Standard Arithmetic with Polynomials and Rational Expressions Benchmark Number MAFS.912.A-APR.3.4 Benchmark Prove polynomial identities and use them to describe numerical relationships. For example, the polynomial identity can be used to generate Pythagorean Triples. Also Assesses N/A Item Types Selected Response (Multiple Choice ), Gridded Response Cognitive Complexity Level Low Benchmark Clarification Students will apply common identities for sum, difference, and multiplication of polynomials. Content Limits Items will be limited to quadratic, cubic, and quartic polynomials. Stimulus Attributes Items may be set in either mathematical contexts or real-world applications. Response Attributes None specified Sample Items Which polynomial identity is demonstrated below? cube of a binomial cube of a trinomial square of a binomial square of a trinomial Correct Answer: D Which of the following is the equivalent of ?
Also Assesses MAFS.912.A-REI.2.4 Item Types Selected Response (Multiple Choice), Gridded Response Cognitive Complexity Level Moderate Benchmark Clarification Students will solve systems of equations involving a linear equation and a quadratic equation with two variables using a graph or algebraic reasoning. Content Limits Items will only include systems of two variables. Items will include systems consisting of one linear and one quadratic equation. Stimulus Attributes Item should be set in mathematical context. Include systems that lead to work with fractions. For example, finding the intersections between and leads to the point on the unit circle, corresponding to the Pythagorean Triple, . Response Attributes None specified Sample Items The following system has two solutions. What is the y-coordinate of the solution found in the first quadrant? Correct Answer: 8 Reporting Category Algebra Standard Seeing Structure in Expressions Benchmark Number MAFS.912.A-SSE.2.3
Sample Items Consider the following sequence of numbers: 3 7 11 15… Which of the following equations best models this sequence where represents the term number and represents the value of the term? Correct Answer: C Reporting Category Functions Standard Linear, Quadratic, & Exponential Models Benchmark Number MAFS.912.F-LE.1.3 Benchmark Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. Also Assesses MAFS.912.F-LE.1.1 Item Types Selected Response (Multiple Choice), Gridded Response Cognitive Complexity Level Moderate
Focus: and directrix: Correct Answer: B Which of the following is the equation for the parabola that has a vertex at and a focus at ? Correct Answer: A Reporting Category Geometry Standard Expressing Geometric Properties with Equations Benchmark Number MAFS.912.G-GPE.2.4 Benchmark Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point lies on the circle centered at the origin and containing the point . Also Assesses N/A Item Types Selected Response (Multiple Choice), Gridded Response Cognitive Complexity Level Moderate
Correct Answer: D Reporting Category Number & Quantity Standard The Complex Number System Benchmark Number MAFS.912.N-CN.1.1 Benchmark Know there is a complex number such that, and every complex number has the form with and real. Also Assesses MAFS.912.N-CN.1.2 Item Types Selected Response (Multiple Choice) Cognitive Complexity Level Low Benchmark Clarification Students will use the equation and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. Content Limits None specified Stimulus Attributes Items should be set in a mathematical context. Response Attributes None specified Sample Items What is the product of the following complex conjugates?