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26 | eureka Math algebra II Study guIde
extenSionS to the algebRa ii couRSe
The (+) standards below are included in the Algebra II course to provide coherence to the
curriculum. They can be used to effectively extend a topic or to introduce a theme/concept
that will be fully covered in the Precalculus course.
Module 1. Students will be working with zeros of
polynomials in this module, which offers teachers
an opportunity to introduce Standard N-CN.C.9.A major theme of the module is A-APR.D.7.
Teachers should continually remind students of
the connections between rational expressions
and rational numbers as students add, subtract,
multiply, and divide rational expressions.use complex numbers in polynomial identities and equations.
N-CN.C.8 (+) Extend polynomial identities to the complex numbers.
For example, rewrite x^2 + 4 as (x + 2i)(x – 2i).
N-CN.C.9 (+) Know the Fundamental Theorem of Algebra; show that
it is true for quadratic polynomials.
rewrite rational expressions.
A-APR.D.7 (+) Understand that rational expressions form a system
analogous to the rational numbers, closed under addition,
subtraction, multiplication, and division by a nonzero rational
expression; add, subtract, multiply, and divide rational expressions.Module 2. In F-TF.A.3, students begin fluency
exercises with trigonometric ratios of the special
angles.Teachers present proofs of formulas in F-TF.C.9.
Students use the formulas in Algebra II; they prove
the formulas in Precalculus.extend the domain of trigonometric functions using the unit circle.
F-TF.A.3 (+) Use special triangles to determine geometrically the
values of sine, cosine, tangent for π/3, π/4 and π/6, and use the
unit circle to express the values of sine, cosine, and tangent for
π – x, π + x, and 2π – x in terms of their values for x, where x is any
real number.
prove and apply trigonometric identities.
F-TF.C.9 (+) Prove the addition and subtraction formulas for sine,
cosine, and tangent and use them to solve problems.