved
• determine the probabilities for two or more events in which permutations or
combinations are involved
• solve probability problems
8. Statistics
7 classes
Review of Mean and Standard Deviation
• definitions and terminology – mean, median, mode, range, standard
deviation
• use technology to calculate the mean and standard deviation using
ungrouped and grouped data
The Normal Distribution Curve
• definition and properties of the normal curve
• use and apply the z-score formula
• use and apply the area under the normal curve chart to solve problems
• solve manufacturers’ guarantees problems
The Binomial Distribution
• definition and terminology related to a binomial experiment
• solve and apply binomial experiment problems with and without
technology
LTCHS M30P Course Outline Sept2011
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