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Common Core: Standard
Common Core: ELA
Common Core: Math
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 Students revisit the fundamental theorem of algebra as they explore complex roots of polynomial functions. They use polynomial identities, the binomial theorem, and Pascal’s Triangle to find roots...

 This module revisits trigonometry that was introduced in Geometry and Algebra II, uniting and further expanding the ideas of right triangle trigonometry and the unit circle. New tools are introduced...

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

 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 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 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.

 Topic A helps students recall how to use special triangles positioned within the unit circle to determine geometrically the values of sine, cosine, and tangent at special angles. The unit circle is...

 Student Outcomes Students construct a tangent line from a point outside a given circle to the circle.

 Students derive sophisticated applications of the trigonometric functions in Topic B including: the area formula for a general triangle, the law of sines, the law of cosines, and Heron’s formula. ...

 Student Outcomes Students prove the formula Area = 1/2 bc sin(A) for a triangle. They reason geometrically and numerically to find the areas of various triangles.

 Student Outcomes Students prove the law of sines and use it to solve problems.

 Student Outcomes Students prove the law of cosines and use it to solve problems.

 Student Outcomes Students apply the law of sines or the law of cosines to determine missing measurements in realworld situations that can be modeled using nonright triangles, including situations...

 In this topic, students extend their understanding of probability, building on work from Grade 11. The multiplication rule for independent events introduced in Grade 11 is generalized to a rule that...

 In this topic, students first distinguish between discrete and continuous random variables and then focus on probability distributions for discrete random variables. In the early lessons of this...