II. Individual Benchmark Specifications Reporting Category Calculus Standard Limits and Continuity Benchmark Number MAFS.912.C.1.2 Benchmark Find limits by substitution. Also Assesses MAFS.912.C.1.11 Item Types Selected Response (Multiple Choice), Gridded Response, Short Answer Cognitive Complexity Level Low Benchmark Clarification Students will demonstrate their knowledge of evaluating limits by substituting values within the functions. Content Limits The function must be defined at the value the limit is to be evaluated on the real number system.
Stimulus Attributes Items may be set in real world or mathematical context. Graphs of the function may be provided but are not required. Functions may include polynomial, trigonometric, rational, logarithmic, and exponential. Response Attributes None Specified Sample Items Evaluate the following: Correct Answer: Evaluate the following: Correct Answer: - Which of the following limits are undefined? i only ii only i and ii i, ii, and iii Correct Answer: A Reporting Category Calculus Standard Limits and Continuity Benchmark Number MAFS.912.C.1.3 Benchmark Find limits of sums, differences, products, and quotients.
Limits that are to be estimated graphically must be provided with a clearly labeled graph. Stimulus Attributes Item should be set in mathematical context. Response Attributes Responses may include pictures or values. Sample Items What is ? Correct Answer: 0 Consider the following graph of : Evaluate 2 -1 0 Undefined Correct Answer: B Reporting Category Algebra Standard Arithmetic with Polynomials and Rational Expressions Benchmark Number MAFS.912.A-APR.4.6 Benchmark Rewrite simple rational expressions in different forms; write in the form , where , , , and are polynomials with the degree of less than the degree of , using inspection, long division, or, for the more complicated examples, a computer algebra system. Also Assesses MAFS.912.A-APR.4.7 Item Types Selected Response (Multiple Choice), Gridded Response
Sample Items Over what domain should the function be restricted in order for to exist? Correct Answer: D Reporting Category Functions Standard Trigonometric Functions Benchmark Number MAFS.912.F-TF.3.8 Benchmark Prove the Pythagorean identity and use it to find trigonometric ratios. Also Assesses N/A Item Types Selected Response (Multiple Choice), Gridded Response, Short Answer Cognitive Complexity Level Moderate Benchmark Clarification Students will be able to use the relationship expressed through the Pythagorean identity to help solve trigonometric problems. Students will be able to reconstruct triangles based on the given, , or and the quadrant of the angle and use that information in conjunction with the Pythagorean identity to solve trigonometric problems. Content Limits Items should not involve identities beyond the Pythagorean identity other than . Stimulus Attributes Angles may be measured in radians or degrees. Reciprocal trigonometric functions may be used. Graphics may be provided.
Students will be able to use the addition and subtraction, half-angle, and double-angle formulas to find the values of trigonometric functions at angles that are not necessarily multiples of 30, 45, 60, or 90 degrees. Content Limits None Specified Stimulus Attributes Items may be set in real world or mathematical context. Angle measures may be in degrees or radians. Items should be assessed without the use of technology. Response Attributes Answers must be in exact radical form rather than decimal form. Answers do not necessarily have to be in simplest radical form. Sample Items What is the exact value of cos · cos + sin· sin ? Correct Answer: What is the exact value of cos 75˚? Correct Answer: B Reporting Category Geometry Standard Expressing Geometric Properties with Equations Benchmark Number MAFS.912.G-GPE.1.1 Benchmark 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.
A. B. C. D. Correct Answer: B Reporting Category Number and Quantity Standard Complex Number System Benchmark Number MAFS.912.N-CN.2.5 Benchmark Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representation for computation. For example, because has modulus 2 and argument 120°. Also Assesses N/A Item Types Selected Response (Multiple Choice), Gridded Response, Short Answer Cognitive Complexity Level Moderate Benchmark Clarification Students will find powers of complex numbers written in rectangular form or in polar (trigonometric form) by applying DeMoivre's Theorem. Content Limits Arguments may be in degree or radian measures between (0π) and (2π). Items written to be solved without the use of a calculator should have arguments that are multiples of 30, 45, 60, or 90 degrees. Exponential form of complex numbers will not be used or assessed. Stimulus Attributes Items must be set in a mathematical context. Complex numbers may be written in either rectangular form or polar (trigonometric) form. Polar forms of complex numbers may be written in form or form.