Precalculus
Fall Semester | ||||
Unit Title | Unit 1: Functions and Their Graphs | Unit 2: Polynomial and Rational Functions | Unit 3: Exponential and Logarithmic Functions | Unit 4: Series and Sequences |
Time | ~ 4 weeks | ~ 5 weeks | ~ 5 weeks | ~ 4 weeks |
Understandings | Exploring, describing, and analyzing attributes of functions serve as a foundation for connections between multiple representations and construction of algebraic functions.
Combinations of functions can be used to model and solve real-world problems using the functions’ characteristics and attributes.
Function composition results depend on which function is being substituted and which function receives the substitution.
| Functions have key attributes that can be used to analyze, describe, write, graph and solve functions related to real-world problems.
Applying characteristics and attributes of polynomial and rational functions helps analyze, graph, and solve real world problems.
There are a variety of methods used to graph and solve rational functions that can also be used to solve real-world situations.
| Exponential and Logarithmic Functions have key attributes that can be used to analyze, describe, write, graph and solve problems in mathematics and related to real-world situations.
Exponential functions with base a and with base e (natural exponential) can be analyzed and evaluated for defining characteristics.
Logarithmic (with base a) and natural (ln x) functions can be analyzed and evaluated for defining characteristics.
| Formulas can be written to represent series and sequences that model real-world problems and can be used for evaluating.
The nth partial sums of arithmetic series can be evaluated using formulas.
Sums of infinite geometric series can be algebraically and numerically evaluated.
The Binomial Theorem can be used to calculate binomial coefficients for each term in the expansion.
|
TEKS | P.2 A, B, C, D, E, F, G, I, J, N | P.2 F, G, I, J, K, L, M, N P.5 J, K, L | P.2 F, G, I, J, N P.5 G, H, I | P.5 A, B, C, D, E, F |
Process Standards | P.1 A, B, C, D, E, F, G | |||
Precalculus
Spring Semester | |||||
Unit Title | Unit 5: Trigonometric Functions | Unit 6: Analytic Trigonometry | Unit 7: Additional Trigonometry Topics | Unit 8: Conics | Unit 9: Parametric Equations and Polar Coordinates |
Time | ~ 4 weeks | ~ 4 weeks | ~ 3 weeks | ~ 2 weeks | ~ 4 weeks |
Understandings | Trigonometric functions assign real numbers to angle measures based on certain ratios and are simplified when studied along the unit circle.
Special angles allow for evaluating trigonometric functions using the unit circle.
The unit circle, with its specific angle measures and sine and cosine values, helps in evaluating all trigonometric functions at special angles.
The trigonometric values obtained from the unit circle apply to solving real-world situations.
| Trigonometric identities preserve the relationship between functions and can be based on ratios from Pythagoras’ Theorem.
Fundamental trigonometric identities can be used to evaluate trigonometric functions, simplifY trigonometric expressions and equations, and rewrite trigonometric expressions and equations.
Sum and difference formulas can be used to evaluate trigonometric functions, verify trigonometric identities, and solve trigonometric equations.
| Trigonometry can be applied to oblique triangles and vectors to solve real-world problems.
the direction angles and magnitude of vectors can be calculated and analyzed to model and solve real-world problems.
Basic mathematical operations can be performed on vectors in component form and represented symbolically and graphically.
| Conic sections connect algebraic and geometric relations.
A conic section is determined and identified by the different orientations of intersections of a plane and double-napped cone.
The general equations of conic sections aid in classifying and graphing the conic sections and their attributes.
Properties of circles and parabolas can be applied to solve real-world problems.
| Parametric equations and polar coordinates offer a different mathematical perspective on graphing representations of real-world figures.
Parametric equations and their graphs can be used to model and solve real-world situations.
Equations can be converted from rectangular to polar form and vice versa.
Special polar graphs and their characteristics can be recognized and evaluated.
|
TEKS | P.2 F, I, G, H, O, P P.4 A, B, C, D, E, F P.5 F | P.5 M, N | P.4 G, H, I, J, K | P.3 F, G, H, I | P.3 A, B, C, D, E |
Process Standards | G.1 A, B, C, D, E, F, G | ||||