Common Core State Standards for Mathematics Accelerated Precalculus (V09)  Semester One 


Domain: Interpreting Functions (FIF)  
Learning Standard: Interpret functions that arise in applications in terms of the context  Test Questions 
FIF0912.04 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 maximum and minimums; symmetries; end behavior; and periodicity.  1, 2, 8, 10 
FIF0912.05 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 personhours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.  3, 4, 5, 6, 7, 22 
Learning Standard: Analyze functions using different representations  Test Questions 
FIF0912.07 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

11, 23, 24, 25, 26, 27 
Domain: Building Functions (FBF)  
Learning Standard: Build a function that models a relationship between two quantities  Test Questions 
FBF0912.01 Write a function that describes a relationship between two quantities.

13, 14, 15, 16, 18 
Learning Standard: Build new functions from existing functions  Test Questions 
FBF0912.03 Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing events and odd functions from their graphs and algebraic expressions for them.  9, 12 
FBF0912.04 Find inverse functions.

17, 19, 20, 21 
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 
Domain: Trigonometric Functions (FTF)  
Learning Standard: Extend the domain of trigonometric functions using the unit circle 
Test Questions 
FTF0912.01 Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.  51, 52 
FTF0912.02 Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.  48, 49, 50, 53, 54, 55, 62, 63 
FTF0912.03 Use special triangles to determine geometrically the values of sine, cosine, tangent for π/3, π/4 and π/6, and use the unit circle to express the values of sine, cosines, and tangent for x, π + x, and 2π – x in terms of their values for x, where x is any real number.  56, 57, 58 
Learning Standard: Prove and apply trigonometric identities  Test Questions 
FTF0912.08 Prove the Pythagorean identity sin^{2}(θ) + cos^{2}(θ) = 1 and use it to find sin(θ), cos(θ), or tan(θ) given sin(θ), cos(θ), or tan(θ) and the quadrant of the angle.  59, 60, 61 
Domain: Vector & Matrix quantities (NVM)  
Learning Standard: Perform operations on matrices and matrices in applications  Test Questions 
NVM0912.06 Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network.  39 
NVM0912.08 Add, subtract, and multiply matrices of appropriate dimensions.  37, 38 
NVM0912.09 Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive properties.  41 
NVM0912.12 Work with 2 x 2 matrices as transformations of the plane, and interpret the absolute value of the determinant in terms of area.  36 
Domain: Reasoning with equations & inequalities (AREI)  
Learning Standard: Solve systems of equations  Test Questions 
AREI0912.08 Represent a system of linear equations as a single matrix equation in a vector variable.  33, 40 
AREI0912.09 Find the inverse of a matrix if it exists and use it to solve systems of linear equations (using technology for matrices of dimension 3 x3 or greater).  34, 35 
Domain: Expressing Geometric Properties with Equations (GGPE)  
Learning Standard: Translate between the geometric description and the equation for a conic section  Test Questions 
GGPE0912.03 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.  42, 43, 44, 45, 46, 47 
Total: 63 points
Free Response: 10 points
Overall: 73 points