Students will explore the equations of circles, their transformations, and derivation from ...

Students will explore the equations of circles, their transformations, and derivation from the Pythagorean Theorem. Students will create circles on graph paper with specified center, radius, and containing 3 points. Students will determine the best location for a hospital to best serve the needs of Moore County.

Sample Item provided by Smarter Balanced as preliminary examples of the types ...

Sample Item provided by Smarter Balanced as preliminary examples of the types of items that students might encounter on the summative assessment. The item assesses whether the student has a solid understanding of writing equations to model a real-life situations and use the equations to find answers to questions within a context. MAT.HS.CR.2.0ACED.A.225

A Constructed Response Item provided by Smarter Balanced as preliminary examples of ...

A Constructed Response Item provided by Smarter Balanced as preliminary examples of the types of items that students might encounter on the summative assessment. The item prompt students to produce a text or numerical response in order to collect evidence about their knowledge or understanding of representing constraints by equations and systems of equations, solving systems of linear equations and interpreting solutions as viable or nonviable options in a modeling context. MAT.HS.CR.2.0AREI.A.032

A Constructed Response Item provided by Smarter Balanced as preliminary examples of ...

A Constructed Response Item provided by Smarter Balanced as preliminary examples of the types of items that students might encounter on the summative assessment. The item prompt students to produce a text or numerical response in order to collect evidence about their knowledge or understanding of using structure of an expression to identify ways to rewrite it and rearrange formulas to highlight a specific quantity of interest. MAT.HS.CR.2.0ASSE.A.005

Students find solutions to polynomial equations where the polynomial expression is not ...

Students find solutions to polynomial equations where the polynomial expression is not factored into linear factors. Students construct a polynomial function that has a specified set of zeros with stated multiplicity.

Students develop the distributive property for application to polynomial multiplication. Students connect ...

Students develop the distributive property for application to polynomial multiplication. Students connect multiplication of polynomials with multiplication of multi-digit integers.

Students perform arithmetic operations on polynomials and write them in standard form. ...

Students perform arithmetic operations on polynomials and write them in standard form. Students understand the structure of polynomial expressions by quickly determining the first and last terms if the polynomial were to be written in standard form.

Students understand that the sum of two square roots (or two cube ...

Students understand that the sum of two square roots (or two cube roots) is not equal to the square root (or cube root) of their sum. Students convert expressions to simplest radical form. Students understand that the product of conjugate radicals can be viewed as the difference of two squares.

Students will use the factored forms of polynomials to find zeros of ...

Students will use the factored forms of polynomials to find zeros of a function. Students will use the factored forms of polynomials to sketch the components of graphs between zeros.

Students solve simple radical equations and understand the possibility of extraneous solutions. ...

Students solve simple radical equations and understand the possibility of extraneous solutions. They understand that care must be taken with the role of square roots so as to avoid apparent paradoxes. Students explain and justify the steps taken in solving simple radical equations.

Students define a complex number in the form a + bi, where ...

Students define a complex number in the form a + bi, where a and b are real numbers and the imaginary unit i satisfies i 2 = −1. Students geometrically identify i as a multiplicand effecting a 90° counterclockwise rotation of the real number line. Students locate points corresponding to complex numbers in the complex plane. Students understand complex numbers as a superset of the real numbers; i.e., a complex number a + bi is real when b = 0. Students learn that complex numbers share many similar properties of the real numbers: associative, commutative, distributive, addition/subtraction, multiplication, etc.

Students understand the Fundamental Theorem of Algebra; that all polynomial expressions factor ...

Students understand the Fundamental Theorem of Algebra; that all polynomial expressions factor into linear terms in the realm of complex numbers. Consequences, in particular, for quadratic and cubic equations are understood.

Students apply geometric concepts in modeling situations. Specifically, they find distances between ...

Students apply geometric concepts in modeling situations. Specifically, they find distances between points of a circle and a given line to represent the height above the ground of a passenger car on a Ferris wheel as it is rotated a number of degrees about the origin from an initial reference point. Students sketch the graph of a nonlinear relationship between variables

Students observe identities from graphs of sine and cosine basic trigonometric identities ...

Students observe identities from graphs of sine and cosine basic trigonometric identities and relate those identities to periodicity, even and odd properties, intercepts, end behavior, and the fact that cosine is a horizontal translation of sine.

Students explore the historical context of trigonometry as motion of celestial bodies ...

Students explore the historical context of trigonometry as motion of celestial bodies in a presumed circular arc. Students describe the position of an object along a line of sight in the context of circular motion. Students understand the naming of the quadrants and why counterclockwise motion is deemed the positive direction of turning in mathematics.

Students define the tangent function and understand the historic reason for its ...

Students define the tangent function and understand the historic reason for its name. Students use special triangles to determine geometrically the values of the tangent function for 30°, 45°, and 60°.

Students define the secant function and the co-functions in terms of points ...

Students define the secant function and the co-functions in terms of points on the unit circle. They relate these names for these functions to the geometric relationships among lines, angles, and right triangles in a unit circle diagram. Students use reciprocal relationships to relate the trigonometric functions and use these relationships to evaluate trigonometric functions for multiples of 30, 45, and 60 degrees.

Students graph the sine and cosine functions and analyze the shape of ...

Students graph the sine and cosine functions and analyze the shape of these curves. For the sine and cosine functions, students sketch graphs showing key features, which include intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maxima and minima; symmetries; end behavior; and periodicity.

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