Measurement and Geometry
1. Students understand and use periodic functions and trigonometric
relationships.
1.1 use similarity, right triangles, the Law of Sines, and the Law of
Cosines to determine measurements of objects which are difficult to measure
directly
2. Students use vectors to represent and answer questions about
quantities.
2.1 draw a system of vectors and find the resultant graphically
2.2 identify, create, and solve practical problems using a system of
vectors and their horizontal and vertical components
Functions
1. Students investigate, identify the characteristics of, and
graph polynomial and rational functions.
1.1 determine the zeros, y-intercepts, end behavior, relative maximum
and minimum points, and symmetry of polynomial functions and graph them
1.2 determine the zeros, asymptotes, y-intercepts, end behavior, relative
maximum and minimum points, symmetry of rational functions and graph them
1.3 determine the intervals where a polynomial function is increasing
or decreasing
1.4 given the graph of a function, graph its reciprocal
2. Students perform operations on functions and determine the
domain and range of the results.
2.1 determine the composition of two or more functions and the composition
of a function with itself and determine the domain and range of the resultant
function
2.2 determine the inverse of a function given as an equation, a graph,
or a set of ordered pairs, determine its domain and range and discuss the
relationships among these representations
3. Students analyze and explain the reasons behind the effect
changing coefficients, exponents, and other parameters has on functions
and their graphs.
3.1 apply transformations to the graph of a basic function (e.g., trigonometric
functions), predict and analyze the results on the graph of the function
3.2 graph polar equations (e.g., roses, limniscates), analyze the results
of parameter changes on the graphs, and classify the equations according
to their graph
4. Students investigate periodic behavior, identify the characteristics
of, and graph trigonometric functions.
4.1 understand and explain the relationship between triangle trigonometry
and the unit circle/wrapping function approach to trigonometry
4.2 find the exact values of the trigonometric functions of multiples
of 30° ([pi]/6) and 45° ([pi]/4) and their related angles as found
in the unit circle, including converting radians to degrees and vice versa
4.3 given the value of one trigonometric function, find the values of
other trigonometric functions
4.4 solve trigonometric equations that include both infinite solutions
and restricted domain solutions and solve basic trigonometric inequalities
4.5 prove basic trigonometric identities and make substitutions using
the basic identities
4.6 identify key characteristics (e.g., domain, range, amplitude, period,
phase shift, and vertical shift) of and graph trigonometric functions and
their inverse
4.7 analyze and solve problems involving periodic phenomena (e.g., biological
rhythms, sound waves, tidal variations)
5. Students use graphs to investigate and describe continuity
of functions.
5.1 graph and analyze step and piecewise defined functions
5.2 define and apply the properties of limits of functions including
infinite sequences, series, and areas under curves
Statistics, Data Analysis, and Probability
1. Students formulate and test hypotheses and demonstrate understanding
that statistics is used to estimate the uncertainty involved in any conclusions
which are drawn.
1.1 create, implement, defend a plan (including survey design, sampling
procedures, control groups) for gathering data to answer a relevant question
1.2 analyze and evaluate surveys (for clarity, bias, return rate, specialized
audiences and experiments (for protocol, randomness, analysis, interpretation)
done by others
1.3 interpret and evaluate graphical/tabular data displays for their
consistency with the data and appropriateness of the type of display, scale,
and overall message
1.4 describe the normal curve and use it to predict such things as percentiles
and probabilities
1.5 explain and use the Central Limit Theorem and confidence intervals
in the formation of conclusions based on sample data
1.6 use inferential statistics (e.g., x-square, t-test) and probability
distributions to compare two sets of data
2. Students demonstrate an understanding of experimental and theoretical
probability in more complex situations.
2.1 apply the addition and multiplication principles to determine probability
of compound, complementary, independent, and dependent events
2.2 compute simple, compound, and conditional probabilities
2.3 design, implement, and interpret simulations to estimate probabilities
of events (e.g., Design a simulation to predict the average wait time in
a line at an airport.)
Credits
The Draft Standards were prepared by:
The State of California Academic Standards Commission
The Commission for the Establishment of Academic Content and Performance Standards
Comments may be addressed to The Commission
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