District Assessment Connection for South Dakota Core Standards
Precalculus (V06) - Semester 2
Domain: Building Functions (FBF)
Learning Standard: Build new functions from existing functions Test Questions
FBF09-12.05 Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents (simplifying trigonometric functions and limits). 19-26, 54, 55, 56
Domain: Trigonometric Functions (FTF)
Learning Standard Test Questions
FTF0912.01 Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle. 1
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. 2, 3, 5, 7
Learning Standard: Model periodic phenomena with trigonometric functions Test Questions
FTF0912.05 Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline. 10, 11, 12, 13, 14, 15, 16, 17
FTF0912.07 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. 18, 27, 28, 29, 30, 31
Learning Standard: Prove and apply trigonometric identities Test Questions
FTF0912.08 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. 4, 6, 9
FTF0912.09 Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems. 32, 33
Domain: Similarity, Right Triangles, & Trigonometry (GSRT)
Learning Standard: Define trigonometric ratios and solve problems involving right triangles Test Questions
GSRT0912.08 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems 8
Learning Standard: Apply trigonometry to general triangles Test Questions
GSRT0912.09 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. 37, 38
GSRT0912.10 Prove the Laws of Sines and Cosines and use them to solve problems. 34, 35
GSRT0912.11 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). 36
Domain: The Complex Number System (NCN)
Learning Standard: Represent complex numbers and their operations on the complex plane Test Questions
NCN0912.04 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. 45, 46, 47, 48, 49, 50
NCN0912.05 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°. 51, 52, 53
Domain: Vector and Matrix Quantities (NVM)
Learning Standard: Represent and model with vector quantities Test Questions
NVM0912.01 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). 40, 41
NVM0912.02 Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point. 39
NVM0912.03 Solve problems involving velocity and other quantities that can be represented by vectors. 43, 44
Learning Standard: Perform operations on vectors Test Questions
• 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.
42

Total Multiple Choice: 56 points
Free Response: 7 points
Overall: 63 points

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