Main Menu Units by Performance Expectation Units by Strand Units by Topic About the Capstone Course

Procedure and Calculation

Students will be able to perform and justify steps in mathematical procedures and calculations and graph and solve a range
of equations types. Students will reason from a variety of representations such as graphs, tables, and charts and will use
displays of univariate data to identify and interpret patterns. Students will be able to calculate probabilities and analyze
distributions of data to make decisions.

  1. The student, given rational, radical, or polynomial expressions, will Δ

    a) add, subtract, multiply, divide, and simplify rational algebraic expressions;

    b) add, subtract, multiply, divide, and simplify radical expressions containing
    rational numbers and variables, and expressions containing rational exponents;

    c) write radical expressions as expressions containing rational exponents and vice versa; and

    d) factor polynomials completely.

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  2. The student will graph linear equations and linear inequalities in two variables, including

    a) determining the slope of a line when given an equation of the line, the graph of the line, or two points on the line. Slope will be
    described as rate of change and will be positive, negative, zero, or undefined; and

    b) writing the equation of a line when given the graph of the line, two points on the line, or the slope and a point on the line.

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  3. The student, given a point other than the origin on the terminal side of an angle, will use the definitions of the six trigonometric functions
    to find the sine, cosine, tangent, cotangent, secant, and cosecant of the angle in standard position. Trigonometric functions defined on
    the unit circle will be related to trigonometric functions defined in right triangles. Δ
  4. The student, given the coordinates of the center of a circle and a point on the circle, will write the equation of the circle. Δ

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  5. The student will analyze graphical displays of univariate data, including dotplots, stemplots, and histograms, to identify and describe
    patterns and departures from patterns, using central tendency, spread, clusters, gaps, and outliers. Appropriate technology will be
    used to create graphical displays. Δ

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  6. The student will analyze the normal distribution. Key concepts include Δ

    a) characteristics of normally distributed data;

    b) percentiles;

    c) normalizing data, using z-scores; and

    d) area under the standard normal curve and probability.

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  7. The student will describe orally and in writing the relationships between the subsets of the real number system.
  8. The student will perform operations on complex numbers, express the results in simplest form using patterns of the powers of i, and
    identify field properties that are valid for the complex numbers.
  9. The student will solve, algebraically and graphically,

    a) absolute value equations and inequalities;

    b) quadratic equations over the set of complex numbers;

    c) equations containing rational algebraic expressions; and

    d) equations containing radical expressions.

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    Graphing calculators will be used for solving and for confirming the algebraic solutions.

  10. The student, given one of the six trigonometric functions in standard form, will

    a) state the domain and the range of the function;

    b) determine the amplitude, period, phase shift, vertical shift, and asymptotes;

    c) sketch the graph of the function by using transformations for at least a two-period interval; and

    d) investigate the effect of changing the parameters in a trigonometric function on the graph of the function.

  11. The student will find, without the aid of a calculator, the values of the trigonometric functions of the special angles and their related angles
    as found in the unit circle. This will include converting angle measures from radians to degrees and vice versa.
  12. The student will investigate and identify the characteristics of conic section equations in (h, k) and standard forms. Transformations in the coordinate plane will be used to graph conic sections.
  13. The student, using two-way tables, will analyze categorical data to describe patterns and departure from patterns and to find marginal frequency and relative frequencies, including conditional frequencies.
  14. The student will calculate probabilities. Key concepts include

    a) conditional probability;

    b) dependent and independent events;

    c) addition and multiplication rules;

    d) counting techniques (permutations and combinations); and

    e) Law of Large Numbers.

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