Common Core State Standards for Mathematics
Accelerated Precalculus (V06) - Semester Two
Domain: Trigonometric Functions (FTF)
Learning Standard: Model periodic phenomena with trigonometric functions Test Questions
FTF09-12.05 Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline. (AII) 1, 2, 3, 4, 5, 6
FTF09-12.07 Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms of the context. 7, 8, 9, 10, 18, 19, 20, 21, 24, 25
Learning Standard: Prove and apply trigonometric identities Test Questions
FTF09-12.08 Prove the Pythagorean identity sin2(?) + cos2(?) = 1 and use it to find sin(?), cos(?), or tan(?) given sin(?), cos(?), or tan(?) and the quadrant of the angle. 13, 15, 17
FR2
FTF09-12.09 Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems. 11, 12, 14, 16, 22, 23
Domain: Similarity, Right Triangles, and Trigonometry (GSRT)
Learning Standard: Apply trigonometry to general triangles Test Questions
GSRT09-12.09 Derive the formula A = 1/2 ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side. 29
GSRT09-12.10 Prove the Laws of Sines and Cosines and use them to solve problems. 26, 27
GSRT09-12.11 Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles (e.g., surveying problems, resultant forces). 28
Indicator A4: Describe and use properties and behaviors of relations, functions, and inverses Test Questions
11A4-05 Describe characteristics of nonlinear functions and relations. 35, 36, 40, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57
FR3, FR4
Domain: The Complex Number System (NCN)
Learning Standard: Represent complex numbers and their operations on the complex plane Test Questions
NCN09-12.04 Represent complex numbers on the complex plane in rectangular and polar form (including real and imaginary numbers), and explain why the rectangular and polar forms of a given complex number represent the same number. 41, 42, 43, 44
NCN09-12.05 Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representation for computation. For example, (-1 + ?3 i)3 = 8 because (-1 + ?3 i) has modulus 2 and argument 120°. 45, 46
Domain: Vector and Matrix Quantities (NVM)
Learning Standard: Represent and model with vector quantities Test Questions
NVM09-12.01 Recognize vector quantities as having both magnitude and direction. Represent vector quantities by directed line segments, and use appropriate symbols for vectors and their magnitudes (e.g., v, |v|, ||v||, v). 31, 32, 37
NVM09-12.02 Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point. 30
NVM09-12.03 Solve problems involving velocity and other quantities that can be represented by vectors. 38, 39
FR1
Learning Standard: Perform operations on vectors Test Questions
NVM09-12.04 Add and subtract vectors.
  • Add vectors end-to-end, component-wise, and by the parallelogram rule. Understand that the magnitude of a sum of two vectors is typically not the sum of the magnitudes.
  • Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum.
  • Understand vector subtraction vw as v + (–w), where –w is the additive inverse of w, with the same magnitude as w and pointing in the opposite direction. Represent vector subtraction graphically by connecting the tips in the appropriate order, and perform vector subtraction component-wise.
33, 34

Test Questions: 57 points
Free Response: 15 points
Overall: 72 points

 

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