Precalculus (Texas TEKS)

111.42(c)(1) Mathematical process standards

• 111.42(c)(1) Student applies mathematical processes to build and show understanding: real-world use, problem solving, tools, representations, communication, and justification.
• 111.42(c)(1)(A) Use mathematics to solve problems that come up in daily life, society, and the workplace.
• 111.42(c)(1)(B) Follow a problem-solving model: analyze, plan, solve, justify, and check that the answer is reasonable.
• 111.42(c)(1)(C) Pick suitable tools and techniques, including mental math and estimation, to solve problems.
• 111.42(c)(1)(D) Communicate mathematical ideas with several kinds of representation.
• 111.42(c)(1)(E) Make and use representations to organize and record mathematical ideas.
• 111.42(c)(1)(F) Analyze how mathematical ideas relate in order to connect and explain them.
• 111.42(c)(1)(G) Show, explain, and justify mathematical ideas and arguments with precise language.

111.42(c)(2) Functions

• 111.42(c)(2) Student studies attributes of functions, links their representations, builds new functions, and uses them to model real problems.
• 111.42(c)(2)(A) Use the composition of functions to model and solve real-world problems.
• 111.42(c)(2)(B) Show that composing functions is not always commutative.
• 111.42(c)(2)(C) Express a given function as the composition of two or more simpler functions.
• 111.42(c)(2)(D) Describe the symmetry shown by the graphs of even and odd functions.
• 111.42(c)(2)(E) Find inverse functions where they exist and show them in several representations.
• 111.42(c)(2)(F) Graph exponential, logarithmic, rational, polynomial, power, trigonometric, inverse trigonometric, and piecewise functions, including step functions.
• 111.42(c)(2)(G) Graph transformations of functions of the forms af(x), f(x) + d, f(x − c), and f(bx).
• 111.42(c)(2)(H) Graph inverse sine and inverse cosine and explain the domain limits they need.
• 111.42(c)(2)(I) Find domain, range, symmetry, extrema, zeros, asymptotes, and where a function increases or decreases.
• 111.42(c)(2)(J) Analyze end behavior using infinity notation.
• 111.42(c)(2)(K) Analyze how rational functions behave near horizontal, vertical, and oblique (slant) asymptotes.
• 111.42(c)(2)(L) Identify types of discontinuity over all real numbers and the limits of graphing calculators near them.
• 111.42(c)(2)(M) Describe the left-hand and right-hand behavior of a graph near a discontinuity.
• 111.42(c)(2)(N) Analyze real situations modeled by exponential, logarithmic, rational, polynomial, and power functions.
• 111.42(c)(2)(O) Build and use a sinusoidal function to model a situation.
• 111.42(c)(2)(P) Find exact trigonometric values at special angles and use them in problems.

111.42(c)(3) Relations and geometric reasoning

• 111.42(c)(3) Student links algebraic and geometric relations, including parametric, polar, and conic forms.
• 111.42(c)(3)(A) Graph a set of parametric equations.
• 111.42(c)(3)(B) Change relations between parametric and rectangular form.
• 111.42(c)(3)(C) Model and solve problems using parametric equations.
• 111.42(c)(3)(D) Plot points in polar form and convert between polar and rectangular coordinates.
• 111.42(c)(3)(E) Graph polar equations by plotting points and with technology.
• 111.42(c)(3)(F) Name the conic section made when a plane cuts a double-napped cone.
• 111.42(c)(3)(G) Connect the locus definition of each conic to its equation in rectangular form.
• 111.42(c)(3)(H) Write the equation of an ellipse centered at (h, k) from given information.
• 111.42(c)(3)(I) Write the equation of a hyperbola centered at (h, k) from given information.

111.42(c)(4) Number and measure

• 111.42(c)(4) Student uses methods, tools, and formulas to find measures in mathematical and real situations.
• 111.42(c)(4)(A) Use the unit circle and periodic functions to evaluate trigonometric functions.
• 111.42(c)(4)(B) Describe how degree and radian measure relate on the unit circle.
• 111.42(c)(4)(C) Give angle measures in radians or degrees and find reference angles and angles in standard position.
• 111.42(c)(4)(D) Represent rotation in problems, including linear and angular speed.
• 111.42(c)(4)(E) Find the values of trigonometric ratios and use them to solve problems.
• 111.42(c)(4)(F) Solve problems with trigonometry, including direction and bearing.
• 111.42(c)(4)(G) Use the Law of Sines to solve problems.
• 111.42(c)(4)(H) Use the Law of Cosines to solve problems.
• 111.42(c)(4)(I) Use vectors to model situations with magnitude and direction.
• 111.42(c)(4)(J) Show vector addition and multiplying a vector by a scalar both with diagrams and symbols.
• 111.42(c)(4)(K) Apply vector addition and scalar multiplication to solve problems.

111.42(c)(5) Algebraic reasoning

• 111.42(c)(5) Student evaluates expressions, describes patterns, builds models, and solves equations and inequalities.
• 111.42(c)(5)(A) Evaluate finite sums and geometric series written in sigma notation.
• 111.42(c)(5)(B) Write arithmetic and geometric sequences recursively.
• 111.42(c)(5)(C) Find the nth term and the nth partial sum of an arithmetic series.
• 111.42(c)(5)(D) Write arithmetic and geometric series using sigma notation.
• 111.42(c)(5)(E) Find the nth term, the nth partial sum, and, where it exists, the infinite sum of a geometric series.
• 111.42(c)(5)(F) Use the Binomial Theorem to expand (a + b) to a positive whole-number power.
• 111.42(c)(5)(G) Use properties of logarithms to evaluate or rewrite logarithmic expressions.
• 111.42(c)(5)(H) Write and solve logarithmic equations in context.
• 111.42(c)(5)(I) Write and solve exponential equations in context.
• 111.42(c)(5)(J) Solve polynomial equations that have real coefficients.
• 111.42(c)(5)(K) Solve polynomial inequalities and give answers in interval notation.
• 111.42(c)(5)(L) Solve rational inequalities and give answers in interval notation.
• 111.42(c)(5)(M) Simplify trigonometric expressions using trigonometric identities.
• 111.42(c)(5)(N) Write and solve trigonometric equations in context.