EOC Assessment Outline

Transcription

1 EOC Assessment Outline Course Name: Advanced Topics in Math Course Number: Test 50 MAFS.912.F-BF.1.2 Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. Complexity Complexity Complexity Students will be able to write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. Content Limits at the lower level may require students to be able to connect arithmetic sequences to linear functions and geometric sequences to exponential functions. at the higher level may require students to be able to write arithmetic and geometric sequences and use them to model situations. MAFS.912.S-CP.2.6 Find the conditional probability of A given B as the fraction of B s outcomes that also belong to A, and interpret the answer in terms of the model. Complexity Complexity Complexity Students will be able to find the conditional probability of A given B as the fraction of B s outcomes that also belong to A, and interpret the answer in terms of the model. Content Limits may require students at the lower level to be able to find the probability of a simple conditional outcome. may require students at the higher level to be able to find the conditional probability of a two-way table. Use a Venn Diagram to determine a conditional probability.

2 MAFS.912.N-VM.3.12 Work with 2 2 matrices as transformations of the plane, and interpret the absolute value of the determinant in terms of area. Complexity Complexity Complexity Students will be able to work with 2 x 2 matrices as transformations of the plane, and interpret the absolute value of the determinant in terms of area. Content Limits at the lower level may require students to be able to solve system of equations by using matrices (Cramer's Rule). at the higher level may require students to be able to solve the system of equations by using matrices in a real-world context. MAFS.912.N-VM.3.11 Multiply a vector (regarded as a matrix with one column) by a matrix of suitable dimensions to produce another vector. Work with matrices as transformations of vectors. Complexity Complexity Complexity Students will be able to multiply a vector (regarded as a matrix with one column) by a matrix of suitable dimensions to produce another vector. Work with matrices as transformations of vectors. Content Limits at the lower level may require students to be able to multiply a one-column matrix by a constant. at the higher level may require students to be able to multiply a vector using matrices to produce another vector, and make transformations of vectors.

3 MAFS.912.N-CN.3.7 Solve quadratic equations with real coefficients that have complex solutions. Complexity Complexity Complexity Students will be able to solve quadratic equations with real coefficients that have complex solutions. Content Limits at the lower level may require students to be able to solve quadratic functions by any method. at the higher level may require students to be able to solve quadratic functions by interpreting the solutions from a graph. MAFS.912.N-CN.2.6 Calculate the distance between numbers in the complex plane as the modulus of the difference, and the midpoint of a segment as the average of the numbers at its endpoints. Complexity Complexity Complexity Students will be able to calculate the distance between numbers in the complex plane as the modulus of the difference, and the midpoint of a segment as the average of the numbers at its endpoints. Content Limits at the lower level may require students to be able to find the midpoint of a segment and the distance formula by using complex numbers. at the higher level may require students to be able to calculate the distance in a complex plane.

4 MAFS.912.N-CN.2.4 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. Complexity Complexity Complexity Students will be able to 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. Content Limits at the lower level may require students to be able to convert from polar to rectangular form and vice versa. at the higher level may require students to be able to use real and imaginary numbers to explain why these two forms represent the same number. MAFS.912.G-GPE.1.1 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. Complexity Complexity Complexity Students will be able to 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. Content Limits at the lower level may require students to be able to write an equation of a circle given the radius and center. at the higher level may require students to be able to complete the square to find the center and radius of a circle in standard form. Also, derive the equation of a circle.

5 MAFS.912.F-TF.1.3 Use special triangles to determine geometrically the values of sine, cosine, tangent for pi/3, pi/4 and pi/6, and use the unit circle to express the values of sine, cosine, and tangent for pi x, pi+x, and 2pi x in terms of their values for x, where x is any real number. Complexity Complexity Complexity Students will be able to use special triangles to determine geometrically the values of sine, cosine, tangent for pi/3, pi/4 and pi/6, and use the unit circle to express the values of sine, cosine, and tangent for pi x, pi + x, and 2pi x in terms. Content Limits at the lower level may require students to be able to convert from degrees to radians and vice versa. at the higher level may require students to be able to relate periods of trigonometric functions to the unit circle. MAFS.912.F-IF.3.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. Complexity Complexity Complexity Students will be able to graph linear and quadratic functions and show intercepts, maxima, and minima. Graph square root, cube root, and piecewise-defined functions, step functions and absolute value functions. Graph polynomial functions and identify the zero. Content Limits at the lower level may require students to be able to identify the key features of a linear function. at the higher level may require students to be able to graph and interpret linear, square root, cube root, piecewise, exponential, logarithmic, and trigonometric functions.

6 MAFS.912.F-BF.1.1 Write a function that describes a relationship between two quantities. Complexity Complexity Complexity Students will be able to write a function that describes a relationship between two quantities. Determine an explicit expression, a recursive process, or steps for calculation from a context. Combine standard function types using arithmetic operations. Content Limits at the lower level may require students to be able to determine the linear, quadratic, and exponential functions with domains in the integers. at the higher level may require students to be able to write the linear, quadratic, and exponential functions, and use this functions in a real-world problem. MAFS.912.F-IF.3.8 Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. Complexity Complexity Complexity Students will be able to write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. Use the process of factoring and completing the square in a quadratic function to show zero. Content Limits at the lower level may require students to be able to use the process of factoring to write an equivalent expression. at the higher level my require students to be able to use the process of factoring, and completing the square to write an equivalent expression. Identify the zeroes.