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Common Core: ELA
Common Core: Math
2531 Results

 Student Outcomes Students graph rational functions showing intercepts, asymptotes, and end behavior.

 Student Outcomes Students identify vertical and horizontal asymptotes of rational functions.

 Student Outcomes Students describe the end behavior of rational functions.

 Student Outcomes Students reduce rational expressions to lowest terms. Students determine the domain of rational functions.

 Student Outcomes Students understand that rational expressions form a system analogous to the rational numbers, closed underaddition, subtraction, multiplication, and division by a nonzero rational...

 In Topic B, students explore composition of functions in depth and notice that a composition of a polynomial function with the function f(x) = 1/x gives functions that can be written as ratios of...

 Student Outcomes Students will be able to give an informal argument using Cavalieri’s principle for the formula for the volume of a sphere and other solid figures.

 Student Outcomes Students learn to graph equations of the form x2/a2  y2/b2 =1 . Students derive the equations of hyperbolas given the foci, using the fact that the difference of distances from the...

 Student Outcomes Students derive the equations of ellipses given the foci, using the fact that the sum of distances from the foci is constant.

 Student Outcomes Students convert between the real and complex forms of equations for ellipses. Students write equations of ellipses and represent them graphically.

 Student Outcomes Students observe patterns in the coefficients of the terms in binomial expansions. They formalize their observations and explore the mathematical basis for them. Students use the...

 Student Outcomes Students discover patterns in the expansion of binomials, leading to the understanding of the binomial theorem. Students use Pascal’s triangle to find the coefficients of binomial...

 Student Outcomes Students determine the complex roots of polynomial equations of the form xn = 1 and, more generally, equations of the form xn = k positive integers n and positive real numbers k....

 Student Outcomes Students apply their understanding of polynomial identities that have been extended to the complex numbers to find the square roots of complex numbers.

 Student Outcomes Students determine all solutions of polynomial equations over the set of complex numbers and understand the implications of the fundamental theorem of algebra, especially for...

 Topic A brings students back to the study of complex roots of polynomial functions. Students briefly review quadratic and cubic functions and then extend familiar polynomial identities to both...

 Student Outcomes Students determine the area of a cyclic quadrilateral as a function of its side lengths and the acute angle formed by its diagonals. Students prove Ptolemy’s theorem, which states...

 Student Outcomes Students show that a quadrilateral is cyclic if and only if its opposite angles are supplementary. Students derive and apply the area of cyclic quadrilateral ABCD as 1/2 AB·CD·sin(w...

 The module concludes with Topic E focusing on the properties of quadrilaterals inscribed in circles and establishing Ptolemy's theorem. This result codifies the Pythagorean theorem, curious facts...

 Student Outcomes Given a circle, students find the equations of two lines tangent to the circle with specified slopes. Given a circle and a point outside the circle, students find the equation of the...

 Student Outcomes Students complete the square in order to write the equation of a circle in centerradius form. Students recognize when a quadratic in x and y is the equation for a circle.

 Student Outcomes Students write the equation for a circle in centerradius form, (x  a)2 (y  b)2 = r2 using the Pythagorean theorem or the distance formula. Students write the equation of a circle...

 Topic D brings in coordinate geometry to establish the equation of a circle. Students solve problems to find the equations of specific tangent lines or the coordinates of specific points of contact...

 Student Outcomes Students find “missing lengths” in circlesecant or circlesecanttangent diagrams.