Common Core State Standards for Mathematics
Precalculus (V05) - Semester One
Domain: Interpreting Functions (FIF)
Learning Standard: Interpret functions that arise in applications in terms of the context Test Questions
FIF09-12.04 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 7, 8, 9, 10
FIF09-12.05 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function. 1, 2, 3, 4, 5, 6, 11, 12, 13
Learning Standard: Analyze functions using different representations Test Questions
FIF09-12.07 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.
  • Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.
18, 19, 20, 21, 22
FR1, FR2
Domain: Arithmetic with Polynomials and Rational Expressions (AAPR)
Learning Standard: Rewrite rational expressions Test Questions
AAPR09-12.07 Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions.  23, 24, 25
Domain: Building Functions (FBF)
Learning Standard: Build a function that models a relationship between two quantities Test Questions
FBF09-12.01 Write a function that describes a relationship between two quantities.
  • Compose functions. For example, if T(y) is the temperature in the atmosphere as a function of height, and h(t) is the height of a weather balloon as a function of time, then T(h(t)) is the temperature at the location of the weather balloon as a function of time.
14, 15, 16, 26, 27
Learning Standard: Build new functions from existing functions Test Questions
FBF0912.04 Find inverse functions.
  • Verify by composition that one function is the inverse of another.
  • Read values of an inverse function from a graph or a table, given that the function has an inverse.
  • Produce an invertible function from a non-invertible function by restricting the domain.
FBF0912.05 Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents. 28, 29, 30, 31, 32, 33, 34, 35
Domain: Vector and Matrix Quantities (NVM)
Learning Standard: Perform operations on matrices and use matrices in applications Test Questions
NVM0912.07 Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are doubled. 42
NVM0912.08 Add, subtract, and multiply matrices of appropriate dimensions. 36, 37, 38
Domain: Reasoning With Equations And Inequalities (AREI)
Learning Standard: Solve systems of equations Test Questions
AREI09-12.08 Represent a system of linear equations as a single matrix equation in a vector variable. 39, 41, 43
AREI09-12.09 Find the inverse of a matrix if it exists and use it to solve systems of linear equations (using technology for matrices of dimension 3x3 or greater). 40
Domain: Expressing Geometric Properties With Equations (GGPE)
Learning Standard: Translate between the geometric description and the equation for a conic section Test Questions
GGPE09-12.01 Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation. 44, 51, 52
GGPE09-12.03 Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant. 45, 46, 47, 48, 49, 50


Total: 52 points
Free Response: 9 points
Overall: 61 points