Precalculus

  • Functions

    Students explore, describe, and analyze the attributes of functions. Students make connections between multiple representations of functions and algebraically construct new functions. Students analyze and use functions to model real-world problems.

    New TEKS:

    • Use the composition of two functions to model and solve real-world problems
    • Demonstrate that function composition is not always commutative
    • Graph piecewise-defined functions, including step functions

    Relations and Geometric Reasoning

    Students model and make connections between algebraic and geometric relations.

    New TEKS:

    • Graph a set of parametric equations
    • Graph points in the polar coordinate system and convert between rectangular coordinates and polar coordinates
    • Graph polar equations by plotting points and using technology
    • Determine the conic section formed when a plane intersects a double-napped cone
    • Make connections between the locus definition of conic sections and their equations in rectangular coordinates
    • Use the characteristics of an ellipse to write the equation of an ellipse
    • Use the characteristics of a hyperbola to write the equation of a hyperbola

    Number and Measure

    Students apply appropriate techniques, tools, and formulas to calculate measures in mathematical and real-world problems.

    New TEKS:

    • Represent the addition of vectors and the multiplication of a vector by a scalar geometrically and symbolically

    Algebraic Reasoning

    Students evaluate expressions, describe patterns, formulate models, and solve equations and inequalities using properties, procedures, or algorithms.

    New TEKS:

    • Generate and solve logarithmic equations in mathematical and real-world problems
    • Generate and solve exponential equations in mathematical and real-world problems
    • Solve polynomial equations in mathematical and real-world problems
    • Solve polynomial inequalities and write the solutions set in interval notation
    • Solve rational inequalities and write the solution set in interval notation